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a/_images/fe30aac9519fd5e8e2f5cb9122683f55fc56e645a1346c5b1c1112e809ead0c5.png b/_images/fe30aac9519fd5e8e2f5cb9122683f55fc56e645a1346c5b1c1112e809ead0c5.png new file mode 100644 index 0000000..28f81cd Binary files /dev/null and b/_images/fe30aac9519fd5e8e2f5cb9122683f55fc56e645a1346c5b1c1112e809ead0c5.png differ diff --git a/_notebooks/ar1_bayes.ipynb b/_notebooks/ar1_bayes.ipynb index fc23d3a..4cb65b3 100644 --- a/_notebooks/ar1_bayes.ipynb +++ b/_notebooks/ar1_bayes.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "6101b12d", + "id": "e3c19ac4", "metadata": {}, "source": [ "# Posterior Distributions for AR(1) Parameters\n", @@ -13,7 +13,7 @@ { "cell_type": "code", "execution_count": null, - "id": "088fb117", + "id": "194738d6", "metadata": { "hide-output": false }, @@ -25,7 +25,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cbeb1a42", + "id": "a810f395", "metadata": { "hide-output": false }, @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "7f68f108", + "id": "8903c2ed", "metadata": {}, "source": [ "This lecture uses Bayesian methods offered by [pymc](https://www.pymc.io/projects/docs/en/stable/) and [numpyro](https://num.pyro.ai/en/stable/) to make statistical inferences about two parameters of a univariate first-order autoregression.\n", @@ -145,7 +145,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4d968167", + "id": "6080c7e5", "metadata": { "hide-output": false }, @@ -175,7 +175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ff374b4", + "id": "2ec5bab0", "metadata": { "hide-output": false }, @@ -187,7 +187,7 @@ }, { "cell_type": "markdown", - "id": "6594b515", + "id": "0329be6f", "metadata": {}, "source": [ "Now we shall use Bayes’ law to construct a posterior distribution, conditioning on the initial value of $ y_0 $.\n", @@ -199,7 +199,7 @@ }, { "cell_type": "markdown", - "id": "00b542c4", + "id": "287851ae", "metadata": {}, "source": [ "## PyMC Implementation\n", @@ -211,7 +211,7 @@ { "cell_type": "code", "execution_count": null, - "id": "22bc8a05", + "id": "e3ebfdd8", "metadata": { "hide-output": false }, @@ -234,7 +234,7 @@ }, { "cell_type": "markdown", - "id": "b0f47a54", + "id": "90996156", "metadata": {}, "source": [ "[pmc.sample](https://www.pymc.io/projects/docs/en/v5.10.0/api/generated/pymc.sample.html#pymc-sample) by default uses the NUTS samplers to generate samples as shown in the below cell:" @@ -243,7 +243,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5750f3a9", + "id": "356d6214", "metadata": { "hide-output": false }, @@ -256,7 +256,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f00983c", + "id": "770f0cde", "metadata": { "hide-output": false }, @@ -268,14 +268,14 @@ }, { "cell_type": "markdown", - "id": "c85dd51b", + "id": "658500ab", "metadata": {}, "source": [ "Evidently, the posteriors aren’t centered on the true values of $ .5, 1 $ that we used to generate the data.\n", "\n", - "This is a symptom of the classic **Hurwicz bias** for first order autoregressive processes (see Leonid Hurwicz [[Hur50](https://python.quantecon.org/zreferences.html#id244)].)\n", + "This is a symptom of the classic **Hurwicz bias** for first order autoregressive processes (see Leonid Hurwicz [[Hur50](https://python.quantecon.org/zreferences.html#id246)].)\n", "\n", - "The Hurwicz bias is worse the smaller is the sample (see [[OW69](https://python.quantecon.org/zreferences.html#id243)]).\n", + "The Hurwicz bias is worse the smaller is the sample (see [[OW69](https://python.quantecon.org/zreferences.html#id245)]).\n", "\n", "Be that as it may, here is more information about the posterior." ] @@ -283,7 +283,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ecc856c2", + "id": "a2f4febf", "metadata": { "hide-output": false }, @@ -297,7 +297,7 @@ }, { "cell_type": "markdown", - "id": "31e05ee2", + "id": "f7465ac3", "metadata": {}, "source": [ "Now we shall compute a posterior distribution after seeing the same data but instead assuming that $ y_0 $ is drawn from the stationary distribution.\n", @@ -314,7 +314,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eaef1c61", + "id": "b629c3d3", "metadata": { "hide-output": false }, @@ -340,7 +340,7 @@ { "cell_type": "code", "execution_count": null, - "id": "80cd1aa8", + "id": "8be43f79", "metadata": { "hide-output": false }, @@ -355,7 +355,7 @@ { "cell_type": "code", "execution_count": null, - "id": "34b8b76f", + "id": "1139dd10", "metadata": { "hide-output": false }, @@ -368,7 +368,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f1baae3c", + "id": "b696cc4e", "metadata": { "hide-output": false }, @@ -382,7 +382,7 @@ }, { "cell_type": "markdown", - "id": "00f3dd34", + "id": "c4b2d8df", "metadata": {}, "source": [ "Please note how the posterior for $ \\rho $ has shifted to the right relative to when we conditioned on $ y_0 $ instead of assuming that $ y_0 $ is drawn from the stationary distribution.\n", @@ -399,7 +399,7 @@ }, { "cell_type": "markdown", - "id": "133d1d92", + "id": "728ea887", "metadata": {}, "source": [ "## Numpyro Implementation" @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49a4da18", + "id": "15ad0d76", "metadata": { "hide-output": false }, @@ -444,7 +444,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb696090", + "id": "5c2dc83b", "metadata": { "hide-output": false }, @@ -465,7 +465,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d68e8c33", + "id": "d04c5e88", "metadata": { "hide-output": false }, @@ -485,7 +485,7 @@ { "cell_type": "code", "execution_count": null, - "id": "70aff6ac", + "id": "9d6d5ac3", "metadata": { "hide-output": false }, @@ -497,7 +497,7 @@ { "cell_type": "code", "execution_count": null, - "id": "addfc73b", + "id": "b365d10f", "metadata": { "hide-output": false }, @@ -508,7 +508,7 @@ }, { "cell_type": "markdown", - "id": "b4d12b8e", + "id": "1f29a3d6", "metadata": {}, "source": [ "Next, we again compute the posterior under the assumption that $ y_0 $ is drawn from the stationary distribution, so that\n", @@ -523,7 +523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0dfc979", + "id": "236f75ac", "metadata": { "hide-output": false }, @@ -548,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69a309ec", + "id": "434a6c10", "metadata": { "hide-output": false }, @@ -568,7 +568,7 @@ { "cell_type": "code", "execution_count": null, - "id": "236344e9", + "id": "04f5d399", "metadata": { "hide-output": false }, @@ -580,7 +580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "576d58cf", + "id": "5b948fb9", "metadata": { "hide-output": false }, @@ -591,7 +591,7 @@ }, { "cell_type": "markdown", - "id": "6248f9d1", + "id": "072e44cf", "metadata": {}, "source": [ "Look what happened to the posterior!\n", @@ -606,7 +606,7 @@ } ], "metadata": { - "date": 1706246574.4990308, + "date": 1706493928.679338, "filename": "ar1_bayes.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/ar1_turningpts.ipynb b/_notebooks/ar1_turningpts.ipynb index 7022cad..8a2a505 100644 --- a/_notebooks/ar1_turningpts.ipynb +++ b/_notebooks/ar1_turningpts.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "bcc5866c", + "id": "e373f7e3", "metadata": {}, "source": [ "# Forecasting an AR(1) Process" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bfa5e73e", + "id": "9c351c21", "metadata": { "hide-output": false }, @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "fadd3ad9", + "id": "20f7aa25", "metadata": {}, "source": [ "This lecture describes methods for forecasting statistics that are functions of future values of a univariate autogressive process.\n", @@ -41,7 +41,7 @@ "\n", "**Sample path properties** are things like “time to next turning point” or “time to next recession”.\n", "\n", - "To investigate sample path properties we’ll use a simulation procedure recommended by Wecker [[Wec79](https://python.quantecon.org/zreferences.html#id245)].\n", + "To investigate sample path properties we’ll use a simulation procedure recommended by Wecker [[Wec79](https://python.quantecon.org/zreferences.html#id247)].\n", "\n", "To acknowledge uncertainty about parameters, we’ll deploy `pymc` to construct a Bayesian joint posterior distribution for unknown parameters.\n", "\n", @@ -51,7 +51,7 @@ { "cell_type": "code", "execution_count": null, - "id": "93a0ef61", + "id": "85e80db4", "metadata": { "hide-output": false }, @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "77acc4dc", + "id": "f0451e68", "metadata": {}, "source": [ "## A Univariate First-Order Autoregressive Process\n", @@ -134,7 +134,7 @@ "- the time until the next turning point (positive or negative). \n", "\n", "\n", - "To accomplish that for situations in which we are uncertain about parameter values, we shall extend Wecker’s [[Wec79](https://python.quantecon.org/zreferences.html#id245)] approach in the following way.\n", + "To accomplish that for situations in which we are uncertain about parameter values, we shall extend Wecker’s [[Wec79](https://python.quantecon.org/zreferences.html#id247)] approach in the following way.\n", "\n", "- first simulate an initial path of length $ T_0 $; \n", "- for a given prior, draw a sample of size $ N $ from the posterior joint distribution of parameters $ \\left(\\rho,\\sigma\\right) $ after observing the initial path; \n", @@ -144,7 +144,7 @@ }, { "cell_type": "markdown", - "id": "e61dc8e6", + "id": "f100e5c4", "metadata": {}, "source": [ "## Implementation\n", @@ -161,7 +161,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ecc1589", + "id": "db4fde4d", "metadata": { "hide-output": false }, @@ -227,7 +227,7 @@ }, { "cell_type": "markdown", - "id": "ed493402", + "id": "4d7eda9a", "metadata": {}, "source": [ "As functions of forecast horizon, the coverage intervals have shapes like those described in\n", @@ -236,12 +236,12 @@ }, { "cell_type": "markdown", - "id": "0ac694b1", + "id": "d00fb744", "metadata": {}, "source": [ "## Predictive Distributions of Path Properties\n", "\n", - "Wecker [[Wec79](https://python.quantecon.org/zreferences.html#id245)] proposed using simulation techniques to characterize predictive distribution of some statistics that are non-linear functions of $ y $.\n", + "Wecker [[Wec79](https://python.quantecon.org/zreferences.html#id247)] proposed using simulation techniques to characterize predictive distribution of some statistics that are non-linear functions of $ y $.\n", "\n", "He called these functions “path properties” to contrast them with properties of single data points.\n", "\n", @@ -268,7 +268,7 @@ "W_t(\\omega):= \\inf \\{ k\\geq 1 \\mid Z_{t+k}(\\omega) = 1\\}\n", "$$\n", "\n", - "Wecker [[Wec79](https://python.quantecon.org/zreferences.html#id245)] also studied **the minimum value of $ Y $ over the next 8 quarters**\n", + "Wecker [[Wec79](https://python.quantecon.org/zreferences.html#id247)] also studied **the minimum value of $ Y $ over the next 8 quarters**\n", "which can be defined as the random variable.\n", "\n", "$$\n", @@ -303,12 +303,12 @@ "- ``after one or two decrease(s), $ Y $ will grow for two consecutive quarters’’ \n", "\n", "\n", - "Following [[Wec79](https://python.quantecon.org/zreferences.html#id245)], we can use simulations to calculate probabilities of $ P_t $ and $ N_t $ for each period $ t $." + "Following [[Wec79](https://python.quantecon.org/zreferences.html#id247)], we can use simulations to calculate probabilities of $ P_t $ and $ N_t $ for each period $ t $." ] }, { "cell_type": "markdown", - "id": "55d1731e", + "id": "d4ff7e21", "metadata": {}, "source": [ "## A Wecker-Like Algorithm\n", @@ -329,7 +329,7 @@ }, { "cell_type": "markdown", - "id": "0039313e", + "id": "e58e2a64", "metadata": {}, "source": [ "## Using Simulations to Approximate a Posterior Distribution\n", @@ -342,7 +342,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43ac9332", + "id": "6ddbe5ef", "metadata": { "hide-output": false }, @@ -389,7 +389,7 @@ }, { "cell_type": "markdown", - "id": "23fdf09c", + "id": "55706166", "metadata": {}, "source": [ "The graphs on the left portray posterior marginal distributions." @@ -397,7 +397,7 @@ }, { "cell_type": "markdown", - "id": "554fde0b", + "id": "fa412f9a", "metadata": {}, "source": [ "## Calculating Sample Path Statistics\n", @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "52b65021", + "id": "4e825520", "metadata": { "hide-output": false }, @@ -470,7 +470,7 @@ }, { "cell_type": "markdown", - "id": "e2088f69", + "id": "943c508e", "metadata": {}, "source": [ "## Original Wecker Method\n", @@ -482,7 +482,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7dd366e5", + "id": "ee67b851", "metadata": { "hide-output": false }, @@ -550,7 +550,7 @@ }, { "cell_type": "markdown", - "id": "7faa592f", + "id": "bc5d1d3d", "metadata": {}, "source": [ "## Extended Wecker Method\n", @@ -564,7 +564,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2d097eb7", + "id": "64f71414", "metadata": { "hide-output": false }, @@ -625,7 +625,7 @@ }, { "cell_type": "markdown", - "id": "a0215de8", + "id": "f6c8f70e", "metadata": {}, "source": [ "## Comparison\n", @@ -636,7 +636,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2d63c21", + "id": "be9adb16", "metadata": { "hide-output": false }, @@ -652,7 +652,7 @@ } ], "metadata": { - "date": 1706246574.5286124, + "date": 1706493928.7100508, "filename": "ar1_turningpts.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/back_prop.ipynb b/_notebooks/back_prop.ipynb index 692f0a3..bdfd122 100644 --- a/_notebooks/back_prop.ipynb +++ b/_notebooks/back_prop.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "0ed444c9", + "id": "bbf985dc", "metadata": {}, "source": [ "# Introduction to Artificial Neural Networks" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99db6905", + "id": "eb1d7741", "metadata": { "hide-output": false }, @@ -23,7 +23,7 @@ }, { "cell_type": "markdown", - "id": "9b2df5dc", + "id": "7e2f04d1", "metadata": {}, "source": [ ">**Note**\n", @@ -36,7 +36,7 @@ }, { "cell_type": "markdown", - "id": "5ef32dd8", + "id": "6464b4e5", "metadata": {}, "source": [ "## Overview\n", @@ -63,7 +63,7 @@ }, { "cell_type": "markdown", - "id": "7786318a", + "id": "bc8f6f03", "metadata": {}, "source": [ "## A Deep (but not Wide) Artificial Neural Network\n", @@ -148,7 +148,7 @@ }, { "cell_type": "markdown", - "id": "978e270f", + "id": "0d75d938", "metadata": {}, "source": [ "## Calibrating Parameters\n", @@ -211,7 +211,7 @@ }, { "cell_type": "markdown", - "id": "5cab155c", + "id": "1f42fa6c", "metadata": {}, "source": [ "## Back Propagation and the Chain Rule\n", @@ -308,7 +308,7 @@ }, { "cell_type": "markdown", - "id": "57f3ed76", + "id": "e2865c60", "metadata": {}, "source": [ "## Training Set\n", @@ -330,7 +330,7 @@ { "cell_type": "code", "execution_count": null, - "id": "02e18a67", + "id": "303220a9", "metadata": { "hide-output": false }, @@ -347,7 +347,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8507dbbe", + "id": "f25e415a", "metadata": { "hide-output": false }, @@ -368,7 +368,7 @@ { "cell_type": "code", "execution_count": null, - "id": "00015a65", + "id": "b1eb633b", "metadata": { "hide-output": false }, @@ -416,7 +416,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9a9490b6", + "id": "8192e54c", "metadata": { "hide-output": false }, @@ -433,7 +433,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea3063af", + "id": "0bb68d92", "metadata": { "hide-output": false }, @@ -447,7 +447,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f9f007c", + "id": "3a3f56e1", "metadata": { "hide-output": false }, @@ -460,7 +460,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8271c3e8", + "id": "acf074b0", "metadata": { "hide-output": false }, @@ -472,7 +472,7 @@ { "cell_type": "code", "execution_count": null, - "id": "31fb14ab", + "id": "ca992d2c", "metadata": { "hide-output": false }, @@ -489,7 +489,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b7442084", + "id": "90099c23", "metadata": { "hide-output": false }, @@ -503,7 +503,7 @@ { "cell_type": "code", "execution_count": null, - "id": "13d33edf", + "id": "57b7ca9e", "metadata": { "hide-output": false }, @@ -515,7 +515,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b9c2a3e", + "id": "808cb991", "metadata": { "hide-output": false }, @@ -528,7 +528,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c77c8a2c", + "id": "997ba87f", "metadata": { "hide-output": false }, @@ -560,7 +560,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5daea87b", + "id": "2c929dd2", "metadata": { "hide-output": false }, @@ -573,7 +573,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fa5bfc79", + "id": "c8abee49", "metadata": { "hide-output": false }, @@ -584,7 +584,7 @@ }, { "cell_type": "markdown", - "id": "e48dbef3", + "id": "6ef5e78c", "metadata": {}, "source": [ "## Example 1\n", @@ -607,7 +607,7 @@ { "cell_type": "code", "execution_count": null, - "id": "94147690", + "id": "7a45ae02", "metadata": { "hide-output": false }, @@ -624,7 +624,7 @@ { "cell_type": "code", "execution_count": null, - "id": "444f0e8a", + "id": "45d73be8", "metadata": { "hide-output": false }, @@ -646,7 +646,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e365e4cc", + "id": "ff857f24", "metadata": { "hide-output": false }, @@ -661,7 +661,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f1ef12a2", + "id": "9fef20f8", "metadata": { "hide-output": false }, @@ -674,7 +674,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a9a077a", + "id": "5fdb5d61", "metadata": { "hide-output": false }, @@ -686,7 +686,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6de3923", + "id": "81e23382", "metadata": { "hide-output": false }, @@ -704,7 +704,7 @@ }, { "cell_type": "markdown", - "id": "962bae09", + "id": "2effd7d3", "metadata": {}, "source": [ "## How Deep?\n", @@ -718,7 +718,7 @@ }, { "cell_type": "markdown", - "id": "202a4794", + "id": "e17f104f", "metadata": {}, "source": [ "## Example 2\n", @@ -733,7 +733,7 @@ { "cell_type": "code", "execution_count": null, - "id": "90832740", + "id": "07f4f0e7", "metadata": { "hide-output": false }, @@ -749,7 +749,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3b43656", + "id": "6e387a3b", "metadata": { "hide-output": false }, @@ -764,7 +764,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f668bf0a", + "id": "255a0d18", "metadata": { "hide-output": false }, @@ -779,7 +779,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3132241a", + "id": "9b1924f3", "metadata": { "hide-output": false }, @@ -794,7 +794,7 @@ { "cell_type": "code", "execution_count": null, - "id": "14d8b94d", + "id": "92cd3823", "metadata": { "hide-output": false }, @@ -806,7 +806,7 @@ { "cell_type": "code", "execution_count": null, - "id": "028895c0", + "id": "eae9575b", "metadata": { "hide-output": false }, @@ -818,7 +818,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2996715", + "id": "18d03c1d", "metadata": { "hide-output": false }, @@ -830,7 +830,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da0b4bd3", + "id": "67bb9ed8", "metadata": { "hide-output": false }, @@ -844,7 +844,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4db688d3", + "id": "06e23c19", "metadata": { "hide-output": false }, @@ -865,7 +865,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5d08512", + "id": "71fd495f", "metadata": { "hide-output": false }, @@ -879,7 +879,7 @@ }, { "cell_type": "markdown", - "id": "87f11f04", + "id": "9d1f7dc4", "metadata": {}, "source": [ ">**Note**\n", @@ -891,7 +891,7 @@ } ], "metadata": { - "date": 1706246574.5728967, + "date": 1706493928.7554488, "filename": "back_prop.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/bayes_nonconj.ipynb b/_notebooks/bayes_nonconj.ipynb index 84d9c06..003f31d 100644 --- a/_notebooks/bayes_nonconj.ipynb +++ b/_notebooks/bayes_nonconj.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ef7bd4e6", + "id": "6fcfe07b", "metadata": {}, "source": [ "# Non-Conjugate Priors\n", @@ -45,7 +45,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c4a8d8e", + "id": "fb400b98", "metadata": { "hide-output": false }, @@ -58,7 +58,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66997200", + "id": "76031d10", "metadata": { "hide-output": false }, @@ -96,7 +96,7 @@ }, { "cell_type": "markdown", - "id": "fca57ad9", + "id": "d41cd0ca", "metadata": {}, "source": [ "## Unleashing MCMC on a Binomial Likelihood\n", @@ -123,7 +123,7 @@ }, { "cell_type": "markdown", - "id": "66123d94", + "id": "8e525c8b", "metadata": {}, "source": [ "### Analytical Posterior\n", @@ -175,7 +175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f50e0e1", + "id": "3ae326d5", "metadata": { "hide-output": false }, @@ -214,7 +214,7 @@ }, { "cell_type": "markdown", - "id": "3c5a6930", + "id": "4ad4e712", "metadata": {}, "source": [ "### Two Ways to Approximate Posteriors\n", @@ -252,7 +252,7 @@ }, { "cell_type": "markdown", - "id": "688bb839", + "id": "3d1c100d", "metadata": {}, "source": [ "## Prior Distributions\n", @@ -285,7 +285,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35107e27", + "id": "bbf0a121", "metadata": { "hide-output": false }, @@ -364,7 +364,7 @@ }, { "cell_type": "markdown", - "id": "ac1548e9", + "id": "817bd2e3", "metadata": {}, "source": [ "### Variational Inference\n", @@ -451,7 +451,7 @@ }, { "cell_type": "markdown", - "id": "2dcc5a01", + "id": "7b97b24a", "metadata": {}, "source": [ "## Implementation\n", @@ -494,7 +494,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4bb53647", + "id": "a50d7115", "metadata": { "hide-output": false }, @@ -745,7 +745,7 @@ }, { "cell_type": "markdown", - "id": "e236f7d0", + "id": "ab3699aa", "metadata": {}, "source": [ "## Alternative Prior Distributions\n", @@ -764,7 +764,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0d0e8112", + "id": "d916a0be", "metadata": { "hide-output": false }, @@ -781,7 +781,7 @@ }, { "cell_type": "markdown", - "id": "dda86315", + "id": "26d148b7", "metadata": {}, "source": [ "The above graphs show that sampling seems to work well with both distributions.\n", @@ -792,7 +792,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59ec49b5", + "id": "b9701fc7", "metadata": { "hide-output": false }, @@ -809,7 +809,7 @@ }, { "cell_type": "markdown", - "id": "0ebe6130", + "id": "e09c2eb4", "metadata": {}, "source": [ "These graphs look good too.\n", @@ -820,7 +820,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0eaa4425", + "id": "46000bbe", "metadata": { "hide-output": false }, @@ -833,7 +833,7 @@ }, { "cell_type": "markdown", - "id": "f11b6b88", + "id": "d6f118de", "metadata": {}, "source": [ "Having assured ourselves that our sampler seems to do a good job, let’s put it to work in using MCMC to compute posterior probabilities." @@ -841,7 +841,7 @@ }, { "cell_type": "markdown", - "id": "0a1c8563", + "id": "d6c6ab77", "metadata": {}, "source": [ "## Posteriors Via MCMC and VI\n", @@ -859,7 +859,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9170047", + "id": "32ee69c2", "metadata": { "hide-output": false }, @@ -992,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "92329529", + "id": "bd31eae3", "metadata": {}, "source": [ "Let’s set some parameters that we’ll use in all of the examples below.\n", @@ -1005,7 +1005,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5afbb60e", + "id": "d47aa76a", "metadata": { "hide-output": false }, @@ -1021,7 +1021,7 @@ }, { "cell_type": "markdown", - "id": "635d09ea", + "id": "94aeb23c", "metadata": {}, "source": [ "### Beta Prior and Posteriors:\n", @@ -1041,7 +1041,7 @@ { "cell_type": "code", "execution_count": null, - "id": "65479244", + "id": "ec8b2d43", "metadata": { "hide-output": false }, @@ -1078,7 +1078,7 @@ }, { "cell_type": "markdown", - "id": "90ba9803", + "id": "e1647c84", "metadata": {}, "source": [ "Now let’s use MCMC while still using a beta prior.\n", @@ -1089,7 +1089,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d604c24c", + "id": "03785d88", "metadata": { "hide-output": false }, @@ -1101,7 +1101,7 @@ }, { "cell_type": "markdown", - "id": "4d6b91a0", + "id": "30169cbc", "metadata": {}, "source": [ "Here the MCMC approximation looks good.\n", @@ -1122,7 +1122,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6924f736", + "id": "0055cc5b", "metadata": { "hide-output": false }, @@ -1133,7 +1133,7 @@ }, { "cell_type": "markdown", - "id": "dee8d593", + "id": "a7254848", "metadata": {}, "source": [ "## Non-conjugate Prior Distributions\n", @@ -1146,7 +1146,7 @@ }, { "cell_type": "markdown", - "id": "bac28673", + "id": "5fd4220e", "metadata": {}, "source": [ "### MCMC\n", @@ -1159,7 +1159,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ee32687b", + "id": "23b9fe05", "metadata": { "hide-output": false }, @@ -1187,7 +1187,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6841e2fd", + "id": "374e90ef", "metadata": { "hide-output": false }, @@ -1205,7 +1205,7 @@ }, { "cell_type": "markdown", - "id": "ac095f07", + "id": "1ae9ec73", "metadata": {}, "source": [ "In the situation depicted above, we have assumed a $ Uniform(\\underline{\\theta}, \\overline{\\theta}) $ prior that puts zero probability outside a bounded support that excludes the true value.\n", @@ -1218,7 +1218,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87fe4bcd", + "id": "9b696fd4", "metadata": { "hide-output": false }, @@ -1237,7 +1237,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f6f85e61", + "id": "33af741b", "metadata": { "hide-output": false }, @@ -1258,7 +1258,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6695a4d8", + "id": "4361f739", "metadata": { "hide-output": false }, @@ -1272,7 +1272,7 @@ }, { "cell_type": "markdown", - "id": "ad2310f2", + "id": "08388f8b", "metadata": {}, "source": [ "To get more accuracy we will now increase the number of steps for Variational Inference (VI)" @@ -1281,7 +1281,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75cc857d", + "id": "ccc04736", "metadata": { "hide-output": false }, @@ -1292,7 +1292,7 @@ }, { "cell_type": "markdown", - "id": "c120b6ec", + "id": "8bc72bd3", "metadata": {}, "source": [ "#### VI with a Truncated Normal Guide" @@ -1301,7 +1301,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c24aba4a", + "id": "11ff4f7d", "metadata": { "hide-output": false }, @@ -1316,7 +1316,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd1f760e", + "id": "50daaafd", "metadata": { "hide-output": false }, @@ -1331,7 +1331,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aaec2414", + "id": "e61b14fd", "metadata": { "hide-output": false }, @@ -1347,7 +1347,7 @@ { "cell_type": "code", "execution_count": null, - "id": "913fa9c3", + "id": "3839b160", "metadata": { "hide-output": false }, @@ -1361,7 +1361,7 @@ }, { "cell_type": "markdown", - "id": "9a5aca3f", + "id": "fe76231b", "metadata": {}, "source": [ "#### Variational Inference with a Beta Guide Distribution" @@ -1370,7 +1370,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f1960b6", + "id": "30d6fc50", "metadata": { "hide-output": false }, @@ -1385,7 +1385,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ba17add", + "id": "2fbe1edf", "metadata": { "hide-output": false }, @@ -1404,7 +1404,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b25b6282", + "id": "32717e7e", "metadata": { "hide-output": false }, @@ -1425,7 +1425,7 @@ { "cell_type": "code", "execution_count": null, - "id": "148a34f8", + "id": "2cc76fb6", "metadata": { "hide-output": false }, @@ -1439,7 +1439,7 @@ } ], "metadata": { - "date": 1706246574.7847593, + "date": 1706493928.8501415, "filename": "bayes_nonconj.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/exchangeable.ipynb b/_notebooks/exchangeable.ipynb index bbfbd5e..7ceb737 100644 --- a/_notebooks/exchangeable.ipynb +++ b/_notebooks/exchangeable.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ebf0f625", + "id": "0042c2d0", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "e6db4a59", + "id": "f77e3355", "metadata": {}, "source": [ "# Exchangeability and Bayesian Updating" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "d8e4435f", + "id": "e4cac594", "metadata": {}, "source": [ "## Contents\n", @@ -38,7 +38,7 @@ }, { "cell_type": "markdown", - "id": "499ec0af", + "id": "0b2e6e9e", "metadata": {}, "source": [ "## Overview\n", @@ -89,7 +89,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4d9e49d", + "id": "1f0c2c4b", "metadata": { "hide-output": false }, @@ -106,7 +106,7 @@ }, { "cell_type": "markdown", - "id": "749d3edb", + "id": "dfcf48e1", "metadata": {}, "source": [ "## Independently and Identically Distributed\n", @@ -141,7 +141,7 @@ }, { "cell_type": "markdown", - "id": "91081ebe", + "id": "8104a019", "metadata": {}, "source": [ "### IID Means Past Observations Don’t Tell Us Anything About Future Observations\n", @@ -193,7 +193,7 @@ }, { "cell_type": "markdown", - "id": "42505b0a", + "id": "19d82827", "metadata": {}, "source": [ "## A Setting in Which Past Observations Are Informative\n", @@ -247,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "9e509fa3", + "id": "1f487a60", "metadata": {}, "source": [ "## Relationship Between IID and Exchangeable\n", @@ -313,7 +313,7 @@ }, { "cell_type": "markdown", - "id": "a47852ae", + "id": "4c437e31", "metadata": {}, "source": [ "## Exchangeability\n", @@ -346,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "2f5131db", + "id": "9036b2d5", "metadata": {}, "source": [ "## Bayes’ Law\n", @@ -422,7 +422,7 @@ }, { "cell_type": "markdown", - "id": "768f5344", + "id": "78597fd6", "metadata": {}, "source": [ "## More Details about Bayesian Updating\n", @@ -475,7 +475,7 @@ { "cell_type": "code", "execution_count": null, - "id": "173d9c22", + "id": "a736f881", "metadata": { "hide-output": false }, @@ -566,7 +566,7 @@ }, { "cell_type": "markdown", - "id": "9c42117f", + "id": "858927b0", "metadata": {}, "source": [ "Now we’ll create a group of graphs that illustrate dynamics induced by Bayes’ Law.\n", @@ -577,7 +577,7 @@ { "cell_type": "code", "execution_count": null, - "id": "65141c32", + "id": "379fb84a", "metadata": { "hide-output": false }, @@ -588,7 +588,7 @@ }, { "cell_type": "markdown", - "id": "48e22d5c", + "id": "dbcfdaff", "metadata": {}, "source": [ "Please look at the three graphs above created for an instance in which $ f $ is a uniform distribution on $ [0,1] $\n", @@ -632,7 +632,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8834f388", + "id": "e11a9bca", "metadata": { "hide-output": false }, @@ -643,7 +643,7 @@ }, { "cell_type": "markdown", - "id": "8405fce5", + "id": "b60e74da", "metadata": {}, "source": [ "Notice how the likelihood ratio, the middle graph, and the arrows compare with the previous instance of our example." @@ -651,7 +651,7 @@ }, { "cell_type": "markdown", - "id": "2560beab", + "id": "9e8299ea", "metadata": {}, "source": [ "## Appendix" @@ -659,7 +659,7 @@ }, { "cell_type": "markdown", - "id": "31660954", + "id": "d836ad7d", "metadata": {}, "source": [ "### Sample Paths of $ \\pi_t $\n", @@ -680,7 +680,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d62ed6d", + "id": "ab2bb000", "metadata": { "hide-output": false }, @@ -741,7 +741,7 @@ { "cell_type": "code", "execution_count": null, - "id": "204847c1", + "id": "30660b8e", "metadata": { "hide-output": false }, @@ -752,7 +752,7 @@ }, { "cell_type": "markdown", - "id": "9d4d2bd6", + "id": "fd5cc8be", "metadata": {}, "source": [ "We begin by generating $ N $ simulated $ \\{\\pi_t\\} $ paths with $ T $\n", @@ -762,7 +762,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5a5a5d1", + "id": "7bdd0602", "metadata": { "hide-output": false }, @@ -774,7 +774,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7734f059", + "id": "44dcba96", "metadata": { "hide-output": false }, @@ -786,7 +786,7 @@ }, { "cell_type": "markdown", - "id": "cf722f06", + "id": "2149f294", "metadata": {}, "source": [ "In the above example, for most paths $ \\pi_t \\rightarrow 1 $.\n", @@ -801,7 +801,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e772dd4a", + "id": "31f521dd", "metadata": { "hide-output": false }, @@ -813,7 +813,7 @@ }, { "cell_type": "markdown", - "id": "d984f1e1", + "id": "27749b8e", "metadata": {}, "source": [ "In the above graph we observe that now most paths $ \\pi_t \\rightarrow 0 $." @@ -821,7 +821,7 @@ }, { "cell_type": "markdown", - "id": "37ed83a5", + "id": "0b27f0d7", "metadata": {}, "source": [ "### Rates of convergence\n", @@ -839,7 +839,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1979fa14", + "id": "e03981d0", "metadata": { "hide-output": false }, @@ -853,7 +853,7 @@ }, { "cell_type": "markdown", - "id": "17f9bc51", + "id": "f5873b2f", "metadata": {}, "source": [ "From the above graph, rates of convergence appear not to depend on whether $ F $ or $ G $ generates the data." @@ -861,7 +861,7 @@ }, { "cell_type": "markdown", - "id": "ac06cbfa", + "id": "c9639594", "metadata": {}, "source": [ "### Graph of Ensemble Dynamics of $ \\pi_t $\n", @@ -885,7 +885,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f88f9c3f", + "id": "1f546b9b", "metadata": { "hide-output": false }, @@ -919,7 +919,7 @@ }, { "cell_type": "markdown", - "id": "aff57997", + "id": "813b71e9", "metadata": {}, "source": [ "First, consider the case where $ F_a=F_b=1 $ and\n", @@ -929,7 +929,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ebe6607", + "id": "5c9f39ea", "metadata": { "hide-output": false }, @@ -940,7 +940,7 @@ }, { "cell_type": "markdown", - "id": "f5befd3a", + "id": "84b979ca", "metadata": {}, "source": [ "The above graphs shows that when $ F $ generates the data, $ \\pi_t $ on average always heads north, while\n", @@ -956,7 +956,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b8722c56", + "id": "34e5e842", "metadata": { "hide-output": false }, @@ -967,7 +967,7 @@ }, { "cell_type": "markdown", - "id": "fe5cd97a", + "id": "6ab96c57", "metadata": {}, "source": [ "The above graph says that $ \\pi_t $ is inert and remains at its initial value.\n", @@ -980,7 +980,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c51585d8", + "id": "16938de0", "metadata": { "hide-output": false }, @@ -991,7 +991,7 @@ }, { "cell_type": "markdown", - "id": "6b14099f", + "id": "e06f2007", "metadata": {}, "source": [ "## Sequels\n", @@ -1007,7 +1007,7 @@ } ], "metadata": { - "date": 1706246574.841498, + "date": 1706493928.9074676, "filename": "exchangeable.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/hoist_failure.ipynb b/_notebooks/hoist_failure.ipynb index d241162..09cea0e 100644 --- a/_notebooks/hoist_failure.ipynb +++ b/_notebooks/hoist_failure.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "01e9bf3e", + "id": "870ea79d", "metadata": {}, "source": [ "# Fault Tree Uncertainties" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "fa24505d", + "id": "d88dddbb", "metadata": {}, "source": [ "## Overview\n", @@ -35,9 +35,9 @@ "For more about Fourier transforms see this quantecon lecture [Circulant Matrices](https://python.quantecon.org/eig_circulant.html)\n", "as well as these lecture [Covariance Stationary Processes](https://python-advanced.quantecon.org/arma.html) and [Estimation of Spectra](https://python-advanced.quantecon.org/estspec.html).\n", "\n", - "El-Shanawany, Ardron, and Walker [[ESAW18](https://python.quantecon.org/zreferences.html#id259)] and Greenfield and Sargent [[GS93](https://python.quantecon.org/zreferences.html#id258)] used some of the methods described here to approximate probabilities of failures of safety systems in nuclear facilities.\n", + "El-Shanawany, Ardron, and Walker [[ESAW18](https://python.quantecon.org/zreferences.html#id261)] and Greenfield and Sargent [[GS93](https://python.quantecon.org/zreferences.html#id260)] used some of the methods described here to approximate probabilities of failures of safety systems in nuclear facilities.\n", "\n", - "These methods respond to some of the recommendations made by Apostolakis [[Apo90](https://python.quantecon.org/zreferences.html#id257)] for constructing procedures for quantifying\n", + "These methods respond to some of the recommendations made by Apostolakis [[Apo90](https://python.quantecon.org/zreferences.html#id259)] for constructing procedures for quantifying\n", "uncertainty about the reliability of a safety system.\n", "\n", "We’ll start by bringing in some Python machinery." @@ -46,7 +46,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c02b875", + "id": "f101a0e7", "metadata": { "hide-output": false }, @@ -58,7 +58,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f8c8521", + "id": "c53d4e3e", "metadata": { "hide-output": false }, @@ -74,7 +74,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8fd18497", + "id": "a5a1a95b", "metadata": { "hide-output": false }, @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "eda0c0ca", + "id": "566f10a8", "metadata": {}, "source": [ "## Log normal distribution\n", @@ -147,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "8455bfe1", + "id": "59dcd1b5", "metadata": {}, "source": [ "## The Convolution Property\n", @@ -220,7 +220,7 @@ { "cell_type": "code", "execution_count": null, - "id": "19c741f1", + "id": "89553a3b", "metadata": { "hide-output": false }, @@ -239,7 +239,7 @@ }, { "cell_type": "markdown", - "id": "96481332", + "id": "5d65f973", "metadata": {}, "source": [ "A little later we’ll explain some advantages that come from using `scipy.signal.ftconvolve` rather than `numpy.convolve`.numpy program convolve.\n", @@ -251,7 +251,7 @@ }, { "cell_type": "markdown", - "id": "1f9d5e92", + "id": "3904ffc2", "metadata": {}, "source": [ "## Approximating Distributions\n", @@ -267,7 +267,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b4eeda8", + "id": "f3c4dd97", "metadata": { "hide-output": false }, @@ -295,7 +295,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79d99209", + "id": "0f8127bb", "metadata": { "hide-output": false }, @@ -307,7 +307,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d7dd5a5e", + "id": "7405be47", "metadata": { "hide-output": false }, @@ -319,7 +319,7 @@ { "cell_type": "code", "execution_count": null, - "id": "52657ac3", + "id": "b68e1ec8", "metadata": { "hide-output": false }, @@ -333,7 +333,7 @@ }, { "cell_type": "markdown", - "id": "81a43813", + "id": "8a90da78", "metadata": {}, "source": [ "Here are helper functions that create a discretized version of a log normal\n", @@ -343,7 +343,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3dd1c180", + "id": "81342045", "metadata": { "hide-output": false }, @@ -362,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "adda3220", + "id": "c987e2f7", "metadata": {}, "source": [ "Now we shall set a grid length $ I $ and a grid increment size $ m =1 $ for our discretizations.\n", @@ -380,7 +380,7 @@ { "cell_type": "code", "execution_count": null, - "id": "225af04d", + "id": "ed766276", "metadata": { "hide-output": false }, @@ -394,7 +394,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb0fd43b", + "id": "6b9d1a26", "metadata": { "hide-output": false }, @@ -419,7 +419,7 @@ { "cell_type": "code", "execution_count": null, - "id": "258ddfee", + "id": "fac2ab99", "metadata": { "hide-output": false }, @@ -434,7 +434,7 @@ }, { "cell_type": "markdown", - "id": "5e5dc4e6", + "id": "ea402c32", "metadata": {}, "source": [ "## Convolving Probability Mass Functions\n", @@ -497,7 +497,7 @@ { "cell_type": "code", "execution_count": null, - "id": "499a8489", + "id": "a16b8bde", "metadata": { "hide-output": false }, @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "f70f42b3", + "id": "65eab260", "metadata": {}, "source": [ "The fast Fourier transform is two orders of magnitude faster than `numpy.convolve`\n", @@ -544,7 +544,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e31c52b0", + "id": "edcb0e0e", "metadata": { "hide-output": false }, @@ -566,7 +566,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4238f159", + "id": "1e1653ac", "metadata": { "hide-output": false }, @@ -587,7 +587,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35468d03", + "id": "0914270b", "metadata": { "hide-output": false }, @@ -602,7 +602,7 @@ { "cell_type": "code", "execution_count": null, - "id": "64186b83", + "id": "ec43b9ca", "metadata": { "hide-output": false }, @@ -616,7 +616,7 @@ }, { "cell_type": "markdown", - "id": "0f91c8b3", + "id": "706e2384", "metadata": {}, "source": [ "## Failure Tree Analysis\n", @@ -626,7 +626,7 @@ "Before applying the convolution theorem, we first describe the model that connects constituent events to the **top** end whose\n", "failure rate we seek to quantify.\n", "\n", - "The model is an example of the widely used **failure tree analysis** described by El-Shanawany, Ardron, and Walker [[ESAW18](https://python.quantecon.org/zreferences.html#id259)].\n", + "The model is an example of the widely used **failure tree analysis** described by El-Shanawany, Ardron, and Walker [[ESAW18](https://python.quantecon.org/zreferences.html#id261)].\n", "\n", "To construct the statistical model, we repeatedly use what is called the **rare event approximation**.\n", "\n", @@ -663,7 +663,7 @@ }, { "cell_type": "markdown", - "id": "3d3d6da8", + "id": "15398062", "metadata": {}, "source": [ "## Application\n", @@ -694,13 +694,13 @@ }, { "cell_type": "markdown", - "id": "16244e3a", + "id": "00ed4bf6", "metadata": {}, "source": [ "## Failure Rates Unknown\n", "\n", - "Now we come to the problem that really interests us, following [[ESAW18](https://python.quantecon.org/zreferences.html#id259)] and Greenfield and Sargent\n", - "[[GS93](https://python.quantecon.org/zreferences.html#id258)] in the spirit of Apostolakis [[Apo90](https://python.quantecon.org/zreferences.html#id257)].\n", + "Now we come to the problem that really interests us, following [[ESAW18](https://python.quantecon.org/zreferences.html#id261)] and Greenfield and Sargent\n", + "[[GS93](https://python.quantecon.org/zreferences.html#id260)] in the spirit of Apostolakis [[Apo90](https://python.quantecon.org/zreferences.html#id259)].\n", "\n", "The constituent probabilities or failure rates $ P(A_i) $ are not known a priori and have to be estimated.\n", "\n", @@ -740,7 +740,7 @@ }, { "cell_type": "markdown", - "id": "53f42a0e", + "id": "1081274c", "metadata": {}, "source": [ "## Waste Hoist Failure Rate\n", @@ -751,18 +751,18 @@ "\n", "A regulatory agency wants the sytem to be designed in a way that makes the failure rate of the top event small with high probability.\n", "\n", - "This example is Design Option B-2 (Case I) described in Table 10 on page 27 of [[GS93](https://python.quantecon.org/zreferences.html#id258)].\n", + "This example is Design Option B-2 (Case I) described in Table 10 on page 27 of [[GS93](https://python.quantecon.org/zreferences.html#id260)].\n", "\n", "The table describes parameters $ \\mu_i, \\sigma_i $ for fourteen log normal random variables that consist of **seven pairs** of random variables that are identically and independently distributed.\n", "\n", "- Within a pair, parameters $ \\mu_i, \\sigma_i $ are the same \n", - "- As described in table 10 of [[GS93](https://python.quantecon.org/zreferences.html#id258)] p. 27, parameters of log normal distributions for the seven unique probabilities $ P(A_i) $ have been calibrated to be the values in the following Python code: " + "- As described in table 10 of [[GS93](https://python.quantecon.org/zreferences.html#id260)] p. 27, parameters of log normal distributions for the seven unique probabilities $ P(A_i) $ have been calibrated to be the values in the following Python code: " ] }, { "cell_type": "code", "execution_count": null, - "id": "6b18fd05", + "id": "b57a2c76", "metadata": { "hide-output": false }, @@ -779,7 +779,7 @@ }, { "cell_type": "markdown", - "id": "3853f544", + "id": "3be88529", "metadata": {}, "source": [ ">**Note**\n", @@ -795,7 +795,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2440cedc", + "id": "055ebd41", "metadata": { "hide-output": false }, @@ -809,7 +809,7 @@ }, { "cell_type": "markdown", - "id": "aceb0c46", + "id": "83ceec4a", "metadata": {}, "source": [ "We compute the required thirteen convolutions in the following code.\n", @@ -817,14 +817,14 @@ "(Please feel free to try different values of the power parameter $ p $ that we use to set the number of points in our grid for constructing\n", "the probability mass functions that discretize the continuous log normal distributions.)\n", "\n", - "We’ll plot a counterpart to the cumulative distribution function (CDF) in figure 5 on page 29 of [[GS93](https://python.quantecon.org/zreferences.html#id258)]\n", + "We’ll plot a counterpart to the cumulative distribution function (CDF) in figure 5 on page 29 of [[GS93](https://python.quantecon.org/zreferences.html#id260)]\n", "and we’ll also present a counterpart to their Table 11 on page 28." ] }, { "cell_type": "code", "execution_count": null, - "id": "e5cc7e21", + "id": "7ac4de91", "metadata": { "hide-output": false }, @@ -878,7 +878,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d9059a3e", + "id": "4d935123", "metadata": { "hide-output": false }, @@ -925,10 +925,10 @@ }, { "cell_type": "markdown", - "id": "31533cf6", + "id": "c2a78a49", "metadata": {}, "source": [ - "The above table agrees closely with column 2 of Table 11 on p. 28 of of [[GS93](https://python.quantecon.org/zreferences.html#id258)].\n", + "The above table agrees closely with column 2 of Table 11 on p. 28 of of [[GS93](https://python.quantecon.org/zreferences.html#id260)].\n", "\n", "Discrepancies are probably due to slight differences in the number of digits retained in inputting $ \\mu_i, \\sigma_i, i = 1, \\ldots, 14 $\n", "and in the number of points deployed in the discretizations." @@ -936,7 +936,7 @@ } ], "metadata": { - "date": 1706246574.892568, + "date": 1706493929.079273, "filename": "hoist_failure.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/imp_sample.ipynb b/_notebooks/imp_sample.ipynb index 784ffd1..6f95de5 100644 --- a/_notebooks/imp_sample.ipynb +++ b/_notebooks/imp_sample.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "15568c37", + "id": "16ec93c5", "metadata": {}, "source": [ "# Computing Mean of a Likelihood Ratio Process" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "8fc8f70e", + "id": "eb9f0f99", "metadata": {}, "source": [ "## Contents\n", @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "3c7b7e2a", + "id": "98b1197c", "metadata": {}, "source": [ "## Overview\n", @@ -46,7 +46,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5dbb3b12", + "id": "01cbc8ca", "metadata": { "hide-output": false }, @@ -60,7 +60,7 @@ }, { "cell_type": "markdown", - "id": "58948ac2", + "id": "53203b74", "metadata": {}, "source": [ "## Mathematical Expectation of Likelihood Ratio\n", @@ -101,7 +101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "636ccfd0", + "id": "d42cab99", "metadata": { "hide-output": false }, @@ -124,7 +124,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e679efe5", + "id": "a1fc0fb6", "metadata": { "hide-output": false }, @@ -142,7 +142,7 @@ }, { "cell_type": "markdown", - "id": "b9a23c79", + "id": "8d47aca1", "metadata": {}, "source": [ "The likelihood ratio is `l(w)=f(w)/g(w)`." @@ -151,7 +151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4d5020d", + "id": "b037e565", "metadata": { "hide-output": false }, @@ -163,7 +163,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2bf936a9", + "id": "9fa26faa", "metadata": { "hide-output": false }, @@ -177,7 +177,7 @@ }, { "cell_type": "markdown", - "id": "84c3ee03", + "id": "3df71eda", "metadata": {}, "source": [ "The above plots shows that as $ \\omega \\rightarrow 0 $, $ f \\left(\\omega\\right) $ is unchanged and $ g \\left(\\omega\\right) \\rightarrow 0 $, so the likelihood ratio approaches infinity.\n", @@ -191,7 +191,7 @@ }, { "cell_type": "markdown", - "id": "b342f081", + "id": "e0a37d51", "metadata": {}, "source": [ "## Importance sampling\n", @@ -236,7 +236,7 @@ }, { "cell_type": "markdown", - "id": "6aa1efa5", + "id": "8f9fd387", "metadata": {}, "source": [ "## Selecting a Sampling Distribution\n", @@ -249,7 +249,7 @@ { "cell_type": "code", "execution_count": null, - "id": "38155753", + "id": "65d46900", "metadata": { "hide-output": false }, @@ -262,7 +262,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f3c5922", + "id": "83ac96dc", "metadata": { "hide-output": false }, @@ -280,7 +280,7 @@ }, { "cell_type": "markdown", - "id": "02c6e5af", + "id": "5435215d", "metadata": {}, "source": [ "## Approximating a cumulative likelihood ratio\n", @@ -305,7 +305,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06fef33a", + "id": "13175a75", "metadata": { "hide-output": false }, @@ -335,7 +335,7 @@ }, { "cell_type": "markdown", - "id": "96902743", + "id": "279bdee8", "metadata": {}, "source": [ "Consider the case when $ T=1 $, which amounts to approximating $ E_0\\left[\\ell\\left(\\omega\\right)\\right] $\n", @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8d902a5", + "id": "2a847707", "metadata": { "hide-output": false }, @@ -357,7 +357,7 @@ }, { "cell_type": "markdown", - "id": "2804c57a", + "id": "46e7c1d4", "metadata": {}, "source": [ "For our importance sampling estimate, we set $ q = h $." @@ -366,7 +366,7 @@ { "cell_type": "code", "execution_count": null, - "id": "89b2fa7d", + "id": "1f29f742", "metadata": { "hide-output": false }, @@ -377,7 +377,7 @@ }, { "cell_type": "markdown", - "id": "cd5b1180", + "id": "6475c977", "metadata": {}, "source": [ "Evidently, even at T=1, our importance sampling estimate is closer to $ 1 $ than is the Monte Carlo estimate.\n", @@ -391,7 +391,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9184defa", + "id": "98b756b4", "metadata": { "hide-output": false }, @@ -403,7 +403,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cee07b2f", + "id": "fe8f4128", "metadata": { "hide-output": false }, @@ -414,7 +414,7 @@ }, { "cell_type": "markdown", - "id": "732cf4af", + "id": "94172979", "metadata": {}, "source": [ "## Distribution of Sample Mean\n", @@ -427,7 +427,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b63c4396", + "id": "a089fb9f", "metadata": { "hide-output": false }, @@ -448,7 +448,7 @@ }, { "cell_type": "markdown", - "id": "597f7c09", + "id": "4ade12ee", "metadata": {}, "source": [ "Again, we first consider estimating $ {E} \\left[\\ell\\left(\\omega\\right)\\right] $ by setting T=1.\n", @@ -459,7 +459,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f9228be0", + "id": "6941e666", "metadata": { "hide-output": false }, @@ -472,7 +472,7 @@ { "cell_type": "code", "execution_count": null, - "id": "97e63799", + "id": "5e57b4cf", "metadata": { "hide-output": false }, @@ -485,7 +485,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bcb383b8", + "id": "f3e5c005", "metadata": { "hide-output": false }, @@ -497,7 +497,7 @@ }, { "cell_type": "markdown", - "id": "e4284d68", + "id": "73c0a315", "metadata": {}, "source": [ "Although both methods tend to provide a mean estimate of $ {E} \\left[\\ell\\left(\\omega\\right)\\right] $ close to $ 1 $, the importance sampling estimates have smaller variance.\n", @@ -508,7 +508,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1f38bc49", + "id": "7cb7055d", "metadata": { "hide-output": false }, @@ -543,7 +543,7 @@ }, { "cell_type": "markdown", - "id": "37a14afd", + "id": "582bc95e", "metadata": {}, "source": [ "The simulation exercises above show that the importance sampling estimates are unbiased under all $ T $\n", @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "820106cb", + "id": "74fb4540", "metadata": {}, "source": [ "## More Thoughts about Choice of Sampling Distribution\n", @@ -579,7 +579,7 @@ { "cell_type": "code", "execution_count": null, - "id": "78a02415", + "id": "c561fe63", "metadata": { "hide-output": false }, @@ -591,7 +591,7 @@ { "cell_type": "code", "execution_count": null, - "id": "acd0af29", + "id": "75185a78", "metadata": { "hide-output": false }, @@ -603,7 +603,7 @@ }, { "cell_type": "markdown", - "id": "ce59f6f0", + "id": "0368fd8c", "metadata": {}, "source": [ "We could also use other distributions as our importance distribution.\n", @@ -614,7 +614,7 @@ { "cell_type": "code", "execution_count": null, - "id": "898197d2", + "id": "7494132c", "metadata": { "hide-output": false }, @@ -627,7 +627,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35fa417f", + "id": "dc78b05e", "metadata": { "hide-output": false }, @@ -647,7 +647,7 @@ }, { "cell_type": "markdown", - "id": "aa17dcf0", + "id": "ec21a26f", "metadata": {}, "source": [ "We consider two additonal distributions.\n", @@ -672,7 +672,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ebd86369", + "id": "36e2eee0", "metadata": { "hide-output": false }, @@ -709,7 +709,7 @@ }, { "cell_type": "markdown", - "id": "3f4a0051", + "id": "5217ac59", "metadata": {}, "source": [ "Our simulations suggest that indeed $ h_2 $ is a quite good importance sampling distribution for our problem.\n", @@ -720,7 +720,7 @@ { "cell_type": "code", "execution_count": null, - "id": "52ea0267", + "id": "aa132e38", "metadata": { "hide-output": false }, @@ -757,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "5fae3089", + "id": "a281d16e", "metadata": {}, "source": [ "However, $ h_3 $ is evidently a poor importance sampling distribution forpir problem,\n", @@ -771,7 +771,7 @@ } ], "metadata": { - "date": 1706246574.9296286, + "date": 1706493929.1163507, "filename": "imp_sample.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/intro.ipynb b/_notebooks/intro.ipynb index f419efb..0357b1a 100644 --- a/_notebooks/intro.ipynb +++ b/_notebooks/intro.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "bb31902a", + "id": "9c85db7a", "metadata": {}, "source": [ "# Statistics for Computational Economics\n", @@ -12,7 +12,7 @@ }, { "cell_type": "markdown", - "id": "b40c5d2d", + "id": "47fcce9b", "metadata": {}, "source": [ "# Elementary Statistics\n", @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "97763615", + "id": "3ce55cf9", "metadata": {}, "source": [ "# Information & Bayesian Statistics\n", @@ -47,7 +47,7 @@ }, { "cell_type": "markdown", - "id": "7e8070d4", + "id": "5fc69e8d", "metadata": {}, "source": [ "# Applications of Statistics\n", @@ -61,7 +61,7 @@ }, { "cell_type": "markdown", - "id": "560263a4", + "id": "96763865", "metadata": {}, "source": [ "# Other\n", @@ -73,7 +73,7 @@ } ], "metadata": { - "date": 1706246574.9499836, + "date": 1706493929.1364436, "filename": "intro.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/likelihood_bayes.ipynb b/_notebooks/likelihood_bayes.ipynb index 2efba89..989efe3 100644 --- a/_notebooks/likelihood_bayes.ipynb +++ b/_notebooks/likelihood_bayes.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "42344dcf", + "id": "799b3ba6", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "8ca882eb", + "id": "6800193a", "metadata": {}, "source": [ "# Likelihood Ratio Processes and Bayesian Learning" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "c69883da", + "id": "1a4a3e04", "metadata": {}, "source": [ "## Overview\n", @@ -50,7 +50,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d89c974c", + "id": "e4afd376", "metadata": { "hide-output": false }, @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "afd390d8", + "id": "d32ad790", "metadata": {}, "source": [ "## The Setting\n", @@ -140,7 +140,7 @@ "\n", "The likelihood ratio and its logarithm are key tools for making\n", "inferences using a classic frequentist approach due to Neyman and\n", - "Pearson [[NP33](https://python.quantecon.org/zreferences.html#id276)].\n", + "Pearson [[NP33](https://python.quantecon.org/zreferences.html#id278)].\n", "\n", "We’ll again deploy the following Python code from [this lecture](https://python.quantecon.org/likelihood_ratio_process.html) that\n", "evaluates $ f $ and $ g $ as two different\n", @@ -152,7 +152,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e8a4d0a1", + "id": "e0915c84", "metadata": { "hide-output": false }, @@ -175,7 +175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b1a6babc", + "id": "e6d03431", "metadata": { "hide-output": false }, @@ -202,7 +202,7 @@ }, { "cell_type": "markdown", - "id": "c2a1444e", + "id": "18f02a6f", "metadata": {}, "source": [ "We’ll also use the following Python code to prepare some informative simulations" @@ -211,7 +211,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cf9894ae", + "id": "307fb96c", "metadata": { "hide-output": false }, @@ -224,7 +224,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7bc699f6", + "id": "043fa007", "metadata": { "hide-output": false }, @@ -236,7 +236,7 @@ }, { "cell_type": "markdown", - "id": "74233dff", + "id": "56c2fc42", "metadata": {}, "source": [ "## Likelihood Ratio Process and Bayes’ Law\n", @@ -268,7 +268,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da1a571f", + "id": "e6f8c2fe", "metadata": { "hide-output": false }, @@ -286,7 +286,7 @@ }, { "cell_type": "markdown", - "id": "f8b0e0df", + "id": "484f0378", "metadata": {}, "source": [ "Formula [(15.1)](#equation-eq-recur1) can be generalized by iterating on it and thereby deriving an\n", @@ -367,7 +367,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55161e89", + "id": "955e7f23", "metadata": { "hide-output": false }, @@ -378,7 +378,7 @@ }, { "cell_type": "markdown", - "id": "29390b5d", + "id": "26753641", "metadata": {}, "source": [ "Next we generate paths of the likelihood ratio process $ L_t $ and the posterior $ \\pi_t $ for a\n", @@ -388,7 +388,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ba26a8e", + "id": "ec40bec8", "metadata": { "hide-output": false }, @@ -406,7 +406,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ed877adf", + "id": "d238713c", "metadata": { "hide-output": false }, @@ -431,7 +431,7 @@ }, { "cell_type": "markdown", - "id": "e88ae74c", + "id": "6108d0da", "metadata": {}, "source": [ "The dotted line in the graph above records the logarithm of the likelihood ratio process $ \\log L(w^t) $.\n", @@ -444,7 +444,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3d1ddba5", + "id": "7664fea4", "metadata": { "hide-output": false }, @@ -462,7 +462,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ecea72c1", + "id": "41e77034", "metadata": { "hide-output": false }, @@ -487,7 +487,7 @@ }, { "cell_type": "markdown", - "id": "2148f97f", + "id": "72e7cb6b", "metadata": {}, "source": [ "Below we offer Python code that verifies that nature chose permanently to draw from density $ f $." @@ -496,7 +496,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1bd8d346", + "id": "9639bffb", "metadata": { "hide-output": false }, @@ -513,7 +513,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75b4c36c", + "id": "3a7bbdfa", "metadata": { "hide-output": false }, @@ -524,7 +524,7 @@ }, { "cell_type": "markdown", - "id": "5e2dee7e", + "id": "76ccbc00", "metadata": {}, "source": [ "We thus conclude that the likelihood ratio process is a key ingredient of the formula [(15.2)](#equation-eq-bayeslaw103) for\n", @@ -534,7 +534,7 @@ }, { "cell_type": "markdown", - "id": "a746fd24", + "id": "c3cc109c", "metadata": {}, "source": [ "## Behavior of posterior probability $ \\{\\pi_t\\} $ under the subjective probability distribution\n", @@ -571,7 +571,7 @@ }, { "cell_type": "markdown", - "id": "d7077d3b", + "id": "45832b2a", "metadata": {}, "source": [ "### Mechanical details again\n", @@ -722,7 +722,7 @@ }, { "cell_type": "markdown", - "id": "0531eeb4", + "id": "cc378185", "metadata": {}, "source": [ "### Some simulations\n", @@ -741,7 +741,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e840696b", + "id": "f228139b", "metadata": { "hide-output": false }, @@ -797,7 +797,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8bcc3001", + "id": "bc5e7c1b", "metadata": { "hide-output": false }, @@ -814,7 +814,7 @@ }, { "cell_type": "markdown", - "id": "db4a4cfe", + "id": "1e55d300", "metadata": {}, "source": [ "The above graph indicates that\n", @@ -831,7 +831,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de2c62d7", + "id": "2d92a188", "metadata": { "hide-output": false }, @@ -849,7 +849,7 @@ }, { "cell_type": "markdown", - "id": "ead5ab22", + "id": "29010bb2", "metadata": {}, "source": [ "Evidently, by $ t = 199 $, $ \\pi_t $ has converged to either $ 0 $ or $ 1 $.\n", @@ -870,7 +870,7 @@ { "cell_type": "code", "execution_count": null, - "id": "afcf7947", + "id": "a0b86dcb", "metadata": { "hide-output": false }, @@ -886,7 +886,7 @@ { "cell_type": "code", "execution_count": null, - "id": "174eff5c", + "id": "b0e9a52b", "metadata": { "hide-output": false }, @@ -904,7 +904,7 @@ }, { "cell_type": "markdown", - "id": "e6edde47", + "id": "67f073a6", "metadata": {}, "source": [ "For the preceding ensemble that assumed $ \\pi_0 = .5 $, the following graph shows two paths of\n", @@ -919,7 +919,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ca85e30", + "id": "545a7526", "metadata": { "hide-output": false }, @@ -940,7 +940,7 @@ }, { "cell_type": "markdown", - "id": "5f6d04da", + "id": "54f3fa07", "metadata": {}, "source": [ "## Initial Prior is Verified by Paths Drawn from Subjective Conditional Densities\n", @@ -960,7 +960,7 @@ { "cell_type": "code", "execution_count": null, - "id": "85088178", + "id": "52804ee8", "metadata": { "hide-output": false }, @@ -973,7 +973,7 @@ }, { "cell_type": "markdown", - "id": "a2e94b11", + "id": "6bf9bdba", "metadata": {}, "source": [ "The fraction of simulations for which $ \\pi_{t} $ had converged to $ 1 $ is indeed always close to $ \\pi_{-1} $, as anticipated." @@ -981,7 +981,7 @@ }, { "cell_type": "markdown", - "id": "cffeb965", + "id": "0658235e", "metadata": {}, "source": [ "## Drilling Down a Little Bit\n", @@ -1005,7 +1005,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9981f66b", + "id": "5774a08c", "metadata": { "hide-output": false }, @@ -1040,7 +1040,7 @@ }, { "cell_type": "markdown", - "id": "eff58dfd", + "id": "7f81df9e", "metadata": {}, "source": [ "The shape of the the conditional variance as a function of $ \\pi_{t-1} $ is informative about the behavior of sample paths of $ \\{\\pi_t\\} $.\n", @@ -1052,7 +1052,7 @@ }, { "cell_type": "markdown", - "id": "953e7b33", + "id": "2072f2d8", "metadata": {}, "source": [ "## Sequels\n", @@ -1063,7 +1063,7 @@ } ], "metadata": { - "date": 1706246575.0007012, + "date": 1706493929.1878185, "filename": "likelihood_bayes.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/likelihood_ratio_process.ipynb b/_notebooks/likelihood_ratio_process.ipynb index d6562f9..f98d3a3 100644 --- a/_notebooks/likelihood_ratio_process.ipynb +++ b/_notebooks/likelihood_ratio_process.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "65192a05", + "id": "16d56880", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "15066ecd", + "id": "60164b35", "metadata": {}, "source": [ "# Likelihood Ratio Processes" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "9489813b", + "id": "c75536b7", "metadata": {}, "source": [ "## Contents\n", @@ -37,7 +37,7 @@ }, { "cell_type": "markdown", - "id": "707bcdd2", + "id": "447ada06", "metadata": {}, "source": [ "## Overview\n", @@ -60,7 +60,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6083d473", + "id": "eb95eb69", "metadata": { "hide-output": false }, @@ -76,7 +76,7 @@ }, { "cell_type": "markdown", - "id": "d68cb243", + "id": "58e8bf91", "metadata": {}, "source": [ "## Likelihood Ratio Process\n", @@ -141,7 +141,7 @@ "\n", "The likelihood ratio and its logarithm are key tools for making\n", "inferences using a classic frequentist approach due to Neyman and\n", - "Pearson [[NP33](https://python.quantecon.org/zreferences.html#id276)].\n", + "Pearson [[NP33](https://python.quantecon.org/zreferences.html#id278)].\n", "\n", "To help us appreciate how things work, the following Python code evaluates $ f $ and $ g $ as two different\n", "beta distributions, then computes and simulates an associated likelihood\n", @@ -152,7 +152,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c4473828", + "id": "f3c6c858", "metadata": { "hide-output": false }, @@ -175,7 +175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "555817c2", + "id": "a1b38f13", "metadata": { "hide-output": false }, @@ -202,7 +202,7 @@ }, { "cell_type": "markdown", - "id": "efc02eeb", + "id": "19b4c8b5", "metadata": {}, "source": [ "## Nature Permanently Draws from Density g\n", @@ -214,7 +214,7 @@ { "cell_type": "code", "execution_count": null, - "id": "80005d97", + "id": "52482a44", "metadata": { "hide-output": false }, @@ -227,7 +227,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f6497b8", + "id": "abcd56d6", "metadata": { "hide-output": false }, @@ -245,7 +245,7 @@ }, { "cell_type": "markdown", - "id": "9f206591", + "id": "22fdeb1e", "metadata": {}, "source": [ "Evidently, as sample length $ T $ grows, most probability mass\n", @@ -259,7 +259,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b97f837e", + "id": "e2043094", "metadata": { "hide-output": false }, @@ -270,7 +270,7 @@ }, { "cell_type": "markdown", - "id": "98440d48", + "id": "f15a9104", "metadata": {}, "source": [ "Despite the evident convergence of most probability mass to a\n", @@ -320,7 +320,7 @@ }, { "cell_type": "markdown", - "id": "6c3dce27", + "id": "c462977d", "metadata": {}, "source": [ "## Peculiar Property\n", @@ -343,7 +343,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ca3f575", + "id": "039b8420", "metadata": { "hide-output": false }, @@ -355,7 +355,7 @@ }, { "cell_type": "markdown", - "id": "f394903c", + "id": "440eaafc", "metadata": {}, "source": [ "It would be useful to use simulations to verify that unconditional means\n", @@ -375,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "6ba78a11", + "id": "b0ce6ea5", "metadata": {}, "source": [ "## Nature Permanently Draws from Density f\n", @@ -409,7 +409,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c756b896", + "id": "0af3bfe8", "metadata": { "hide-output": false }, @@ -422,7 +422,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16b2c446", + "id": "f3b12a1c", "metadata": { "hide-output": false }, @@ -434,7 +434,7 @@ }, { "cell_type": "markdown", - "id": "809e6671", + "id": "6238db0c", "metadata": {}, "source": [ "We also plot the probability that $ L\\left(w^t\\right) $ falls into\n", @@ -445,7 +445,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fd09eaff", + "id": "279e8ad8", "metadata": { "hide-output": false }, @@ -456,13 +456,13 @@ }, { "cell_type": "markdown", - "id": "76833785", + "id": "b7fe3c18", "metadata": {}, "source": [ "## Likelihood Ratio Test\n", "\n", "We now describe how to employ the machinery\n", - "of Neyman and Pearson [[NP33](https://python.quantecon.org/zreferences.html#id276)] to test the hypothesis that history $ w^t $ is generated by repeated\n", + "of Neyman and Pearson [[NP33](https://python.quantecon.org/zreferences.html#id278)] to test the hypothesis that history $ w^t $ is generated by repeated\n", "IID draws from density $ g $.\n", "\n", "Denote $ q $ as the data generating process, so that\n", @@ -543,7 +543,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ec06e6d7", + "id": "e3bb94b3", "metadata": { "hide-output": false }, @@ -554,7 +554,7 @@ }, { "cell_type": "markdown", - "id": "ea57c8bf", + "id": "48d98d91", "metadata": {}, "source": [ "Below we plot empirical distributions of logarithms of the cumulative\n", @@ -580,7 +580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ca84137", + "id": "9305fa34", "metadata": { "hide-output": false }, @@ -613,7 +613,7 @@ }, { "cell_type": "markdown", - "id": "6f36ff04", + "id": "3e24320a", "metadata": {}, "source": [ "The graph below shows more clearly that, when we hold the threshold\n", @@ -624,7 +624,7 @@ { "cell_type": "code", "execution_count": null, - "id": "417386c2", + "id": "14afb885", "metadata": { "hide-output": false }, @@ -647,7 +647,7 @@ }, { "cell_type": "markdown", - "id": "225fb6b7", + "id": "056c1c01", "metadata": {}, "source": [ "For a given sample size $ t $, the threshold $ c $ uniquely pins down probabilities\n", @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f9f8b38f", + "id": "57556277", "metadata": { "hide-output": false }, @@ -694,7 +694,7 @@ }, { "cell_type": "markdown", - "id": "e9f1715a", + "id": "ead88974", "metadata": {}, "source": [ "Notice that as $ t $ increases, we are assured a larger probability\n", @@ -726,7 +726,7 @@ { "cell_type": "code", "execution_count": null, - "id": "abfbd8f1", + "id": "f6eda06c", "metadata": { "hide-output": false }, @@ -751,7 +751,7 @@ }, { "cell_type": "markdown", - "id": "37b95a3b", + "id": "d1cd5774", "metadata": {}, "source": [ "The United States Navy evidently used a procedure like this to select a sample size $ t $ for doing quality\n", @@ -763,7 +763,7 @@ }, { "cell_type": "markdown", - "id": "49e3a515", + "id": "073fc9c6", "metadata": {}, "source": [ "## Kullback–Leibler Divergence\n", @@ -826,7 +826,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ff0f28f7", + "id": "106a0281", "metadata": { "hide-output": false }, @@ -840,7 +840,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2b0f439", + "id": "7921ae62", "metadata": { "hide-output": false }, @@ -857,7 +857,7 @@ }, { "cell_type": "markdown", - "id": "132a4814", + "id": "fe98cb79", "metadata": {}, "source": [ "Let’s compute the Kullback–Leibler discrepancies by quadrature\n", @@ -867,7 +867,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf791e9d", + "id": "e949d716", "metadata": { "hide-output": false }, @@ -883,7 +883,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8dd7f64c", + "id": "0aff2a76", "metadata": { "hide-output": false }, @@ -900,7 +900,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dfdc3e6d", + "id": "b6ab0e37", "metadata": { "hide-output": false }, @@ -912,7 +912,7 @@ }, { "cell_type": "markdown", - "id": "3570a53f", + "id": "3fdeb322", "metadata": {}, "source": [ "We have $ K_g < K_f $.\n", @@ -924,7 +924,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c590b895", + "id": "4d65bd10", "metadata": { "hide-output": false }, @@ -936,7 +936,7 @@ }, { "cell_type": "markdown", - "id": "7f1535a2", + "id": "044dea18", "metadata": {}, "source": [ "The figure below plots over time the fraction of paths\n", @@ -949,7 +949,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e7732f75", + "id": "5e0a70a8", "metadata": { "hide-output": false }, @@ -961,7 +961,7 @@ }, { "cell_type": "markdown", - "id": "d44b29b6", + "id": "cfaa566a", "metadata": {}, "source": [ "We can also try an $ h $ that is closer to $ f $ than is\n", @@ -971,7 +971,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99cdc8ed", + "id": "c0aa047b", "metadata": { "hide-output": false }, @@ -984,7 +984,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0314dec7", + "id": "99f73687", "metadata": { "hide-output": false }, @@ -997,7 +997,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06587cb2", + "id": "46a5d6a7", "metadata": { "hide-output": false }, @@ -1009,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "a2c6338e", + "id": "f401a09e", "metadata": {}, "source": [ "Now probability mass of $ L\\left(w^t\\right) $ falling above\n", @@ -1019,7 +1019,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c149c9d1", + "id": "7d42931e", "metadata": { "hide-output": false }, @@ -1031,7 +1031,7 @@ }, { "cell_type": "markdown", - "id": "cc10ef96", + "id": "b7d305c9", "metadata": {}, "source": [ "## Sequels\n", @@ -1045,7 +1045,7 @@ } ], "metadata": { - "date": 1706246575.0539515, + "date": 1706493929.2431805, "filename": "likelihood_ratio_process.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/lln_clt.ipynb b/_notebooks/lln_clt.ipynb index 0f04085..e38c31f 100644 --- a/_notebooks/lln_clt.ipynb +++ b/_notebooks/lln_clt.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e232946b", + "id": "32fb8ee1", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "d3593b30", + "id": "771b5c44", "metadata": {}, "source": [ "# LLN and CLT\n", @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "d9f75ab3", + "id": "be6ea30e", "metadata": {}, "source": [ "## Contents\n", @@ -37,7 +37,7 @@ }, { "cell_type": "markdown", - "id": "12c10bd1", + "id": "61165b2d", "metadata": {}, "source": [ "## Overview\n", @@ -65,7 +65,7 @@ { "cell_type": "code", "execution_count": null, - "id": "20f0bc9d", + "id": "52d210e0", "metadata": { "hide-output": false }, @@ -84,7 +84,7 @@ }, { "cell_type": "markdown", - "id": "fbdae437", + "id": "d94cc6b7", "metadata": {}, "source": [ "## Relationships\n", @@ -101,7 +101,7 @@ }, { "cell_type": "markdown", - "id": "54fb8b58", + "id": "a793231c", "metadata": {}, "source": [ "## LLN\n", @@ -117,7 +117,7 @@ }, { "cell_type": "markdown", - "id": "03064a37", + "id": "51e28790", "metadata": {}, "source": [ "### The Classical LLN\n", @@ -165,7 +165,7 @@ }, { "cell_type": "markdown", - "id": "43474177", + "id": "c0f85e2a", "metadata": {}, "source": [ "### Proof\n", @@ -254,7 +254,7 @@ }, { "cell_type": "markdown", - "id": "7b46e6e5", + "id": "2e5eaad2", "metadata": {}, "source": [ "### Illustration\n", @@ -278,7 +278,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98c4305b", + "id": "fc442523", "metadata": { "hide-output": false }, @@ -333,7 +333,7 @@ }, { "cell_type": "markdown", - "id": "34eb2988", + "id": "80d3b796", "metadata": {}, "source": [ "The three distributions are chosen at random from a selection stored in the dictionary `distributions`." @@ -341,7 +341,7 @@ }, { "cell_type": "markdown", - "id": "b378e229", + "id": "bd5cfb53", "metadata": {}, "source": [ "## CLT\n", @@ -353,7 +353,7 @@ }, { "cell_type": "markdown", - "id": "a456185b", + "id": "536edbab", "metadata": {}, "source": [ "### Statement of the Theorem\n", @@ -380,7 +380,7 @@ }, { "cell_type": "markdown", - "id": "c6db1f87", + "id": "98fd3c32", "metadata": {}, "source": [ "### Intuition\n", @@ -414,7 +414,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ad64c3eb", + "id": "a02c6af8", "metadata": { "hide-output": false }, @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "235523e6", + "id": "50c72720", "metadata": {}, "source": [ "When $ n = 1 $, the distribution is flat — one success or no successes\n", @@ -469,7 +469,7 @@ }, { "cell_type": "markdown", - "id": "dbd600f9", + "id": "59b10f4a", "metadata": {}, "source": [ "### Simulation 1\n", @@ -496,7 +496,7 @@ { "cell_type": "code", "execution_count": null, - "id": "91d66f17", + "id": "f7df547d", "metadata": { "hide-output": false }, @@ -529,7 +529,7 @@ }, { "cell_type": "markdown", - "id": "f5ef0cdd", + "id": "520945ea", "metadata": {}, "source": [ "Notice the absence of for loops — every operation is vectorized, meaning that the major calculations are all shifted to highly optimized C code.\n", @@ -541,7 +541,7 @@ }, { "cell_type": "markdown", - "id": "39e10193", + "id": "788ad830", "metadata": {}, "source": [ "### Simulation 2\n", @@ -570,7 +570,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb4d8994", + "id": "0bf65b1f", "metadata": { "hide-output": false }, @@ -639,7 +639,7 @@ }, { "cell_type": "markdown", - "id": "406b7c2d", + "id": "aee25f0e", "metadata": {}, "source": [ "As expected, the distribution smooths out into a bell curve as $ n $\n", @@ -657,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "023bef11", + "id": "6741b720", "metadata": {}, "source": [ "### The Multivariate Case\n", @@ -772,7 +772,7 @@ }, { "cell_type": "markdown", - "id": "7ed84788", + "id": "c9430ab1", "metadata": {}, "source": [ "## Exercises" @@ -780,7 +780,7 @@ }, { "cell_type": "markdown", - "id": "f99acbd8", + "id": "1832af3a", "metadata": {}, "source": [ "## Exercise 5.1\n", @@ -817,7 +817,7 @@ }, { "cell_type": "markdown", - "id": "4987958a", + "id": "2e460d40", "metadata": {}, "source": [ "## Solution to[ Exercise 5.1](https://python.quantecon.org/#lln_ex1)\n", @@ -828,7 +828,7 @@ { "cell_type": "code", "execution_count": null, - "id": "46e0a335", + "id": "7e25e5fe", "metadata": { "hide-output": false }, @@ -868,7 +868,7 @@ }, { "cell_type": "markdown", - "id": "39829c2d", + "id": "1475057a", "metadata": {}, "source": [ "What happens when you replace $ [0, \\pi / 2] $ with\n", @@ -882,7 +882,7 @@ }, { "cell_type": "markdown", - "id": "5d802cc3", + "id": "1f474318", "metadata": {}, "source": [ "## Exercise 5.2\n", @@ -993,7 +993,7 @@ }, { "cell_type": "markdown", - "id": "92c2c1e4", + "id": "c107db91", "metadata": {}, "source": [ "## Solution to[ Exercise 5.2](https://python.quantecon.org/#lln_ex2)\n", @@ -1049,7 +1049,7 @@ { "cell_type": "code", "execution_count": null, - "id": "507ee9a1", + "id": "2a1c3b39", "metadata": { "hide-output": false }, @@ -1099,7 +1099,7 @@ } ], "metadata": { - "date": 1706246575.2237282, + "date": 1706493929.2944622, "filename": "lln_clt.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/mix_model.ipynb b/_notebooks/mix_model.ipynb index a084928..4c71d78 100644 --- a/_notebooks/mix_model.ipynb +++ b/_notebooks/mix_model.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c1fa7c5b", + "id": "40361045", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "5a3a6881", + "id": "e17b9e81", "metadata": {}, "source": [ "# Incorrect Models\n", @@ -22,7 +22,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7cf3c80d", + "id": "4b4a2b7c", "metadata": { "hide-output": false }, @@ -33,7 +33,7 @@ }, { "cell_type": "markdown", - "id": "27c6975f", + "id": "611c9bc1", "metadata": {}, "source": [ "## Overview\n", @@ -136,7 +136,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5dc2db89", + "id": "de30ed8a", "metadata": { "hide-output": false }, @@ -171,7 +171,7 @@ }, { "cell_type": "markdown", - "id": "f0240bcd", + "id": "493a26f6", "metadata": {}, "source": [ "Let’s use Python to generate two beta distributions" @@ -180,7 +180,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4383c559", + "id": "59c0bb3f", "metadata": { "hide-output": false }, @@ -203,7 +203,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a00e76b3", + "id": "d0a9b420", "metadata": { "hide-output": false }, @@ -230,7 +230,7 @@ }, { "cell_type": "markdown", - "id": "347165f3", + "id": "43475f18", "metadata": {}, "source": [ "We’ll also use the following Python code to prepare some informative simulations" @@ -239,7 +239,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84f91558", + "id": "ac6a2d7e", "metadata": { "hide-output": false }, @@ -252,7 +252,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f99544dc", + "id": "e622dcb1", "metadata": { "hide-output": false }, @@ -264,7 +264,7 @@ }, { "cell_type": "markdown", - "id": "14551113", + "id": "549602d2", "metadata": {}, "source": [ "## Sampling from Compound Lottery $ H $\n", @@ -308,7 +308,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d42d38ba", + "id": "f412b2bf", "metadata": { "hide-output": false }, @@ -341,7 +341,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b7d7662d", + "id": "6ea65f4e", "metadata": { "hide-output": false }, @@ -368,7 +368,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5bcf8f46", + "id": "676ec116", "metadata": { "hide-output": false }, @@ -381,7 +381,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2247e23", + "id": "b9ab4c0a", "metadata": { "hide-output": false }, @@ -393,7 +393,7 @@ }, { "cell_type": "markdown", - "id": "233c95f2", + "id": "6d443753", "metadata": {}, "source": [ "**Note:** With numba acceleration the first method is actually only slightly slower than the second when we generated 1,000,000 samples." @@ -401,7 +401,7 @@ }, { "cell_type": "markdown", - "id": "f15b5317", + "id": "c4762eff", "metadata": {}, "source": [ "## Type 1 Agent\n", @@ -441,7 +441,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b7c8c961", + "id": "5f71808c", "metadata": { "hide-output": false }, @@ -459,7 +459,7 @@ }, { "cell_type": "markdown", - "id": "302f1750", + "id": "026cb72f", "metadata": {}, "source": [ "Formula [(16.1)](#equation-equation-eq-recur1) can be generalized by iterating on it and thereby deriving an\n", @@ -526,7 +526,7 @@ }, { "cell_type": "markdown", - "id": "726fee6b", + "id": "f0ff1de7", "metadata": {}, "source": [ "## What a type 1 Agent Learns when Mixture $ H $ Generates Data\n", @@ -548,7 +548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "00d0b3fd", + "id": "77badcf9", "metadata": { "hide-output": false }, @@ -603,7 +603,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f97e9c8b", + "id": "80bd7d1a", "metadata": { "hide-output": false }, @@ -614,7 +614,7 @@ }, { "cell_type": "markdown", - "id": "30cfe281", + "id": "611fb249", "metadata": {}, "source": [ "The above graph shows a sample path of the log likelihood ratio process as the blue dotted line, together with\n", @@ -626,7 +626,7 @@ { "cell_type": "code", "execution_count": null, - "id": "261f4a05", + "id": "453ad2e6", "metadata": { "hide-output": false }, @@ -637,7 +637,7 @@ }, { "cell_type": "markdown", - "id": "655952e8", + "id": "d6b2938d", "metadata": {}, "source": [ "Evidently, $ \\alpha $ is having a big effect on the destination of $ \\pi_t $ as $ t \\rightarrow + \\infty $" @@ -645,7 +645,7 @@ }, { "cell_type": "markdown", - "id": "444d7aab", + "id": "eea832ec", "metadata": {}, "source": [ "## Kullback-Leibler Divergence Governs Limit of $ \\pi_t $\n", @@ -685,7 +685,7 @@ { "cell_type": "code", "execution_count": null, - "id": "130b56ba", + "id": "c4414544", "metadata": { "hide-output": false }, @@ -742,7 +742,7 @@ }, { "cell_type": "markdown", - "id": "75480e0c", + "id": "ec7594bb", "metadata": {}, "source": [ "Let us first plot the KL divergences $ KL_g\\left(\\alpha\\right), KL_f\\left(\\alpha\\right) $ for each $ \\alpha $." @@ -751,7 +751,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c2aafaaf", + "id": "96bc3c70", "metadata": { "hide-output": false }, @@ -775,7 +775,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3fad9513", + "id": "8857b0d8", "metadata": { "hide-output": false }, @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "2866e834", + "id": "d3c0836d", "metadata": {}, "source": [ "Let’s compute an $ \\alpha $ for which the KL divergence between $ h $ and $ g $ is the same as that between $ h $ and $ f $." @@ -808,7 +808,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c47fb858", + "id": "2445df82", "metadata": { "hide-output": false }, @@ -820,7 +820,7 @@ }, { "cell_type": "markdown", - "id": "86592da3", + "id": "6e112dec", "metadata": {}, "source": [ "We can compute and plot the convergence point $ \\pi_{\\infty} $ for each $ \\alpha $ to verify that the convergence is indeed governed by the KL divergence.\n", @@ -834,7 +834,7 @@ { "cell_type": "code", "execution_count": null, - "id": "504708fb", + "id": "5ad3a4d7", "metadata": { "hide-output": false }, @@ -864,7 +864,7 @@ }, { "cell_type": "markdown", - "id": "98486c46", + "id": "1f31c250", "metadata": {}, "source": [ "Evidently, our type 1 learner who applies Bayes’ law to his misspecified set of statistical models eventually learns an approximating model that is as close as possible to the true model, as measured by its\n", @@ -873,7 +873,7 @@ }, { "cell_type": "markdown", - "id": "4a75f230", + "id": "831b1e03", "metadata": {}, "source": [ "## Type 2 Agent\n", @@ -919,7 +919,7 @@ { "cell_type": "code", "execution_count": null, - "id": "24a657c1", + "id": "7a9e148d", "metadata": { "hide-output": false }, @@ -950,7 +950,7 @@ }, { "cell_type": "markdown", - "id": "b0f9d71c", + "id": "76368ed9", "metadata": {}, "source": [ "The following code generates the graph below that displays Bayesian posteriors for $ \\alpha $ at various history lengths." @@ -959,7 +959,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fdcf2c63", + "id": "a593a43f", "metadata": { "hide-output": false }, @@ -981,7 +981,7 @@ }, { "cell_type": "markdown", - "id": "79e91345", + "id": "791e577a", "metadata": {}, "source": [ "Evidently, the Bayesian posterior narrows in on the true value $ \\alpha = .8 $ of the mixing parameter as the length of a history of observations grows." @@ -989,7 +989,7 @@ }, { "cell_type": "markdown", - "id": "7a9a86b7", + "id": "098cf577", "metadata": {}, "source": [ "## Concluding Remarks\n", @@ -1028,7 +1028,7 @@ } ], "metadata": { - "date": 1706246575.270256, + "date": 1706493929.3413239, "filename": "mix_model.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/mle.ipynb b/_notebooks/mle.ipynb index 42ca876..156609f 100644 --- a/_notebooks/mle.ipynb +++ b/_notebooks/mle.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "9cf79ea6", + "id": "83f6f5da", "metadata": {}, "source": [ "# Maximum Likelihood Estimation" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "0c1d075a", + "id": "d75ce149", "metadata": {}, "source": [ "## Contents\n", @@ -28,7 +28,7 @@ }, { "cell_type": "markdown", - "id": "91d68b46", + "id": "e286bc11", "metadata": {}, "source": [ "## Overview\n", @@ -54,7 +54,7 @@ { "cell_type": "code", "execution_count": null, - "id": "567790fc", + "id": "04ef30c6", "metadata": { "hide-output": false }, @@ -75,7 +75,7 @@ }, { "cell_type": "markdown", - "id": "2830f1c1", + "id": "baf88feb", "metadata": {}, "source": [ "### Prerequisites\n", @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "7eda09a7", + "id": "889343e2", "metadata": {}, "source": [ "## Set Up and Assumptions\n", @@ -95,7 +95,7 @@ }, { "cell_type": "markdown", - "id": "74346cd3", + "id": "fe13505d", "metadata": {}, "source": [ "### Flow of Ideas\n", @@ -120,7 +120,7 @@ }, { "cell_type": "markdown", - "id": "464b4a71", + "id": "8c17303b", "metadata": {}, "source": [ "### Counting Billionaires\n", @@ -147,7 +147,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b14e4fad", + "id": "46e51627", "metadata": { "hide-output": false }, @@ -180,7 +180,7 @@ }, { "cell_type": "markdown", - "id": "7c0ae9ca", + "id": "220d7d54", "metadata": {}, "source": [ "Notice that the Poisson distribution begins to resemble a normal distribution as the mean of $ y $ increases.\n", @@ -196,7 +196,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ecdce105", + "id": "d5e0bf9d", "metadata": { "hide-output": false }, @@ -211,7 +211,7 @@ }, { "cell_type": "markdown", - "id": "589eae2b", + "id": "da225f2a", "metadata": {}, "source": [ "Using a histogram, we can view the distribution of the number of\n", @@ -222,7 +222,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1527f6f8", + "id": "d6dcb593", "metadata": { "hide-output": false }, @@ -242,7 +242,7 @@ }, { "cell_type": "markdown", - "id": "35e27d0b", + "id": "f0bf78ee", "metadata": {}, "source": [ "From the histogram, it appears that the Poisson assumption is not unreasonable (albeit with a very low $ \\mu $ and some outliers)." @@ -250,7 +250,7 @@ }, { "cell_type": "markdown", - "id": "05ed136b", + "id": "030c8a98", "metadata": {}, "source": [ "## Conditional Distributions\n", @@ -283,7 +283,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88b887bc", + "id": "477c5a39", "metadata": { "hide-output": false }, @@ -325,7 +325,7 @@ }, { "cell_type": "markdown", - "id": "2b89441e", + "id": "efeebf22", "metadata": {}, "source": [ "We can see that the distribution of $ y_i $ is conditional on\n", @@ -334,7 +334,7 @@ }, { "cell_type": "markdown", - "id": "25cc1aae", + "id": "c8b7aa58", "metadata": {}, "source": [ "## Maximum Likelihood Estimation\n", @@ -373,7 +373,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5315d7b", + "id": "ad3391c7", "metadata": { "hide-output": false }, @@ -401,7 +401,7 @@ }, { "cell_type": "markdown", - "id": "a831db9a", + "id": "9efccc75", "metadata": {}, "source": [ "Similarly, the joint pmf of our data (which is distributed as a\n", @@ -477,7 +477,7 @@ }, { "cell_type": "markdown", - "id": "8e226dd9", + "id": "82bda339", "metadata": {}, "source": [ "## MLE with Numerical Methods\n", @@ -502,7 +502,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09e3de13", + "id": "74db12af", "metadata": { "hide-output": false }, @@ -533,7 +533,7 @@ }, { "cell_type": "markdown", - "id": "d1b0a4e2", + "id": "9fe9d1cc", "metadata": {}, "source": [ "The plot shows that the maximum likelihood value (the top plot) occurs\n", @@ -587,7 +587,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36a03281", + "id": "d7d23e31", "metadata": { "hide-output": false }, @@ -624,7 +624,7 @@ }, { "cell_type": "markdown", - "id": "ae46ea60", + "id": "768bc245", "metadata": {}, "source": [ "Our function `newton_raphson` will take a `PoissonRegression` object\n", @@ -648,7 +648,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23927ca4", + "id": "38ca19bf", "metadata": { "hide-output": false }, @@ -690,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "fdec7695", + "id": "54bd27df", "metadata": {}, "source": [ "Let’s try out our algorithm with a small dataset of 5 observations and 3\n", @@ -700,7 +700,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab515bae", + "id": "5373702c", "metadata": { "hide-output": false }, @@ -726,7 +726,7 @@ }, { "cell_type": "markdown", - "id": "968881c2", + "id": "ba61c081", "metadata": {}, "source": [ "As this was a simple model with few observations, the algorithm achieved\n", @@ -749,7 +749,7 @@ { "cell_type": "code", "execution_count": null, - "id": "193559e9", + "id": "de7601e8", "metadata": { "hide-output": false }, @@ -760,7 +760,7 @@ }, { "cell_type": "markdown", - "id": "0f5e166f", + "id": "dd00744b", "metadata": {}, "source": [ "The iterative process can be visualized in the following diagram, where\n", @@ -770,7 +770,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e60cfd94", + "id": "bbb18ecd", "metadata": { "hide-output": false }, @@ -810,7 +810,7 @@ }, { "cell_type": "markdown", - "id": "d4be0424", + "id": "bc202373", "metadata": {}, "source": [ "Note that our implementation of the Newton-Raphson algorithm is rather\n", @@ -820,7 +820,7 @@ }, { "cell_type": "markdown", - "id": "25fbe6c9", + "id": "ff8f2379", "metadata": {}, "source": [ "## Maximum Likelihood Estimation with `statsmodels`\n", @@ -840,7 +840,7 @@ { "cell_type": "code", "execution_count": null, - "id": "be38b07b", + "id": "31b0ac41", "metadata": { "hide-output": false }, @@ -860,7 +860,7 @@ }, { "cell_type": "markdown", - "id": "dc2d24bd", + "id": "d1a338e2", "metadata": {}, "source": [ "Now let’s replicate results from Daniel Treisman’s paper, [Russia’s\n", @@ -884,7 +884,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0660915c", + "id": "cd3550d8", "metadata": { "hide-output": false }, @@ -906,7 +906,7 @@ }, { "cell_type": "markdown", - "id": "619a2d62", + "id": "b305c9b2", "metadata": {}, "source": [ "Then we can use the `Poisson` function from `statsmodels` to fit the\n", @@ -918,7 +918,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83a98883", + "id": "22bb5c5c", "metadata": { "hide-output": false }, @@ -932,7 +932,7 @@ }, { "cell_type": "markdown", - "id": "42690ccf", + "id": "4c3df58f", "metadata": {}, "source": [ "Success! The algorithm was able to achieve convergence in 9 iterations.\n", @@ -949,7 +949,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e75f53bc", + "id": "8e52992a", "metadata": { "hide-output": false }, @@ -989,7 +989,7 @@ }, { "cell_type": "markdown", - "id": "410f542c", + "id": "418acccd", "metadata": {}, "source": [ "The output suggests that the frequency of billionaires is positively\n", @@ -1005,7 +1005,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3fffc94", + "id": "71e50e17", "metadata": { "hide-output": false }, @@ -1034,7 +1034,7 @@ }, { "cell_type": "markdown", - "id": "ceed2eb2", + "id": "5228e66e", "metadata": {}, "source": [ "As we can see, Russia has by far the highest number of billionaires in\n", @@ -1048,7 +1048,7 @@ }, { "cell_type": "markdown", - "id": "69e78e29", + "id": "d8231ad9", "metadata": {}, "source": [ "## Summary\n", @@ -1069,7 +1069,7 @@ }, { "cell_type": "markdown", - "id": "956cd2d4", + "id": "6a6e932a", "metadata": {}, "source": [ "## Exercises" @@ -1077,7 +1077,7 @@ }, { "cell_type": "markdown", - "id": "62aaddb0", + "id": "988bf3a2", "metadata": {}, "source": [ "## Exercise 3.1\n", @@ -1112,7 +1112,7 @@ }, { "cell_type": "markdown", - "id": "fc865400", + "id": "4483be28", "metadata": {}, "source": [ "## Solution to[ Exercise 3.1](https://python.quantecon.org/#mle_ex1)\n", @@ -1164,7 +1164,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d97ad65c", + "id": "48df6adc", "metadata": { "hide-output": false }, @@ -1204,7 +1204,7 @@ }, { "cell_type": "markdown", - "id": "4b493453", + "id": "6c26ee46", "metadata": {}, "source": [ "## Exercise 3.2\n", @@ -1247,7 +1247,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8df8caba", + "id": "60bf0ac6", "metadata": { "hide-output": false }, @@ -1258,7 +1258,7 @@ }, { "cell_type": "markdown", - "id": "152cd20c", + "id": "dfc328f1", "metadata": {}, "source": [ "Note that the simple Newton-Raphson algorithm developed in this lecture\n", @@ -1268,7 +1268,7 @@ }, { "cell_type": "markdown", - "id": "57dd0cd4", + "id": "85b9f667", "metadata": {}, "source": [ "## Solution to[ Exercise 3.2](https://python.quantecon.org/#mle_ex2)\n", @@ -1279,7 +1279,7 @@ { "cell_type": "code", "execution_count": null, - "id": "53ca3d28", + "id": "749a2eab", "metadata": { "hide-output": false }, @@ -1306,7 +1306,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6dd8cc1e", + "id": "15d3767d", "metadata": { "hide-output": false }, @@ -1319,7 +1319,7 @@ } ], "metadata": { - "date": 1706246575.3195305, + "date": 1706493929.3915737, "filename": "mle.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/multi_hyper.ipynb b/_notebooks/multi_hyper.ipynb index 26c9dbc..d0aa7df 100644 --- a/_notebooks/multi_hyper.ipynb +++ b/_notebooks/multi_hyper.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "927fcab2", + "id": "aa550aff", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "50c0b1a3", + "id": "41682b2f", "metadata": {}, "source": [ "# Multivariate Hypergeometric Distribution" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "c99f90bd", + "id": "5b2e9002", "metadata": {}, "source": [ "## Contents\n", @@ -32,7 +32,7 @@ }, { "cell_type": "markdown", - "id": "27021402", + "id": "84bfb580", "metadata": {}, "source": [ "## Overview\n", @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "23e1ac3e", + "id": "52e9fe1a", "metadata": {}, "source": [ "## The Administrator’s Problem\n", @@ -82,7 +82,7 @@ }, { "cell_type": "markdown", - "id": "d0136f1d", + "id": "df6e5485", "metadata": {}, "source": [ "### Details of the Awards Procedure Under Study\n", @@ -132,7 +132,7 @@ }, { "cell_type": "markdown", - "id": "cee50a85", + "id": "d3d982f9", "metadata": {}, "source": [ "### Multivariate Hypergeometric Distribution\n", @@ -143,7 +143,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f71c8b05", + "id": "eeb362d6", "metadata": { "hide-output": false }, @@ -159,7 +159,7 @@ }, { "cell_type": "markdown", - "id": "2a5025c8", + "id": "773c7317", "metadata": {}, "source": [ "To recapitulate, we assume there are in total $ c $ types of objects in an urn.\n", @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a416e4f2", + "id": "b4408b48", "metadata": { "hide-output": false }, @@ -305,7 +305,7 @@ }, { "cell_type": "markdown", - "id": "84476908", + "id": "508808c8", "metadata": {}, "source": [ "## Usage" @@ -313,7 +313,7 @@ }, { "cell_type": "markdown", - "id": "c52e9ff0", + "id": "2daf5b5a", "metadata": {}, "source": [ "### First example\n", @@ -333,7 +333,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ebe9e69", + "id": "03e71c4f", "metadata": { "hide-output": false }, @@ -346,7 +346,7 @@ }, { "cell_type": "markdown", - "id": "1abda759", + "id": "80cc83ba", "metadata": {}, "source": [ "Now use the Urn Class method `pmf` to compute the probability of the outcome $ X = \\begin{pmatrix} 2 & 2 & 2 \\end{pmatrix} $" @@ -355,7 +355,7 @@ { "cell_type": "code", "execution_count": null, - "id": "841d36cd", + "id": "90030cb8", "metadata": { "hide-output": false }, @@ -367,7 +367,7 @@ }, { "cell_type": "markdown", - "id": "b89b54ac", + "id": "bddc5178", "metadata": {}, "source": [ "We can use the code to compute probabilities of a list of possible outcomes by\n", @@ -379,7 +379,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b9c6983b", + "id": "45fec20d", "metadata": { "hide-output": false }, @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "3a99fe7c", + "id": "d1b6879c", "metadata": {}, "source": [ "Now let’s compute the mean vector and variance-covariance matrix." @@ -400,7 +400,7 @@ { "cell_type": "code", "execution_count": null, - "id": "262daf34", + "id": "781abfeb", "metadata": { "hide-output": false }, @@ -413,7 +413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84a455d6", + "id": "fabb6366", "metadata": { "hide-output": false }, @@ -425,7 +425,7 @@ { "cell_type": "code", "execution_count": null, - "id": "955b9d05", + "id": "28c6a565", "metadata": { "hide-output": false }, @@ -436,7 +436,7 @@ }, { "cell_type": "markdown", - "id": "fba92a21", + "id": "7d2f259e", "metadata": {}, "source": [ "### Back to The Administrator’s Problem\n", @@ -451,7 +451,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2d19be79", + "id": "743f25ae", "metadata": { "hide-output": false }, @@ -463,7 +463,7 @@ }, { "cell_type": "markdown", - "id": "44a4471f", + "id": "d098e49f", "metadata": {}, "source": [ "Let’s compute the probability of the outcome $ \\left(10, 1, 4, 0 \\right) $." @@ -472,7 +472,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b28ba76", + "id": "f780e023", "metadata": { "hide-output": false }, @@ -484,7 +484,7 @@ }, { "cell_type": "markdown", - "id": "6b3c8053", + "id": "fb63fc9d", "metadata": {}, "source": [ "We can compute probabilities of three possible outcomes by constructing a 3-dimensional\n", @@ -494,7 +494,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f861355a", + "id": "caef2fb7", "metadata": { "hide-output": false }, @@ -506,7 +506,7 @@ }, { "cell_type": "markdown", - "id": "d100b162", + "id": "237231f6", "metadata": {}, "source": [ "Now let’s compute the mean and variance-covariance matrix of $ X $ when $ n=6 $." @@ -515,7 +515,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c035a722", + "id": "cf6d3a58", "metadata": { "hide-output": false }, @@ -528,7 +528,7 @@ { "cell_type": "code", "execution_count": null, - "id": "10f39730", + "id": "27419aa4", "metadata": { "hide-output": false }, @@ -541,7 +541,7 @@ { "cell_type": "code", "execution_count": null, - "id": "61361f69", + "id": "8d97e0e6", "metadata": { "hide-output": false }, @@ -553,7 +553,7 @@ }, { "cell_type": "markdown", - "id": "5c5b6d8b", + "id": "59596deb", "metadata": {}, "source": [ "We can simulate a large sample and verify that sample means and covariances closely approximate the population means and covariances." @@ -562,7 +562,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47fde3e4", + "id": "5082b086", "metadata": { "hide-output": false }, @@ -575,7 +575,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc8a5283", + "id": "eaa4825a", "metadata": { "hide-output": false }, @@ -588,7 +588,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c47c93b", + "id": "2e05fb65", "metadata": { "hide-output": false }, @@ -600,7 +600,7 @@ }, { "cell_type": "markdown", - "id": "e74a25ad", + "id": "d95efb08", "metadata": {}, "source": [ "Evidently, the sample means and covariances approximate their population counterparts well." @@ -608,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "9749e4b2", + "id": "5b21105c", "metadata": {}, "source": [ "### Quality of Normal Approximation\n", @@ -619,7 +619,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b94f0cf", + "id": "8c26624c", "metadata": { "hide-output": false }, @@ -631,7 +631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "494b5f8f", + "id": "d1cf1c1c", "metadata": { "hide-output": false }, @@ -656,7 +656,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5d4f265", + "id": "a0cb08c2", "metadata": { "hide-output": false }, @@ -676,7 +676,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a9ab3b4", + "id": "5f507d95", "metadata": { "hide-output": false }, @@ -714,7 +714,7 @@ }, { "cell_type": "markdown", - "id": "a8f12957", + "id": "7e5934c9", "metadata": {}, "source": [ "The diagonal graphs plot the marginal distributions of $ k_i $ for\n", @@ -740,7 +740,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c1e4ff9c", + "id": "e8e07b61", "metadata": { "hide-output": false }, @@ -752,7 +752,7 @@ }, { "cell_type": "markdown", - "id": "269dcfa7", + "id": "534c1da6", "metadata": {}, "source": [ "As we can see, all the p-values are almost $ 0 $ and the null hypothesis is soundly rejected.\n", @@ -763,7 +763,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f27613d", + "id": "85abefc9", "metadata": { "hide-output": false }, @@ -775,7 +775,7 @@ }, { "cell_type": "markdown", - "id": "98ed5898", + "id": "f1d65485", "metadata": {}, "source": [ "The lesson to take away from this is that the normal approximation is imperfect." @@ -783,7 +783,7 @@ } ], "metadata": { - "date": 1706246575.3554652, + "date": 1706493929.5398035, "filename": "multi_hyper.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/multivariate_normal.ipynb b/_notebooks/multivariate_normal.ipynb index 7d4cd9c..4898dd6 100644 --- a/_notebooks/multivariate_normal.ipynb +++ b/_notebooks/multivariate_normal.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "3b48a312", + "id": "57f326ce", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "3d09f1d5", + "id": "70115167", "metadata": {}, "source": [ "# Multivariate Normal Distribution" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "e871894a", + "id": "6daab581", "metadata": {}, "source": [ "## Contents\n", @@ -43,7 +43,7 @@ }, { "cell_type": "markdown", - "id": "42516209", + "id": "d657b872", "metadata": {}, "source": [ "## Overview\n", @@ -70,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "0a6c22a4", + "id": "941c2b36", "metadata": {}, "source": [ "## The Multivariate Normal Distribution\n", @@ -94,7 +94,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af3577cd", + "id": "910b0bd2", "metadata": { "hide-output": false }, @@ -109,7 +109,7 @@ }, { "cell_type": "markdown", - "id": "0131eeef", + "id": "a504dd5f", "metadata": {}, "source": [ "Assume that an $ N \\times 1 $ random vector $ z $ has a\n", @@ -131,7 +131,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ec70bc63", + "id": "72dcd13b", "metadata": { "hide-output": false }, @@ -166,7 +166,7 @@ }, { "cell_type": "markdown", - "id": "7ee96d9c", + "id": "99356320", "metadata": {}, "source": [ "For some integer $ k\\in \\{1,\\dots, N-1\\} $, partition\n", @@ -242,7 +242,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af482c24", + "id": "813e5168", "metadata": { "hide-output": false }, @@ -320,7 +320,7 @@ }, { "cell_type": "markdown", - "id": "a6f1f29d", + "id": "4b1b812d", "metadata": {}, "source": [ "Let’s put this code to work on a suite of examples.\n", @@ -341,7 +341,7 @@ }, { "cell_type": "markdown", - "id": "11f0689b", + "id": "ab2e4a3a", "metadata": {}, "source": [ "## Bivariate Example\n", @@ -362,7 +362,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab7d078d", + "id": "aabcb404", "metadata": { "hide-output": false }, @@ -378,7 +378,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ace54688", + "id": "979674a7", "metadata": { "hide-output": false }, @@ -393,7 +393,7 @@ }, { "cell_type": "markdown", - "id": "b0ee7c55", + "id": "b24acc51", "metadata": {}, "source": [ "Let’s illustrate the fact that you *can regress anything on anything else*.\n", @@ -430,7 +430,7 @@ { "cell_type": "code", "execution_count": null, - "id": "19aa35a6", + "id": "3f2824cf", "metadata": { "hide-output": false }, @@ -447,7 +447,7 @@ }, { "cell_type": "markdown", - "id": "f53e5de3", + "id": "9af1b6ae", "metadata": {}, "source": [ "Let’s print out the intercepts and slopes.\n", @@ -458,7 +458,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e7e5a4d", + "id": "17c7cd7f", "metadata": { "hide-output": false }, @@ -470,7 +470,7 @@ }, { "cell_type": "markdown", - "id": "12ff75ce", + "id": "6928624a", "metadata": {}, "source": [ "For the regression of $ z_2 $ on $ z_1 $ we have" @@ -479,7 +479,7 @@ { "cell_type": "code", "execution_count": null, - "id": "762f9301", + "id": "7fb0d68b", "metadata": { "hide-output": false }, @@ -491,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "a38bf9fc", + "id": "4379760f", "metadata": {}, "source": [ "Now let’s plot the two regression lines and stare at them." @@ -500,7 +500,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2ddab68", + "id": "50c5d3a1", "metadata": { "hide-output": false }, @@ -541,7 +541,7 @@ }, { "cell_type": "markdown", - "id": "f22ce4cd", + "id": "4bc8ea6e", "metadata": {}, "source": [ "The red line is the expectation of $ z_1 $ conditional on $ z_2 $.\n", @@ -552,7 +552,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d948a73e", + "id": "ae7fb023", "metadata": { "hide-output": false }, @@ -564,7 +564,7 @@ }, { "cell_type": "markdown", - "id": "79cd1706", + "id": "4a964ff8", "metadata": {}, "source": [ "The blue line is the expectation of $ z_2 $ conditional on $ z_1 $.\n", @@ -575,7 +575,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f31eab3", + "id": "a8552634", "metadata": { "hide-output": false }, @@ -587,7 +587,7 @@ }, { "cell_type": "markdown", - "id": "e906b794", + "id": "392cedf7", "metadata": {}, "source": [ "We can use these regression lines or our code to compute conditional expectations.\n", @@ -601,7 +601,7 @@ { "cell_type": "code", "execution_count": null, - "id": "70542f90", + "id": "415ef349", "metadata": { "hide-output": false }, @@ -617,7 +617,7 @@ }, { "cell_type": "markdown", - "id": "d8aa0e51", + "id": "f153e48b", "metadata": {}, "source": [ "Now let’s compute the mean and variance of the distribution of $ z_1 $\n", @@ -627,7 +627,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87102233", + "id": "4782c096", "metadata": { "hide-output": false }, @@ -643,7 +643,7 @@ }, { "cell_type": "markdown", - "id": "c08208ff", + "id": "d476666f", "metadata": {}, "source": [ "Let’s compare the preceding population mean and variance with outcomes\n", @@ -670,7 +670,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0814774e", + "id": "b830a13b", "metadata": { "hide-output": false }, @@ -690,7 +690,7 @@ }, { "cell_type": "markdown", - "id": "889bccbe", + "id": "c7c47da0", "metadata": {}, "source": [ "Let’s compare the preceding population $ \\beta $ with the OLS sample\n", @@ -700,7 +700,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32b78620", + "id": "3e7fa9b2", "metadata": { "hide-output": false }, @@ -711,7 +711,7 @@ }, { "cell_type": "markdown", - "id": "cba36efd", + "id": "d1f155b1", "metadata": {}, "source": [ "Let’s compare our population $ \\hat{\\Sigma}_1 $ with the\n", @@ -721,7 +721,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3436716c", + "id": "5f935fd8", "metadata": { "hide-output": false }, @@ -732,7 +732,7 @@ }, { "cell_type": "markdown", - "id": "a6615616", + "id": "c61670e1", "metadata": {}, "source": [ "Lastly, let’s compute the estimate of $ \\hat{E z_1 | z_2} $ and\n", @@ -742,7 +742,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dffc6019", + "id": "c374472f", "metadata": { "hide-output": false }, @@ -753,7 +753,7 @@ }, { "cell_type": "markdown", - "id": "8f60a4ae", + "id": "537a1bff", "metadata": {}, "source": [ "Thus, in each case, for our very large sample size, the sample analogues\n", @@ -765,7 +765,7 @@ }, { "cell_type": "markdown", - "id": "5882b4fc", + "id": "78063527", "metadata": {}, "source": [ "## Trivariate Example\n", @@ -778,7 +778,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b55101e6", + "id": "4beda62b", "metadata": { "hide-output": false }, @@ -794,7 +794,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f367579c", + "id": "237b3e5b", "metadata": { "hide-output": false }, @@ -806,7 +806,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f91fb71", + "id": "7217a400", "metadata": { "hide-output": false }, @@ -818,7 +818,7 @@ }, { "cell_type": "markdown", - "id": "c18737cb", + "id": "9daa7782", "metadata": {}, "source": [ "Let’s compute the distribution of $ z_1 $ conditional on\n", @@ -828,7 +828,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77fb46a8", + "id": "8b0e7d26", "metadata": { "hide-output": false }, @@ -843,7 +843,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2d81358a", + "id": "518f5c8a", "metadata": { "hide-output": false }, @@ -858,7 +858,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c1c3e004", + "id": "3a552051", "metadata": { "hide-output": false }, @@ -870,7 +870,7 @@ }, { "cell_type": "markdown", - "id": "41ad1f06", + "id": "0de7102a", "metadata": {}, "source": [ "As above, we compare population and sample regression coefficients, the\n", @@ -881,7 +881,7 @@ { "cell_type": "code", "execution_count": null, - "id": "828c0b0b", + "id": "9743264c", "metadata": { "hide-output": false }, @@ -893,7 +893,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8e37c3e", + "id": "b98b45d1", "metadata": { "hide-output": false }, @@ -905,7 +905,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0de3a1c", + "id": "ca59c90d", "metadata": { "hide-output": false }, @@ -916,7 +916,7 @@ }, { "cell_type": "markdown", - "id": "b3571183", + "id": "21d05400", "metadata": {}, "source": [ "Once again, sample analogues do a good job of approximating their\n", @@ -925,7 +925,7 @@ }, { "cell_type": "markdown", - "id": "acd15f97", + "id": "8c6d7c83", "metadata": {}, "source": [ "## One Dimensional Intelligence (IQ)\n", @@ -1019,7 +1019,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3689ee85", + "id": "6eec1a30", "metadata": { "hide-output": false }, @@ -1040,7 +1040,7 @@ }, { "cell_type": "markdown", - "id": "e3e61b9d", + "id": "c832be02", "metadata": {}, "source": [ "Now let’s consider a specific instance of this model.\n", @@ -1056,7 +1056,7 @@ { "cell_type": "code", "execution_count": null, - "id": "67299121", + "id": "a3d9b7d5", "metadata": { "hide-output": false }, @@ -1071,7 +1071,7 @@ }, { "cell_type": "markdown", - "id": "3acf028d", + "id": "d6c71d9a", "metadata": {}, "source": [ "We can now use our `MultivariateNormal` class to construct an\n", @@ -1086,7 +1086,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fb4f39f", + "id": "9bf08031", "metadata": { "hide-output": false }, @@ -1100,7 +1100,7 @@ }, { "cell_type": "markdown", - "id": "2a05e8d7", + "id": "0db39734", "metadata": {}, "source": [ "Using the generator `multivariate_normal`, we can make one draw of the\n", @@ -1113,7 +1113,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4036ff1", + "id": "f7f88e1f", "metadata": { "hide-output": false }, @@ -1127,7 +1127,7 @@ { "cell_type": "code", "execution_count": null, - "id": "225bcc8a", + "id": "993f02c5", "metadata": { "hide-output": false }, @@ -1139,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "a81c7260", + "id": "2c1dda48", "metadata": {}, "source": [ "The method `cond_dist` takes test scores $ y $ as input and returns the\n", @@ -1154,7 +1154,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ab1f458", + "id": "8e4fe716", "metadata": { "hide-output": false }, @@ -1166,7 +1166,7 @@ }, { "cell_type": "markdown", - "id": "51f93b6f", + "id": "ce2aa748", "metadata": {}, "source": [ "The first number is the conditional mean $ \\hat{\\mu}_{\\theta} $ and\n", @@ -1185,7 +1185,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cb06c12a", + "id": "f0ec3dfc", "metadata": { "hide-output": false }, @@ -1217,7 +1217,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dcd02383", + "id": "270a099d", "metadata": { "hide-output": false }, @@ -1242,7 +1242,7 @@ }, { "cell_type": "markdown", - "id": "16cc1c7f", + "id": "9cb668f4", "metadata": {}, "source": [ "The solid blue line in the plot above shows $ \\hat{\\mu}_{\\theta} $\n", @@ -1274,7 +1274,7 @@ }, { "cell_type": "markdown", - "id": "042b8f9e", + "id": "13673b4b", "metadata": {}, "source": [ "## Information as Surprise\n", @@ -1364,7 +1364,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fae9bc0d", + "id": "774442c4", "metadata": { "hide-output": false }, @@ -1379,7 +1379,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b592db87", + "id": "b281fe56", "metadata": { "hide-output": false }, @@ -1394,7 +1394,7 @@ }, { "cell_type": "markdown", - "id": "6c417643", + "id": "1e2e7918", "metadata": {}, "source": [ "To confirm that these formulas give the same answers that we computed\n", @@ -1408,7 +1408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aff34708", + "id": "9a135b15", "metadata": { "hide-output": false }, @@ -1421,7 +1421,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17ab5448", + "id": "eb9675bb", "metadata": { "hide-output": false }, @@ -1433,7 +1433,7 @@ }, { "cell_type": "markdown", - "id": "b0f926a1", + "id": "2d3a8ace", "metadata": {}, "source": [ "## Cholesky Factor Magic\n", @@ -1455,7 +1455,7 @@ }, { "cell_type": "markdown", - "id": "fe84c507", + "id": "888bdbc0", "metadata": {}, "source": [ "## Math and Verbal Intelligence\n", @@ -1523,7 +1523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0d04604", + "id": "7814c1c5", "metadata": { "hide-output": false }, @@ -1552,7 +1552,7 @@ }, { "cell_type": "markdown", - "id": "d1050915", + "id": "5c80544b", "metadata": {}, "source": [ "Let’s put the function to work." @@ -1561,7 +1561,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23b98100", + "id": "61de1909", "metadata": { "hide-output": false }, @@ -1578,7 +1578,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8dda1385", + "id": "6b9ae46e", "metadata": { "hide-output": false }, @@ -1597,7 +1597,7 @@ }, { "cell_type": "markdown", - "id": "535adf7c", + "id": "14e205b8", "metadata": {}, "source": [ "We first compute the joint normal distribution of\n", @@ -1607,7 +1607,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ac899b87", + "id": "c3952790", "metadata": { "hide-output": false }, @@ -1623,7 +1623,7 @@ }, { "cell_type": "markdown", - "id": "6f953c7b", + "id": "c6b6b366", "metadata": {}, "source": [ "Now let’s compute distributions of $ \\theta $ and $ \\mu $\n", @@ -1636,7 +1636,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6d657e6", + "id": "ff841a19", "metadata": { "hide-output": false }, @@ -1655,7 +1655,7 @@ }, { "cell_type": "markdown", - "id": "c632d47c", + "id": "fe1ab28e", "metadata": {}, "source": [ "Let’s see how things work for an example." @@ -1664,7 +1664,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26390315", + "id": "15691f2d", "metadata": { "hide-output": false }, @@ -1684,7 +1684,7 @@ }, { "cell_type": "markdown", - "id": "166b0322", + "id": "c6803e14", "metadata": {}, "source": [ "Evidently, math tests provide no information about $ \\mu $ and\n", @@ -1693,7 +1693,7 @@ }, { "cell_type": "markdown", - "id": "5142baf5", + "id": "c6507adf", "metadata": {}, "source": [ "## Univariate Time Series Analysis\n", @@ -1794,7 +1794,7 @@ { "cell_type": "code", "execution_count": null, - "id": "14667757", + "id": "b144460f", "metadata": { "hide-output": false }, @@ -1807,7 +1807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4c71fc06", + "id": "f40a228e", "metadata": { "hide-output": false }, @@ -1826,7 +1826,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3babbb81", + "id": "d0075f64", "metadata": { "hide-output": false }, @@ -1846,7 +1846,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4731e1c3", + "id": "51b469c7", "metadata": { "hide-output": false }, @@ -1858,7 +1858,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8bc6307e", + "id": "593c6f28", "metadata": { "hide-output": false }, @@ -1874,7 +1874,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9be403cf", + "id": "4cfae7e4", "metadata": { "hide-output": false }, @@ -1892,7 +1892,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f92adc0", + "id": "45a3ea0a", "metadata": { "hide-output": false }, @@ -1904,7 +1904,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09f3bf75", + "id": "274b9c59", "metadata": { "hide-output": false }, @@ -1916,7 +1916,7 @@ }, { "cell_type": "markdown", - "id": "5103bcf8", + "id": "6c624269", "metadata": {}, "source": [ "The following Python code lets us sample random vectors $ X $ and\n", @@ -1929,7 +1929,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59681125", + "id": "e9eede8b", "metadata": { "hide-output": false }, @@ -1943,7 +1943,7 @@ }, { "cell_type": "markdown", - "id": "c50f0a7c", + "id": "977d28c6", "metadata": {}, "source": [ "### Smoothing Example\n", @@ -1962,7 +1962,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3edea18e", + "id": "048a8373", "metadata": { "hide-output": false }, @@ -1977,7 +1977,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c77ec9b", + "id": "79796362", "metadata": { "hide-output": false }, @@ -1990,7 +1990,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ccab067", + "id": "4d1c66ef", "metadata": { "hide-output": false }, @@ -2007,7 +2007,7 @@ }, { "cell_type": "markdown", - "id": "509d483b", + "id": "85313e3f", "metadata": {}, "source": [ "### Filtering Exercise\n", @@ -2025,7 +2025,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9ff67c7", + "id": "ad7d2ebc", "metadata": { "hide-output": false }, @@ -2037,7 +2037,7 @@ { "cell_type": "code", "execution_count": null, - "id": "725ed8f3", + "id": "2c2020f8", "metadata": { "hide-output": false }, @@ -2058,7 +2058,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4949377d", + "id": "1c10b709", "metadata": { "hide-output": false }, @@ -2070,7 +2070,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b7f24596", + "id": "fe1ad522", "metadata": { "hide-output": false }, @@ -2083,7 +2083,7 @@ { "cell_type": "code", "execution_count": null, - "id": "95db1f51", + "id": "17154e18", "metadata": { "hide-output": false }, @@ -2096,7 +2096,7 @@ }, { "cell_type": "markdown", - "id": "a6d1258c", + "id": "7fe99682", "metadata": {}, "source": [ "### Prediction Exercise\n", @@ -2113,7 +2113,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aafd9c0b", + "id": "92ff7ac7", "metadata": { "hide-output": false }, @@ -2126,7 +2126,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8c355a7a", + "id": "e67a02c9", "metadata": { "hide-output": false }, @@ -2144,7 +2144,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7fbeb2d6", + "id": "0527a0b9", "metadata": { "hide-output": false }, @@ -2156,7 +2156,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5b2735c2", + "id": "08681527", "metadata": { "hide-output": false }, @@ -2169,7 +2169,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43648bbb", + "id": "131615bd", "metadata": { "hide-output": false }, @@ -2182,7 +2182,7 @@ }, { "cell_type": "markdown", - "id": "a671684e", + "id": "55edfc15", "metadata": {}, "source": [ "### Constructing a Wold Representation\n", @@ -2204,7 +2204,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8a5f0eb", + "id": "f05a8ba8", "metadata": { "hide-output": false }, @@ -2218,7 +2218,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3f60736c", + "id": "faec22f5", "metadata": { "hide-output": false }, @@ -2232,7 +2232,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd418643", + "id": "752efdb0", "metadata": { "hide-output": false }, @@ -2243,7 +2243,7 @@ }, { "cell_type": "markdown", - "id": "c5c250ad", + "id": "20a77cec", "metadata": {}, "source": [ "This example is an instance of what is known as a **Wold representation** in time series analysis." @@ -2251,7 +2251,7 @@ }, { "cell_type": "markdown", - "id": "4f102c1a", + "id": "7da7c7bb", "metadata": {}, "source": [ "## Stochastic Difference Equation\n", @@ -2349,7 +2349,7 @@ { "cell_type": "code", "execution_count": null, - "id": "587c9684", + "id": "0c1aab91", "metadata": { "hide-output": false }, @@ -2375,7 +2375,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea6dcaf8", + "id": "915d14f7", "metadata": { "hide-output": false }, @@ -2399,7 +2399,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76d0970e", + "id": "3ea54e14", "metadata": { "hide-output": false }, @@ -2416,7 +2416,7 @@ { "cell_type": "code", "execution_count": null, - "id": "44a42741", + "id": "25239d3e", "metadata": { "hide-output": false }, @@ -2435,7 +2435,7 @@ }, { "cell_type": "markdown", - "id": "4c644573", + "id": "8620cfb7", "metadata": {}, "source": [ "## Application to Stock Price Model\n", @@ -2483,7 +2483,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c082784a", + "id": "86032680", "metadata": { "hide-output": false }, @@ -2495,7 +2495,7 @@ { "cell_type": "code", "execution_count": null, - "id": "58b8d898", + "id": "99bc50bb", "metadata": { "hide-output": false }, @@ -2510,7 +2510,7 @@ }, { "cell_type": "markdown", - "id": "b85b3a2d", + "id": "5b8ebfd9", "metadata": {}, "source": [ "Denote\n", @@ -2541,7 +2541,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b3b70ffa", + "id": "e7f88db8", "metadata": { "hide-output": false }, @@ -2553,7 +2553,7 @@ { "cell_type": "code", "execution_count": null, - "id": "72e05d7a", + "id": "19c6adc5", "metadata": { "hide-output": false }, @@ -2565,7 +2565,7 @@ }, { "cell_type": "markdown", - "id": "4c6076c2", + "id": "3bfe9b62", "metadata": {}, "source": [ "We can simulate paths of $ y_{t} $ and $ p_{t} $ and compute the\n", @@ -2576,7 +2576,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2fa22ef7", + "id": "9c5f8666", "metadata": { "hide-output": false }, @@ -2589,7 +2589,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d2b069a", + "id": "e9ff9603", "metadata": { "hide-output": false }, @@ -2612,7 +2612,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3af8763b", + "id": "6c181275", "metadata": { "hide-output": false }, @@ -2630,7 +2630,7 @@ }, { "cell_type": "markdown", - "id": "da1fa2bb", + "id": "cf1ef1a2", "metadata": {}, "source": [ "In the above graph, the green line is what the price of the stock would\n", @@ -2643,7 +2643,7 @@ }, { "cell_type": "markdown", - "id": "dce8c9b3", + "id": "ae4173e5", "metadata": {}, "source": [ "## Filtering Foundations\n", @@ -2710,7 +2710,7 @@ }, { "cell_type": "markdown", - "id": "596bca95", + "id": "9d676683", "metadata": {}, "source": [ "### Step toward dynamics\n", @@ -2770,7 +2770,7 @@ }, { "cell_type": "markdown", - "id": "8e6eb5ce", + "id": "756395b1", "metadata": {}, "source": [ "### Dynamic version\n", @@ -2847,7 +2847,7 @@ }, { "cell_type": "markdown", - "id": "55367bf4", + "id": "5902f40a", "metadata": {}, "source": [ "### An example\n", @@ -2860,7 +2860,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f1cb6a5a", + "id": "4ba9f5ae", "metadata": { "hide-output": false }, @@ -2879,7 +2879,7 @@ { "cell_type": "code", "execution_count": null, - "id": "01abf788", + "id": "bc162eaa", "metadata": { "hide-output": false }, @@ -2892,7 +2892,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ff5083a0", + "id": "2b016f30", "metadata": { "hide-output": false }, @@ -2904,7 +2904,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2dae561", + "id": "35ca731d", "metadata": { "hide-output": false }, @@ -2921,7 +2921,7 @@ { "cell_type": "code", "execution_count": null, - "id": "81b4c726", + "id": "7514adb2", "metadata": { "hide-output": false }, @@ -2938,7 +2938,7 @@ }, { "cell_type": "markdown", - "id": "9e4a65ba", + "id": "78ad5646", "metadata": {}, "source": [ "### Code for Iterating\n", @@ -2950,7 +2950,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c763859f", + "id": "b9f7b5df", "metadata": { "hide-output": false }, @@ -2988,7 +2988,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5ff07e0a", + "id": "d16f4ffa", "metadata": { "hide-output": false }, @@ -2999,7 +2999,7 @@ }, { "cell_type": "markdown", - "id": "d3654a65", + "id": "6d6417c6", "metadata": {}, "source": [ "The iterative algorithm just described is a version of the celebrated **Kalman filter**.\n", @@ -3009,7 +3009,7 @@ }, { "cell_type": "markdown", - "id": "5f3de41e", + "id": "d22fcae4", "metadata": {}, "source": [ "## Classic Factor Analysis Model\n", @@ -3077,7 +3077,7 @@ { "cell_type": "code", "execution_count": null, - "id": "57967553", + "id": "0bd1786c", "metadata": { "hide-output": false }, @@ -3089,7 +3089,7 @@ }, { "cell_type": "markdown", - "id": "1d7e24b9", + "id": "e1bc714f", "metadata": {}, "source": [ "We set the coefficient matrix $ \\Lambda $ and the covariance matrix\n", @@ -3122,7 +3122,7 @@ { "cell_type": "code", "execution_count": null, - "id": "426a4489", + "id": "83074055", "metadata": { "hide-output": false }, @@ -3139,7 +3139,7 @@ { "cell_type": "code", "execution_count": null, - "id": "31da8e13", + "id": "306163d8", "metadata": { "hide-output": false }, @@ -3151,7 +3151,7 @@ }, { "cell_type": "markdown", - "id": "6cc314f9", + "id": "5cc57a4e", "metadata": {}, "source": [ "We can now construct the mean vector and the covariance matrix for\n", @@ -3161,7 +3161,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b86c5f77", + "id": "7f6ef1de", "metadata": { "hide-output": false }, @@ -3180,7 +3180,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75c9bba1", + "id": "63e5749e", "metadata": { "hide-output": false }, @@ -3195,7 +3195,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3594676b", + "id": "ab07fcd0", "metadata": { "hide-output": false }, @@ -3207,7 +3207,7 @@ }, { "cell_type": "markdown", - "id": "004876c6", + "id": "42244d51", "metadata": {}, "source": [ "Let’s compute the conditional distribution of the hidden factor\n", @@ -3217,7 +3217,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e44d39e5", + "id": "e3e88859", "metadata": { "hide-output": false }, @@ -3228,7 +3228,7 @@ }, { "cell_type": "markdown", - "id": "211f5bb6", + "id": "4f137932", "metadata": {}, "source": [ "We can verify that the conditional mean\n", @@ -3239,7 +3239,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f5f4f16", + "id": "a35c73ea", "metadata": { "hide-output": false }, @@ -3252,7 +3252,7 @@ }, { "cell_type": "markdown", - "id": "3157b460", + "id": "6db2a3dc", "metadata": {}, "source": [ "Similarly, we can compute the conditional distribution $ Y \\mid f $." @@ -3261,7 +3261,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0dd32590", + "id": "4f5f1f80", "metadata": { "hide-output": false }, @@ -3272,7 +3272,7 @@ }, { "cell_type": "markdown", - "id": "37609bd8", + "id": "22bd07b0", "metadata": {}, "source": [ "It can be verified that the mean is\n", @@ -3282,7 +3282,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d370bc9c", + "id": "8357ed2e", "metadata": { "hide-output": false }, @@ -3293,7 +3293,7 @@ }, { "cell_type": "markdown", - "id": "a374409e", + "id": "492e2a8f", "metadata": {}, "source": [ "## PCA and Factor Analysis\n", @@ -3340,7 +3340,7 @@ { "cell_type": "code", "execution_count": null, - "id": "19ca2277", + "id": "ef81a82c", "metadata": { "hide-output": false }, @@ -3361,7 +3361,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55909a75", + "id": "7085cbb0", "metadata": { "hide-output": false }, @@ -3374,7 +3374,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a8d70bc", + "id": "2fa526b9", "metadata": { "hide-output": false }, @@ -3387,7 +3387,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2bd3f37d", + "id": "fa30f849", "metadata": { "hide-output": false }, @@ -3401,7 +3401,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2e3bd6ce", + "id": "bb0e83df", "metadata": { "hide-output": false }, @@ -3414,7 +3414,7 @@ }, { "cell_type": "markdown", - "id": "741b1539", + "id": "2a00d8f6", "metadata": {}, "source": [ "Below we’ll plot several things\n", @@ -3432,7 +3432,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77729807", + "id": "d1d47e3f", "metadata": { "hide-output": false }, @@ -3449,7 +3449,7 @@ }, { "cell_type": "markdown", - "id": "5874ef54", + "id": "9bbf9a97", "metadata": {}, "source": [ "Consequently, the first two $ \\epsilon_{j} $ correspond to the\n", @@ -3461,7 +3461,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd61b146", + "id": "1c73c5d5", "metadata": { "hide-output": false }, @@ -3473,7 +3473,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d39d4cd6", + "id": "73af913a", "metadata": { "hide-output": false }, @@ -3485,7 +3485,7 @@ }, { "cell_type": "markdown", - "id": "1b0f5a0f", + "id": "014076e9", "metadata": {}, "source": [ "The fraction of variance in $ y_{t} $ explained by the first two\n", @@ -3495,7 +3495,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48111373", + "id": "2c79a679", "metadata": { "hide-output": false }, @@ -3506,7 +3506,7 @@ }, { "cell_type": "markdown", - "id": "1a25853d", + "id": "f635b819", "metadata": {}, "source": [ "Compute\n", @@ -3522,7 +3522,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9264ecca", + "id": "0a4d4647", "metadata": { "hide-output": false }, @@ -3533,7 +3533,7 @@ }, { "cell_type": "markdown", - "id": "d7689ab2", + "id": "91c8bd8c", "metadata": {}, "source": [ "In this example, it turns out that the projection $ \\hat{Y} $ of\n", @@ -3548,7 +3548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a45426d", + "id": "2f15e84e", "metadata": { "hide-output": false }, @@ -3569,7 +3569,7 @@ }, { "cell_type": "markdown", - "id": "0eda3b2c", + "id": "8651c7a6", "metadata": {}, "source": [ "The covariance matrix of $ \\hat{Y} $ can be computed by first\n", @@ -3580,7 +3580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b72f2e8", + "id": "8139380d", "metadata": { "hide-output": false }, @@ -3596,7 +3596,7 @@ } ], "metadata": { - "date": 1706246575.4925556, + "date": 1706493929.6796315, "filename": "multivariate_normal.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/navy_captain.ipynb b/_notebooks/navy_captain.ipynb index b8c51b7..226b434 100644 --- a/_notebooks/navy_captain.ipynb +++ b/_notebooks/navy_captain.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "aff2ee6a", + "id": "322b9444", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "3c0ed10a", + "id": "ef790bf3", "metadata": {}, "source": [ "# Bayesian versus Frequentist Decision Rules" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "f731d05d", + "id": "df00d53b", "metadata": {}, "source": [ "## Contents\n", @@ -38,7 +38,7 @@ }, { "cell_type": "markdown", - "id": "d4aae9de", + "id": "b9c2a2bf", "metadata": {}, "source": [ "In addition to what’s in Anaconda, this lecture will need the following libraries:" @@ -47,7 +47,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2245c2a", + "id": "a39a24c7", "metadata": { "hide-output": false }, @@ -59,7 +59,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d5cff6dd", + "id": "a48a26d1", "metadata": { "hide-output": false }, @@ -77,7 +77,7 @@ }, { "cell_type": "markdown", - "id": "8fa3b74c", + "id": "62eafda2", "metadata": {}, "source": [ "## Overview\n", @@ -116,7 +116,7 @@ }, { "cell_type": "markdown", - "id": "3c5016ff", + "id": "b6d014b6", "metadata": {}, "source": [ "## Setup\n", @@ -168,7 +168,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7e7b2211", + "id": "d733ba0f", "metadata": { "hide-output": false }, @@ -185,7 +185,7 @@ }, { "cell_type": "markdown", - "id": "4faf6e3c", + "id": "90dceaf2", "metadata": {}, "source": [ "We start with defining a `jitclass` that stores parameters and\n", @@ -196,7 +196,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7549a70e", + "id": "4975a522", "metadata": { "hide-output": false }, @@ -221,7 +221,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e60cee4e", + "id": "f1f755e3", "metadata": { "hide-output": false }, @@ -274,7 +274,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9efb2a15", + "id": "90a74066", "metadata": { "hide-output": false }, @@ -300,7 +300,7 @@ }, { "cell_type": "markdown", - "id": "6e9eedbc", + "id": "873be0b0", "metadata": {}, "source": [ "Above, we plot the two possible probability densities $ f_0 $ and\n", @@ -309,7 +309,7 @@ }, { "cell_type": "markdown", - "id": "6dd32804", + "id": "dd79d235", "metadata": {}, "source": [ "## Frequentist Decision Rule\n", @@ -382,7 +382,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35f28c17", + "id": "52d96be9", "metadata": { "hide-output": false }, @@ -395,7 +395,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d9c479f", + "id": "eaa8597b", "metadata": { "hide-output": false }, @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0932b072", + "id": "0d884dda", "metadata": { "hide-output": false }, @@ -422,7 +422,7 @@ }, { "cell_type": "markdown", - "id": "033f3776", + "id": "997bd593", "metadata": {}, "source": [ "We can compute sequences of likelihood ratios using simulated samples." @@ -431,7 +431,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7e6cf892", + "id": "d7ba0381", "metadata": { "hide-output": false }, @@ -443,7 +443,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26242842", + "id": "59fbd152", "metadata": { "hide-output": false }, @@ -458,7 +458,7 @@ }, { "cell_type": "markdown", - "id": "e31930b5", + "id": "352ae540", "metadata": {}, "source": [ "With an empirical distribution of likelihood ratios in hand, we can draw\n", @@ -469,7 +469,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c323fd05", + "id": "d785ba58", "metadata": { "hide-output": false }, @@ -497,7 +497,7 @@ }, { "cell_type": "markdown", - "id": "6d101ac6", + "id": "197c1f9c", "metadata": {}, "source": [ "Our frequentist minimizes the expected total loss presented in equation\n", @@ -523,7 +523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1fa5f802", + "id": "f1823f02", "metadata": { "hide-output": false }, @@ -545,7 +545,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c34d5022", + "id": "7998be44", "metadata": { "hide-output": false }, @@ -566,7 +566,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06466dca", + "id": "a421054b", "metadata": { "hide-output": false }, @@ -592,7 +592,7 @@ { "cell_type": "code", "execution_count": null, - "id": "844f730d", + "id": "89d0f0a7", "metadata": { "hide-output": false }, @@ -611,7 +611,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1c3c4d2e", + "id": "e1cdc6fd", "metadata": { "hide-output": false }, @@ -623,7 +623,7 @@ { "cell_type": "code", "execution_count": null, - "id": "95d986fb", + "id": "9d1c6433", "metadata": { "hide-output": false }, @@ -635,7 +635,7 @@ }, { "cell_type": "markdown", - "id": "6558fdfe", + "id": "f2b7591f", "metadata": {}, "source": [ "Let’s now change the value of $ \\pi^{*} $ and watch how the decision\n", @@ -645,7 +645,7 @@ { "cell_type": "code", "execution_count": null, - "id": "427dec28", + "id": "609d9db4", "metadata": { "hide-output": false }, @@ -672,7 +672,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5631b035", + "id": "2e7d2d4b", "metadata": { "hide-output": false }, @@ -687,7 +687,7 @@ }, { "cell_type": "markdown", - "id": "73c82544", + "id": "04578613", "metadata": {}, "source": [ "The following shows how optimal sample size $ t $ and targeted\n", @@ -697,7 +697,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5283ccb5", + "id": "c45aeb0f", "metadata": { "hide-output": false }, @@ -720,7 +720,7 @@ }, { "cell_type": "markdown", - "id": "0d4be2b4", + "id": "372b1633", "metadata": {}, "source": [ "## Bayesian Decision Rule\n", @@ -742,7 +742,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2571302e", + "id": "bc5e20b0", "metadata": { "hide-output": false }, @@ -783,7 +783,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ca37112", + "id": "38866918", "metadata": { "hide-output": false }, @@ -817,7 +817,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ffad9d8a", + "id": "1ed8e148", "metadata": { "hide-output": false }, @@ -829,7 +829,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce4dfa3d", + "id": "d6c39a18", "metadata": { "hide-output": false }, @@ -892,7 +892,7 @@ }, { "cell_type": "markdown", - "id": "4c93022c", + "id": "36cfdd3e", "metadata": {}, "source": [ "The above figure portrays the value function plotted against the decision\n", @@ -948,7 +948,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f551ab6", + "id": "19d11f5e", "metadata": { "hide-output": false }, @@ -991,7 +991,7 @@ { "cell_type": "code", "execution_count": null, - "id": "43c71c59", + "id": "bc2f3aa4", "metadata": { "hide-output": false }, @@ -1014,7 +1014,7 @@ }, { "cell_type": "markdown", - "id": "bdd95eb8", + "id": "a89a49ea", "metadata": {}, "source": [ "Given an assumed value for\n", @@ -1033,7 +1033,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1c6a5a79", + "id": "f538e675", "metadata": { "hide-output": false }, @@ -1052,7 +1052,7 @@ { "cell_type": "code", "execution_count": null, - "id": "251dae87", + "id": "4674eb31", "metadata": { "hide-output": false }, @@ -1083,7 +1083,7 @@ }, { "cell_type": "markdown", - "id": "c60d3570", + "id": "0bd78e5f", "metadata": {}, "source": [ "This pattern of outcomes holds more generally.\n", @@ -1096,7 +1096,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49d319a7", + "id": "06fc83c2", "metadata": { "hide-output": false }, @@ -1132,7 +1132,7 @@ }, { "cell_type": "markdown", - "id": "007dbc5f", + "id": "f4536010", "metadata": {}, "source": [ "## Was the Navy Captain’s Hunch Correct?\n", @@ -1147,7 +1147,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0361207f", + "id": "0d01289d", "metadata": { "hide-output": false }, @@ -1159,7 +1159,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8749cc54", + "id": "a07c4e1e", "metadata": { "hide-output": false }, @@ -1176,7 +1176,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da0cb110", + "id": "bdb35a6a", "metadata": { "hide-output": false }, @@ -1192,7 +1192,7 @@ }, { "cell_type": "markdown", - "id": "5c72db1f", + "id": "71b949cf", "metadata": {}, "source": [ "Evidently, there is no sample size $ t $ at which the frequentist\n", @@ -1205,7 +1205,7 @@ { "cell_type": "code", "execution_count": null, - "id": "08695f75", + "id": "39437e45", "metadata": { "hide-output": false }, @@ -1227,7 +1227,7 @@ }, { "cell_type": "markdown", - "id": "7bc863df", + "id": "43146e4d", "metadata": {}, "source": [ "The right panel of the above graph plots the difference\n", @@ -1238,7 +1238,7 @@ }, { "cell_type": "markdown", - "id": "1d0fcf93", + "id": "69b228e2", "metadata": {}, "source": [ "## More Details\n", @@ -1250,7 +1250,7 @@ { "cell_type": "code", "execution_count": null, - "id": "656914fb", + "id": "b007d5aa", "metadata": { "hide-output": false }, @@ -1261,7 +1261,7 @@ }, { "cell_type": "markdown", - "id": "c1b9e9d5", + "id": "b3f8eecc", "metadata": {}, "source": [ "Recall that when $ \\pi^*=0.5 $, the frequentist decision rule sets a\n", @@ -1273,7 +1273,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4a4e8c9b", + "id": "0efd7c0b", "metadata": { "hide-output": false }, @@ -1284,7 +1284,7 @@ }, { "cell_type": "markdown", - "id": "07e69c82", + "id": "919ceb2c", "metadata": {}, "source": [ "For convenience, let’s define `t_idx` as the Python array index\n", @@ -1294,7 +1294,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5a186cd", + "id": "fb8f5b6a", "metadata": { "hide-output": false }, @@ -1305,7 +1305,7 @@ }, { "cell_type": "markdown", - "id": "f7fb9f8e", + "id": "70a9bc45", "metadata": {}, "source": [ "## Distribution of Bayesian Decision Rule’s Time to Decide\n", @@ -1330,7 +1330,7 @@ { "cell_type": "code", "execution_count": null, - "id": "147f4b68", + "id": "51c85922", "metadata": { "hide-output": false }, @@ -1359,7 +1359,7 @@ { "cell_type": "code", "execution_count": null, - "id": "edcbe989", + "id": "3c2a5976", "metadata": { "hide-output": false }, @@ -1376,7 +1376,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f75493a", + "id": "95f9bf68", "metadata": { "hide-output": false }, @@ -1400,7 +1400,7 @@ }, { "cell_type": "markdown", - "id": "9f36f09a", + "id": "e4448f1a", "metadata": {}, "source": [ "Later we’ll figure out how these distributions ultimately affect\n", @@ -1416,7 +1416,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3279fd6f", + "id": "6ef758a4", "metadata": { "hide-output": false }, @@ -1429,7 +1429,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d1f0c789", + "id": "c8aadc91", "metadata": { "hide-output": false }, @@ -1456,7 +1456,7 @@ }, { "cell_type": "markdown", - "id": "1a7f6514", + "id": "1bf9cf8f", "metadata": {}, "source": [ "The above figures compare averages and variances of updated Bayesian\n", @@ -1485,7 +1485,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d9bec83", + "id": "ef9f1c4e", "metadata": { "hide-output": false }, @@ -1506,7 +1506,7 @@ }, { "cell_type": "markdown", - "id": "f4fd98ef", + "id": "d940e2d6", "metadata": {}, "source": [ "## Probability of Making Correct Decision\n", @@ -1527,7 +1527,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5e2f0c6", + "id": "7f6294d8", "metadata": { "hide-output": false }, @@ -1540,7 +1540,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc4640c3", + "id": "2ce58f3e", "metadata": { "hide-output": false }, @@ -1567,7 +1567,7 @@ }, { "cell_type": "markdown", - "id": "2b9676eb", + "id": "01429527", "metadata": {}, "source": [ "By averaging using $ \\pi^{*} $, we also plot the unconditional\n", @@ -1577,7 +1577,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4e3e9c2", + "id": "ccd65ddd", "metadata": { "hide-output": false }, @@ -1601,7 +1601,7 @@ }, { "cell_type": "markdown", - "id": "16a3cd7d", + "id": "fecf5072", "metadata": {}, "source": [ "## Distribution of Likelihood Ratios at Frequentist’s $ t $\n", @@ -1623,7 +1623,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b45d2706", + "id": "bfda7193", "metadata": { "hide-output": false }, @@ -1636,7 +1636,7 @@ { "cell_type": "code", "execution_count": null, - "id": "038c4346", + "id": "adaeca02", "metadata": { "hide-output": false }, @@ -1661,7 +1661,7 @@ }, { "cell_type": "markdown", - "id": "d6102fee", + "id": "affd69de", "metadata": {}, "source": [ "The next graph plots the unconditional distribution of Bayesian times to\n", @@ -1672,7 +1672,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1d618081", + "id": "c98f243a", "metadata": { "hide-output": false }, @@ -1693,7 +1693,7 @@ } ], "metadata": { - "date": 1706246575.5658276, + "date": 1706493929.7554166, "filename": "navy_captain.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/ols.ipynb b/_notebooks/ols.ipynb index 42aa722..8ea2dc9 100644 --- a/_notebooks/ols.ipynb +++ b/_notebooks/ols.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "90e19f69", + "id": "b1ef2185", "metadata": {}, "source": [ "# Linear Regression in Python" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "6b181e56", + "id": "20774f06", "metadata": {}, "source": [ "## Contents\n", @@ -26,7 +26,7 @@ }, { "cell_type": "markdown", - "id": "4d095eff", + "id": "253c9eea", "metadata": {}, "source": [ "In addition to what’s in Anaconda, this lecture will need the following libraries:" @@ -35,7 +35,7 @@ { "cell_type": "code", "execution_count": null, - "id": "25382673", + "id": "63791c59", "metadata": { "hide-output": false }, @@ -46,7 +46,7 @@ }, { "cell_type": "markdown", - "id": "93c69cec", + "id": "34332ae1", "metadata": {}, "source": [ "## Overview\n", @@ -80,7 +80,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b9da7433", + "id": "58413909", "metadata": { "hide-output": false }, @@ -99,7 +99,7 @@ }, { "cell_type": "markdown", - "id": "b4c567f6", + "id": "c585312c", "metadata": {}, "source": [ "### Prerequisites\n", @@ -112,7 +112,7 @@ }, { "cell_type": "markdown", - "id": "7a081dd8", + "id": "c4c3b209", "metadata": {}, "source": [ "## Simple Linear Regression\n", @@ -135,7 +135,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3d5656cf", + "id": "fc2206ff", "metadata": { "hide-output": false }, @@ -147,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "b7f27d7b", + "id": "cab97d74", "metadata": {}, "source": [ "Let’s use a scatterplot to see whether any obvious relationship exists\n", @@ -158,7 +158,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0e2e4754", + "id": "96d6f812", "metadata": { "hide-output": false }, @@ -170,7 +170,7 @@ }, { "cell_type": "markdown", - "id": "5ec1e75f", + "id": "3404422a", "metadata": {}, "source": [ "The plot shows a fairly strong positive relationship between\n", @@ -207,7 +207,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4e77daf", + "id": "8f401cfa", "metadata": { "hide-output": false }, @@ -246,7 +246,7 @@ }, { "cell_type": "markdown", - "id": "d1587b7c", + "id": "52b759be", "metadata": {}, "source": [ "The most common technique to estimate the parameters ($ \\beta $’s)\n", @@ -270,7 +270,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2546a036", + "id": "7823053d", "metadata": { "hide-output": false }, @@ -281,7 +281,7 @@ }, { "cell_type": "markdown", - "id": "4a8570a0", + "id": "bbf9571f", "metadata": {}, "source": [ "Now we can construct our model in `statsmodels` using the OLS function.\n", @@ -292,7 +292,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5be757c", + "id": "3636be74", "metadata": { "hide-output": false }, @@ -305,7 +305,7 @@ }, { "cell_type": "markdown", - "id": "eeb2ca82", + "id": "1307a1c3", "metadata": {}, "source": [ "So far we have simply constructed our model.\n", @@ -317,7 +317,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c86b138f", + "id": "3aa431a9", "metadata": { "hide-output": false }, @@ -329,7 +329,7 @@ }, { "cell_type": "markdown", - "id": "63a92318", + "id": "01eb00f6", "metadata": {}, "source": [ "We now have the fitted regression model stored in `results`.\n", @@ -345,7 +345,7 @@ { "cell_type": "code", "execution_count": null, - "id": "65ee1fe7", + "id": "ff275f74", "metadata": { "hide-output": false }, @@ -356,7 +356,7 @@ }, { "cell_type": "markdown", - "id": "74a34361", + "id": "20bc4e9f", "metadata": {}, "source": [ "From our results, we see that\n", @@ -395,7 +395,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ededff9c", + "id": "defb2934", "metadata": { "hide-output": false }, @@ -408,7 +408,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5aef75a", + "id": "8285bf41", "metadata": { "hide-output": false }, @@ -420,7 +420,7 @@ }, { "cell_type": "markdown", - "id": "ecbc9669", + "id": "ef6d549e", "metadata": {}, "source": [ "An easier (and more accurate) way to obtain this result is to use\n", @@ -431,7 +431,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7a8b4bce", + "id": "c74bf6f3", "metadata": { "hide-output": false }, @@ -442,7 +442,7 @@ }, { "cell_type": "markdown", - "id": "e526afa3", + "id": "427a0960", "metadata": {}, "source": [ "We can obtain an array of predicted $ {logpgp95}_i $ for every value\n", @@ -459,7 +459,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce9072c6", + "id": "32b19571", "metadata": { "hide-output": false }, @@ -489,7 +489,7 @@ }, { "cell_type": "markdown", - "id": "04982c26", + "id": "7b44d9e7", "metadata": {}, "source": [ "## Extending the Linear Regression Model\n", @@ -518,7 +518,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a831b18a", + "id": "c6cc2976", "metadata": { "hide-output": false }, @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "ff793c7b", + "id": "05c0d159", "metadata": {}, "source": [ "Now that we have fitted our model, we will use `summary_col` to\n", @@ -553,7 +553,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1266bcb0", + "id": "f65fe620", "metadata": { "hide-output": false }, @@ -582,7 +582,7 @@ }, { "cell_type": "markdown", - "id": "faa98cfd", + "id": "9963b9ab", "metadata": {}, "source": [ "## Endogeneity\n", @@ -634,7 +634,7 @@ { "cell_type": "code", "execution_count": null, - "id": "531a34fa", + "id": "33e29798", "metadata": { "hide-output": false }, @@ -670,7 +670,7 @@ }, { "cell_type": "markdown", - "id": "623c975e", + "id": "9fe9e32b", "metadata": {}, "source": [ "The second condition may not be satisfied if settler mortality rates in the 17th to 19th centuries have a direct effect on current GDP (in addition to their indirect effect through institutions).\n", @@ -714,7 +714,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fce65620", + "id": "1c36cabf", "metadata": { "hide-output": false }, @@ -736,7 +736,7 @@ }, { "cell_type": "markdown", - "id": "6e8f0fa3", + "id": "c7d9e3e3", "metadata": {}, "source": [ "**Second stage**\n", @@ -757,7 +757,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e4746b1", + "id": "12503176", "metadata": { "hide-output": false }, @@ -772,7 +772,7 @@ }, { "cell_type": "markdown", - "id": "b7354655", + "id": "e1ba6f1d", "metadata": {}, "source": [ "The second-stage regression results give us an unbiased and consistent\n", @@ -796,7 +796,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04dd11e8", + "id": "8e8ea060", "metadata": { "hide-output": false }, @@ -812,7 +812,7 @@ }, { "cell_type": "markdown", - "id": "34b0395a", + "id": "6d2bd390", "metadata": {}, "source": [ "Given that we now have consistent and unbiased estimates, we can infer\n", @@ -828,7 +828,7 @@ }, { "cell_type": "markdown", - "id": "b43b4fe0", + "id": "a85764cf", "metadata": {}, "source": [ "## Summary\n", @@ -840,7 +840,7 @@ }, { "cell_type": "markdown", - "id": "2238337a", + "id": "0f89eae5", "metadata": {}, "source": [ "## Exercises" @@ -848,7 +848,7 @@ }, { "cell_type": "markdown", - "id": "ba948dae", + "id": "9bd6d2c4", "metadata": {}, "source": [ "## Exercise 2.1\n", @@ -895,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "23b44102", + "id": "925270a1", "metadata": {}, "source": [ "## Solution to[ Exercise 2.1](https://python.quantecon.org/#ols_ex1)" @@ -904,7 +904,7 @@ { "cell_type": "code", "execution_count": null, - "id": "908f9c3a", + "id": "59973270", "metadata": { "hide-output": false }, @@ -934,7 +934,7 @@ }, { "cell_type": "markdown", - "id": "1824726c", + "id": "14455608", "metadata": {}, "source": [ "The output shows that the coefficient on the residuals is statistically\n", @@ -943,7 +943,7 @@ }, { "cell_type": "markdown", - "id": "d67a3177", + "id": "c3081c05", "metadata": {}, "source": [ "## Exercise 2.2\n", @@ -987,7 +987,7 @@ }, { "cell_type": "markdown", - "id": "31ac157d", + "id": "89d17731", "metadata": {}, "source": [ "## Solution to[ Exercise 2.2](https://python.quantecon.org/#ols_ex2)" @@ -996,7 +996,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e377e6f7", + "id": "a54401f8", "metadata": { "hide-output": false }, @@ -1023,7 +1023,7 @@ }, { "cell_type": "markdown", - "id": "2620945b", + "id": "cb44fd73", "metadata": {}, "source": [ "It is also possible to use `np.linalg.inv(X.T @ X) @ X.T @ y` to solve\n", @@ -1033,7 +1033,7 @@ } ], "metadata": { - "date": 1706246575.7381618, + "date": 1706493929.8142025, "filename": "ols.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/pandas_panel.ipynb b/_notebooks/pandas_panel.ipynb index dcd29cf..2cad495 100644 --- a/_notebooks/pandas_panel.ipynb +++ b/_notebooks/pandas_panel.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "18760771", + "id": "b9bb8240", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "717aa28e", + "id": "a64dbfa8", "metadata": {}, "source": [ "# Pandas for Panel Data\n", @@ -22,7 +22,7 @@ }, { "cell_type": "markdown", - "id": "e9b7ee2b", + "id": "b69b72df", "metadata": {}, "source": [ "## Contents\n", @@ -38,7 +38,7 @@ }, { "cell_type": "markdown", - "id": "11a54bab", + "id": "88f7cfce", "metadata": {}, "source": [ "## Overview\n", @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "cc2338b5", + "id": "1b002abf", "metadata": {}, "source": [ "## Slicing and Reshaping Data\n", @@ -88,7 +88,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4da8100", + "id": "d7dfba16", "metadata": { "hide-output": false }, @@ -100,7 +100,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26ea99fd", + "id": "d1221ec5", "metadata": { "hide-output": false }, @@ -119,7 +119,7 @@ }, { "cell_type": "markdown", - "id": "ca2d23df", + "id": "f7f80249", "metadata": {}, "source": [ "Let’s have a look at what we’ve got to work with" @@ -128,7 +128,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f993cb2", + "id": "bed44559", "metadata": { "hide-output": false }, @@ -139,7 +139,7 @@ }, { "cell_type": "markdown", - "id": "81462f8e", + "id": "140e238a", "metadata": {}, "source": [ "The data is currently in long format, which is difficult to analyze when there are several dimensions to the data.\n", @@ -154,7 +154,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f0f45c0", + "id": "f20f979c", "metadata": { "hide-output": false }, @@ -168,7 +168,7 @@ }, { "cell_type": "markdown", - "id": "7e2f6bce", + "id": "dbb020e3", "metadata": {}, "source": [ "To more easily filter our time series data, later on, we will convert the index into a `DateTimeIndex`" @@ -177,7 +177,7 @@ { "cell_type": "code", "execution_count": null, - "id": "75150b6d", + "id": "6fd2e995", "metadata": { "hide-output": false }, @@ -189,7 +189,7 @@ }, { "cell_type": "markdown", - "id": "e66334c4", + "id": "74b0c75b", "metadata": {}, "source": [ "The columns contain multiple levels of indexing, known as a\n", @@ -203,7 +203,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b16f796", + "id": "14b4153f", "metadata": { "hide-output": false }, @@ -215,7 +215,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1556c648", + "id": "78507dd5", "metadata": { "hide-output": false }, @@ -226,7 +226,7 @@ }, { "cell_type": "markdown", - "id": "4429b1b0", + "id": "6a9519a6", "metadata": {}, "source": [ "Like before, we can select the country (the top level of our\n", @@ -236,7 +236,7 @@ { "cell_type": "code", "execution_count": null, - "id": "233fa2dc", + "id": "dc65ced3", "metadata": { "hide-output": false }, @@ -247,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "d7ce535f", + "id": "7e8d464e", "metadata": {}, "source": [ "Stacking and unstacking levels of the `MultiIndex` will be used\n", @@ -261,7 +261,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f99d3a7", + "id": "aed69b5b", "metadata": { "hide-output": false }, @@ -272,7 +272,7 @@ }, { "cell_type": "markdown", - "id": "bbfedc83", + "id": "aaecd97e", "metadata": {}, "source": [ "We can also pass in an argument to select the level we would like to\n", @@ -282,7 +282,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6209aac5", + "id": "9a826447", "metadata": { "hide-output": false }, @@ -293,7 +293,7 @@ }, { "cell_type": "markdown", - "id": "050539ac", + "id": "27d87fcd", "metadata": {}, "source": [ "Using a `DatetimeIndex` makes it easy to select a particular time\n", @@ -306,7 +306,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cef0f500", + "id": "36bd1dbf", "metadata": { "hide-output": false }, @@ -317,7 +317,7 @@ }, { "cell_type": "markdown", - "id": "0b069c5f", + "id": "cf31c144", "metadata": {}, "source": [ "For the rest of lecture, we will work with a dataframe of the hourly\n", @@ -332,7 +332,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e06f09b", + "id": "498d5fa4", "metadata": { "hide-output": false }, @@ -345,7 +345,7 @@ }, { "cell_type": "markdown", - "id": "227b4cb8", + "id": "b1af3614", "metadata": {}, "source": [ "## Merging Dataframes and Filling NaNs\n", @@ -364,7 +364,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c5c908e", + "id": "c6eb111a", "metadata": { "hide-output": false }, @@ -376,7 +376,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3d9a9c8e", + "id": "695cd8e1", "metadata": { "hide-output": false }, @@ -388,7 +388,7 @@ }, { "cell_type": "markdown", - "id": "e3b48df3", + "id": "6af34f1f", "metadata": {}, "source": [ "First, we’ll select just the country and continent variables from\n", @@ -398,7 +398,7 @@ { "cell_type": "code", "execution_count": null, - "id": "abf810ff", + "id": "a099c8c6", "metadata": { "hide-output": false }, @@ -411,7 +411,7 @@ }, { "cell_type": "markdown", - "id": "c80894bd", + "id": "ee633a76", "metadata": {}, "source": [ "We want to merge our new dataframe, `worlddata`, with `realwage_f`.\n", @@ -427,7 +427,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c64dade", + "id": "f177d4ce", "metadata": { "hide-output": false }, @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "3072595f", + "id": "45c68ede", "metadata": {}, "source": [ "We can use either left, right, inner, or outer join to merge our\n", @@ -475,7 +475,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6452f3e2", + "id": "bcf16b86", "metadata": { "hide-output": false }, @@ -488,7 +488,7 @@ }, { "cell_type": "markdown", - "id": "319ef5d1", + "id": "a707ab0d", "metadata": {}, "source": [ "Countries that appeared in `realwage_f` but not in `worlddata` will\n", @@ -501,7 +501,7 @@ { "cell_type": "code", "execution_count": null, - "id": "054634e9", + "id": "c8d05a4f", "metadata": { "hide-output": false }, @@ -512,7 +512,7 @@ }, { "cell_type": "markdown", - "id": "6d33b34a", + "id": "24681433", "metadata": {}, "source": [ "We have three missing values!\n", @@ -529,7 +529,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0bf06528", + "id": "376b0b4d", "metadata": { "hide-output": false }, @@ -544,7 +544,7 @@ }, { "cell_type": "markdown", - "id": "c7497b7e", + "id": "e58d6a9d", "metadata": {}, "source": [ "We don’t want to overwrite the entire series with this mapping.\n", @@ -556,7 +556,7 @@ { "cell_type": "code", "execution_count": null, - "id": "960d8f34", + "id": "5f3a5f32", "metadata": { "hide-output": false }, @@ -571,7 +571,7 @@ }, { "cell_type": "markdown", - "id": "160c6118", + "id": "62e985c2", "metadata": {}, "source": [ "We will also combine the Americas into a single continent - this will make our visualization nicer later on.\n", @@ -582,7 +582,7 @@ { "cell_type": "code", "execution_count": null, - "id": "70580f98", + "id": "de00f84e", "metadata": { "hide-output": false }, @@ -598,7 +598,7 @@ }, { "cell_type": "markdown", - "id": "7b373267", + "id": "252ebc38", "metadata": {}, "source": [ "Now that we have all the data we want in a single `DataFrame`, we will\n", @@ -613,7 +613,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5911b1b", + "id": "77a3b167", "metadata": { "hide-output": false }, @@ -625,7 +625,7 @@ }, { "cell_type": "markdown", - "id": "9aef9cf7", + "id": "b2b8bd00", "metadata": {}, "source": [ "While merging, we lost our `DatetimeIndex`, as we merged columns that\n", @@ -635,7 +635,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7502d33f", + "id": "cde3e25c", "metadata": { "hide-output": false }, @@ -646,7 +646,7 @@ }, { "cell_type": "markdown", - "id": "a3521348", + "id": "16ed2944", "metadata": {}, "source": [ "Now that we have set the merged columns as the index, we can recreate a\n", @@ -656,7 +656,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48040b79", + "id": "8d1c1aa5", "metadata": { "hide-output": false }, @@ -669,7 +669,7 @@ }, { "cell_type": "markdown", - "id": "c80985bc", + "id": "48fa7ced", "metadata": {}, "source": [ "The `DatetimeIndex` tends to work more smoothly in the row axis, so we\n", @@ -679,7 +679,7 @@ { "cell_type": "code", "execution_count": null, - "id": "492368e3", + "id": "0ba19c4d", "metadata": { "hide-output": false }, @@ -691,7 +691,7 @@ }, { "cell_type": "markdown", - "id": "0f40d3cc", + "id": "85b1feee", "metadata": {}, "source": [ "## Grouping and Summarizing Data\n", @@ -711,7 +711,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bafced34", + "id": "9c846cf8", "metadata": { "hide-output": false }, @@ -722,7 +722,7 @@ }, { "cell_type": "markdown", - "id": "41dc7892", + "id": "fe79829c", "metadata": {}, "source": [ "Using this series, we can plot the average real minimum wage over the\n", @@ -732,7 +732,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9ca8894", + "id": "ede72e2e", "metadata": { "hide-output": false }, @@ -746,7 +746,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ffb1c9b", + "id": "809d6a3f", "metadata": { "hide-output": false }, @@ -765,7 +765,7 @@ }, { "cell_type": "markdown", - "id": "ab0802ce", + "id": "5f6f838e", "metadata": {}, "source": [ "Passing in `axis=1` to `.mean()` will aggregate over columns (giving\n", @@ -775,7 +775,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77d4c238", + "id": "72925e90", "metadata": { "hide-output": false }, @@ -786,7 +786,7 @@ }, { "cell_type": "markdown", - "id": "39df21f2", + "id": "cf6f83e8", "metadata": {}, "source": [ "We can plot this time series as a line graph" @@ -795,7 +795,7 @@ { "cell_type": "code", "execution_count": null, - "id": "286940c8", + "id": "8c043b18", "metadata": { "hide-output": false }, @@ -810,7 +810,7 @@ }, { "cell_type": "markdown", - "id": "baf9df65", + "id": "573b167a", "metadata": {}, "source": [ "We can also specify a level of the `MultiIndex` (in the column axis)\n", @@ -820,7 +820,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b59022d", + "id": "6e8546a2", "metadata": { "hide-output": false }, @@ -831,7 +831,7 @@ }, { "cell_type": "markdown", - "id": "da731558", + "id": "46e59816", "metadata": {}, "source": [ "We can plot the average minimum wages in each continent as a time series" @@ -840,7 +840,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4010846c", + "id": "49d31984", "metadata": { "hide-output": false }, @@ -855,7 +855,7 @@ }, { "cell_type": "markdown", - "id": "bb994428", + "id": "d279a322", "metadata": {}, "source": [ "We will drop Australia as a continent for plotting purposes" @@ -864,7 +864,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1224a59a", + "id": "27aa4091", "metadata": { "hide-output": false }, @@ -880,7 +880,7 @@ }, { "cell_type": "markdown", - "id": "a222d69b", + "id": "24e82879", "metadata": {}, "source": [ "`.describe()` is useful for quickly retrieving a number of common\n", @@ -890,7 +890,7 @@ { "cell_type": "code", "execution_count": null, - "id": "722369fc", + "id": "5121803f", "metadata": { "hide-output": false }, @@ -901,7 +901,7 @@ }, { "cell_type": "markdown", - "id": "09cb80fe", + "id": "cbed5084", "metadata": {}, "source": [ "This is a simplified way to use `groupby`.\n", @@ -923,7 +923,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f7ea34a8", + "id": "5ebb5760", "metadata": { "hide-output": false }, @@ -935,7 +935,7 @@ }, { "cell_type": "markdown", - "id": "6cb9f6d1", + "id": "f7074547", "metadata": {}, "source": [ "Calling an aggregation method on the object applies the function to each\n", @@ -950,7 +950,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4e675268", + "id": "d99eb919", "metadata": { "hide-output": false }, @@ -961,7 +961,7 @@ }, { "cell_type": "markdown", - "id": "021bd3b6", + "id": "c7d43387", "metadata": {}, "source": [ "Calling `.get_group()` to return just the countries in a single group,\n", @@ -975,7 +975,7 @@ { "cell_type": "code", "execution_count": null, - "id": "698c8b94", + "id": "5922040b", "metadata": { "hide-output": false }, @@ -994,7 +994,7 @@ }, { "cell_type": "markdown", - "id": "8432a71b", + "id": "9e83a200", "metadata": {}, "source": [ "## Final Remarks\n", @@ -1009,7 +1009,7 @@ }, { "cell_type": "markdown", - "id": "abbf2559", + "id": "a9572d08", "metadata": {}, "source": [ "## Exercises" @@ -1017,7 +1017,7 @@ }, { "cell_type": "markdown", - "id": "ddb7464d", + "id": "b9736924", "metadata": {}, "source": [ "## Exercise 1.1\n", @@ -1031,7 +1031,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a54745e5", + "id": "25ee9549", "metadata": { "hide-output": false }, @@ -1042,7 +1042,7 @@ }, { "cell_type": "markdown", - "id": "af7c77aa", + "id": "96cdd656", "metadata": {}, "source": [ "Reading in the CSV file returns a panel dataset in long format. Use `.pivot_table()` to construct\n", @@ -1056,7 +1056,7 @@ }, { "cell_type": "markdown", - "id": "6f15febc", + "id": "ad3a7625", "metadata": {}, "source": [ "## Solution to[ Exercise 1.1](https://python.quantecon.org/#pp_ex1)" @@ -1065,7 +1065,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1d587481", + "id": "564760d0", "metadata": { "hide-output": false }, @@ -1081,7 +1081,7 @@ }, { "cell_type": "markdown", - "id": "ddfad513", + "id": "8a683dc1", "metadata": {}, "source": [ "This is a large dataset so it is useful to explore the levels and\n", @@ -1091,7 +1091,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84d2f49d", + "id": "b1154bd2", "metadata": { "hide-output": false }, @@ -1102,7 +1102,7 @@ }, { "cell_type": "markdown", - "id": "95dc7c1f", + "id": "3cc200d5", "metadata": {}, "source": [ "Variables within levels can be quickly retrieved with a loop" @@ -1111,7 +1111,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d6fffdf4", + "id": "e9eb847f", "metadata": { "hide-output": false }, @@ -1123,7 +1123,7 @@ }, { "cell_type": "markdown", - "id": "beec957e", + "id": "a34c5f0b", "metadata": {}, "source": [ "## Exercise 1.2\n", @@ -1139,7 +1139,7 @@ }, { "cell_type": "markdown", - "id": "80d0f841", + "id": "613545c5", "metadata": {}, "source": [ "## Solution to[ Exercise 1.2](https://python.quantecon.org/#pp_ex2)\n", @@ -1151,7 +1151,7 @@ { "cell_type": "code", "execution_count": null, - "id": "30b56e93", + "id": "a1707c0d", "metadata": { "hide-output": false }, @@ -1163,7 +1163,7 @@ }, { "cell_type": "markdown", - "id": "2a916ba0", + "id": "c7d65ede", "metadata": {}, "source": [ "We need to get rid of a few items in `GEO` which are not countries.\n", @@ -1175,7 +1175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e92c6314", + "id": "a3783972", "metadata": { "hide-output": false }, @@ -1189,7 +1189,7 @@ }, { "cell_type": "markdown", - "id": "b08063b9", + "id": "2871ff21", "metadata": {}, "source": [ "Select only percentage employed in the active population from the\n", @@ -1199,7 +1199,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc0fad3d", + "id": "bff0742b", "metadata": { "hide-output": false }, @@ -1213,7 +1213,7 @@ }, { "cell_type": "markdown", - "id": "51130027", + "id": "09bbb430", "metadata": {}, "source": [ "Drop the ‘Total’ value before creating the grouped boxplot" @@ -1222,7 +1222,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c7ad36cf", + "id": "1afbecf6", "metadata": { "hide-output": false }, @@ -1234,7 +1234,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5b6059c8", + "id": "a87957ad", "metadata": { "hide-output": false }, @@ -1252,7 +1252,7 @@ } ], "metadata": { - "date": 1706246575.7992496, + "date": 1706493929.873617, "filename": "pandas_panel.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/prob_matrix.ipynb b/_notebooks/prob_matrix.ipynb index 077398f..abff42d 100644 --- a/_notebooks/prob_matrix.ipynb +++ b/_notebooks/prob_matrix.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "861de990", + "id": "6fd319c3", "metadata": {}, "source": [ "# Elementary Probability with Matrices\n", @@ -34,7 +34,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b9ae3c5c", + "id": "1ebaf3b0", "metadata": { "hide-output": false }, @@ -45,7 +45,7 @@ }, { "cell_type": "markdown", - "id": "cd681780", + "id": "b4856150", "metadata": {}, "source": [ "As usual, we’ll start with some imports" @@ -54,7 +54,7 @@ { "cell_type": "code", "execution_count": null, - "id": "78cfb796", + "id": "30d280b0", "metadata": { "hide-output": false }, @@ -70,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "cc170ccc", + "id": "e7fbfdaf", "metadata": {}, "source": [ "## Sketch of Basic Concepts\n", @@ -110,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "ecfbeb9a", + "id": "86204cd5", "metadata": {}, "source": [ "## What Does Probability Mean?\n", @@ -188,7 +188,7 @@ }, { "cell_type": "markdown", - "id": "4825b3b2", + "id": "db9227b8", "metadata": {}, "source": [ "## Representing Probability Distributions\n", @@ -230,7 +230,7 @@ }, { "cell_type": "markdown", - "id": "7dc8bc33", + "id": "501e08a5", "metadata": {}, "source": [ "## Univariate Probability Distributions\n", @@ -241,7 +241,7 @@ }, { "cell_type": "markdown", - "id": "d5f91486", + "id": "e6456890", "metadata": {}, "source": [ "### Discrete random variable\n", @@ -315,7 +315,7 @@ }, { "cell_type": "markdown", - "id": "cb35f959", + "id": "64f6a9d6", "metadata": {}, "source": [ "### Continuous random variable\n", @@ -335,7 +335,7 @@ }, { "cell_type": "markdown", - "id": "05f5f439", + "id": "342665bd", "metadata": {}, "source": [ "## Bivariate Probability Distributions\n", @@ -375,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "6156036c", + "id": "511402e4", "metadata": {}, "source": [ "## Marginal Probability Distributions\n", @@ -426,7 +426,7 @@ }, { "cell_type": "markdown", - "id": "43b60c1b", + "id": "f33f1f16", "metadata": {}, "source": [ "## Conditional Probability Distributions\n", @@ -470,7 +470,7 @@ }, { "cell_type": "markdown", - "id": "4d1bf70e", + "id": "93286b4d", "metadata": {}, "source": [ "## Statistical Independence\n", @@ -502,7 +502,7 @@ }, { "cell_type": "markdown", - "id": "8ce22fcc", + "id": "5a7426c7", "metadata": {}, "source": [ "## Means and Variances\n", @@ -529,7 +529,7 @@ }, { "cell_type": "markdown", - "id": "d475934c", + "id": "b01090ad", "metadata": {}, "source": [ "## Generating Random Numbers\n", @@ -640,7 +640,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1d06f802", + "id": "10a7b76f", "metadata": { "hide-output": false }, @@ -665,7 +665,7 @@ { "cell_type": "code", "execution_count": null, - "id": "095d2783", + "id": "91630c7b", "metadata": { "hide-output": false }, @@ -677,7 +677,7 @@ }, { "cell_type": "markdown", - "id": "8fd552ba", + "id": "51cfcb6e", "metadata": {}, "source": [ "**Geometric distribution**\n", @@ -738,7 +738,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0fca3d43", + "id": "76d3cf24", "metadata": { "hide-output": false }, @@ -763,7 +763,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35937981", + "id": "c6c0133f", "metadata": { "hide-output": false }, @@ -775,7 +775,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c4249078", + "id": "4a625799", "metadata": { "hide-output": false }, @@ -787,7 +787,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb21bbe3", + "id": "5e8d7e83", "metadata": { "hide-output": false }, @@ -799,7 +799,7 @@ }, { "cell_type": "markdown", - "id": "2a72f522", + "id": "bdae28c8", "metadata": {}, "source": [ "## Some Discrete Probability Distributions\n", @@ -815,7 +815,7 @@ }, { "cell_type": "markdown", - "id": "0800ba7f", + "id": "ef5f0f8e", "metadata": {}, "source": [ "## Geometric distribution\n", @@ -838,7 +838,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1ea12f5", + "id": "a4d33f9e", "metadata": { "hide-output": false }, @@ -863,7 +863,7 @@ }, { "cell_type": "markdown", - "id": "b4df0fa4", + "id": "b50e3a12", "metadata": {}, "source": [ "### Newcomb–Benford distribution\n", @@ -902,7 +902,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84f3afe8", + "id": "9f6b6190", "metadata": { "hide-output": false }, @@ -926,7 +926,7 @@ { "cell_type": "code", "execution_count": null, - "id": "22c15271", + "id": "f3f0b242", "metadata": { "hide-output": false }, @@ -940,7 +940,7 @@ }, { "cell_type": "markdown", - "id": "655b2880", + "id": "ff2f2c34", "metadata": {}, "source": [ "### Pascal (negative binomial) distribution\n", @@ -975,7 +975,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c170da31", + "id": "50e25d83", "metadata": { "hide-output": false }, @@ -998,7 +998,7 @@ }, { "cell_type": "markdown", - "id": "f8e259dc", + "id": "8ce24fc3", "metadata": {}, "source": [ "## Continuous Random Variables" @@ -1006,7 +1006,7 @@ }, { "cell_type": "markdown", - "id": "67716ef3", + "id": "d6476aa9", "metadata": {}, "source": [ "### Univariate Gaussian distribution\n", @@ -1029,7 +1029,7 @@ { "cell_type": "code", "execution_count": null, - "id": "914d6b8d", + "id": "51f9a5db", "metadata": { "hide-output": false }, @@ -1055,7 +1055,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0d8fc46", + "id": "58843363", "metadata": { "hide-output": false }, @@ -1068,7 +1068,7 @@ }, { "cell_type": "markdown", - "id": "92cc6174", + "id": "3ce6352e", "metadata": {}, "source": [ "### Uniform Distribution\n", @@ -1093,7 +1093,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e4cbac5", + "id": "efe5ecc8", "metadata": { "hide-output": false }, @@ -1119,7 +1119,7 @@ }, { "cell_type": "markdown", - "id": "2ec43a4a", + "id": "cf278c15", "metadata": {}, "source": [ "## A Mixed Discrete-Continuous Distribution\n", @@ -1150,7 +1150,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cbaad9e2", + "id": "284839a1", "metadata": { "hide-output": false }, @@ -1169,7 +1169,7 @@ }, { "cell_type": "markdown", - "id": "5fc124eb", + "id": "3d4ce5d3", "metadata": {}, "source": [ "The analytical mean and variance can be computed:\n", @@ -1194,7 +1194,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2b8e7659", + "id": "42dbc11b", "metadata": { "hide-output": false }, @@ -1208,7 +1208,7 @@ }, { "cell_type": "markdown", - "id": "21d63f26", + "id": "48c9ea7f", "metadata": {}, "source": [ "## Matrix Representation of Some Bivariate Distributions\n", @@ -1242,7 +1242,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7a1047b3", + "id": "8bede1c8", "metadata": { "hide-output": false }, @@ -1272,7 +1272,7 @@ }, { "cell_type": "markdown", - "id": "a4f62d77", + "id": "fd830f40", "metadata": {}, "source": [ "Here, we use exactly the inverse CDF technique to generate sample from the joint distribution $ F $." @@ -1281,7 +1281,7 @@ { "cell_type": "code", "execution_count": null, - "id": "84581d04", + "id": "70b60202", "metadata": { "hide-output": false }, @@ -1310,7 +1310,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69ae6629", + "id": "383d6a4a", "metadata": { "hide-output": false }, @@ -1345,7 +1345,7 @@ }, { "cell_type": "markdown", - "id": "135a5d60", + "id": "816a6f43", "metadata": {}, "source": [ "Let’s calculate population marginal and conditional probabilities using matrix algebra.\n", @@ -1405,7 +1405,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3f24436", + "id": "6d9646d1", "metadata": { "hide-output": false }, @@ -1525,7 +1525,7 @@ }, { "cell_type": "markdown", - "id": "1f7d33dc", + "id": "c662eef5", "metadata": {}, "source": [ "Let’s apply our code to some examples.\n", @@ -1536,7 +1536,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df37e57b", + "id": "fed03c11", "metadata": { "hide-output": false }, @@ -1550,7 +1550,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36c28bd6", + "id": "31192c16", "metadata": { "hide-output": false }, @@ -1564,7 +1564,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5106844", + "id": "24c040f9", "metadata": { "hide-output": false }, @@ -1576,7 +1576,7 @@ }, { "cell_type": "markdown", - "id": "db852492", + "id": "3bc1c065", "metadata": {}, "source": [ "**Example 2**" @@ -1585,7 +1585,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a8a8cc77", + "id": "e2a76d82", "metadata": { "hide-output": false }, @@ -1601,7 +1601,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f85f3486", + "id": "704342c6", "metadata": { "hide-output": false }, @@ -1614,7 +1614,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc5a0204", + "id": "dc548dda", "metadata": { "hide-output": false }, @@ -1625,7 +1625,7 @@ }, { "cell_type": "markdown", - "id": "6cbb709e", + "id": "cddab70b", "metadata": {}, "source": [ "## A Continuous Bivariate Random Vector\n", @@ -1656,7 +1656,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87abe2c0", + "id": "40b6f764", "metadata": { "hide-output": false }, @@ -1675,7 +1675,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1627a0a3", + "id": "ab168fac", "metadata": { "hide-output": false }, @@ -1691,7 +1691,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87e186eb", + "id": "c4d53939", "metadata": { "hide-output": false }, @@ -1704,7 +1704,7 @@ }, { "cell_type": "markdown", - "id": "7c92b6bc", + "id": "edf61728", "metadata": {}, "source": [ "**Joint Distribution**\n", @@ -1715,7 +1715,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2a2ff985", + "id": "e40b7f43", "metadata": { "hide-output": false }, @@ -1733,7 +1733,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4c40c95c", + "id": "c0811759", "metadata": { "hide-output": false }, @@ -1753,7 +1753,7 @@ }, { "cell_type": "markdown", - "id": "d505bf4f", + "id": "b0112a15", "metadata": {}, "source": [ "Next we can simulate from a built-in `numpy` function and calculate a **sample** marginal distribution from the sample mean and variance." @@ -1762,7 +1762,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83bc7667", + "id": "0e4949ff", "metadata": { "hide-output": false }, @@ -1778,7 +1778,7 @@ }, { "cell_type": "markdown", - "id": "3d65d966", + "id": "c83120d1", "metadata": {}, "source": [ "**Marginal distribution**" @@ -1787,7 +1787,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e5b73c55", + "id": "111cde24", "metadata": { "hide-output": false }, @@ -1804,7 +1804,7 @@ { "cell_type": "code", "execution_count": null, - "id": "90071e8a", + "id": "440d913e", "metadata": { "hide-output": false }, @@ -1820,7 +1820,7 @@ }, { "cell_type": "markdown", - "id": "46bc2d2c", + "id": "8ec3ee19", "metadata": {}, "source": [ "**Conditional distribution**\n", @@ -1848,7 +1848,7 @@ { "cell_type": "code", "execution_count": null, - "id": "157af71f", + "id": "25cf4c93", "metadata": { "hide-output": false }, @@ -1863,7 +1863,7 @@ }, { "cell_type": "markdown", - "id": "6aabce4e", + "id": "f259c792", "metadata": {}, "source": [ "The mean and variance are computed by\n", @@ -1881,7 +1881,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5df999b0", + "id": "ea9ca8a8", "metadata": { "hide-output": false }, @@ -1901,7 +1901,7 @@ }, { "cell_type": "markdown", - "id": "3e946707", + "id": "573afa9c", "metadata": {}, "source": [ "Fix $ x=1 $." @@ -1910,7 +1910,7 @@ { "cell_type": "code", "execution_count": null, - "id": "584e494e", + "id": "3ca7542c", "metadata": { "hide-output": false }, @@ -1925,7 +1925,7 @@ { "cell_type": "code", "execution_count": null, - "id": "12b1c14e", + "id": "22f3c9b2", "metadata": { "hide-output": false }, @@ -1943,7 +1943,7 @@ }, { "cell_type": "markdown", - "id": "c0d067e6", + "id": "d57d071e", "metadata": {}, "source": [ "We compare with the analytically computed parameters and note that they are close." @@ -1952,7 +1952,7 @@ { "cell_type": "code", "execution_count": null, - "id": "29a40fb8", + "id": "b2e3704e", "metadata": { "hide-output": false }, @@ -1967,7 +1967,7 @@ }, { "cell_type": "markdown", - "id": "a9e0b953", + "id": "9c0913b3", "metadata": {}, "source": [ "## Sum of Two Independently Distributed Random Variables\n", @@ -2014,7 +2014,7 @@ }, { "cell_type": "markdown", - "id": "6ba22ad7", + "id": "e14a4ffc", "metadata": {}, "source": [ "## Transition Probability Matrix\n", @@ -2068,7 +2068,7 @@ }, { "cell_type": "markdown", - "id": "98a5487d", + "id": "46dffcbe", "metadata": {}, "source": [ "## Coupling\n", @@ -2192,7 +2192,7 @@ }, { "cell_type": "markdown", - "id": "701a296f", + "id": "f14aea52", "metadata": {}, "source": [ "## Copula Functions\n", @@ -2245,7 +2245,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b02b33c2", + "id": "f44ff8be", "metadata": { "hide-output": false }, @@ -2273,7 +2273,7 @@ { "cell_type": "code", "execution_count": null, - "id": "44796063", + "id": "4010b53e", "metadata": { "hide-output": false }, @@ -2301,7 +2301,7 @@ }, { "cell_type": "markdown", - "id": "ac7ffa33", + "id": "28b2a0b7", "metadata": {}, "source": [ "Let’s now take our two marginal distributions, one for $ X $, the other for $ Y $, and construct two distinct couplings.\n", @@ -2327,7 +2327,7 @@ { "cell_type": "code", "execution_count": null, - "id": "89e14ce2", + "id": "e342faec", "metadata": { "hide-output": false }, @@ -2362,7 +2362,7 @@ { "cell_type": "code", "execution_count": null, - "id": "232b8c75", + "id": "b5ef18ca", "metadata": { "hide-output": false }, @@ -2388,7 +2388,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b5419be", + "id": "c249bc7c", "metadata": { "hide-output": false }, @@ -2416,7 +2416,7 @@ }, { "cell_type": "markdown", - "id": "8df1d77d", + "id": "0a6a398e", "metadata": {}, "source": [ "Now, let’s construct another joint distribution that is also a coupling of $ X $ and $ Y $\n", @@ -2432,7 +2432,7 @@ { "cell_type": "code", "execution_count": null, - "id": "771c7d33", + "id": "3bdad6a7", "metadata": { "hide-output": false }, @@ -2467,7 +2467,7 @@ { "cell_type": "code", "execution_count": null, - "id": "099613d9", + "id": "83e5222a", "metadata": { "hide-output": false }, @@ -2493,7 +2493,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ce99685", + "id": "a32a8e34", "metadata": { "hide-output": false }, @@ -2521,7 +2521,7 @@ }, { "cell_type": "markdown", - "id": "c4bff8b0", + "id": "d9295172", "metadata": {}, "source": [ "We have verified that both joint distributions, $ c_1 $ and $ c_2 $, have identical marginal distributions of $ X $ and $ Y $, respectively.\n", @@ -2531,7 +2531,7 @@ }, { "cell_type": "markdown", - "id": "812bd5b2", + "id": "c1e7bbc1", "metadata": {}, "source": [ "## Time Series\n", @@ -2568,7 +2568,7 @@ } ], "metadata": { - "date": 1706246575.8898537, + "date": 1706493930.085523, "filename": "prob_matrix.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/prob_meaning.ipynb b/_notebooks/prob_meaning.ipynb index 3c1785a..2827be1 100644 --- a/_notebooks/prob_meaning.ipynb +++ b/_notebooks/prob_meaning.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c3e94433", + "id": "9d3bcc72", "metadata": {}, "source": [ "# Two Meanings of Probability" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "7b9fd89d", + "id": "e8e95e04", "metadata": {}, "source": [ "## Overview\n", @@ -46,7 +46,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b8477ad7", + "id": "ffb7fa78", "metadata": { "hide-output": false }, @@ -57,7 +57,7 @@ }, { "cell_type": "markdown", - "id": "5494e58a", + "id": "e1b105a0", "metadata": {}, "source": [ "To answer our coding questions, we’ll start with some imports" @@ -66,7 +66,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2c40cde", + "id": "021615cf", "metadata": { "hide-output": false }, @@ -82,7 +82,7 @@ }, { "cell_type": "markdown", - "id": "60cce1a4", + "id": "3130758b", "metadata": {}, "source": [ "Empowered with these Python tools, we’ll now explore the two meanings described above." @@ -90,7 +90,7 @@ }, { "cell_type": "markdown", - "id": "fb2451c5", + "id": "8b2cc3b8", "metadata": {}, "source": [ "## Frequentist Interpretation\n", @@ -147,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "07db6be5", + "id": "29170932", "metadata": {}, "source": [ "## Exercise 7.1\n", @@ -160,7 +160,7 @@ }, { "cell_type": "markdown", - "id": "1eb0a614", + "id": "2d60577e", "metadata": {}, "source": [ "## Solution to[ Exercise 7.1](https://python.quantecon.org/#pm_ex1)\n", @@ -171,7 +171,7 @@ { "cell_type": "code", "execution_count": null, - "id": "61925eb7", + "id": "5b614a27", "metadata": { "hide-output": false }, @@ -238,7 +238,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4e709dbd", + "id": "507a2c0a", "metadata": { "hide-output": false }, @@ -253,7 +253,7 @@ }, { "cell_type": "markdown", - "id": "d737367d", + "id": "414da3f8", "metadata": {}, "source": [ "From the table above, can you see the law of large numbers at work?\n", @@ -274,7 +274,7 @@ { "cell_type": "code", "execution_count": null, - "id": "608a2ad2", + "id": "2f97311f", "metadata": { "hide-output": false }, @@ -296,7 +296,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8270b44f", + "id": "01a71cf0", "metadata": { "hide-output": false }, @@ -316,7 +316,7 @@ }, { "cell_type": "markdown", - "id": "f6d0f4e0", + "id": "036e7dd7", "metadata": {}, "source": [ "**Comparison with different $ n $**\n", @@ -329,7 +329,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49163bd2", + "id": "abe15751", "metadata": { "hide-output": false }, @@ -351,7 +351,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9951e116", + "id": "3475c638", "metadata": { "hide-output": false }, @@ -371,7 +371,7 @@ }, { "cell_type": "markdown", - "id": "6d1d7608", + "id": "5f7276fe", "metadata": {}, "source": [ "**Comparison with different $ I $**\n", @@ -382,7 +382,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f664aca8", + "id": "a964e736", "metadata": { "hide-output": false }, @@ -405,7 +405,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef33d97a", + "id": "93329d3a", "metadata": { "hide-output": false }, @@ -425,7 +425,7 @@ }, { "cell_type": "markdown", - "id": "51321878", + "id": "1979231f", "metadata": {}, "source": [ "From the above graphs, we can see that **$ I $, the number of independent sequences,** plays an important role.\n", @@ -454,7 +454,7 @@ }, { "cell_type": "markdown", - "id": "803eb4cf", + "id": "176197d5", "metadata": {}, "source": [ "## Bayesian Interpretation\n", @@ -487,7 +487,7 @@ }, { "cell_type": "markdown", - "id": "bb0ce93c", + "id": "ed0cd0fb", "metadata": {}, "source": [ "## Exercise 7.2\n", @@ -511,7 +511,7 @@ }, { "cell_type": "markdown", - "id": "023f50a9", + "id": "a67d97a4", "metadata": {}, "source": [ "## Solution to[ Exercise 7.2](https://python.quantecon.org/#pm_ex2)\n", @@ -560,7 +560,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3e6fde2", + "id": "80d6eed3", "metadata": { "hide-output": false }, @@ -629,7 +629,7 @@ }, { "cell_type": "markdown", - "id": "5631a1f7", + "id": "8b4cd9f9", "metadata": {}, "source": [ "**d)** Please plot the posterior distribution for $ \\theta $ as a function of $ \\theta $ as $ n $ grows from $ 1, 2, \\ldots $." @@ -638,7 +638,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5dc8b607", + "id": "626dc8f4", "metadata": { "hide-output": false }, @@ -670,7 +670,7 @@ }, { "cell_type": "markdown", - "id": "8449c704", + "id": "3332fba1", "metadata": {}, "source": [ "**e)** For various $ n $’s, please describe and compute $ .05 $ and $ .95 $ quantiles for posterior probabilities." @@ -679,7 +679,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e99a4579", + "id": "430a7723", "metadata": { "hide-output": false }, @@ -698,7 +698,7 @@ }, { "cell_type": "markdown", - "id": "326c0f82", + "id": "33e1fa24", "metadata": {}, "source": [ "As $ n $ increases, we can see that Bayesian coverage intervals narrow and move toward $ 0.4 $.\n", @@ -721,7 +721,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f1e57f36", + "id": "6bfc653e", "metadata": { "hide-output": false }, @@ -744,7 +744,7 @@ }, { "cell_type": "markdown", - "id": "a75dc6ca", + "id": "c75cc3e8", "metadata": {}, "source": [ "Notice that in the graph above the posterior probabililty that $ \\theta \\in [.45, .55] $ typically exhibits a hump shape as $ n $ increases.\n", @@ -771,7 +771,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1834f284", + "id": "7c9bcb08", "metadata": { "hide-output": false }, @@ -794,7 +794,7 @@ }, { "cell_type": "markdown", - "id": "aa8b5d53", + "id": "0ffb977f", "metadata": {}, "source": [ "As $ n $ increases, we can see that the probability density functions *concentrate* on $ 0.4 $, the true value of $ \\theta $.\n", @@ -807,7 +807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "67ee7337", + "id": "567515ae", "metadata": { "hide-output": false }, @@ -835,7 +835,7 @@ }, { "cell_type": "markdown", - "id": "0c287ae3", + "id": "ae293170", "metadata": {}, "source": [ "How shall we interpret the patterns above?\n", @@ -882,7 +882,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef4fe30c", + "id": "564d3075", "metadata": { "hide-output": false }, @@ -906,7 +906,7 @@ }, { "cell_type": "markdown", - "id": "9a23079a", + "id": "78cc464a", "metadata": {}, "source": [ "After observing a large number of outcomes, the posterior distribution collapses around $ 0.4 $.\n", @@ -920,7 +920,7 @@ }, { "cell_type": "markdown", - "id": "c712ba0f", + "id": "d4e4fcdb", "metadata": {}, "source": [ "## Role of a Conjugate Prior\n", @@ -955,7 +955,7 @@ } ], "metadata": { - "date": 1706246575.9432917, + "date": 1706493930.1414871, "filename": "prob_meaning.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/rand_resp.ipynb b/_notebooks/rand_resp.ipynb index d54894a..0a82a91 100644 --- a/_notebooks/rand_resp.ipynb +++ b/_notebooks/rand_resp.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d7ca9a16", + "id": "a943b8d5", "metadata": {}, "source": [ "# Randomized Response Surveys" @@ -10,7 +10,7 @@ }, { "cell_type": "markdown", - "id": "9247aadc", + "id": "32d5add1", "metadata": {}, "source": [ "## Overview\n", @@ -21,7 +21,7 @@ "\n", "These problems induce **selection** biases that present challenges to interpreting and designing surveys.\n", "\n", - "To illustrate how social scientists have thought about estimating the prevalence of such embarrassing activities and opinions, this lecture describes a classic approach of S. L. Warner [[War65](https://python.quantecon.org/zreferences.html#id247)].\n", + "To illustrate how social scientists have thought about estimating the prevalence of such embarrassing activities and opinions, this lecture describes a classic approach of S. L. Warner [[War65](https://python.quantecon.org/zreferences.html#id249)].\n", "\n", "Warner used elementary probability to construct a way to protect the privacy of **individual** respondents to surveys while still estimating the fraction of a **collection** of individuals who have a socially stigmatized characteristic or who engage in a socially stigmatized activity.\n", "\n", @@ -38,7 +38,7 @@ }, { "cell_type": "markdown", - "id": "e265d9ae", + "id": "4d635ffe", "metadata": {}, "source": [ "## Warner’s Strategy\n", @@ -49,7 +49,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1deef233", + "id": "aa7cc3e6", "metadata": { "hide-output": false }, @@ -61,14 +61,14 @@ }, { "cell_type": "markdown", - "id": "81938830", + "id": "c2168337", "metadata": {}, "source": [ "Suppose that every person in population either belongs to Group A or Group B.\n", "\n", "We want to estimate the proportion $ \\pi $ who belong to Group A while protecting individual respondents’ privacy.\n", "\n", - "Warner [[War65](https://python.quantecon.org/zreferences.html#id247)] proposed and analyzed the following procedure.\n", + "Warner [[War65](https://python.quantecon.org/zreferences.html#id249)] proposed and analyzed the following procedure.\n", "\n", "- A random sample of $ n $ people is drawn with replacement from the population and each person is interviewed. \n", "- Draw $ n $ random samples from the population with replacement and interview each person. \n", @@ -182,7 +182,7 @@ }, { "cell_type": "markdown", - "id": "3b6b6aee", + "id": "52afdc53", "metadata": {}, "source": [ "## Comparing Two Survey Designs\n", @@ -245,7 +245,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c9bed5f", + "id": "c9cf6b0a", "metadata": { "hide-output": false }, @@ -306,7 +306,7 @@ }, { "cell_type": "markdown", - "id": "a84b4a9d", + "id": "24f907c1", "metadata": {}, "source": [ "Let’s put the code to work for parameter values\n", @@ -323,7 +323,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a0679038", + "id": "553b50be", "metadata": { "hide-output": false }, @@ -337,7 +337,7 @@ { "cell_type": "code", "execution_count": null, - "id": "03d61fcb", + "id": "0e5eb1ad", "metadata": { "hide-output": false }, @@ -349,7 +349,7 @@ }, { "cell_type": "markdown", - "id": "ee684d7c", + "id": "3974eb7d", "metadata": {}, "source": [ "The theoretical calculations do a good job of predicting Monte Carlo results.\n", @@ -360,7 +360,7 @@ "\n", "By adjusting parameters $ \\pi_A $ and $ n $, we can study outcomes in different situations.\n", "\n", - "For example, for another situation described in Warner [[War65](https://python.quantecon.org/zreferences.html#id247)]:\n", + "For example, for another situation described in Warner [[War65](https://python.quantecon.org/zreferences.html#id249)]:\n", "\n", "- $ \\pi_A=0.5 $ \n", "- $ n=1000 $ \n", @@ -372,7 +372,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5715a611", + "id": "4db8edf3", "metadata": { "hide-output": false }, @@ -386,7 +386,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ae5f667", + "id": "777ff7e1", "metadata": { "hide-output": false }, @@ -398,10 +398,10 @@ }, { "cell_type": "markdown", - "id": "6eb9f874", + "id": "21f6b468", "metadata": {}, "source": [ - "We can also revisit a calculation in the concluding section of Warner [[War65](https://python.quantecon.org/zreferences.html#id247)] in which\n", + "We can also revisit a calculation in the concluding section of Warner [[War65](https://python.quantecon.org/zreferences.html#id249)] in which\n", "\n", "- $ \\pi_A=0.6 $ \n", "- $ n=2000 $ \n", @@ -413,7 +413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f304f51d", + "id": "ced4dab0", "metadata": { "hide-output": false }, @@ -427,7 +427,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b048e536", + "id": "5d4debb8", "metadata": { "hide-output": false }, @@ -439,7 +439,7 @@ }, { "cell_type": "markdown", - "id": "625dc858", + "id": "03e792cc", "metadata": {}, "source": [ "Evidently, as $ n $ increases, the randomized response method does better performance in more situations." @@ -447,7 +447,7 @@ }, { "cell_type": "markdown", - "id": "c48ceaf2", + "id": "5471cd03", "metadata": {}, "source": [ "## Concluding Remarks\n", @@ -455,12 +455,12 @@ "[This QuantEcon lecture](https://python.quantecon.org/util_rand_resp.html) describes some alternative randomized response surveys.\n", "\n", "That lecture presents a utilitarian analysis of those alternatives conducted by Lars Ljungqvist\n", - "[[Lju93](https://python.quantecon.org/zreferences.html#id248)]." + "[[Lju93](https://python.quantecon.org/zreferences.html#id250)]." ] } ], "metadata": { - "date": 1706246575.9701364, + "date": 1706493930.170094, "filename": "rand_resp.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/status.ipynb b/_notebooks/status.ipynb index 7b48ff7..21cb43e 100644 --- a/_notebooks/status.ipynb +++ b/_notebooks/status.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d5af20ae", + "id": "59ab8029", "metadata": {}, "source": [ "# Execution Statistics\n", @@ -11,32 +11,32 @@ "\n", "[](https://python.quantecon.org/ar1_bayes.html)[](https://python.quantecon.org/ar1_turningpts.html)[](https://python.quantecon.org/back_prop.html)[](https://python.quantecon.org/bayes_nonconj.html)[](https://python.quantecon.org/exchangeable.html)[](https://python.quantecon.org/hoist_failure.html)[](https://python.quantecon.org/imp_sample.html)[](https://python.quantecon.org/intro.html)[](https://python.quantecon.org/likelihood_bayes.html)[](https://python.quantecon.org/likelihood_ratio_process.html)[](https://python.quantecon.org/lln_clt.html)[](https://python.quantecon.org/mix_model.html)[](https://python.quantecon.org/mle.html)[](https://python.quantecon.org/multi_hyper.html)[](https://python.quantecon.org/multivariate_normal.html)[](https://python.quantecon.org/navy_captain.html)[](https://python.quantecon.org/ols.html)[](https://python.quantecon.org/pandas_panel.html)[](https://python.quantecon.org/prob_matrix.html)[](https://python.quantecon.org/prob_meaning.html)[](https://python.quantecon.org/rand_resp.html)[](https://python.quantecon.org/.html)[](https://python.quantecon.org/troubleshooting.html)[](https://python.quantecon.org/util_rand_resp.html)[](https://python.quantecon.org/wald_friedman.html)[](https://python.quantecon.org/zreferences.html)|Document|Modified|Method|Run Time (s)|Status|\n", "|:------------------:|:------------------:|:------------------:|:------------------:|:------------------:|\n", - "|ar1_bayes|2024-01-24 00:50|cache|572.23|✅|\n", - "|ar1_turningpts|2024-01-24 00:51|cache|60.45|✅|\n", - "|back_prop|2024-01-24 00:54|cache|133.16|✅|\n", - "|bayes_nonconj|2024-01-24 02:01|cache|4027.08|✅|\n", - "|exchangeable|2024-01-24 02:01|cache|9.97|✅|\n", - "|hoist_failure|2024-01-24 02:02|cache|76.49|✅|\n", - "|imp_sample|2024-01-24 02:07|cache|277.73|✅|\n", - "|intro|2024-01-24 02:07|cache|1.14|✅|\n", - "|likelihood_bayes|2024-01-24 02:08|cache|49.06|✅|\n", - "|likelihood_ratio_process|2024-01-24 02:08|cache|10.38|✅|\n", - "|lln_clt|2024-01-24 02:08|cache|14.75|✅|\n", - "|mix_model|2024-01-24 02:09|cache|38.99|✅|\n", - "|mle|2024-01-24 02:09|cache|6.04|✅|\n", - "|multi_hyper|2024-01-24 02:09|cache|25.55|✅|\n", - "|multivariate_normal|2024-01-24 02:09|cache|5.39|✅|\n", - "|navy_captain|2024-01-24 02:10|cache|37.81|✅|\n", - "|ols|2024-01-24 02:10|cache|17.24|✅|\n", - "|pandas_panel|2024-01-24 02:10|cache|5.86|✅|\n", - "|prob_matrix|2024-01-24 02:11|cache|18.06|✅|\n", - "|prob_meaning|2024-01-24 02:12|cache|76.02|✅|\n", - "|rand_resp|2024-01-24 02:12|cache|3.02|✅|\n", - "|status|2024-01-24 02:07|cache|1.14|✅|\n", - "|troubleshooting|2024-01-24 02:07|cache|1.14|✅|\n", - "|util_rand_resp|2024-01-24 02:12|cache|3.73|✅|\n", - "|wald_friedman|2024-01-24 02:12|cache|20.09|✅|\n", - "|zreferences|2024-01-24 02:07|cache|1.14|✅|\n", + "|ar1_bayes|2024-01-29 00:22|cache|598.32|✅|\n", + "|ar1_turningpts|2024-01-29 00:23|cache|62.53|✅|\n", + "|back_prop|2024-01-29 00:26|cache|136.09|✅|\n", + "|bayes_nonconj|2024-01-29 01:37|cache|4279.22|✅|\n", + "|exchangeable|2024-01-29 01:37|cache|10.17|✅|\n", + "|hoist_failure|2024-01-29 01:38|cache|75.62|✅|\n", + "|imp_sample|2024-01-29 01:43|cache|275.9|✅|\n", + "|intro|2024-01-29 01:43|cache|4.02|✅|\n", + "|likelihood_bayes|2024-01-29 01:44|cache|49.22|✅|\n", + "|likelihood_ratio_process|2024-01-29 01:44|cache|10.98|✅|\n", + "|lln_clt|2024-01-29 01:44|cache|15.36|✅|\n", + "|mix_model|2024-01-29 01:45|cache|39.68|✅|\n", + "|mle|2024-01-29 01:45|cache|6.2|✅|\n", + "|multi_hyper|2024-01-29 01:45|cache|26.26|✅|\n", + "|multivariate_normal|2024-01-29 01:46|cache|5.87|✅|\n", + "|navy_captain|2024-01-29 01:46|cache|39.27|✅|\n", + "|ols|2024-01-29 01:47|cache|17.47|✅|\n", + "|pandas_panel|2024-01-29 01:47|cache|5.98|✅|\n", + "|prob_matrix|2024-01-29 01:47|cache|18.14|✅|\n", + "|prob_meaning|2024-01-29 01:48|cache|76.77|✅|\n", + "|rand_resp|2024-01-29 01:48|cache|3.08|✅|\n", + "|status|2024-01-29 01:43|cache|4.02|✅|\n", + "|troubleshooting|2024-01-29 01:43|cache|4.02|✅|\n", + "|util_rand_resp|2024-01-29 01:48|cache|3.54|✅|\n", + "|wald_friedman|2024-01-29 01:49|cache|20.53|✅|\n", + "|zreferences|2024-01-29 01:43|cache|4.02|✅|\n", "\n", "\n", "These lectures are built on `linux` instances through `github actions` and `amazon web services (aws)` to\n", @@ -46,7 +46,7 @@ } ], "metadata": { - "date": 1706246575.9886668, + "date": 1706493930.1897492, "filename": "status.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/troubleshooting.ipynb b/_notebooks/troubleshooting.ipynb index 7285aa4..a1fdd55 100644 --- a/_notebooks/troubleshooting.ipynb +++ b/_notebooks/troubleshooting.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c886537b", + "id": "063fa416", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "02bc5b95", + "id": "f01e5de1", "metadata": {}, "source": [ "# Troubleshooting" @@ -19,7 +19,7 @@ }, { "cell_type": "markdown", - "id": "3bc0bd50", + "id": "f9f20e8a", "metadata": {}, "source": [ "## Contents\n", @@ -31,7 +31,7 @@ }, { "cell_type": "markdown", - "id": "01cb6927", + "id": "e806091a", "metadata": {}, "source": [ "This page is for readers experiencing errors when running the code from the lectures." @@ -39,7 +39,7 @@ }, { "cell_type": "markdown", - "id": "6fa27073", + "id": "7aee9b33", "metadata": {}, "source": [ "## Fixing Your Local Environment\n", @@ -81,7 +81,7 @@ }, { "cell_type": "markdown", - "id": "1b62594c", + "id": "1ad65732", "metadata": {}, "source": [ "## Reporting an Issue\n", @@ -98,7 +98,7 @@ } ], "metadata": { - "date": 1706246575.9946697, + "date": 1706493930.1959321, "filename": "troubleshooting.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/util_rand_resp.ipynb b/_notebooks/util_rand_resp.ipynb index 0a21a0b..7812058 100644 --- a/_notebooks/util_rand_resp.ipynb +++ b/_notebooks/util_rand_resp.ipynb @@ -3,7 +3,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af2fda85", + "id": "a562d1b8", "metadata": { "hide-output": false }, @@ -15,7 +15,7 @@ }, { "cell_type": "markdown", - "id": "fd5d48f1", + "id": "64b9afbc", "metadata": {}, "source": [ "# Expected Utilities of Random Responses" @@ -23,24 +23,24 @@ }, { "cell_type": "markdown", - "id": "381bf48b", + "id": "a9e8795a", "metadata": {}, "source": [ "## Overview\n", "\n", - "[This QuantEcon lecture](https://python.quantecon.org/rand_resp.html) describes randomized response surveys in the tradition of Warner [[War65](https://python.quantecon.org/zreferences.html#id247)] that are designed to protect respondents’ privacy.\n", + "[This QuantEcon lecture](https://python.quantecon.org/rand_resp.html) describes randomized response surveys in the tradition of Warner [[War65](https://python.quantecon.org/zreferences.html#id249)] that are designed to protect respondents’ privacy.\n", "\n", - "Lars Ljungqvist [[Lju93](https://python.quantecon.org/zreferences.html#id248)] analyzed how a respondent’s decision about whether to answer truthfully depends on **expected utility**.\n", + "Lars Ljungqvist [[Lju93](https://python.quantecon.org/zreferences.html#id250)] analyzed how a respondent’s decision about whether to answer truthfully depends on **expected utility**.\n", "\n", "The lecture tells how Ljungqvist used his framework to shed light on alternative randomized response survey techniques\n", - "proposed, for example, by [[Lan75](https://python.quantecon.org/zreferences.html#id255)], [[Lan76](https://python.quantecon.org/zreferences.html#id249)], [[LW76](https://python.quantecon.org/zreferences.html#id250)],\n", - "[[And76](https://python.quantecon.org/zreferences.html#id251)], [[FPS77](https://python.quantecon.org/zreferences.html#id252)], [[GKAH77](https://python.quantecon.org/zreferences.html#id253)],\n", - "[[GAESH69](https://python.quantecon.org/zreferences.html#id254)]." + "proposed, for example, by [[Lan75](https://python.quantecon.org/zreferences.html#id257)], [[Lan76](https://python.quantecon.org/zreferences.html#id251)], [[LW76](https://python.quantecon.org/zreferences.html#id252)],\n", + "[[And76](https://python.quantecon.org/zreferences.html#id253)], [[FPS77](https://python.quantecon.org/zreferences.html#id254)], [[GKAH77](https://python.quantecon.org/zreferences.html#id255)],\n", + "[[GAESH69](https://python.quantecon.org/zreferences.html#id256)]." ] }, { "cell_type": "markdown", - "id": "e52290f1", + "id": "5739d219", "metadata": {}, "source": [ "## Privacy Measures\n", @@ -67,7 +67,7 @@ }, { "cell_type": "markdown", - "id": "fcc9a1b1", + "id": "2bffd2af", "metadata": {}, "source": [ "## Zoo of Concepts\n", @@ -77,7 +77,7 @@ }, { "cell_type": "markdown", - "id": "81da951d", + "id": "1b4eccdf", "metadata": {}, "source": [ "### Leysieffer and Warner(1976)\n", @@ -145,14 +145,14 @@ }, { "cell_type": "markdown", - "id": "e520b108", + "id": "7a61735b", "metadata": {}, "source": [ "### Lanke(1976)\n", "\n", - "Lanke (1975) [[Lan75](https://python.quantecon.org/zreferences.html#id255)] argued that “it is membership in Group A that people may want to hide, not membership in the complementary Group A’.”\n", + "Lanke (1975) [[Lan75](https://python.quantecon.org/zreferences.html#id257)] argued that “it is membership in Group A that people may want to hide, not membership in the complementary Group A’.”\n", "\n", - "For that reason, Lanke (1976) [[Lan76](https://python.quantecon.org/zreferences.html#id249)] argued that an appropriate measure of protection is to minimize\n", + "For that reason, Lanke (1976) [[Lan76](https://python.quantecon.org/zreferences.html#id251)] argued that an appropriate measure of protection is to minimize\n", "\n", "\n", "\n", @@ -165,12 +165,12 @@ }, { "cell_type": "markdown", - "id": "c9eecdc7", + "id": "559f2968", "metadata": {}, "source": [ "### 2.3 Fligner, Policello, and Singh\n", "\n", - "Fligner, Policello, and Singh reached similar conclusion as Lanke (1976). [[FPS77](https://python.quantecon.org/zreferences.html#id252)]\n", + "Fligner, Policello, and Singh reached similar conclusion as Lanke (1976). [[FPS77](https://python.quantecon.org/zreferences.html#id254)]\n", "\n", "They measured “private protection” as\n", "\n", @@ -183,12 +183,12 @@ }, { "cell_type": "markdown", - "id": "d11cef81", + "id": "a8fcbcc8", "metadata": {}, "source": [ "### 2.4 Greenberg, Kuebler, Abernathy, and Horvitz (1977)\n", "\n", - "[[GKAH77](https://python.quantecon.org/zreferences.html#id253)]\n", + "[[GKAH77](https://python.quantecon.org/zreferences.html#id255)]\n", "\n", "Greenberg, Kuebler, Abernathy, and Horvitz (1977) stressed the importance of examining the risk to respondents who do not belong to $ A $ as well as the risk to those who do belong to the sensitive group.\n", "\n", @@ -231,7 +231,7 @@ }, { "cell_type": "markdown", - "id": "b73c5068", + "id": "4b73ddb7", "metadata": {}, "source": [ "## Respondent’s Expected Utility" @@ -239,7 +239,7 @@ }, { "cell_type": "markdown", - "id": "36b11125", + "id": "9b53b83d", "metadata": {}, "source": [ "### Truth Border\n", @@ -343,7 +343,7 @@ }, { "cell_type": "markdown", - "id": "eeb9ee52", + "id": "1fbd2067", "metadata": {}, "source": [ "### Drawing a Truth Border\n", @@ -360,7 +360,7 @@ { "cell_type": "code", "execution_count": null, - "id": "afd02f7b", + "id": "9d18b5d5", "metadata": { "hide-output": false }, @@ -395,7 +395,7 @@ }, { "cell_type": "markdown", - "id": "03fc895a", + "id": "95f1971f", "metadata": {}, "source": [ "Figure 1.1 three types of truth border.\n", @@ -412,7 +412,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aecc442c", + "id": "13d5b5db", "metadata": { "hide-output": false }, @@ -442,7 +442,7 @@ }, { "cell_type": "markdown", - "id": "1487b386", + "id": "44bf1b28", "metadata": {}, "source": [ "## Utilitarian View of Survey Design" @@ -450,7 +450,7 @@ }, { "cell_type": "markdown", - "id": "9399dc07", + "id": "3bbde676", "metadata": {}, "source": [ "### Iso-variance Curves\n", @@ -460,7 +460,7 @@ "- to find a randomized response survey design that minimizes the bias and the variance of the estimator. \n", "\n", "\n", - "Given a design that ensures truthful answers by all respondents, Anderson(1976, Theorem 1) [[And76](https://python.quantecon.org/zreferences.html#id251)] showed that the minimum variance estimate in the two-response model has variance\n", + "Given a design that ensures truthful answers by all respondents, Anderson(1976, Theorem 1) [[And76](https://python.quantecon.org/zreferences.html#id253)] showed that the minimum variance estimate in the two-response model has variance\n", "\n", "\n", "\n", @@ -497,7 +497,7 @@ }, { "cell_type": "markdown", - "id": "0376a8b2", + "id": "91a5a568", "metadata": {}, "source": [ "### Drawing Iso-variance Curves\n", @@ -515,7 +515,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5bc6a121", + "id": "e035b882", "metadata": { "hide-output": false }, @@ -559,7 +559,7 @@ }, { "cell_type": "markdown", - "id": "c9aa9c21", + "id": "e2a78374", "metadata": {}, "source": [ "Properties of iso-variance curves are:\n", @@ -568,7 +568,7 @@ "- From $ V_1 $ to $ V_9 $, the variance of the iso-variance curve increase monotonically, as colors brighten monotonically \n", "\n", "\n", - "Suppose the parameters of the iso-variance model follow those in Ljungqvist [[Lju93](https://python.quantecon.org/zreferences.html#id248)], which are:\n", + "Suppose the parameters of the iso-variance model follow those in Ljungqvist [[Lju93](https://python.quantecon.org/zreferences.html#id250)], which are:\n", "\n", "- $ \\pi=0.3 $ \n", "- $ n=100 $ \n", @@ -580,7 +580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd66ef1b", + "id": "c0f1d9cd", "metadata": { "hide-output": false }, @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "9399ad61", + "id": "7bc9a248", "metadata": {}, "source": [ "### Optimal Survey\n", @@ -625,7 +625,7 @@ }, { "cell_type": "markdown", - "id": "d64e9c6d", + "id": "c0893f79", "metadata": {}, "source": [ "## Criticisms of Proposed Privacy Measures\n", @@ -637,7 +637,7 @@ }, { "cell_type": "markdown", - "id": "21e59906", + "id": "baaef5af", "metadata": {}, "source": [ "### Analysis of Method of Lanke’s (1976)\n", @@ -658,7 +658,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62d193fb", + "id": "cdcb62b3", "metadata": { "hide-output": false }, @@ -703,7 +703,7 @@ }, { "cell_type": "markdown", - "id": "990d9a34", + "id": "8e4340f5", "metadata": {}, "source": [ "### Method of Leysieffer and Warner (1976)\n", @@ -725,12 +725,12 @@ }, { "cell_type": "markdown", - "id": "76f159c4", + "id": "6e43b116", "metadata": {}, "source": [ "### Analysis on the Method of Chaudhuri and Mukerjee’s (1988)\n", "\n", - "[[CM88](https://python.quantecon.org/zreferences.html#id246)]\n", + "[[CM88](https://python.quantecon.org/zreferences.html#id248)]\n", "\n", "Chaudhuri and Mukerjee (1988) argued that the individual may find that since “yes” may sometimes relate to the sensitive group A, a clever respondent may falsely but safely always be inclined to respond “no”. In this situation, the truth border is such that individuals choose to lie whenever the truthful answer is “yes” and\n", "\n", @@ -760,7 +760,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a657094c", + "id": "d7db609a", "metadata": { "hide-output": false }, @@ -776,7 +776,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cacea3d4", + "id": "e65fed39", "metadata": { "hide-output": false }, @@ -820,12 +820,12 @@ }, { "cell_type": "markdown", - "id": "161071ac", + "id": "f1af97c5", "metadata": {}, "source": [ "### Method of Greenberg et al. (1977)\n", "\n", - "[[GKAH77](https://python.quantecon.org/zreferences.html#id253)]\n", + "[[GKAH77](https://python.quantecon.org/zreferences.html#id255)]\n", "\n", "Greenberg et al. (1977) defined the hazard for an individual in $ A $ as the probability that he or she is perceived as belonging to $ A $:\n", "\n", @@ -888,7 +888,7 @@ }, { "cell_type": "markdown", - "id": "c6f2d90b", + "id": "31eab138", "metadata": {}, "source": [ "## Concluding Remarks\n", @@ -909,12 +909,12 @@ "- The optimal model design is obtained at the point where the truth border touches the lowest possible iso-variance curve. \n", "\n", "\n", - "A practical implication of the analysis of [[Lju93](https://python.quantecon.org/zreferences.html#id248)] is that uncertainty about respondents’ demands for privacy can be acknowledged by **choosing $ \\text{Pr}(A|\\text{yes}) $ and $ \\text{Pr}(A|\\text{no}) $ sufficiently close to each other**." + "A practical implication of the analysis of [[Lju93](https://python.quantecon.org/zreferences.html#id250)] is that uncertainty about respondents’ demands for privacy can be acknowledged by **choosing $ \\text{Pr}(A|\\text{yes}) $ and $ \\text{Pr}(A|\\text{no}) $ sufficiently close to each other**." ] } ], "metadata": { - "date": 1706246576.1626396, + "date": 1706493930.2476246, "filename": "util_rand_resp.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/wald_friedman.ipynb b/_notebooks/wald_friedman.ipynb index 4c7656a..761ad39 100644 --- a/_notebooks/wald_friedman.ipynb +++ b/_notebooks/wald_friedman.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "10f17800", + "id": "d4ddcbbe", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "cd46a53f", + "id": "8837d87c", "metadata": {}, "source": [ "# A Problem that Stumped Milton Friedman\n", @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "191cf489", + "id": "cdd7d85d", "metadata": {}, "source": [ "## Contents\n", @@ -41,7 +41,7 @@ }, { "cell_type": "markdown", - "id": "4965d7cf", + "id": "ce102eec", "metadata": {}, "source": [ "In addition to what’s in Anaconda, this lecture will need the following libraries:" @@ -50,7 +50,7 @@ { "cell_type": "code", "execution_count": null, - "id": "34e0c818", + "id": "6829a5ba", "metadata": { "hide-output": false }, @@ -61,7 +61,7 @@ }, { "cell_type": "markdown", - "id": "29ba9f78", + "id": "e01dad2e", "metadata": {}, "source": [ "## Overview\n", @@ -94,7 +94,7 @@ { "cell_type": "code", "execution_count": null, - "id": "776490f0", + "id": "78894354", "metadata": { "hide-output": false }, @@ -110,7 +110,7 @@ }, { "cell_type": "markdown", - "id": "54ff3497", + "id": "92f1c3ab", "metadata": {}, "source": [ "This lecture uses ideas studied in [this lecture](https://python.quantecon.org/likelihood_ratio_process.html), [this lecture](https://python.quantecon.org/likelihood_bayes.html).\n", @@ -119,7 +119,7 @@ }, { "cell_type": "markdown", - "id": "37ee5257", + "id": "d1f659f4", "metadata": {}, "source": [ "## Origin of the Problem\n", @@ -129,6 +129,11 @@ "during World War II, when they worked at the US Government’s\n", "Statistical Research Group at Columbia University.\n", "\n", + ">**Note**\n", + ">\n", + ">See pages 25 and 26 of Allen Wallis’s 1980 article [[Wal80](https://python.quantecon.org/zreferences.html#id243)] about the Statistical Research Group at Columbia University during World War II for his account of the episode and for important contributions that Harold Hotelling made to formulating the problem. Also see chapter 5 of Jennifer Burns book about\n", + "Milton Friedman [[Bur23](https://python.quantecon.org/zreferences.html#id244)].\n", + "\n", "Let’s listen to Milton Friedman tell us what happened\n", "\n", "> In order to understand the story, it is necessary to have an idea of a\n", @@ -170,7 +175,7 @@ }, { "cell_type": "markdown", - "id": "50acbb39", + "id": "12f2d621", "metadata": {}, "source": [ "## A Dynamic Programming Approach\n", @@ -248,7 +253,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62a7a40d", + "id": "7b447428", "metadata": { "hide-output": false }, @@ -284,7 +289,7 @@ }, { "cell_type": "markdown", - "id": "b26dbfa3", + "id": "a03fd75d", "metadata": {}, "source": [ "### Losses and Costs\n", @@ -311,7 +316,7 @@ }, { "cell_type": "markdown", - "id": "36b0290c", + "id": "6a04f388", "metadata": {}, "source": [ "### Digression on Type I and Type II Errors\n", @@ -333,7 +338,7 @@ }, { "cell_type": "markdown", - "id": "a02d9049", + "id": "3f400552", "metadata": {}, "source": [ "### Intuition\n", @@ -363,7 +368,7 @@ }, { "cell_type": "markdown", - "id": "2ec978d6", + "id": "65015dae", "metadata": {}, "source": [ "### A Bellman Equation\n", @@ -485,7 +490,7 @@ }, { "cell_type": "markdown", - "id": "ca04c5f6", + "id": "62341662", "metadata": {}, "source": [ "## Implementation\n", @@ -496,7 +501,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cd383b7d", + "id": "058c354b", "metadata": { "hide-output": false }, @@ -519,7 +524,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b26feabe", + "id": "8a69cb91", "metadata": { "hide-output": false }, @@ -578,7 +583,7 @@ }, { "cell_type": "markdown", - "id": "fd16c577", + "id": "b71dcfac", "metadata": {}, "source": [ "As in the [optimal growth lecture](https://quantecon.github.io/lecture-dynamics/optgrowth.html), to approximate a continuous value function\n", @@ -593,7 +598,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9986904c", + "id": "f9a76940", "metadata": { "hide-output": false }, @@ -633,7 +638,7 @@ }, { "cell_type": "markdown", - "id": "ef098d77", + "id": "53de5dad", "metadata": {}, "source": [ "To solve the key functional equation, we will iterate using `Q` to find the fixed point" @@ -642,7 +647,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4199568b", + "id": "8eb4424c", "metadata": { "hide-output": false }, @@ -675,7 +680,7 @@ }, { "cell_type": "markdown", - "id": "6c92d958", + "id": "6c27987f", "metadata": {}, "source": [ "## Analysis\n", @@ -688,7 +693,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d60d59df", + "id": "e58db629", "metadata": { "hide-output": false }, @@ -707,7 +712,7 @@ }, { "cell_type": "markdown", - "id": "ec0e403c", + "id": "2b9cc5d0", "metadata": {}, "source": [ "### Value Function\n", @@ -718,7 +723,7 @@ { "cell_type": "code", "execution_count": null, - "id": "237528c2", + "id": "1877fcf0", "metadata": { "hide-output": false }, @@ -729,7 +734,7 @@ }, { "cell_type": "markdown", - "id": "d6291bc7", + "id": "6465b0de", "metadata": {}, "source": [ "We will also set up a function to compute the cutoffs $ \\alpha $ and $ \\beta $\n", @@ -739,7 +744,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cb2e46ee", + "id": "947dff05", "metadata": { "hide-output": false }, @@ -802,7 +807,7 @@ }, { "cell_type": "markdown", - "id": "28349e0c", + "id": "e2223b15", "metadata": {}, "source": [ "The cost function $ J $ equals $ \\pi L_1 $ for $ \\pi \\leq \\beta $, and $ (1-\\pi )L_0 $ for $ \\pi\n", @@ -820,7 +825,7 @@ }, { "cell_type": "markdown", - "id": "5e4b5234", + "id": "75ffaf56", "metadata": {}, "source": [ "### Simulations\n", @@ -839,7 +844,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d956ad1a", + "id": "f3960621", "metadata": { "hide-output": false }, @@ -939,7 +944,7 @@ }, { "cell_type": "markdown", - "id": "8254c5e5", + "id": "b46f10db", "metadata": {}, "source": [ "### Comparative Statics\n", @@ -957,7 +962,7 @@ { "cell_type": "code", "execution_count": null, - "id": "725fabb5", + "id": "bb2d1947", "metadata": { "hide-output": false }, @@ -969,7 +974,7 @@ }, { "cell_type": "markdown", - "id": "bdb7a174", + "id": "bec331c1", "metadata": {}, "source": [ "Increased cost per draw has induced the decision-maker to take fewer draws before deciding.\n", @@ -981,7 +986,7 @@ }, { "cell_type": "markdown", - "id": "1c0180b0", + "id": "2b0b6698", "metadata": {}, "source": [ "### A Notebook Implementation\n", @@ -1003,7 +1008,7 @@ }, { "cell_type": "markdown", - "id": "3b241841", + "id": "c3c3d0d9", "metadata": {}, "source": [ "## Comparison with Neyman-Pearson Formulation\n", @@ -1177,7 +1182,7 @@ }, { "cell_type": "markdown", - "id": "42513b04", + "id": "bca395f0", "metadata": {}, "source": [ "## Sequels\n", @@ -1198,7 +1203,7 @@ } ], "metadata": { - "date": 1706246576.225045, + "date": 1706493930.310227, "filename": "wald_friedman.md", "kernelspec": { "display_name": "Python", diff --git a/_notebooks/zreferences.ipynb b/_notebooks/zreferences.ipynb index 9366ed8..e06bd95 100644 --- a/_notebooks/zreferences.ipynb +++ b/_notebooks/zreferences.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "84ee43af", + "id": "0bca3a17", "metadata": {}, "source": [ "\n", @@ -11,7 +11,7 @@ }, { "cell_type": "markdown", - "id": "67cc1f58", + "id": "fbe55365", "metadata": {}, "source": [ "# References\n", @@ -19,16 +19,19 @@ "\n", "\\[AJR01\\] Daron Acemoglu, Simon Johnson, and James A Robinson. The colonial origins of comparative development: an empirical investigation. *The American Economic Review*, 91(5):1369–1401, 2001.\n", "\n", - "\n", + "\n", "\\[And76\\] Harald Anderson. Estimation of a proportion through randomized response. *International Statistical Review/Revue Internationale de Statistique*, pages 213–217, 1976.\n", "\n", - "\n", + "\n", "\\[Apo90\\] George Apostolakis. The concept of probability in safety assessments of technological systems. *Science*, 250(4986):1359–1364, 1990.\n", "\n", "\n", "\\[Ber75\\] Dmitri Bertsekas. *Dynamic Programming and Stochastic Control*. Academic Press, New York, 1975.\n", "\n", - "\n", + "\n", + "\\[Bur23\\] Jennifer Burns. *Milton Friedman: The Last Conservative by Jennifer Burns*. Farrar, Straus, and Giroux, New York, 2023.\n", + "\n", + "\n", "\\[CM88\\] A Chadhuri and R Mukerjee. *Randomized Response: Theory and Technique*. Marcel Dekker, New York, 1988.\n", "\n", "\n", @@ -37,49 +40,49 @@ "\n", "\\[Dud02\\] R M Dudley. *Real Analysis and Probability*. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2002.\n", "\n", - "\n", + "\n", "\\[ESAW18\\] Ashraf Ben El-Shanawany, Keith H Ardron, and Simon P Walker. Lognormal approximations of fault tree uncertainty distributions. *Risk Analysis*, 38(8):1576–1584, 2018.\n", "\n", - "\n", + "\n", "\\[FPS77\\] Michael A Fligner, George E Policello, and Jagbir Singh. A comparison of two randomized response survey methods with consideration for the level of respondent protection. *Communications in Statistics-Theory and Methods*, 6(15):1511–1524, 1977.\n", "\n", "\n", "\\[FF98\\] Milton Friedman and Rose D Friedman. *Two Lucky People*. University of Chicago Press, 1998.\n", "\n", - "\n", + "\n", "\\[GAESH69\\] Bernard G Greenberg, Abdel-Latif A Abul-Ela, Walt R Simmons, and Daniel G Horvitz. The unrelated question randomized response model: theoretical framework. *Journal of the American Statistical Association*, 64(326):520–539, 1969.\n", "\n", - "\n", + "\n", "\\[GKAH77\\] Bernard G Greenberg, Roy R Kuebler, James R Abernathy, and Daniel G Horvitz. Respondent hazards in the unrelated question randomized response model. *Journal of Statistical Planning and Inference*, 1(1):53–60, 1977.\n", "\n", - "\n", + "\n", "\\[GS93\\] Moses A Greenfield and Thomas J Sargent. A probabilistic analysis of a catastrophic transuranic waste hoise accident at the wipp. Environmental Evaluation Group, Albuquerque, New Mexico, June 1993. URL: [http://www.tomsargent.com/research/EEG-53.pdf](http://www.tomsargent.com/research/EEG-53.pdf).\n", "\n", - "\n", + "\n", "\\[Hur50\\] Leonid Hurwicz. Least squares bias in time series. *Statistical inference in dynamic economic models*, 10:365–383, 1950.\n", "\n", "\n", "\\[Kre88\\] David M. Kreps. *Notes on the Theory of Choice*. Westview Press, Boulder, Colorado, 1988.\n", "\n", - "\n", + "\n", "\\[Lan75\\] Jan Lanke. On the choice of the unrelated question in simmons' version of randomized response. *Journal of the American Statistical Association*, 70(349):80–83, 1975.\n", "\n", - "\n", + "\n", "\\[Lan76\\] Jan Lanke. On the degree of protection in randomized interviews. *International Statistical Review/Revue Internationale de Statistique*, pages 197–203, 1976.\n", "\n", - "\n", + "\n", "\\[LW76\\] Frederick W Leysieffer and Stanley L Warner. Respondent jeopardy and optimal designs in randomized response models. *Journal of the American Statistical Association*, 71(355):649–656, 1976.\n", "\n", - "\n", + "\n", "\\[Lju93\\] Lars Ljungqvist. A unified approach to measures of privacy in randomized response models: a utilitarian perspective. *Journal of the American Statistical Association*, 88(421):97–103, 1993.\n", "\n", "\n", "\\[McC70\\] J J McCall. Economics of Information and Job Search. *The Quarterly Journal of Economics*, 84(1):113–126, 1970.\n", "\n", - "\n", + "\n", "\\[NP33\\] J. Neyman and E. S Pearson. On the problem of the most efficient tests of statistical hypotheses. *Phil. Trans. R. Soc. Lond. A. 231 (694–706)*, pages 289–337, 1933.\n", "\n", - "\n", + "\n", "\\[OW69\\] Guy H. Orcutt and Herbert S. Winokur. First order autoregression: inference, estimation, and prediction. *Econometrica*, 37(1):1–14, 1969.\n", "\n", "\n", @@ -88,10 +91,13 @@ "\n", "\\[Wal47\\] Abraham Wald. *Sequential Analysis*. John Wiley and Sons, New York, 1947.\n", "\n", - "\n", + "\n", + "\\[Wal80\\] W Allen Wallis. The statistical research group, 1942–1945. *Journal of the American Statistical Association*, 75(370):320–330, 1980.\n", + "\n", + "\n", "\\[War65\\] Stanley L Warner. Randomized response: a survey technique for eliminating evasive answer bias. *Journal of the American Statistical Association*, 60(309):63–69, 1965.\n", "\n", - "\n", + "\n", "\\[Wec79\\] William E Wecker. Predicting the turning points of a time series. *Journal of business*, pages 35–50, 1979.\n", "\n", "\n", @@ -100,7 +106,7 @@ } ], "metadata": { - "date": 1706246576.2401505, + "date": 1706493930.325982, "filename": "zreferences.md", "kernelspec": { "display_name": "Python", diff --git a/_pdf/quantecon-python.pdf b/_pdf/quantecon-python.pdf index 3cbf680..f64eba3 100644 Binary files a/_pdf/quantecon-python.pdf and b/_pdf/quantecon-python.pdf differ diff --git a/_sources/ar1_bayes.ipynb b/_sources/ar1_bayes.ipynb index db0fc48..8568e48 100644 --- a/_sources/ar1_bayes.ipynb +++ b/_sources/ar1_bayes.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "e46a9479", + "id": "1f98e638", "metadata": {}, "source": [ "# Posterior Distributions for AR(1) Parameters\n", @@ -13,7 +13,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c61170d5", + "id": "e033712f", "metadata": { "tags": [ "hide-output" @@ -27,7 +27,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d2fff63", + "id": "f979b5fe", "metadata": {}, "outputs": [], "source": [ @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "7f8de345", + "id": "b6f32a01", "metadata": {}, "source": [ "This lecture uses Bayesian methods offered by [pymc](https://www.pymc.io/projects/docs/en/stable/) and [numpyro](https://num.pyro.ai/en/stable/) to make statistical inferences about two parameters of a univariate first-order autoregression.\n", @@ -149,7 +149,7 @@ { "cell_type": "code", "execution_count": null, - "id": "191a3896", + "id": "067fd54e", "metadata": {}, "outputs": [], "source": [ @@ -177,7 +177,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a4b2667d", + "id": "4daba3b4", "metadata": {}, "outputs": [], "source": [ @@ -187,7 +187,7 @@ }, { "cell_type": "markdown", - "id": "852fea4f", + "id": "9bd7e3d9", "metadata": {}, "source": [ "Now we shall use Bayes' law to construct a posterior distribution, conditioning on the initial value of $y_0$.\n", @@ -205,7 +205,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2d26da2", + "id": "806f3399", "metadata": {}, "outputs": [], "source": [ @@ -226,7 +226,7 @@ }, { "cell_type": "markdown", - "id": "537de659", + "id": "bce410a8", "metadata": {}, "source": [ "[pmc.sample](https://www.pymc.io/projects/docs/en/v5.10.0/api/generated/pymc.sample.html#pymc-sample) by default uses the NUTS samplers to generate samples as shown in the below cell:" @@ -235,7 +235,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eef9bd89", + "id": "95a036ed", "metadata": { "tag": [ "hide-output" @@ -250,7 +250,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e36e16b0", + "id": "fa4be87a", "metadata": {}, "outputs": [], "source": [ @@ -260,7 +260,7 @@ }, { "cell_type": "markdown", - "id": "91c41255", + "id": "7a8f7f06", "metadata": {}, "source": [ "Evidently, the posteriors aren't centered on the true values of $.5, 1$ that we used to generate the data.\n", @@ -276,7 +276,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b5eb1cf", + "id": "92b421b1", "metadata": {}, "outputs": [], "source": [ @@ -288,7 +288,7 @@ }, { "cell_type": "markdown", - "id": "60280544", + "id": "6235aeb1", "metadata": {}, "source": [ "Now we shall compute a posterior distribution after seeing the same data but instead assuming that $y_0$ is drawn from the stationary distribution.\n", @@ -305,7 +305,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0e53c9f3", + "id": "56a13b46", "metadata": {}, "outputs": [], "source": [ @@ -329,7 +329,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8ac4ff27", + "id": "8e6896b5", "metadata": { "tag": [ "hide-output" @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f673d37", + "id": "180f5c2f", "metadata": {}, "outputs": [], "source": [ @@ -357,7 +357,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8f93255b", + "id": "4d101fec", "metadata": {}, "outputs": [], "source": [ @@ -369,7 +369,7 @@ }, { "cell_type": "markdown", - "id": "9b9f6867", + "id": "390e7e74", "metadata": {}, "source": [ "Please note how the posterior for $\\rho$ has shifted to the right relative to when we conditioned on $y_0$ instead of assuming that $y_0$ is drawn from the stationary distribution.\n", @@ -391,7 +391,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8e8137a0", + "id": "65e63867", "metadata": {}, "outputs": [], "source": [ @@ -425,7 +425,7 @@ { "cell_type": "code", "execution_count": null, - "id": "46362e24", + "id": "9a8ba976", "metadata": {}, "outputs": [], "source": [ @@ -444,7 +444,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8ffaa7de", + "id": "7b148dd2", "metadata": { "tag": [ "hide-output" @@ -466,7 +466,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f20a8b5", + "id": "823d7349", "metadata": {}, "outputs": [], "source": [ @@ -476,7 +476,7 @@ { "cell_type": "code", "execution_count": null, - "id": "937c5973", + "id": "02e6a834", "metadata": {}, "outputs": [], "source": [ @@ -485,7 +485,7 @@ }, { "cell_type": "markdown", - "id": "b16b3f02", + "id": "bb493a2e", "metadata": {}, "source": [ "Next, we again compute the posterior under the assumption that $y_0$ is drawn from the stationary distribution, so that\n", @@ -500,7 +500,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76afc3bd", + "id": "38452ab5", "metadata": {}, "outputs": [], "source": [ @@ -523,7 +523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d21af18", + "id": "ddf639ac", "metadata": { "tag": [ "hide-output" @@ -545,7 +545,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3241a94", + "id": "0034a1e8", "metadata": {}, "outputs": [], "source": [ @@ -555,7 +555,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdee610f", + "id": "bf85e1e2", "metadata": {}, "outputs": [], "source": [ @@ -564,7 +564,7 @@ }, { "cell_type": "markdown", - "id": "d344f00f", + "id": "294bb810", "metadata": {}, "source": [ "Look what happened to the posterior!\n", diff --git a/_sources/ar1_turningpts.ipynb b/_sources/ar1_turningpts.ipynb index b333499..64be0de 100644 --- a/_sources/ar1_turningpts.ipynb +++ b/_sources/ar1_turningpts.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "f625ee6f", + "id": "13819c44", "metadata": {}, "source": [ "# Forecasting an AR(1) Process" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3539c567", + "id": "d9f2063f", "metadata": { "tags": [ "hide-output" @@ -24,7 +24,7 @@ }, { "cell_type": "markdown", - "id": "0621306e", + "id": "6fecc302", "metadata": {}, "source": [ "This lecture describes methods for forecasting statistics that are functions of future values of a univariate autogressive process. \n", @@ -53,7 +53,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a25a5e90", + "id": "1693be41", "metadata": {}, "outputs": [], "source": [ @@ -74,7 +74,7 @@ }, { "cell_type": "markdown", - "id": "8468881f", + "id": "1fd37860", "metadata": {}, "source": [ "## A Univariate First-Order Autoregressive Process\n", @@ -146,7 +146,7 @@ { "cell_type": "code", "execution_count": null, - "id": "af4a711c", + "id": "c24e0e92", "metadata": {}, "outputs": [], "source": [ @@ -210,7 +210,7 @@ }, { "cell_type": "markdown", - "id": "72f840f7", + "id": "91f6235b", "metadata": {}, "source": [ "As functions of forecast horizon, the coverage intervals have shapes like those described in \n", @@ -339,7 +339,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4caef408", + "id": "94f97291", "metadata": {}, "outputs": [], "source": [ @@ -384,7 +384,7 @@ }, { "cell_type": "markdown", - "id": "616e5e1b", + "id": "f46fc207", "metadata": {}, "source": [ "The graphs on the left portray posterior marginal distributions.\n", @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "317ab48a", + "id": "e3024c5a", "metadata": {}, "outputs": [], "source": [ @@ -457,7 +457,7 @@ }, { "cell_type": "markdown", - "id": "1951cfc7", + "id": "485ebd44", "metadata": {}, "source": [ "## Original Wecker Method\n", @@ -469,7 +469,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ff6b572", + "id": "1cf31057", "metadata": {}, "outputs": [], "source": [ @@ -535,7 +535,7 @@ }, { "cell_type": "markdown", - "id": "a3f5d180", + "id": "ee4c3452", "metadata": {}, "source": [ "## Extended Wecker Method\n", @@ -549,7 +549,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cbf10bd2", + "id": "e54f93e3", "metadata": {}, "outputs": [], "source": [ @@ -608,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "68cef1d0", + "id": "54d1881d", "metadata": {}, "source": [ "## Comparison\n", @@ -619,7 +619,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e6a24eb9", + "id": "7e168b02", "metadata": {}, "outputs": [], "source": [ diff --git a/_sources/back_prop.ipynb b/_sources/back_prop.ipynb index 5238758..449a96a 100644 --- a/_sources/back_prop.ipynb +++ b/_sources/back_prop.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ebbc0b42", + "id": "babb6f97", "metadata": {}, "source": [ "# Introduction to Artificial Neural Networks" @@ -11,7 +11,7 @@ { "cell_type": "code", "execution_count": null, - "id": "45fef513", + "id": "812fe7ee", "metadata": { "tags": [ "hide-output" @@ -25,7 +25,7 @@ }, { "cell_type": "markdown", - "id": "6727101a", + "id": "f4f96252", "metadata": {}, "source": [ "```{note}\n", @@ -315,7 +315,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a1936532", + "id": "5ef0b105", "metadata": {}, "outputs": [], "source": [ @@ -330,7 +330,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9294e5e6", + "id": "784cb63b", "metadata": {}, "outputs": [], "source": [ @@ -349,7 +349,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f171cd5", + "id": "0e912b84", "metadata": {}, "outputs": [], "source": [ @@ -395,7 +395,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2649d961", + "id": "88b33e72", "metadata": {}, "outputs": [], "source": [ @@ -410,7 +410,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e2cd4e96", + "id": "13927ec8", "metadata": {}, "outputs": [], "source": [ @@ -422,7 +422,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a645dbf3", + "id": "38d7462d", "metadata": {}, "outputs": [], "source": [ @@ -433,7 +433,7 @@ { "cell_type": "code", "execution_count": null, - "id": "edf47067", + "id": "02cccd84", "metadata": {}, "outputs": [], "source": [ @@ -443,7 +443,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6f92bf66", + "id": "eb31547f", "metadata": {}, "outputs": [], "source": [ @@ -458,7 +458,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eefb1c3c", + "id": "b49901c8", "metadata": {}, "outputs": [], "source": [ @@ -470,7 +470,7 @@ { "cell_type": "code", "execution_count": null, - "id": "90c3c253", + "id": "5fd5737b", "metadata": {}, "outputs": [], "source": [ @@ -480,7 +480,7 @@ { "cell_type": "code", "execution_count": null, - "id": "586499a5", + "id": "f8048e13", "metadata": {}, "outputs": [], "source": [ @@ -491,7 +491,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1439c3e5", + "id": "1ae4c8ae", "metadata": {}, "outputs": [], "source": [ @@ -522,7 +522,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a45376de", + "id": "a1a3ea4b", "metadata": {}, "outputs": [], "source": [ @@ -533,7 +533,7 @@ { "cell_type": "code", "execution_count": null, - "id": "081bbfd0", + "id": "0d285cf8", "metadata": {}, "outputs": [], "source": [ @@ -542,7 +542,7 @@ }, { "cell_type": "markdown", - "id": "9f873217", + "id": "118f4abb", "metadata": {}, "source": [ "## Example 1\n", @@ -565,7 +565,7 @@ { "cell_type": "code", "execution_count": null, - "id": "12764f89", + "id": "3ceae4d8", "metadata": {}, "outputs": [], "source": [ @@ -580,7 +580,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de3c15dd", + "id": "78b950a5", "metadata": {}, "outputs": [], "source": [ @@ -600,7 +600,7 @@ { "cell_type": "code", "execution_count": null, - "id": "526e53e8", + "id": "bfb7d8a3", "metadata": {}, "outputs": [], "source": [ @@ -613,7 +613,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23982171", + "id": "43200336", "metadata": {}, "outputs": [], "source": [ @@ -624,7 +624,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b7035ea", + "id": "fcb537b0", "metadata": {}, "outputs": [], "source": [ @@ -634,7 +634,7 @@ { "cell_type": "code", "execution_count": null, - "id": "38395abc", + "id": "425395de", "metadata": {}, "outputs": [], "source": [ @@ -650,7 +650,7 @@ }, { "cell_type": "markdown", - "id": "5c3c492b", + "id": "a129488c", "metadata": {}, "source": [ "## How Deep? \n", @@ -677,7 +677,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ee4a309", + "id": "f18a2de1", "metadata": {}, "outputs": [], "source": [ @@ -691,7 +691,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e52b63a", + "id": "66ad17ee", "metadata": {}, "outputs": [], "source": [ @@ -704,7 +704,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e4d1235e", + "id": "0521fe0b", "metadata": {}, "outputs": [], "source": [ @@ -717,7 +717,7 @@ { "cell_type": "code", "execution_count": null, - "id": "361b8640", + "id": "69f266fd", "metadata": {}, "outputs": [], "source": [ @@ -730,7 +730,7 @@ { "cell_type": "code", "execution_count": null, - "id": "28e807f9", + "id": "730d1b45", "metadata": {}, "outputs": [], "source": [ @@ -740,7 +740,7 @@ { "cell_type": "code", "execution_count": null, - "id": "67126b19", + "id": "e234a0ca", "metadata": {}, "outputs": [], "source": [ @@ -750,7 +750,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7e1d72f2", + "id": "b4d989ff", "metadata": {}, "outputs": [], "source": [ @@ -760,7 +760,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76ae84a1", + "id": "b334f734", "metadata": {}, "outputs": [], "source": [ @@ -772,7 +772,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2db811d", + "id": "921954fc", "metadata": {}, "outputs": [], "source": [ @@ -791,7 +791,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5f57e127", + "id": "e5ce6666", "metadata": {}, "outputs": [], "source": [ @@ -803,7 +803,7 @@ }, { "cell_type": "markdown", - "id": "e2c80486", + "id": "5b15cd85", "metadata": {}, "source": [ "```{note}\n", diff --git a/_sources/bayes_nonconj.ipynb b/_sources/bayes_nonconj.ipynb index e2dfd92..43fdc77 100644 --- a/_sources/bayes_nonconj.ipynb +++ b/_sources/bayes_nonconj.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "02cf50fa", + "id": "be3cdbcb", "metadata": {}, "source": [ "# Non-Conjugate Priors\n", @@ -41,7 +41,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f58b993d", + "id": "816d98f0", "metadata": { "tags": [ "hide-output" @@ -56,7 +56,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a1fd05e", + "id": "ab4c4485", "metadata": {}, "outputs": [], "source": [ @@ -92,7 +92,7 @@ }, { "cell_type": "markdown", - "id": "34469a42", + "id": "922239fa", "metadata": {}, "source": [ "## Unleashing MCMC on a Binomial Likelihood\n", @@ -167,7 +167,7 @@ { "cell_type": "code", "execution_count": null, - "id": "39380271", + "id": "05cf4461", "metadata": {}, "outputs": [], "source": [ @@ -204,7 +204,7 @@ }, { "cell_type": "markdown", - "id": "afbb9da4", + "id": "74c12997", "metadata": {}, "source": [ "### Two Ways to Approximate Posteriors\n", @@ -279,7 +279,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3db528c5", + "id": "762d061b", "metadata": {}, "outputs": [], "source": [ @@ -356,7 +356,7 @@ }, { "cell_type": "markdown", - "id": "686ce930", + "id": "41fa3716", "metadata": {}, "source": [ "### Variational Inference\n", @@ -479,7 +479,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04e08333", + "id": "ce3e34a8", "metadata": {}, "outputs": [], "source": [ @@ -728,7 +728,7 @@ }, { "cell_type": "markdown", - "id": "2f9cf136", + "id": "094f06a1", "metadata": {}, "source": [ "## Alternative Prior Distributions\n", @@ -746,7 +746,7 @@ { "cell_type": "code", "execution_count": null, - "id": "772465b6", + "id": "34c40b3c", "metadata": {}, "outputs": [], "source": [ @@ -761,7 +761,7 @@ }, { "cell_type": "markdown", - "id": "617333dc", + "id": "26966da7", "metadata": {}, "source": [ "The above graphs show that sampling seems to work well with both distributions.\n", @@ -773,7 +773,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c8d1d97a", + "id": "61fad1aa", "metadata": {}, "outputs": [], "source": [ @@ -788,7 +788,7 @@ }, { "cell_type": "markdown", - "id": "2084be5f", + "id": "e5ca3637", "metadata": {}, "source": [ "These graphs look good too.\n", @@ -799,7 +799,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50e8cb54", + "id": "8dc96e13", "metadata": {}, "outputs": [], "source": [ @@ -810,7 +810,7 @@ }, { "cell_type": "markdown", - "id": "dfe7ba01", + "id": "b176caf6", "metadata": {}, "source": [ "Having assured ourselves that our sampler seems to do a good job, let's put it to work in using MCMC to compute posterior probabilities.\n", @@ -831,7 +831,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2857d3f4", + "id": "6e30a4a7", "metadata": {}, "outputs": [], "source": [ @@ -962,7 +962,7 @@ }, { "cell_type": "markdown", - "id": "b1973364", + "id": "0426792e", "metadata": {}, "source": [ "Let's set some parameters that we'll use in all of the examples below.\n", @@ -975,7 +975,7 @@ { "cell_type": "code", "execution_count": null, - "id": "deb5e78f", + "id": "374ca567", "metadata": {}, "outputs": [], "source": [ @@ -989,7 +989,7 @@ }, { "cell_type": "markdown", - "id": "06151425", + "id": "c620bea6", "metadata": {}, "source": [ "### Beta Prior and Posteriors:\n", @@ -1008,7 +1008,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f8cdf36", + "id": "a903f838", "metadata": {}, "outputs": [], "source": [ @@ -1043,7 +1043,7 @@ }, { "cell_type": "markdown", - "id": "37383e27", + "id": "9d49b704", "metadata": {}, "source": [ "Now let's use MCMC while still using a beta prior.\n", @@ -1054,7 +1054,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77ef302f", + "id": "7057ce8b", "metadata": {}, "outputs": [], "source": [ @@ -1064,7 +1064,7 @@ }, { "cell_type": "markdown", - "id": "53e071f9", + "id": "54412eab", "metadata": {}, "source": [ "Here the MCMC approximation looks good.\n", @@ -1085,7 +1085,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0762a53a", + "id": "da0b54cb", "metadata": {}, "outputs": [], "source": [ @@ -1094,7 +1094,7 @@ }, { "cell_type": "markdown", - "id": "3172cefa", + "id": "8af9a4d3", "metadata": {}, "source": [ "## Non-conjugate Prior Distributions\n", @@ -1114,7 +1114,7 @@ { "cell_type": "code", "execution_count": null, - "id": "69550e4b", + "id": "1d803743", "metadata": {}, "outputs": [], "source": [ @@ -1140,7 +1140,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f809e421", + "id": "c89b6a50", "metadata": {}, "outputs": [], "source": [ @@ -1156,7 +1156,7 @@ }, { "cell_type": "markdown", - "id": "0b1fdca5", + "id": "2a13a31a", "metadata": {}, "source": [ "In the situation depicted above, we have assumed a $Uniform(\\underline{\\theta}, \\overline{\\theta})$ prior that puts zero probability outside a bounded support that excludes the true value.\n", @@ -1169,7 +1169,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62f46eaa", + "id": "ca28c5da", "metadata": {}, "outputs": [], "source": [ @@ -1186,7 +1186,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0b85cfbb", + "id": "b755fe6c", "metadata": {}, "outputs": [], "source": [ @@ -1205,7 +1205,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aa7fac9a", + "id": "5dc93ecc", "metadata": {}, "outputs": [], "source": [ @@ -1217,7 +1217,7 @@ }, { "cell_type": "markdown", - "id": "d66d33e5", + "id": "b12871db", "metadata": {}, "source": [ "To get more accuracy we will now increase the number of steps for Variational Inference (VI)" @@ -1226,7 +1226,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a63edb8f", + "id": "6d958a4b", "metadata": {}, "outputs": [], "source": [ @@ -1235,7 +1235,7 @@ }, { "cell_type": "markdown", - "id": "9a64a453", + "id": "f818a266", "metadata": {}, "source": [ "#### VI with a Truncated Normal Guide" @@ -1244,7 +1244,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9dce11f9", + "id": "364c5bba", "metadata": {}, "outputs": [], "source": [ @@ -1257,7 +1257,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c5b3f95f", + "id": "58fb44ce", "metadata": {}, "outputs": [], "source": [ @@ -1270,7 +1270,7 @@ { "cell_type": "code", "execution_count": null, - "id": "36f3b3d6", + "id": "f4088831", "metadata": {}, "outputs": [], "source": [ @@ -1284,7 +1284,7 @@ { "cell_type": "code", "execution_count": null, - "id": "22075b10", + "id": "9a6157a6", "metadata": {}, "outputs": [], "source": [ @@ -1296,7 +1296,7 @@ }, { "cell_type": "markdown", - "id": "9e4ef2c7", + "id": "676331cc", "metadata": {}, "source": [ "#### Variational Inference with a Beta Guide Distribution" @@ -1305,7 +1305,7 @@ { "cell_type": "code", "execution_count": null, - "id": "992557f2", + "id": "787a540a", "metadata": {}, "outputs": [], "source": [ @@ -1318,7 +1318,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ac422783", + "id": "bbbc390d", "metadata": {}, "outputs": [], "source": [ @@ -1335,7 +1335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c2bf37f", + "id": "b77a380f", "metadata": {}, "outputs": [], "source": [ @@ -1354,7 +1354,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3cd98213", + "id": "7e50ea4c", "metadata": {}, "outputs": [], "source": [ diff --git a/_sources/exchangeable.ipynb b/_sources/exchangeable.ipynb index 14e8b63..317d14e 100644 --- a/_sources/exchangeable.ipynb +++ b/_sources/exchangeable.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "0afb8a0f", + "id": "f1d8b101", "metadata": {}, "source": [ "(odu_v3)=\n", @@ -66,7 +66,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bb52a87a", + "id": "2ceffa2f", "metadata": { "tags": [ "hide-output" @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "d3c27e63", + "id": "aaa6c80f", "metadata": {}, "source": [ "## Independently and Identically Distributed\n", @@ -416,7 +416,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e76d2d43", + "id": "0a9c2833", "metadata": {}, "outputs": [], "source": [ @@ -505,7 +505,7 @@ }, { "cell_type": "markdown", - "id": "fdb0dfa0", + "id": "14ba5c8b", "metadata": {}, "source": [ "Now we'll create a group of graphs that illustrate dynamics induced by Bayes' Law.\n", @@ -516,7 +516,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f812d792", + "id": "836c8a2c", "metadata": {}, "outputs": [], "source": [ @@ -525,7 +525,7 @@ }, { "cell_type": "markdown", - "id": "02bbe190", + "id": "cb4e7d06", "metadata": {}, "source": [ "Please look at the three graphs above created for an instance in which $f$ is a uniform distribution on $[0,1]$\n", @@ -569,7 +569,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6b3e886", + "id": "e5f2f6ed", "metadata": {}, "outputs": [], "source": [ @@ -578,7 +578,7 @@ }, { "cell_type": "markdown", - "id": "85f5ad1d", + "id": "17d29f0d", "metadata": {}, "source": [ "Notice how the likelihood ratio, the middle graph, and the arrows compare with the previous instance of our example.\n", @@ -602,7 +602,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3430b6b", + "id": "d9d82a22", "metadata": {}, "outputs": [], "source": [ @@ -661,7 +661,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e10a2702", + "id": "d3c1aa63", "metadata": {}, "outputs": [], "source": [ @@ -670,7 +670,7 @@ }, { "cell_type": "markdown", - "id": "27fa3d01", + "id": "f5487dbd", "metadata": {}, "source": [ "We begin by generating $N$ simulated $\\{\\pi_t\\}$ paths with $T$\n", @@ -680,7 +680,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d8d500df", + "id": "61d315b4", "metadata": {}, "outputs": [], "source": [ @@ -690,7 +690,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c7eec5b", + "id": "6ee60c46", "metadata": {}, "outputs": [], "source": [ @@ -700,7 +700,7 @@ }, { "cell_type": "markdown", - "id": "2df9d1b8", + "id": "f27309b1", "metadata": {}, "source": [ "In the above example, for most paths $\\pi_t \\rightarrow 1$.\n", @@ -715,7 +715,7 @@ { "cell_type": "code", "execution_count": null, - "id": "50b823a6", + "id": "69eed82a", "metadata": {}, "outputs": [], "source": [ @@ -725,7 +725,7 @@ }, { "cell_type": "markdown", - "id": "e0eccf11", + "id": "2b8a4181", "metadata": {}, "source": [ "In the above graph we observe that now most paths $\\pi_t \\rightarrow 0$.\n", @@ -745,7 +745,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b04adaec", + "id": "01fce03b", "metadata": {}, "outputs": [], "source": [ @@ -757,7 +757,7 @@ }, { "cell_type": "markdown", - "id": "0a9b77ff", + "id": "8652cd75", "metadata": {}, "source": [ "From the above graph, rates of convergence appear not to depend on whether $F$ or $G$ generates the data.\n", @@ -783,7 +783,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ba5d8012", + "id": "77d885e8", "metadata": {}, "outputs": [], "source": [ @@ -815,7 +815,7 @@ }, { "cell_type": "markdown", - "id": "77726fe4", + "id": "4ee3e578", "metadata": {}, "source": [ "First, consider the case where $F_a=F_b=1$ and\n", @@ -825,7 +825,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d58eb357", + "id": "a2fd1906", "metadata": {}, "outputs": [], "source": [ @@ -834,7 +834,7 @@ }, { "cell_type": "markdown", - "id": "4daa07ff", + "id": "9beb334e", "metadata": {}, "source": [ "The above graphs shows that when $F$ generates the data, $\\pi_t$ on average always heads north, while\n", @@ -850,7 +850,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5fb3a886", + "id": "37b95e97", "metadata": {}, "outputs": [], "source": [ @@ -859,7 +859,7 @@ }, { "cell_type": "markdown", - "id": "90c5cf79", + "id": "d646d88f", "metadata": {}, "source": [ "The above graph says that $\\pi_t$ is inert and remains at its initial value.\n", @@ -872,7 +872,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c7202a28", + "id": "4ab72307", "metadata": {}, "outputs": [], "source": [ @@ -881,7 +881,7 @@ }, { "cell_type": "markdown", - "id": "f8b90fb3", + "id": "16edf984", "metadata": {}, "source": [ "## Sequels\n", diff --git a/_sources/hoist_failure.ipynb b/_sources/hoist_failure.ipynb index cc34561..ab8d8c7 100644 --- a/_sources/hoist_failure.ipynb +++ b/_sources/hoist_failure.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "58469abb", + "id": "85027c80", "metadata": {}, "source": [ "# Fault Tree Uncertainties\n", @@ -43,7 +43,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f151a76f", + "id": "f221b9c4", "metadata": {}, "outputs": [], "source": [ @@ -53,7 +53,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b44bdf69", + "id": "1e2fbe30", "metadata": {}, "outputs": [], "source": [ @@ -67,7 +67,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88ff5481", + "id": "3328a7b5", "metadata": {}, "outputs": [], "source": [ @@ -76,7 +76,7 @@ }, { "cell_type": "markdown", - "id": "a1803154", + "id": "35823095", "metadata": {}, "source": [ "\n", @@ -202,7 +202,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ab8ce2c8", + "id": "2992e3d7", "metadata": {}, "outputs": [], "source": [ @@ -219,7 +219,7 @@ }, { "cell_type": "markdown", - "id": "55d8a631", + "id": "0b6b4ead", "metadata": {}, "source": [ "A little later we'll explain some advantages that come from using `scipy.signal.ftconvolve` rather than `numpy.convolve`.numpy program convolve.\n", @@ -242,7 +242,7 @@ { "cell_type": "code", "execution_count": null, - "id": "065464a3", + "id": "71bde1d5", "metadata": {}, "outputs": [], "source": [ @@ -269,7 +269,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ea577920", + "id": "aa66b9b4", "metadata": {}, "outputs": [], "source": [ @@ -279,7 +279,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ff715d4c", + "id": "bd0d6e07", "metadata": {}, "outputs": [], "source": [ @@ -289,7 +289,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c377dd4", + "id": "19ac6bb9", "metadata": {}, "outputs": [], "source": [ @@ -301,7 +301,7 @@ }, { "cell_type": "markdown", - "id": "b1d3567a", + "id": "b408f6a6", "metadata": {}, "source": [ "Here are helper functions that create a discretized version of a log normal\n", @@ -311,7 +311,7 @@ { "cell_type": "code", "execution_count": null, - "id": "77d669a0", + "id": "ba3f8b42", "metadata": {}, "outputs": [], "source": [ @@ -328,7 +328,7 @@ }, { "cell_type": "markdown", - "id": "f4dd5ca3", + "id": "c5ff9a87", "metadata": {}, "source": [ "\n", @@ -349,7 +349,7 @@ { "cell_type": "code", "execution_count": null, - "id": "532a13a4", + "id": "c0138cb0", "metadata": {}, "outputs": [], "source": [ @@ -361,7 +361,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c11a7aa", + "id": "425b212f", "metadata": {}, "outputs": [], "source": [ @@ -384,7 +384,7 @@ { "cell_type": "code", "execution_count": null, - "id": "32d90583", + "id": "dea49405", "metadata": {}, "outputs": [], "source": [ @@ -397,7 +397,7 @@ }, { "cell_type": "markdown", - "id": "90cc5265", + "id": "37733b55", "metadata": {}, "source": [ "## Convolving Probability Mass Functions\n", @@ -459,7 +459,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e89aa979", + "id": "16a4e88a", "metadata": {}, "outputs": [], "source": [ @@ -494,7 +494,7 @@ }, { "cell_type": "markdown", - "id": "86ffc443", + "id": "4dcb4dcf", "metadata": {}, "source": [ "The fast Fourier transform is two orders of magnitude faster than `numpy.convolve`\n", @@ -506,7 +506,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f0fb215", + "id": "6be8b1bb", "metadata": {}, "outputs": [], "source": [ @@ -526,7 +526,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4f6df38", + "id": "b368ed56", "metadata": {}, "outputs": [], "source": [ @@ -545,7 +545,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fedf091e", + "id": "e3869808", "metadata": {}, "outputs": [], "source": [ @@ -558,7 +558,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c0c29f83", + "id": "045168e4", "metadata": {}, "outputs": [], "source": [ @@ -570,7 +570,7 @@ }, { "cell_type": "markdown", - "id": "b06d1fe1", + "id": "4459769f", "metadata": {}, "source": [ "\n", @@ -695,7 +695,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b42e63f6", + "id": "4df6d6b3", "metadata": {}, "outputs": [], "source": [ @@ -710,7 +710,7 @@ }, { "cell_type": "markdown", - "id": "5ac908cf", + "id": "f0c1f851", "metadata": {}, "source": [ "```{note}\n", @@ -727,7 +727,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4def5f1e", + "id": "b52c31f0", "metadata": {}, "outputs": [], "source": [ @@ -739,7 +739,7 @@ }, { "cell_type": "markdown", - "id": "1978be0c", + "id": "a1398613", "metadata": {}, "source": [ "We compute the required thirteen convolutions in the following code.\n", @@ -754,7 +754,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5b03e738", + "id": "c2312888", "metadata": {}, "outputs": [], "source": [ @@ -806,7 +806,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ee4a71a3", + "id": "1bcf5979", "metadata": {}, "outputs": [], "source": [ @@ -851,7 +851,7 @@ }, { "cell_type": "markdown", - "id": "107dd503", + "id": "8df12170", "metadata": {}, "source": [ "The above table agrees closely with column 2 of Table 11 on p. 28 of of {cite}`Greenfield_Sargent_1993`.\n", diff --git a/_sources/imp_sample.ipynb b/_sources/imp_sample.ipynb index 92570f0..60b177e 100644 --- a/_sources/imp_sample.ipynb +++ b/_sources/imp_sample.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "6e5604ad", + "id": "75d122ee", "metadata": {}, "source": [ "# Computing Mean of a Likelihood Ratio Process\n", @@ -27,7 +27,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c2a1a15b", + "id": "03c1ccb7", "metadata": {}, "outputs": [], "source": [ @@ -39,7 +39,7 @@ }, { "cell_type": "markdown", - "id": "7ef4d82c", + "id": "505b2644", "metadata": {}, "source": [ "## Mathematical Expectation of Likelihood Ratio\n", @@ -80,7 +80,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8dfd93ee", + "id": "17cc9bef", "metadata": {}, "outputs": [], "source": [ @@ -101,7 +101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e856dc3b", + "id": "c7cf2be5", "metadata": {}, "outputs": [], "source": [ @@ -117,7 +117,7 @@ }, { "cell_type": "markdown", - "id": "abce1c31", + "id": "80a7d1f4", "metadata": {}, "source": [ "The likelihood ratio is `l(w)=f(w)/g(w)`." @@ -126,7 +126,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9bd5df94", + "id": "8ed2733c", "metadata": {}, "outputs": [], "source": [ @@ -136,7 +136,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c9e53617", + "id": "7379738e", "metadata": {}, "outputs": [], "source": [ @@ -148,7 +148,7 @@ }, { "cell_type": "markdown", - "id": "b0ac0bdf", + "id": "c12ab40e", "metadata": {}, "source": [ "The above plots shows that as $\\omega \\rightarrow 0$, $f \\left(\\omega\\right)$ is unchanged and $g \\left(\\omega\\right) \\rightarrow 0$, so the likelihood ratio approaches infinity.\n", @@ -208,7 +208,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d19dcb80", + "id": "3392072c", "metadata": {}, "outputs": [], "source": [ @@ -219,7 +219,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6cc3a813", + "id": "00f280bd", "metadata": {}, "outputs": [], "source": [ @@ -235,7 +235,7 @@ }, { "cell_type": "markdown", - "id": "54b5d3c3", + "id": "cf97459f", "metadata": {}, "source": [ "## Approximating a cumulative likelihood ratio\n", @@ -260,7 +260,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e2fa0d58", + "id": "32f6ddbe", "metadata": {}, "outputs": [], "source": [ @@ -288,7 +288,7 @@ }, { "cell_type": "markdown", - "id": "3904535a", + "id": "07abf009", "metadata": {}, "source": [ "Consider the case when $T=1$, which amounts to approximating $E_0\\left[\\ell\\left(\\omega\\right)\\right]$\n", @@ -299,7 +299,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5975316d", + "id": "c347fc06", "metadata": {}, "outputs": [], "source": [ @@ -308,7 +308,7 @@ }, { "cell_type": "markdown", - "id": "7c0fee52", + "id": "2ab9a642", "metadata": {}, "source": [ "For our importance sampling estimate, we set $q = h$." @@ -317,7 +317,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3d34fce0", + "id": "e9c126b2", "metadata": {}, "outputs": [], "source": [ @@ -326,7 +326,7 @@ }, { "cell_type": "markdown", - "id": "b042dc5e", + "id": "3489c7a6", "metadata": {}, "source": [ "Evidently, even at T=1, our importance sampling estimate is closer to $1$ than is the Monte Carlo estimate.\n", @@ -340,7 +340,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ddc55a0", + "id": "383a84b7", "metadata": {}, "outputs": [], "source": [ @@ -350,7 +350,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b5e369f6", + "id": "f885955d", "metadata": {}, "outputs": [], "source": [ @@ -359,7 +359,7 @@ }, { "cell_type": "markdown", - "id": "9477a50c", + "id": "3d2b33fd", "metadata": {}, "source": [ "## Distribution of Sample Mean\n", @@ -372,7 +372,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c2009b44", + "id": "f4731ba9", "metadata": {}, "outputs": [], "source": [ @@ -391,7 +391,7 @@ }, { "cell_type": "markdown", - "id": "58e665cf", + "id": "a251741c", "metadata": {}, "source": [ "Again, we first consider estimating ${E} \\left[\\ell\\left(\\omega\\right)\\right]$ by setting T=1.\n", @@ -402,7 +402,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db9cfc82", + "id": "fefc7f77", "metadata": {}, "outputs": [], "source": [ @@ -413,7 +413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b5a6eec", + "id": "615073c9", "metadata": {}, "outputs": [], "source": [ @@ -424,7 +424,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3537fe6", + "id": "f511ec83", "metadata": {}, "outputs": [], "source": [ @@ -434,7 +434,7 @@ }, { "cell_type": "markdown", - "id": "5b4ad276", + "id": "0b71dbd9", "metadata": {}, "source": [ "Although both methods tend to provide a mean estimate of ${E} \\left[\\ell\\left(\\omega\\right)\\right]$ close to $1$, the importance sampling estimates have smaller variance.\n", @@ -445,7 +445,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a7e26441", + "id": "1aaaf694", "metadata": {}, "outputs": [], "source": [ @@ -478,7 +478,7 @@ }, { "cell_type": "markdown", - "id": "ad940d8f", + "id": "4d49040d", "metadata": {}, "source": [ "The simulation exercises above show that the importance sampling estimates are unbiased under all $T$\n", @@ -491,7 +491,7 @@ }, { "cell_type": "markdown", - "id": "3b5242b7", + "id": "e95cbce9", "metadata": {}, "source": [ "Above, we arbitraily chose $h = Beta(0.5,0.5)$ as the importance distribution.\n", @@ -514,7 +514,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ff6c522d", + "id": "cad46c7e", "metadata": {}, "outputs": [], "source": [ @@ -524,7 +524,7 @@ { "cell_type": "code", "execution_count": null, - "id": "673dc0c1", + "id": "138fe65f", "metadata": {}, "outputs": [], "source": [ @@ -534,7 +534,7 @@ }, { "cell_type": "markdown", - "id": "219a52a8", + "id": "b1cb970b", "metadata": {}, "source": [ "We could also use other distributions as our importance distribution.\n", @@ -545,7 +545,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b033d084", + "id": "2f29d33d", "metadata": {}, "outputs": [], "source": [ @@ -556,7 +556,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1096a6da", + "id": "3003fa00", "metadata": {}, "outputs": [], "source": [ @@ -574,7 +574,7 @@ }, { "cell_type": "markdown", - "id": "1c2112bd", + "id": "932a5864", "metadata": {}, "source": [ "We consider two additonal distributions.\n", @@ -600,7 +600,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6364922e", + "id": "6b6c9fda", "metadata": {}, "outputs": [], "source": [ @@ -635,7 +635,7 @@ }, { "cell_type": "markdown", - "id": "739550a9", + "id": "fcabec2e", "metadata": {}, "source": [ "Our simulations suggest that indeed $h_2$ is a quite good importance sampling distribution for our problem.\n", @@ -646,7 +646,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dc55ffa0", + "id": "6cf74ba0", "metadata": {}, "outputs": [], "source": [ @@ -681,7 +681,7 @@ }, { "cell_type": "markdown", - "id": "e90da99b", + "id": "5cdfc742", "metadata": {}, "source": [ "However, $h_3$ is evidently a poor importance sampling distribution forpir problem,\n", diff --git a/_sources/intro.ipynb b/_sources/intro.ipynb index 9eca210..50740e0 100644 --- a/_sources/intro.ipynb +++ b/_sources/intro.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "8af18dce", + "id": "5f146bcf", "metadata": {}, "source": [ "# Statistics for Computational Economics\n", diff --git a/_sources/likelihood_bayes.ipynb b/_sources/likelihood_bayes.ipynb index 9b71221..a5796f7 100644 --- a/_sources/likelihood_bayes.ipynb +++ b/_sources/likelihood_bayes.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "b5c9e350", + "id": "4fb4d1f2", "metadata": {}, "source": [ "(likelihood_ratio_process)=\n", @@ -46,7 +46,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7326443e", + "id": "4087aac7", "metadata": { "hide-output": false }, @@ -70,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "8791b789", + "id": "3cefeb04", "metadata": {}, "source": [ "## The Setting\n", @@ -148,7 +148,7 @@ { "cell_type": "code", "execution_count": null, - "id": "37d60b7f", + "id": "961cd808", "metadata": {}, "outputs": [], "source": [ @@ -169,7 +169,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d3b55d03", + "id": "bb4247be", "metadata": {}, "outputs": [], "source": [ @@ -194,7 +194,7 @@ }, { "cell_type": "markdown", - "id": "95ef6745", + "id": "368a5546", "metadata": {}, "source": [ "We'll also use the following Python code to prepare some informative simulations" @@ -203,7 +203,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d93474e3", + "id": "0193146b", "metadata": {}, "outputs": [], "source": [ @@ -214,7 +214,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d45dc11b", + "id": "57b968cc", "metadata": {}, "outputs": [], "source": [ @@ -224,7 +224,7 @@ }, { "cell_type": "markdown", - "id": "126faab8", + "id": "373455ad", "metadata": {}, "source": [ "## Likelihood Ratio Process and Bayes’ Law\n", @@ -256,7 +256,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e6bc1ecc", + "id": "9575bb46", "metadata": {}, "outputs": [], "source": [ @@ -272,7 +272,7 @@ }, { "cell_type": "markdown", - "id": "5c62613f", + "id": "52272857", "metadata": {}, "source": [ "Formula {eq}`eq_recur1` can be generalized by iterating on it and thereby deriving an\n", @@ -353,7 +353,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8beae613", + "id": "e87c096f", "metadata": {}, "outputs": [], "source": [ @@ -362,7 +362,7 @@ }, { "cell_type": "markdown", - "id": "86b21bf0", + "id": "6427b227", "metadata": {}, "source": [ "Next we generate paths of the likelihood ratio process $L_t$ and the posterior $\\pi_t$ for a\n", @@ -372,7 +372,7 @@ { "cell_type": "code", "execution_count": null, - "id": "236e035c", + "id": "883ed71c", "metadata": {}, "outputs": [], "source": [ @@ -388,7 +388,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6e5060e8", + "id": "800cc1c2", "metadata": {}, "outputs": [], "source": [ @@ -411,7 +411,7 @@ }, { "cell_type": "markdown", - "id": "7618c0f4", + "id": "275f6c10", "metadata": {}, "source": [ "The dotted line in the graph above records the logarithm of the likelihood ratio process $\\log L(w^t)$.\n", @@ -424,7 +424,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2c99ca2", + "id": "7c94ea9d", "metadata": {}, "outputs": [], "source": [ @@ -440,7 +440,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8deb2d1e", + "id": "1e7ec4a6", "metadata": {}, "outputs": [], "source": [ @@ -463,7 +463,7 @@ }, { "cell_type": "markdown", - "id": "9e2f0096", + "id": "fdac4239", "metadata": {}, "source": [ "Below we offer Python code that verifies that nature chose permanently to draw from density $f$." @@ -472,7 +472,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e7d405e7", + "id": "7706b588", "metadata": {}, "outputs": [], "source": [ @@ -487,7 +487,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cbb5d835", + "id": "2a6bb016", "metadata": {}, "outputs": [], "source": [ @@ -496,7 +496,7 @@ }, { "cell_type": "markdown", - "id": "43b5970a", + "id": "0e2548b5", "metadata": {}, "source": [ "We thus conclude that the likelihood ratio process is a key ingredient of the formula {eq}`eq_Bayeslaw103` for\n", @@ -716,7 +716,7 @@ { "cell_type": "code", "execution_count": null, - "id": "25465f3f", + "id": "6e42e131", "metadata": {}, "outputs": [], "source": [ @@ -770,7 +770,7 @@ { "cell_type": "code", "execution_count": null, - "id": "164b6c04", + "id": "39b369d6", "metadata": {}, "outputs": [], "source": [ @@ -785,7 +785,7 @@ }, { "cell_type": "markdown", - "id": "6dd2d55d", + "id": "b57793ac", "metadata": {}, "source": [ "The above graph indicates that\n", @@ -804,7 +804,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c64e160e", + "id": "3d61b03d", "metadata": {}, "outputs": [], "source": [ @@ -820,7 +820,7 @@ }, { "cell_type": "markdown", - "id": "bbb7db91", + "id": "33eff51e", "metadata": {}, "source": [ "Evidently, by $t = 199$, $\\pi_t$ has converged to either $0$ or $1$.\n", @@ -841,7 +841,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1100d3c3", + "id": "e14d7518", "metadata": {}, "outputs": [], "source": [ @@ -855,7 +855,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b1dd190f", + "id": "beb3178a", "metadata": {}, "outputs": [], "source": [ @@ -871,7 +871,7 @@ }, { "cell_type": "markdown", - "id": "add520b6", + "id": "141b6f2e", "metadata": {}, "source": [ "For the preceding ensemble that assumed $\\pi_0 = .5$, the following graph shows two paths of\n", @@ -886,7 +886,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2734d76d", + "id": "c3fe021f", "metadata": {}, "outputs": [], "source": [ @@ -905,7 +905,7 @@ }, { "cell_type": "markdown", - "id": "17c3c37b", + "id": "02e07d47", "metadata": {}, "source": [ "## Initial Prior is Verified by Paths Drawn from Subjective Conditional Densities\n", @@ -927,7 +927,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b1e428d2", + "id": "383479fe", "metadata": {}, "outputs": [], "source": [ @@ -938,7 +938,7 @@ }, { "cell_type": "markdown", - "id": "7ce2b0b2", + "id": "af01a365", "metadata": {}, "source": [ "The fraction of simulations for which $\\pi_{t}$ had converged to $1$ is indeed always close to $\\pi_{-1}$, as anticipated.\n", @@ -965,7 +965,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7de30d29", + "id": "be903024", "metadata": {}, "outputs": [], "source": [ @@ -998,7 +998,7 @@ }, { "cell_type": "markdown", - "id": "4e93a6c8", + "id": "649d9c70", "metadata": {}, "source": [ "The shape of the the conditional variance as a function of $\\pi_{t-1}$ is informative about the behavior of sample paths of $\\{\\pi_t\\}$.\n", diff --git a/_sources/likelihood_ratio_process.ipynb b/_sources/likelihood_ratio_process.ipynb index 0288d36..935246a 100644 --- a/_sources/likelihood_ratio_process.ipynb +++ b/_sources/likelihood_ratio_process.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c0114325", + "id": "59d80087", "metadata": {}, "source": [ "(likelihood_ratio_process)=\n", @@ -41,7 +41,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5574c0c0", + "id": "cd877769", "metadata": {}, "outputs": [], "source": [ @@ -55,7 +55,7 @@ }, { "cell_type": "markdown", - "id": "1a47c04c", + "id": "b33666d8", "metadata": {}, "source": [ "## Likelihood Ratio Process\n", @@ -131,7 +131,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04cf427e", + "id": "27ff6dc7", "metadata": {}, "outputs": [], "source": [ @@ -152,7 +152,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b48530b0", + "id": "439e68cc", "metadata": {}, "outputs": [], "source": [ @@ -177,7 +177,7 @@ }, { "cell_type": "markdown", - "id": "9ef7d39a", + "id": "35176c8d", "metadata": {}, "source": [ "## Nature Permanently Draws from Density g\n", @@ -189,7 +189,7 @@ { "cell_type": "code", "execution_count": null, - "id": "08830cdd", + "id": "dc057df5", "metadata": {}, "outputs": [], "source": [ @@ -200,7 +200,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f3914c1e", + "id": "183dd852", "metadata": {}, "outputs": [], "source": [ @@ -216,7 +216,7 @@ }, { "cell_type": "markdown", - "id": "c7d49675", + "id": "2624c0f0", "metadata": {}, "source": [ "Evidently, as sample length $T$ grows, most probability mass\n", @@ -230,7 +230,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d3e82f5d", + "id": "2479a816", "metadata": {}, "outputs": [], "source": [ @@ -239,7 +239,7 @@ }, { "cell_type": "markdown", - "id": "1529caae", + "id": "c4761e6d", "metadata": {}, "source": [ "Despite the evident convergence of most probability mass to a\n", @@ -306,7 +306,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9fb331fb", + "id": "a82f929e", "metadata": {}, "outputs": [], "source": [ @@ -316,7 +316,7 @@ }, { "cell_type": "markdown", - "id": "78ca14c4", + "id": "8d019f5f", "metadata": {}, "source": [ "It would be useful to use simulations to verify that unconditional means\n", @@ -365,7 +365,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef9ed757", + "id": "632ac82d", "metadata": {}, "outputs": [], "source": [ @@ -376,7 +376,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d71ba197", + "id": "c0956711", "metadata": {}, "outputs": [], "source": [ @@ -386,7 +386,7 @@ }, { "cell_type": "markdown", - "id": "eb84b0d2", + "id": "1abd807e", "metadata": {}, "source": [ "We also plot the probability that $L\\left(w^t\\right)$ falls into\n", @@ -397,7 +397,7 @@ { "cell_type": "code", "execution_count": null, - "id": "006b8702", + "id": "d1f6d44d", "metadata": {}, "outputs": [], "source": [ @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "43f8c310", + "id": "b5b408e1", "metadata": {}, "source": [ "## Likelihood Ratio Test\n", @@ -494,7 +494,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f53b19b0", + "id": "8e297fa0", "metadata": {}, "outputs": [], "source": [ @@ -503,7 +503,7 @@ }, { "cell_type": "markdown", - "id": "01ae2645", + "id": "f1d7dd70", "metadata": {}, "source": [ "Below we plot empirical distributions of logarithms of the cumulative\n", @@ -529,7 +529,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2b6bfe0b", + "id": "9623b656", "metadata": {}, "outputs": [], "source": [ @@ -560,7 +560,7 @@ }, { "cell_type": "markdown", - "id": "48338dba", + "id": "3b7ccc9a", "metadata": {}, "source": [ "The graph below shows more clearly that, when we hold the threshold\n", @@ -571,7 +571,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b4dfe6a", + "id": "101345fc", "metadata": {}, "outputs": [], "source": [ @@ -592,7 +592,7 @@ }, { "cell_type": "markdown", - "id": "e75f9533", + "id": "30c69d58", "metadata": {}, "source": [ "For a given sample size $t$, the threshold $c$ uniquely pins down probabilities\n", @@ -611,7 +611,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb4c7265", + "id": "0e62e1d9", "metadata": {}, "outputs": [], "source": [ @@ -637,7 +637,7 @@ }, { "cell_type": "markdown", - "id": "fe7ada44", + "id": "5aef778f", "metadata": {}, "source": [ "Notice that as $t$ increases, we are assured a larger probability\n", @@ -669,7 +669,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c044b8f6", + "id": "63837c16", "metadata": {}, "outputs": [], "source": [ @@ -692,7 +692,7 @@ }, { "cell_type": "markdown", - "id": "e87b7993", + "id": "1804756b", "metadata": {}, "source": [ "The United States Navy evidently used a procedure like this to select a sample size $t$ for doing quality\n", @@ -759,7 +759,7 @@ { "cell_type": "code", "execution_count": null, - "id": "05194c47", + "id": "94473b24", "metadata": {}, "outputs": [], "source": [ @@ -771,7 +771,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2faf4e4", + "id": "22280b2c", "metadata": {}, "outputs": [], "source": [ @@ -786,7 +786,7 @@ }, { "cell_type": "markdown", - "id": "468e5d1d", + "id": "9b0d7f7f", "metadata": {}, "source": [ "Let’s compute the Kullback–Leibler discrepancies by quadrature\n", @@ -796,7 +796,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fbe0da70", + "id": "4809d3ea", "metadata": {}, "outputs": [], "source": [ @@ -810,7 +810,7 @@ { "cell_type": "code", "execution_count": null, - "id": "01b5222d", + "id": "1deb4da9", "metadata": {}, "outputs": [], "source": [ @@ -825,7 +825,7 @@ { "cell_type": "code", "execution_count": null, - "id": "94670686", + "id": "a8be6544", "metadata": {}, "outputs": [], "source": [ @@ -835,7 +835,7 @@ }, { "cell_type": "markdown", - "id": "d2ee4c48", + "id": "31de1034", "metadata": {}, "source": [ "We have $K_g < K_f$.\n", @@ -847,7 +847,7 @@ { "cell_type": "code", "execution_count": null, - "id": "62fd3e78", + "id": "5e88ca97", "metadata": {}, "outputs": [], "source": [ @@ -857,7 +857,7 @@ }, { "cell_type": "markdown", - "id": "dc924204", + "id": "a7b1d932", "metadata": {}, "source": [ "The figure below plots over time the fraction of paths\n", @@ -870,7 +870,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c057678e", + "id": "b88034bd", "metadata": {}, "outputs": [], "source": [ @@ -880,7 +880,7 @@ }, { "cell_type": "markdown", - "id": "0f97fb59", + "id": "a7003a30", "metadata": {}, "source": [ "We can also try an $h$ that is closer to $f$ than is\n", @@ -890,7 +890,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5c008bae", + "id": "b17af14b", "metadata": {}, "outputs": [], "source": [ @@ -901,7 +901,7 @@ { "cell_type": "code", "execution_count": null, - "id": "29d9c4c4", + "id": "f2e0021c", "metadata": {}, "outputs": [], "source": [ @@ -912,7 +912,7 @@ { "cell_type": "code", "execution_count": null, - "id": "92d77ee6", + "id": "cb9c0c52", "metadata": {}, "outputs": [], "source": [ @@ -922,7 +922,7 @@ }, { "cell_type": "markdown", - "id": "2dc43b53", + "id": "44618927", "metadata": {}, "source": [ "Now probability mass of $L\\left(w^t\\right)$ falling above\n", @@ -932,7 +932,7 @@ { "cell_type": "code", "execution_count": null, - "id": "95a08356", + "id": "4bafedf9", "metadata": {}, "outputs": [], "source": [ @@ -942,7 +942,7 @@ }, { "cell_type": "markdown", - "id": "5f9badff", + "id": "baf8ed14", "metadata": {}, "source": [ "## Sequels\n", diff --git a/_sources/lln_clt.ipynb b/_sources/lln_clt.ipynb index 951a957..5077cc0 100644 --- a/_sources/lln_clt.ipynb +++ b/_sources/lln_clt.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "896c4f69", + "id": "e5db2f0c", "metadata": {}, "source": [ "(lln_clt)=\n", @@ -50,7 +50,7 @@ { "cell_type": "code", "execution_count": null, - "id": "355e9f3b", + "id": "97f521f5", "metadata": {}, "outputs": [], "source": [ @@ -67,7 +67,7 @@ }, { "cell_type": "markdown", - "id": "57406699", + "id": "7652a7e1", "metadata": {}, "source": [ "## Relationships\n", @@ -236,7 +236,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0f738062", + "id": "012f7206", "metadata": {}, "outputs": [], "source": [ @@ -289,7 +289,7 @@ }, { "cell_type": "markdown", - "id": "886dfa6c", + "id": "9c521e75", "metadata": {}, "source": [ "The three distributions are chosen at random from a selection stored in the dictionary `distributions`.\n", @@ -353,7 +353,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d1f52d38", + "id": "f08ace5b", "metadata": {}, "outputs": [], "source": [ @@ -375,7 +375,7 @@ }, { "cell_type": "markdown", - "id": "dcfb76f3", + "id": "68adec50", "metadata": {}, "source": [ "When $n = 1$, the distribution is flat --- one success or no successes\n", @@ -425,7 +425,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ef90f769", + "id": "4f2b8d06", "metadata": {}, "outputs": [], "source": [ @@ -456,7 +456,7 @@ }, { "cell_type": "markdown", - "id": "75fff9df", + "id": "f8d6cb95", "metadata": {}, "source": [ "Notice the absence of for loops --- every operation is vectorized, meaning that the major calculations are all shifted to highly optimized C code.\n", @@ -491,7 +491,7 @@ { "cell_type": "code", "execution_count": null, - "id": "01c41b1a", + "id": "f5865f43", "metadata": {}, "outputs": [], "source": [ @@ -558,7 +558,7 @@ }, { "cell_type": "markdown", - "id": "58646cbb", + "id": "c1e950af", "metadata": {}, "source": [ "As expected, the distribution smooths out into a bell curve as $n$\n", @@ -733,7 +733,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e91e8994", + "id": "eac9fb6c", "metadata": {}, "outputs": [], "source": [ @@ -771,7 +771,7 @@ }, { "cell_type": "markdown", - "id": "3a0c921e", + "id": "e348d490", "metadata": {}, "source": [ "What happens when you replace $[0, \\pi / 2]$ with\n", @@ -953,7 +953,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c7b54d9", + "id": "50c4cec1", "metadata": {}, "outputs": [], "source": [ @@ -1001,7 +1001,7 @@ }, { "cell_type": "markdown", - "id": "e77204c5", + "id": "e6b7b619", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/mix_model.ipynb b/_sources/mix_model.ipynb index f175f9d..40c09af 100644 --- a/_sources/mix_model.ipynb +++ b/_sources/mix_model.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "daa62f45", + "id": "6b3e4958", "metadata": {}, "source": [ "(likelihood-ratio-process)=\n", @@ -14,7 +14,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ca69a93", + "id": "0a9058d0", "metadata": { "tags": [ "hide-output" @@ -27,7 +27,7 @@ }, { "cell_type": "markdown", - "id": "3533ada3", + "id": "cc27a1fb", "metadata": {}, "source": [ "## Overview\n", @@ -131,7 +131,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ed607a4b", + "id": "f212ed4e", "metadata": { "hide-output": false }, @@ -166,7 +166,7 @@ }, { "cell_type": "markdown", - "id": "dd57939b", + "id": "11c4d8fc", "metadata": {}, "source": [ "Let's use Python to generate two beta distributions" @@ -175,7 +175,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e4e651da", + "id": "2f7f2192", "metadata": { "hide-output": false }, @@ -198,7 +198,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9bd420dc", + "id": "d7ed3df7", "metadata": { "hide-output": false }, @@ -225,7 +225,7 @@ }, { "cell_type": "markdown", - "id": "c903497c", + "id": "7bff6c25", "metadata": {}, "source": [ "We’ll also use the following Python code to prepare some informative simulations" @@ -234,7 +234,7 @@ { "cell_type": "code", "execution_count": null, - "id": "20350636", + "id": "c1ee1a3a", "metadata": { "hide-output": false }, @@ -247,7 +247,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7920b77b", + "id": "d1bc9f6e", "metadata": { "hide-output": false }, @@ -259,7 +259,7 @@ }, { "cell_type": "markdown", - "id": "9076f012", + "id": "f8f28ae1", "metadata": {}, "source": [ "## Sampling from Compound Lottery $H$\n", @@ -308,7 +308,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ef4544e", + "id": "fbf5eaf7", "metadata": {}, "outputs": [], "source": [ @@ -339,7 +339,7 @@ { "cell_type": "code", "execution_count": null, - "id": "66824f07", + "id": "61f8df2a", "metadata": {}, "outputs": [], "source": [ @@ -364,7 +364,7 @@ { "cell_type": "code", "execution_count": null, - "id": "26604b87", + "id": "adb83d42", "metadata": {}, "outputs": [], "source": [ @@ -375,7 +375,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f4facad4", + "id": "5253c594", "metadata": {}, "outputs": [], "source": [ @@ -385,7 +385,7 @@ }, { "cell_type": "markdown", - "id": "38e22617", + "id": "e417734d", "metadata": {}, "source": [ "**Note:** With numba acceleration the first method is actually only slightly slower than the second when we generated 1,000,000 samples.\n", @@ -425,7 +425,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9d84d6f6", + "id": "121cb777", "metadata": { "hide-output": false }, @@ -443,7 +443,7 @@ }, { "cell_type": "markdown", - "id": "f6c83bb4", + "id": "8e204fdb", "metadata": {}, "source": [ "Formula {eq}`equation-eq-recur1` can be generalized by iterating on it and thereby deriving an\n", @@ -524,7 +524,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bf0283d6", + "id": "24bcc8c6", "metadata": {}, "outputs": [], "source": [ @@ -577,7 +577,7 @@ { "cell_type": "code", "execution_count": null, - "id": "565e5163", + "id": "48890a09", "metadata": {}, "outputs": [], "source": [ @@ -586,7 +586,7 @@ }, { "cell_type": "markdown", - "id": "b9b8486b", + "id": "749edab1", "metadata": {}, "source": [ "The above graph shows a sample path of the log likelihood ratio process as the blue dotted line, together with\n", @@ -599,7 +599,7 @@ { "cell_type": "code", "execution_count": null, - "id": "11587f15", + "id": "ef18c7aa", "metadata": {}, "outputs": [], "source": [ @@ -608,7 +608,7 @@ }, { "cell_type": "markdown", - "id": "98ef44fb", + "id": "ed4fc9a3", "metadata": {}, "source": [ "Evidently, $\\alpha$ is having a big effect on the destination of $\\pi_t$ as $t \\rightarrow + \\infty$\n", @@ -646,7 +646,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9d99acd1", + "id": "b2258090", "metadata": {}, "outputs": [], "source": [ @@ -701,7 +701,7 @@ }, { "cell_type": "markdown", - "id": "83f5d505", + "id": "66ad5db9", "metadata": {}, "source": [ "Let us first plot the KL divergences $KL_g\\left(\\alpha\\right), KL_f\\left(\\alpha\\right)$ for each $\\alpha$." @@ -710,7 +710,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c58784bc", + "id": "f2124542", "metadata": {}, "outputs": [], "source": [ @@ -732,7 +732,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5b442437", + "id": "d390534c", "metadata": {}, "outputs": [], "source": [ @@ -754,7 +754,7 @@ }, { "cell_type": "markdown", - "id": "ec26734d", + "id": "e68348f3", "metadata": {}, "source": [ "Let's compute an $\\alpha$ for which the KL divergence between $h$ and $g$ is the same as that between $h$ and $f$." @@ -763,7 +763,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de71d4b5", + "id": "e517c6d9", "metadata": {}, "outputs": [], "source": [ @@ -773,7 +773,7 @@ }, { "cell_type": "markdown", - "id": "3fd22d00", + "id": "96baba9e", "metadata": {}, "source": [ "We can compute and plot the convergence point $\\pi_{\\infty}$ for each $\\alpha$ to verify that the convergence is indeed governed by the KL divergence.\n", @@ -787,7 +787,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3e1596b5", + "id": "dae2c9da", "metadata": {}, "outputs": [], "source": [ @@ -815,7 +815,7 @@ }, { "cell_type": "markdown", - "id": "a84de7fd", + "id": "2f936bde", "metadata": {}, "source": [ "Evidently, our type 1 learner who applies Bayes' law to his misspecified set of statistical models eventually learns an approximating model that is as close as possible to the true model, as measured by its\n", @@ -866,7 +866,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d72b937", + "id": "5125d17d", "metadata": {}, "outputs": [], "source": [ @@ -895,7 +895,7 @@ }, { "cell_type": "markdown", - "id": "42614306", + "id": "14593004", "metadata": {}, "source": [ "The following code generates the graph below that displays Bayesian posteriors for $\\alpha$ at various history lengths." @@ -904,7 +904,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ace7c7db", + "id": "2ace74ae", "metadata": {}, "outputs": [], "source": [ @@ -924,7 +924,7 @@ }, { "cell_type": "markdown", - "id": "f8120eed", + "id": "56e4c04d", "metadata": {}, "source": [ "Evidently, the Bayesian posterior narrows in on the true value $\\alpha = .8$ of the mixing parameter as the length of a history of observations grows.\n", diff --git a/_sources/mle.ipynb b/_sources/mle.ipynb index a4a1138..3aeaf24 100644 --- a/_sources/mle.ipynb +++ b/_sources/mle.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7b7a3b46", + "id": "6c765ef6", "metadata": {}, "source": [ "```{raw} html\n", @@ -42,7 +42,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c91249e3", + "id": "371f49e5", "metadata": {}, "outputs": [], "source": [ @@ -61,7 +61,7 @@ }, { "cell_type": "markdown", - "id": "3625379f", + "id": "1714dff6", "metadata": {}, "source": [ "### Prerequisites\n", @@ -113,7 +113,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aaa4fdb9", + "id": "0f81ba39", "metadata": {}, "outputs": [], "source": [ @@ -144,7 +144,7 @@ }, { "cell_type": "markdown", - "id": "cbfd7e44", + "id": "f03bc4ac", "metadata": {}, "source": [ "Notice that the Poisson distribution begins to resemble a normal distribution as the mean of $y$ increases.\n", @@ -160,7 +160,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27dfa834", + "id": "592a72bb", "metadata": {}, "outputs": [], "source": [ @@ -173,7 +173,7 @@ }, { "cell_type": "markdown", - "id": "03d38ddc", + "id": "4b5e4f63", "metadata": {}, "source": [ "Using a histogram, we can view the distribution of the number of\n", @@ -184,7 +184,7 @@ { "cell_type": "code", "execution_count": null, - "id": "aab15145", + "id": "501849d1", "metadata": {}, "outputs": [], "source": [ @@ -202,7 +202,7 @@ }, { "cell_type": "markdown", - "id": "bd8da371", + "id": "28508c72", "metadata": {}, "source": [ "From the histogram, it appears that the Poisson assumption is not unreasonable (albeit with a very low $\\mu$ and some outliers).\n", @@ -237,7 +237,7 @@ { "cell_type": "code", "execution_count": null, - "id": "005ec7f8", + "id": "88259321", "metadata": {}, "outputs": [], "source": [ @@ -277,7 +277,7 @@ }, { "cell_type": "markdown", - "id": "31549dbd", + "id": "fb0da5c3", "metadata": {}, "source": [ "We can see that the distribution of $y_i$ is conditional on\n", @@ -319,7 +319,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3d575224", + "id": "09a2a7de", "metadata": {}, "outputs": [], "source": [ @@ -345,7 +345,7 @@ }, { "cell_type": "markdown", - "id": "b6d7eb30", + "id": "b2091b0b", "metadata": {}, "source": [ "Similarly, the joint pmf of our data (which is distributed as a\n", @@ -440,7 +440,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4ba3824", + "id": "6129d696", "metadata": {}, "outputs": [], "source": [ @@ -469,7 +469,7 @@ }, { "cell_type": "markdown", - "id": "5d8355e4", + "id": "6c8d1f78", "metadata": {}, "source": [ "The plot shows that the maximum likelihood value (the top plot) occurs\n", @@ -525,7 +525,7 @@ { "cell_type": "code", "execution_count": null, - "id": "99cc1af9", + "id": "d5da3ae4", "metadata": {}, "outputs": [], "source": [ @@ -560,7 +560,7 @@ }, { "cell_type": "markdown", - "id": "2b2cc12d", + "id": "a96a0737", "metadata": {}, "source": [ "Our function `newton_raphson` will take a `PoissonRegression` object\n", @@ -583,7 +583,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0baaa051", + "id": "eec1e1d7", "metadata": {}, "outputs": [], "source": [ @@ -623,7 +623,7 @@ }, { "cell_type": "markdown", - "id": "cf3ace66", + "id": "58471bf5", "metadata": {}, "source": [ "Let's try out our algorithm with a small dataset of 5 observations and 3\n", @@ -633,7 +633,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79a16e44", + "id": "871aad49", "metadata": {}, "outputs": [], "source": [ @@ -657,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "9f96601c", + "id": "fcbcaabe", "metadata": {}, "source": [ "As this was a simple model with few observations, the algorithm achieved\n", @@ -680,7 +680,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d72231de", + "id": "67517364", "metadata": {}, "outputs": [], "source": [ @@ -689,7 +689,7 @@ }, { "cell_type": "markdown", - "id": "111cd1db", + "id": "9da11b95", "metadata": {}, "source": [ "The iterative process can be visualized in the following diagram, where\n", @@ -699,7 +699,7 @@ { "cell_type": "code", "execution_count": null, - "id": "35c83a1d", + "id": "6168d0a9", "metadata": { "tags": [ "output_scroll" @@ -741,7 +741,7 @@ }, { "cell_type": "markdown", - "id": "5b8275ec", + "id": "a7c09806", "metadata": {}, "source": [ "Note that our implementation of the Newton-Raphson algorithm is rather\n", @@ -765,7 +765,7 @@ { "cell_type": "code", "execution_count": null, - "id": "33add151", + "id": "df71f486", "metadata": {}, "outputs": [], "source": [ @@ -783,7 +783,7 @@ }, { "cell_type": "markdown", - "id": "3237c81e", + "id": "413199c4", "metadata": {}, "source": [ "Now let's replicate results from Daniel Treisman's paper, [Russia's\n", @@ -806,7 +806,7 @@ { "cell_type": "code", "execution_count": null, - "id": "febc9fd2", + "id": "1bec0291", "metadata": {}, "outputs": [], "source": [ @@ -826,7 +826,7 @@ }, { "cell_type": "markdown", - "id": "8ab21c3e", + "id": "04e9a031", "metadata": {}, "source": [ "Then we can use the `Poisson` function from `statsmodels` to fit the\n", @@ -838,7 +838,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b0a83ccc", + "id": "ee60b0de", "metadata": {}, "outputs": [], "source": [ @@ -850,7 +850,7 @@ }, { "cell_type": "markdown", - "id": "7ee21419", + "id": "acc7cf74", "metadata": {}, "source": [ "Success! The algorithm was able to achieve convergence in 9 iterations.\n", @@ -867,7 +867,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b15b6e6e", + "id": "cb9d31b8", "metadata": {}, "outputs": [], "source": [ @@ -905,7 +905,7 @@ }, { "cell_type": "markdown", - "id": "8d23ccd7", + "id": "3f22bff1", "metadata": {}, "source": [ "The output suggests that the frequency of billionaires is positively\n", @@ -921,7 +921,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a156a4b", + "id": "538370b1", "metadata": {}, "outputs": [], "source": [ @@ -948,7 +948,7 @@ }, { "cell_type": "markdown", - "id": "90212413", + "id": "7b2eb6fd", "metadata": {}, "source": [ "As we can see, Russia has by far the highest number of billionaires in\n", @@ -1059,7 +1059,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dee68a73", + "id": "f6741ceb", "metadata": {}, "outputs": [], "source": [ @@ -1097,7 +1097,7 @@ }, { "cell_type": "markdown", - "id": "55c80c3f", + "id": "d126c26b", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1145,7 +1145,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5629d5f2", + "id": "15de5df5", "metadata": {}, "outputs": [], "source": [ @@ -1154,7 +1154,7 @@ }, { "cell_type": "markdown", - "id": "05dc1f9c", + "id": "487980b2", "metadata": {}, "source": [ "Note that the simple Newton-Raphson algorithm developed in this lecture\n", @@ -1174,7 +1174,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7d5bc5bd", + "id": "b8419999", "metadata": {}, "outputs": [], "source": [ @@ -1199,7 +1199,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0ce77874", + "id": "e5387ad4", "metadata": {}, "outputs": [], "source": [ @@ -1210,7 +1210,7 @@ }, { "cell_type": "markdown", - "id": "ba4247fe", + "id": "6ac6ece3", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/multi_hyper.ipynb b/_sources/multi_hyper.ipynb index 29d5dc8..63c018f 100644 --- a/_sources/multi_hyper.ipynb +++ b/_sources/multi_hyper.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "5b2b5a47", + "id": "e9dae4d7", "metadata": {}, "source": [ "(multi_hyper_v7)=\n", @@ -110,7 +110,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5111d29f", + "id": "fbdfcad6", "metadata": {}, "outputs": [], "source": [ @@ -124,7 +124,7 @@ }, { "cell_type": "markdown", - "id": "198c21c5", + "id": "0ac4f76c", "metadata": {}, "source": [ "To recapitulate, we assume there are in total $c$ types of objects in an urn.\n", @@ -172,7 +172,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3186c1f8", + "id": "5e51c884", "metadata": {}, "outputs": [], "source": [ @@ -268,7 +268,7 @@ }, { "cell_type": "markdown", - "id": "238444c7", + "id": "0abb120a", "metadata": {}, "source": [ "## Usage\n", @@ -290,7 +290,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1aaa9b49", + "id": "5c5bfd69", "metadata": {}, "outputs": [], "source": [ @@ -301,7 +301,7 @@ }, { "cell_type": "markdown", - "id": "7d56d5d3", + "id": "618de41b", "metadata": {}, "source": [ "Now use the Urn Class method `pmf` to compute the probability of the outcome $X = \\begin{pmatrix} 2 & 2 & 2 \\end{pmatrix}$" @@ -310,7 +310,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5e4f80c", + "id": "789370e3", "metadata": {}, "outputs": [], "source": [ @@ -320,7 +320,7 @@ }, { "cell_type": "markdown", - "id": "1186e1eb", + "id": "927ec9e7", "metadata": {}, "source": [ "We can use the code to compute probabilities of a list of possible outcomes by\n", @@ -332,7 +332,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f08706c0", + "id": "75f42b55", "metadata": {}, "outputs": [], "source": [ @@ -342,7 +342,7 @@ }, { "cell_type": "markdown", - "id": "04e20d7d", + "id": "b9efa86a", "metadata": {}, "source": [ "Now let's compute the mean vector and variance-covariance matrix." @@ -351,7 +351,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0cc1ff82", + "id": "cb99bdfb", "metadata": {}, "outputs": [], "source": [ @@ -362,7 +362,7 @@ { "cell_type": "code", "execution_count": null, - "id": "199a9b8c", + "id": "452d62a8", "metadata": {}, "outputs": [], "source": [ @@ -372,7 +372,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3a0385e0", + "id": "b980aad4", "metadata": {}, "outputs": [], "source": [ @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "0eb3a33f", + "id": "34351007", "metadata": {}, "source": [ "### Back to The Administrator's Problem\n", @@ -396,7 +396,7 @@ { "cell_type": "code", "execution_count": null, - "id": "12d83df9", + "id": "6167f3ed", "metadata": {}, "outputs": [], "source": [ @@ -406,7 +406,7 @@ }, { "cell_type": "markdown", - "id": "1209cb19", + "id": "6c63507a", "metadata": {}, "source": [ "Let's compute the probability of the outcome $\\left(10, 1, 4, 0 \\right)$." @@ -415,7 +415,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c276660a", + "id": "06bc93b2", "metadata": {}, "outputs": [], "source": [ @@ -425,7 +425,7 @@ }, { "cell_type": "markdown", - "id": "9b493f9b", + "id": "966d8e5a", "metadata": {}, "source": [ "We can compute probabilities of three possible outcomes by constructing a 3-dimensional\n", @@ -435,7 +435,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9ea2b857", + "id": "2304b72e", "metadata": {}, "outputs": [], "source": [ @@ -445,7 +445,7 @@ }, { "cell_type": "markdown", - "id": "5699ca1d", + "id": "847480b6", "metadata": {}, "source": [ "Now let's compute the mean and variance-covariance matrix of $X$ when $n=6$." @@ -454,7 +454,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0bdc35b2", + "id": "ebf7b9a4", "metadata": {}, "outputs": [], "source": [ @@ -465,7 +465,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5586256b", + "id": "80abef75", "metadata": {}, "outputs": [], "source": [ @@ -476,7 +476,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a82b10ff", + "id": "c79c9759", "metadata": {}, "outputs": [], "source": [ @@ -486,7 +486,7 @@ }, { "cell_type": "markdown", - "id": "76859507", + "id": "7649e359", "metadata": {}, "source": [ "We can simulate a large sample and verify that sample means and covariances closely approximate the population means and covariances." @@ -495,7 +495,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5d9b2434", + "id": "af614129", "metadata": {}, "outputs": [], "source": [ @@ -506,7 +506,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cdbea7b2", + "id": "0b193935", "metadata": {}, "outputs": [], "source": [ @@ -517,7 +517,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4657838", + "id": "45133506", "metadata": {}, "outputs": [], "source": [ @@ -527,7 +527,7 @@ }, { "cell_type": "markdown", - "id": "68bda9f1", + "id": "58d96cd1", "metadata": {}, "source": [ "Evidently, the sample means and covariances approximate their population counterparts well.\n", @@ -540,7 +540,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fca441ea", + "id": "111a3119", "metadata": {}, "outputs": [], "source": [ @@ -550,7 +550,7 @@ { "cell_type": "code", "execution_count": null, - "id": "27d34503", + "id": "a417b232", "metadata": {}, "outputs": [], "source": [ @@ -573,7 +573,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5a7cbe94", + "id": "1f676d2e", "metadata": {}, "outputs": [], "source": [ @@ -591,7 +591,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6756d311", + "id": "ece2df4a", "metadata": {}, "outputs": [], "source": [ @@ -627,7 +627,7 @@ }, { "cell_type": "markdown", - "id": "7600f4ca", + "id": "954e2257", "metadata": {}, "source": [ "The diagonal graphs plot the marginal distributions of $k_i$ for\n", @@ -653,7 +653,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f5f6570f", + "id": "de65ff55", "metadata": {}, "outputs": [], "source": [ @@ -663,7 +663,7 @@ }, { "cell_type": "markdown", - "id": "28bc606f", + "id": "2bee15cc", "metadata": {}, "source": [ "As we can see, all the p-values are almost $0$ and the null hypothesis is soundly rejected.\n", @@ -674,7 +674,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b1ce0af", + "id": "5586c7bb", "metadata": {}, "outputs": [], "source": [ @@ -684,7 +684,7 @@ }, { "cell_type": "markdown", - "id": "b697badd", + "id": "3e45c070", "metadata": {}, "source": [ "The lesson to take away from this is that the normal approximation is imperfect." diff --git a/_sources/multivariate_normal.ipynb b/_sources/multivariate_normal.ipynb index 66e038e..de9806b 100644 --- a/_sources/multivariate_normal.ipynb +++ b/_sources/multivariate_normal.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "c3e4bdd5", + "id": "e94d507c", "metadata": {}, "source": [ "(multivariate_normal_v11)=\n", @@ -60,7 +60,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dab96d75", + "id": "8b6600b9", "metadata": {}, "outputs": [], "source": [ @@ -73,7 +73,7 @@ }, { "cell_type": "markdown", - "id": "2c9c9a6f", + "id": "6d3ce72e", "metadata": {}, "source": [ "Assume that an $N \\times 1$ random vector $z$ has a\n", @@ -95,7 +95,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3778e414", + "id": "4af9f405", "metadata": {}, "outputs": [], "source": [ @@ -128,7 +128,7 @@ }, { "cell_type": "markdown", - "id": "017f8803", + "id": "98998189", "metadata": {}, "source": [ "For some integer $k\\in \\{1,\\dots, N-1\\}$, partition\n", @@ -201,7 +201,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23fd1655", + "id": "5c04669b", "metadata": {}, "outputs": [], "source": [ @@ -277,7 +277,7 @@ }, { "cell_type": "markdown", - "id": "31755925", + "id": "ed12e6ad", "metadata": {}, "source": [ "Let’s put this code to work on a suite of examples.\n", @@ -313,7 +313,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d18ce92a", + "id": "861174fb", "metadata": {}, "outputs": [], "source": [ @@ -327,7 +327,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d057d962", + "id": "826f1f8b", "metadata": {}, "outputs": [], "source": [ @@ -340,7 +340,7 @@ }, { "cell_type": "markdown", - "id": "81964653", + "id": "ad8e01c6", "metadata": {}, "source": [ "Let's illustrate the fact that you _can regress anything on anything else_.\n", @@ -377,7 +377,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9216eb13", + "id": "99457d60", "metadata": {}, "outputs": [], "source": [ @@ -392,7 +392,7 @@ }, { "cell_type": "markdown", - "id": "8b4959b3", + "id": "dd24540a", "metadata": {}, "source": [ "Let's print out the intercepts and slopes.\n", @@ -404,7 +404,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d7baebe6", + "id": "e0f3af92", "metadata": {}, "outputs": [], "source": [ @@ -414,7 +414,7 @@ }, { "cell_type": "markdown", - "id": "648bc2b5", + "id": "fe79eaae", "metadata": {}, "source": [ "For the regression of $z_2$ on $z_1$ we have" @@ -423,7 +423,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47c43c76", + "id": "22afbe95", "metadata": {}, "outputs": [], "source": [ @@ -433,7 +433,7 @@ }, { "cell_type": "markdown", - "id": "e16cd759", + "id": "b6d6f14e", "metadata": {}, "source": [ "Now let's plot the two regression lines and stare at them." @@ -442,7 +442,7 @@ { "cell_type": "code", "execution_count": null, - "id": "543d475d", + "id": "5a1f7833", "metadata": {}, "outputs": [], "source": [ @@ -481,7 +481,7 @@ }, { "cell_type": "markdown", - "id": "48f14961", + "id": "7a18209d", "metadata": {}, "source": [ "The red line is the expectation of $z_1$ conditional on $z_2$.\n", @@ -492,7 +492,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f793ce81", + "id": "887ef696", "metadata": {}, "outputs": [], "source": [ @@ -502,7 +502,7 @@ }, { "cell_type": "markdown", - "id": "ebead5e7", + "id": "5a84a6a7", "metadata": {}, "source": [ "The blue line is the expectation of $z_2$ conditional on $z_1$.\n", @@ -513,7 +513,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a92a16a7", + "id": "ba837efa", "metadata": {}, "outputs": [], "source": [ @@ -523,7 +523,7 @@ }, { "cell_type": "markdown", - "id": "328b2a3b", + "id": "b4d31b40", "metadata": {}, "source": [ "We can use these regression lines or our code to compute conditional expectations.\n", @@ -537,7 +537,7 @@ { "cell_type": "code", "execution_count": null, - "id": "65a306a1", + "id": "b34eb286", "metadata": {}, "outputs": [], "source": [ @@ -551,7 +551,7 @@ }, { "cell_type": "markdown", - "id": "63683e1b", + "id": "60d53994", "metadata": {}, "source": [ "Now let’s compute the mean and variance of the distribution of $z_1$\n", @@ -561,7 +561,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2894216", + "id": "58fad875", "metadata": {}, "outputs": [], "source": [ @@ -575,7 +575,7 @@ }, { "cell_type": "markdown", - "id": "54c95e11", + "id": "42ac0754", "metadata": {}, "source": [ "Let’s compare the preceding population mean and variance with outcomes\n", @@ -602,7 +602,7 @@ { "cell_type": "code", "execution_count": null, - "id": "332b26bc", + "id": "50fe72c9", "metadata": {}, "outputs": [], "source": [ @@ -620,7 +620,7 @@ }, { "cell_type": "markdown", - "id": "7d346985", + "id": "686a6e34", "metadata": {}, "source": [ "Let’s compare the preceding population $\\beta$ with the OLS sample\n", @@ -630,7 +630,7 @@ { "cell_type": "code", "execution_count": null, - "id": "eccb3278", + "id": "836daae6", "metadata": {}, "outputs": [], "source": [ @@ -639,7 +639,7 @@ }, { "cell_type": "markdown", - "id": "0ee2a058", + "id": "a974948f", "metadata": {}, "source": [ "Let’s compare our population $\\hat{\\Sigma}_1$ with the\n", @@ -649,7 +649,7 @@ { "cell_type": "code", "execution_count": null, - "id": "94203e39", + "id": "84dff77a", "metadata": {}, "outputs": [], "source": [ @@ -658,7 +658,7 @@ }, { "cell_type": "markdown", - "id": "24597b64", + "id": "34082f2f", "metadata": {}, "source": [ "Lastly, let’s compute the estimate of $\\hat{E z_1 | z_2}$ and\n", @@ -668,7 +668,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9e2550e0", + "id": "de98d890", "metadata": {}, "outputs": [], "source": [ @@ -677,7 +677,7 @@ }, { "cell_type": "markdown", - "id": "74544422", + "id": "8af5cb9c", "metadata": {}, "source": [ "Thus, in each case, for our very large sample size, the sample analogues\n", @@ -696,7 +696,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b501d622", + "id": "ee314389", "metadata": {}, "outputs": [], "source": [ @@ -710,7 +710,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f3a7268", + "id": "cf72a936", "metadata": {}, "outputs": [], "source": [ @@ -720,7 +720,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b48bfd6e", + "id": "a2dc41b0", "metadata": {}, "outputs": [], "source": [ @@ -730,7 +730,7 @@ }, { "cell_type": "markdown", - "id": "d82a1f0b", + "id": "f873b38a", "metadata": {}, "source": [ "Let’s compute the distribution of $z_1$ conditional on\n", @@ -740,7 +740,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2ee5f191", + "id": "cb642915", "metadata": {}, "outputs": [], "source": [ @@ -753,7 +753,7 @@ { "cell_type": "code", "execution_count": null, - "id": "97c3ab43", + "id": "75762e9d", "metadata": {}, "outputs": [], "source": [ @@ -766,7 +766,7 @@ { "cell_type": "code", "execution_count": null, - "id": "33998abd", + "id": "381d91ff", "metadata": {}, "outputs": [], "source": [ @@ -776,7 +776,7 @@ }, { "cell_type": "markdown", - "id": "a6476b2e", + "id": "6cb3a361", "metadata": {}, "source": [ "As above, we compare population and sample regression coefficients, the\n", @@ -787,7 +787,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a604765d", + "id": "e65f9673", "metadata": {}, "outputs": [], "source": [ @@ -797,7 +797,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fcb6f0e8", + "id": "6c6e839b", "metadata": {}, "outputs": [], "source": [ @@ -807,7 +807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "509dbeae", + "id": "f4bff3e6", "metadata": {}, "outputs": [], "source": [ @@ -816,7 +816,7 @@ }, { "cell_type": "markdown", - "id": "05ccff70", + "id": "a556dd7d", "metadata": {}, "source": [ "Once again, sample analogues do a good job of approximating their\n", @@ -913,7 +913,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ad9ca233", + "id": "1d9d8754", "metadata": {}, "outputs": [], "source": [ @@ -932,7 +932,7 @@ }, { "cell_type": "markdown", - "id": "0c896807", + "id": "1a1bc9c3", "metadata": {}, "source": [ "Now let’s consider a specific instance of this model.\n", @@ -948,7 +948,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59e350be", + "id": "67e3d926", "metadata": {}, "outputs": [], "source": [ @@ -961,7 +961,7 @@ }, { "cell_type": "markdown", - "id": "d3960776", + "id": "97a59ff6", "metadata": {}, "source": [ "We can now use our `MultivariateNormal` class to construct an\n", @@ -976,7 +976,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4a857484", + "id": "37c1bfda", "metadata": {}, "outputs": [], "source": [ @@ -988,7 +988,7 @@ }, { "cell_type": "markdown", - "id": "43325198", + "id": "bdaa8cb3", "metadata": {}, "source": [ "Using the generator `multivariate_normal`, we can make one draw of the\n", @@ -1001,7 +1001,7 @@ { "cell_type": "code", "execution_count": null, - "id": "850e5b4a", + "id": "e75cdcfe", "metadata": {}, "outputs": [], "source": [ @@ -1013,7 +1013,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6b697876", + "id": "d59376b0", "metadata": {}, "outputs": [], "source": [ @@ -1023,7 +1023,7 @@ }, { "cell_type": "markdown", - "id": "0b67cd9e", + "id": "f6322676", "metadata": {}, "source": [ "The method `cond_dist` takes test scores $y$ as input and returns the\n", @@ -1038,7 +1038,7 @@ { "cell_type": "code", "execution_count": null, - "id": "56ae9a7e", + "id": "df93c8cc", "metadata": {}, "outputs": [], "source": [ @@ -1048,7 +1048,7 @@ }, { "cell_type": "markdown", - "id": "dc6b1a54", + "id": "3fb3f6e6", "metadata": {}, "source": [ "The first number is the conditional mean $\\hat{\\mu}_{\\theta}$ and\n", @@ -1067,7 +1067,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e1177658", + "id": "f34dbe2f", "metadata": {}, "outputs": [], "source": [ @@ -1097,7 +1097,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb8f1a64", + "id": "498013e7", "metadata": {}, "outputs": [], "source": [ @@ -1120,7 +1120,7 @@ }, { "cell_type": "markdown", - "id": "3e7327d1", + "id": "3bbf4e60", "metadata": {}, "source": [ "The solid blue line in the plot above shows $\\hat{\\mu}_{\\theta}$\n", @@ -1236,7 +1236,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e2c1b890", + "id": "dc862798", "metadata": {}, "outputs": [], "source": [ @@ -1249,7 +1249,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dafbbd39", + "id": "eb1a8380", "metadata": {}, "outputs": [], "source": [ @@ -1262,7 +1262,7 @@ }, { "cell_type": "markdown", - "id": "dd327dc0", + "id": "3e9a24e3", "metadata": {}, "source": [ "To confirm that these formulas give the same answers that we computed\n", @@ -1276,7 +1276,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16bca6e6", + "id": "2ba297ae", "metadata": {}, "outputs": [], "source": [ @@ -1287,7 +1287,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5dee13e8", + "id": "5b4e836b", "metadata": {}, "outputs": [], "source": [ @@ -1297,7 +1297,7 @@ }, { "cell_type": "markdown", - "id": "fe1ef2ea", + "id": "ff9c6a32", "metadata": {}, "source": [ "## Cholesky Factor Magic\n", @@ -1381,7 +1381,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c9e9489", + "id": "81d2793d", "metadata": {}, "outputs": [], "source": [ @@ -1408,7 +1408,7 @@ }, { "cell_type": "markdown", - "id": "1357d82f", + "id": "d53bee0a", "metadata": {}, "source": [ "Let’s put the function to work." @@ -1417,7 +1417,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2b51734", + "id": "e5869b30", "metadata": {}, "outputs": [], "source": [ @@ -1432,7 +1432,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a3bc8f8", + "id": "3a13d00e", "metadata": {}, "outputs": [], "source": [ @@ -1449,7 +1449,7 @@ }, { "cell_type": "markdown", - "id": "118eedd9", + "id": "af280718", "metadata": {}, "source": [ "We first compute the joint normal distribution of\n", @@ -1459,7 +1459,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f8f54c06", + "id": "6ff88be7", "metadata": {}, "outputs": [], "source": [ @@ -1473,7 +1473,7 @@ }, { "cell_type": "markdown", - "id": "e4223f89", + "id": "00496aa6", "metadata": {}, "source": [ "Now let’s compute distributions of $\\theta$ and $\\mu$\n", @@ -1486,7 +1486,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1ac5d5e9", + "id": "24c1b8a0", "metadata": {}, "outputs": [], "source": [ @@ -1503,7 +1503,7 @@ }, { "cell_type": "markdown", - "id": "6a480c85", + "id": "2e9a9568", "metadata": {}, "source": [ "Let’s see how things work for an example." @@ -1512,7 +1512,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1e60f20e", + "id": "c4088eb9", "metadata": {}, "outputs": [], "source": [ @@ -1530,7 +1530,7 @@ }, { "cell_type": "markdown", - "id": "c031a868", + "id": "ca8fcac7", "metadata": {}, "source": [ "Evidently, math tests provide no information about $\\mu$ and\n", @@ -1633,7 +1633,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f08f345d", + "id": "f7975b99", "metadata": {}, "outputs": [], "source": [ @@ -1644,7 +1644,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9809fe11", + "id": "ccafac1e", "metadata": {}, "outputs": [], "source": [ @@ -1661,7 +1661,7 @@ { "cell_type": "code", "execution_count": null, - "id": "94c0ac92", + "id": "ca619a66", "metadata": {}, "outputs": [], "source": [ @@ -1679,7 +1679,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fb56e761", + "id": "5ad8d095", "metadata": {}, "outputs": [], "source": [ @@ -1689,7 +1689,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41a3272a", + "id": "caea08b8", "metadata": {}, "outputs": [], "source": [ @@ -1703,7 +1703,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4fc06c40", + "id": "b64f3f8e", "metadata": {}, "outputs": [], "source": [ @@ -1719,7 +1719,7 @@ { "cell_type": "code", "execution_count": null, - "id": "090f97bb", + "id": "926482ae", "metadata": {}, "outputs": [], "source": [ @@ -1729,7 +1729,7 @@ { "cell_type": "code", "execution_count": null, - "id": "374de9ee", + "id": "a3e0f732", "metadata": {}, "outputs": [], "source": [ @@ -1739,7 +1739,7 @@ }, { "cell_type": "markdown", - "id": "8181e287", + "id": "f2c0a981", "metadata": {}, "source": [ "The following Python code lets us sample random vectors $X$ and\n", @@ -1752,7 +1752,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7a54326b", + "id": "cc75e3be", "metadata": {}, "outputs": [], "source": [ @@ -1764,7 +1764,7 @@ }, { "cell_type": "markdown", - "id": "10de9d14", + "id": "a815ef58", "metadata": {}, "source": [ "### Smoothing Example\n", @@ -1783,7 +1783,7 @@ { "cell_type": "code", "execution_count": null, - "id": "90334a48", + "id": "14eb09ed", "metadata": {}, "outputs": [], "source": [ @@ -1796,7 +1796,7 @@ { "cell_type": "code", "execution_count": null, - "id": "42587407", + "id": "784202b6", "metadata": {}, "outputs": [], "source": [ @@ -1807,7 +1807,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e65fc443", + "id": "a2fa2931", "metadata": {}, "outputs": [], "source": [ @@ -1822,7 +1822,7 @@ }, { "cell_type": "markdown", - "id": "ed0bd34d", + "id": "5b8d0300", "metadata": {}, "source": [ "### Filtering Exercise\n", @@ -1840,7 +1840,7 @@ { "cell_type": "code", "execution_count": null, - "id": "09aa5bea", + "id": "4af6d1b2", "metadata": {}, "outputs": [], "source": [ @@ -1850,7 +1850,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b17375db", + "id": "fcca1a21", "metadata": {}, "outputs": [], "source": [ @@ -1869,7 +1869,7 @@ { "cell_type": "code", "execution_count": null, - "id": "89ee1e72", + "id": "2093e4a0", "metadata": {}, "outputs": [], "source": [ @@ -1879,7 +1879,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b827b232", + "id": "ee826414", "metadata": {}, "outputs": [], "source": [ @@ -1890,7 +1890,7 @@ { "cell_type": "code", "execution_count": null, - "id": "48888468", + "id": "6f760aa9", "metadata": {}, "outputs": [], "source": [ @@ -1901,7 +1901,7 @@ }, { "cell_type": "markdown", - "id": "db80ba83", + "id": "fd46db4a", "metadata": {}, "source": [ "### Prediction Exercise\n", @@ -1918,7 +1918,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79f5c4a0", + "id": "4d23467e", "metadata": {}, "outputs": [], "source": [ @@ -1929,7 +1929,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c604bfe4", + "id": "6428244b", "metadata": {}, "outputs": [], "source": [ @@ -1945,7 +1945,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8864a9b2", + "id": "a10400b1", "metadata": {}, "outputs": [], "source": [ @@ -1955,7 +1955,7 @@ { "cell_type": "code", "execution_count": null, - "id": "15389e4f", + "id": "23bfa0cb", "metadata": {}, "outputs": [], "source": [ @@ -1966,7 +1966,7 @@ { "cell_type": "code", "execution_count": null, - "id": "33ec9a6c", + "id": "24e4436f", "metadata": {}, "outputs": [], "source": [ @@ -1977,7 +1977,7 @@ }, { "cell_type": "markdown", - "id": "15ed948f", + "id": "bb7d42e7", "metadata": {}, "source": [ "### Constructing a Wold Representation\n", @@ -1999,7 +1999,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d05dbedb", + "id": "63d78841", "metadata": {}, "outputs": [], "source": [ @@ -2011,7 +2011,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0162f447", + "id": "0628a80b", "metadata": {}, "outputs": [], "source": [ @@ -2023,7 +2023,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a4a5d59d", + "id": "61e6a590", "metadata": {}, "outputs": [], "source": [ @@ -2032,7 +2032,7 @@ }, { "cell_type": "markdown", - "id": "01cef4ec", + "id": "09e8044c", "metadata": {}, "source": [ "This example is an instance of what is known as a **Wold representation** in time series analysis.\n", @@ -2133,7 +2133,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d22af02", + "id": "49a6c81e", "metadata": {}, "outputs": [], "source": [ @@ -2157,7 +2157,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9603ebee", + "id": "135f4d82", "metadata": {}, "outputs": [], "source": [ @@ -2179,7 +2179,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a69356c9", + "id": "9b933a3b", "metadata": {}, "outputs": [], "source": [ @@ -2194,7 +2194,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2d44723b", + "id": "59291945", "metadata": {}, "outputs": [], "source": [ @@ -2211,7 +2211,7 @@ }, { "cell_type": "markdown", - "id": "e5adf870", + "id": "0fb57994", "metadata": {}, "source": [ "## Application to Stock Price Model\n", @@ -2259,7 +2259,7 @@ { "cell_type": "code", "execution_count": null, - "id": "22466633", + "id": "c0b884cb", "metadata": {}, "outputs": [], "source": [ @@ -2269,7 +2269,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3c5de931", + "id": "8adc4ee6", "metadata": {}, "outputs": [], "source": [ @@ -2282,7 +2282,7 @@ }, { "cell_type": "markdown", - "id": "31ab84b3", + "id": "bd61a2af", "metadata": {}, "source": [ "Denote\n", @@ -2313,7 +2313,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d2143e8d", + "id": "948b1c36", "metadata": {}, "outputs": [], "source": [ @@ -2323,7 +2323,7 @@ { "cell_type": "code", "execution_count": null, - "id": "41286eeb", + "id": "cdfc9553", "metadata": {}, "outputs": [], "source": [ @@ -2333,7 +2333,7 @@ }, { "cell_type": "markdown", - "id": "89764f2c", + "id": "83ddcb4b", "metadata": {}, "source": [ "We can simulate paths of $y_{t}$ and $p_{t}$ and compute the\n", @@ -2344,7 +2344,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4d1dec96", + "id": "303c3d59", "metadata": {}, "outputs": [], "source": [ @@ -2355,7 +2355,7 @@ { "cell_type": "code", "execution_count": null, - "id": "926ff36b", + "id": "85d8e7af", "metadata": {}, "outputs": [], "source": [ @@ -2376,7 +2376,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f6b2a8dd", + "id": "0f5a3ac1", "metadata": {}, "outputs": [], "source": [ @@ -2392,7 +2392,7 @@ }, { "cell_type": "markdown", - "id": "737daf7b", + "id": "89192784", "metadata": {}, "source": [ "In the above graph, the green line is what the price of the stock would\n", @@ -2603,7 +2603,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2577a456", + "id": "57badefb", "metadata": {}, "outputs": [], "source": [ @@ -2620,7 +2620,7 @@ { "cell_type": "code", "execution_count": null, - "id": "52a4b546", + "id": "acbdc6be", "metadata": {}, "outputs": [], "source": [ @@ -2631,7 +2631,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da8d31d5", + "id": "eaab1033", "metadata": {}, "outputs": [], "source": [ @@ -2641,7 +2641,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4a6545d9", + "id": "bd8119f4", "metadata": {}, "outputs": [], "source": [ @@ -2656,7 +2656,7 @@ { "cell_type": "code", "execution_count": null, - "id": "60621722", + "id": "7d91e41f", "metadata": {}, "outputs": [], "source": [ @@ -2671,7 +2671,7 @@ }, { "cell_type": "markdown", - "id": "5be3b89b", + "id": "6cf81dc7", "metadata": {}, "source": [ "### Code for Iterating\n", @@ -2683,7 +2683,7 @@ { "cell_type": "code", "execution_count": null, - "id": "11de13e6", + "id": "a448d680", "metadata": {}, "outputs": [], "source": [ @@ -2719,7 +2719,7 @@ { "cell_type": "code", "execution_count": null, - "id": "89fa5794", + "id": "25269662", "metadata": {}, "outputs": [], "source": [ @@ -2728,7 +2728,7 @@ }, { "cell_type": "markdown", - "id": "5a70c5dd", + "id": "788679ed", "metadata": {}, "source": [ "The iterative algorithm just described is a version of the celebrated **Kalman filter**.\n", @@ -2800,7 +2800,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8eec752b", + "id": "b7b12746", "metadata": {}, "outputs": [], "source": [ @@ -2810,7 +2810,7 @@ }, { "cell_type": "markdown", - "id": "a115c3dd", + "id": "c9883de8", "metadata": {}, "source": [ "We set the coefficient matrix $\\Lambda$ and the covariance matrix\n", @@ -2843,7 +2843,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f16619d0", + "id": "62a08df6", "metadata": {}, "outputs": [], "source": [ @@ -2858,7 +2858,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dc2a5f4b", + "id": "1d7a9c09", "metadata": {}, "outputs": [], "source": [ @@ -2868,7 +2868,7 @@ }, { "cell_type": "markdown", - "id": "c1ca59d7", + "id": "307c2ba7", "metadata": {}, "source": [ "We can now construct the mean vector and the covariance matrix for\n", @@ -2878,7 +2878,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e66bd0e8", + "id": "684df076", "metadata": {}, "outputs": [], "source": [ @@ -2895,7 +2895,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2495b7da", + "id": "621c0189", "metadata": {}, "outputs": [], "source": [ @@ -2908,7 +2908,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3649a59d", + "id": "6c0c5f00", "metadata": {}, "outputs": [], "source": [ @@ -2918,7 +2918,7 @@ }, { "cell_type": "markdown", - "id": "31181db6", + "id": "a574e3d9", "metadata": {}, "source": [ "Let’s compute the conditional distribution of the hidden factor\n", @@ -2928,7 +2928,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f9811899", + "id": "15a1caac", "metadata": {}, "outputs": [], "source": [ @@ -2937,7 +2937,7 @@ }, { "cell_type": "markdown", - "id": "a8d19452", + "id": "0ee7b4f6", "metadata": {}, "source": [ "We can verify that the conditional mean\n", @@ -2948,7 +2948,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ddf1805b", + "id": "b871086c", "metadata": {}, "outputs": [], "source": [ @@ -2959,7 +2959,7 @@ }, { "cell_type": "markdown", - "id": "88723f56", + "id": "48a20a73", "metadata": {}, "source": [ "Similarly, we can compute the conditional distribution $Y \\mid f$." @@ -2968,7 +2968,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d0d12013", + "id": "267b15b4", "metadata": {}, "outputs": [], "source": [ @@ -2977,7 +2977,7 @@ }, { "cell_type": "markdown", - "id": "7f04dce7", + "id": "29d0ba0f", "metadata": {}, "source": [ "It can be verified that the mean is\n", @@ -2987,7 +2987,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5bdb822b", + "id": "dcff7659", "metadata": {}, "outputs": [], "source": [ @@ -2996,7 +2996,7 @@ }, { "cell_type": "markdown", - "id": "1093befe", + "id": "b5580722", "metadata": {}, "source": [ "## PCA and Factor Analysis\n", @@ -3045,7 +3045,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b6a15df", + "id": "0c603055", "metadata": {}, "outputs": [], "source": [ @@ -3064,7 +3064,7 @@ { "cell_type": "code", "execution_count": null, - "id": "15bd0624", + "id": "24d2ce2a", "metadata": {}, "outputs": [], "source": [ @@ -3075,7 +3075,7 @@ { "cell_type": "code", "execution_count": null, - "id": "276144f6", + "id": "d0168391", "metadata": {}, "outputs": [], "source": [ @@ -3086,7 +3086,7 @@ { "cell_type": "code", "execution_count": null, - "id": "374f6cce", + "id": "d5eb7d36", "metadata": {}, "outputs": [], "source": [ @@ -3098,7 +3098,7 @@ { "cell_type": "code", "execution_count": null, - "id": "de5d6e77", + "id": "ee70c14d", "metadata": {}, "outputs": [], "source": [ @@ -3109,7 +3109,7 @@ }, { "cell_type": "markdown", - "id": "cddc27fa", + "id": "41f75507", "metadata": {}, "source": [ "Below we’ll plot several things\n", @@ -3127,7 +3127,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d27e37cf", + "id": "4032123c", "metadata": {}, "outputs": [], "source": [ @@ -3142,7 +3142,7 @@ }, { "cell_type": "markdown", - "id": "8edbefa9", + "id": "28f13bea", "metadata": {}, "source": [ "Consequently, the first two $\\epsilon_{j}$ correspond to the\n", @@ -3154,7 +3154,7 @@ { "cell_type": "code", "execution_count": null, - "id": "64ff2841", + "id": "a7833200", "metadata": {}, "outputs": [], "source": [ @@ -3164,7 +3164,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7b6d15f8", + "id": "107c2d92", "metadata": {}, "outputs": [], "source": [ @@ -3174,7 +3174,7 @@ }, { "cell_type": "markdown", - "id": "0b051484", + "id": "90f3bb03", "metadata": {}, "source": [ "The fraction of variance in $y_{t}$ explained by the first two\n", @@ -3184,7 +3184,7 @@ { "cell_type": "code", "execution_count": null, - "id": "716ebf3d", + "id": "1aeddb4c", "metadata": {}, "outputs": [], "source": [ @@ -3193,7 +3193,7 @@ }, { "cell_type": "markdown", - "id": "e78aa221", + "id": "ce93ce46", "metadata": {}, "source": [ "Compute\n", @@ -3209,7 +3209,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e02cb0b", + "id": "6ac1f0d9", "metadata": {}, "outputs": [], "source": [ @@ -3218,7 +3218,7 @@ }, { "cell_type": "markdown", - "id": "80b991ad", + "id": "78e49659", "metadata": {}, "source": [ "In this example, it turns out that the projection $\\hat{Y}$ of\n", @@ -3233,7 +3233,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ad259e4", + "id": "492cfada", "metadata": {}, "outputs": [], "source": [ @@ -3252,7 +3252,7 @@ }, { "cell_type": "markdown", - "id": "90c72bdb", + "id": "f51c47d2", "metadata": {}, "source": [ "The covariance matrix of $\\hat{Y}$ can be computed by first\n", @@ -3263,7 +3263,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5206326b", + "id": "22fa6158", "metadata": {}, "outputs": [], "source": [ diff --git a/_sources/navy_captain.ipynb b/_sources/navy_captain.ipynb index 6fa8a2e..1fe52f2 100644 --- a/_sources/navy_captain.ipynb +++ b/_sources/navy_captain.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "6125128d", + "id": "790f7b41", "metadata": {}, "source": [ "(bayesian_vs_frequentist__v1)=\n", @@ -26,7 +26,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dad435a4", + "id": "0c22565a", "metadata": { "tags": [ "hide-output" @@ -40,7 +40,7 @@ { "cell_type": "code", "execution_count": null, - "id": "447ba8f5", + "id": "ec00416d", "metadata": {}, "outputs": [], "source": [ @@ -56,7 +56,7 @@ }, { "cell_type": "markdown", - "id": "5463b910", + "id": "543fb038", "metadata": {}, "source": [ "## Overview\n", @@ -138,7 +138,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e9b4ec3a", + "id": "66d0afae", "metadata": {}, "outputs": [], "source": [ @@ -153,7 +153,7 @@ }, { "cell_type": "markdown", - "id": "cbd7d025", + "id": "b7c6db22", "metadata": {}, "source": [ "We start with defining a `jitclass` that stores parameters and\n", @@ -164,7 +164,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f82ce29", + "id": "ae97be27", "metadata": {}, "outputs": [], "source": [ @@ -187,7 +187,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17604b26", + "id": "841be577", "metadata": {}, "outputs": [], "source": [ @@ -238,7 +238,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7d778160", + "id": "b206d0a3", "metadata": {}, "outputs": [], "source": [ @@ -262,7 +262,7 @@ }, { "cell_type": "markdown", - "id": "1ef77a0d", + "id": "76495798", "metadata": {}, "source": [ "Above, we plot the two possible probability densities $f_0$ and\n", @@ -335,7 +335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "357d63b3", + "id": "f2465658", "metadata": {}, "outputs": [], "source": [ @@ -346,7 +346,7 @@ { "cell_type": "code", "execution_count": null, - "id": "79d8d730", + "id": "c1e9b076", "metadata": {}, "outputs": [], "source": [ @@ -357,7 +357,7 @@ { "cell_type": "code", "execution_count": null, - "id": "38784659", + "id": "758716bd", "metadata": {}, "outputs": [], "source": [ @@ -369,7 +369,7 @@ }, { "cell_type": "markdown", - "id": "8b7bab2b", + "id": "b7afd61f", "metadata": {}, "source": [ "We can compute sequences of likelihood ratios using simulated samples." @@ -378,7 +378,7 @@ { "cell_type": "code", "execution_count": null, - "id": "59b9b91c", + "id": "3476ad77", "metadata": {}, "outputs": [], "source": [ @@ -388,7 +388,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ffa7c88", + "id": "f4ff849a", "metadata": {}, "outputs": [], "source": [ @@ -401,7 +401,7 @@ }, { "cell_type": "markdown", - "id": "67a2a5df", + "id": "8c37acda", "metadata": {}, "source": [ "With an empirical distribution of likelihood ratios in hand, we can draw\n", @@ -412,7 +412,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d64a6ca", + "id": "d2070be6", "metadata": {}, "outputs": [], "source": [ @@ -438,7 +438,7 @@ }, { "cell_type": "markdown", - "id": "336597c5", + "id": "25757f30", "metadata": {}, "source": [ "Our frequentist minimizes the expected total loss presented in equation\n", @@ -464,7 +464,7 @@ { "cell_type": "code", "execution_count": null, - "id": "330781a1", + "id": "8ae8ea4c", "metadata": {}, "outputs": [], "source": [ @@ -484,7 +484,7 @@ { "cell_type": "code", "execution_count": null, - "id": "065b345e", + "id": "26ecf9e6", "metadata": {}, "outputs": [], "source": [ @@ -503,7 +503,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cad31c4e", + "id": "eb05a2db", "metadata": {}, "outputs": [], "source": [ @@ -527,7 +527,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cf6645ac", + "id": "236c36a5", "metadata": {}, "outputs": [], "source": [ @@ -544,7 +544,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0a7b56c3", + "id": "0b002595", "metadata": {}, "outputs": [], "source": [ @@ -554,7 +554,7 @@ { "cell_type": "code", "execution_count": null, - "id": "87036264", + "id": "82392b53", "metadata": {}, "outputs": [], "source": [ @@ -564,7 +564,7 @@ }, { "cell_type": "markdown", - "id": "f6182b04", + "id": "5c43c18b", "metadata": {}, "source": [ "Let’s now change the value of $\\pi^{*}$ and watch how the decision\n", @@ -574,7 +574,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6ed5e570", + "id": "8e244cbf", "metadata": {}, "outputs": [], "source": [ @@ -599,7 +599,7 @@ { "cell_type": "code", "execution_count": null, - "id": "641ce9f4", + "id": "c381e14f", "metadata": {}, "outputs": [], "source": [ @@ -612,7 +612,7 @@ }, { "cell_type": "markdown", - "id": "bb118c67", + "id": "7fff8153", "metadata": {}, "source": [ "The following shows how optimal sample size $t$ and targeted\n", @@ -622,7 +622,7 @@ { "cell_type": "code", "execution_count": null, - "id": "31034367", + "id": "8f64142b", "metadata": {}, "outputs": [], "source": [ @@ -643,7 +643,7 @@ }, { "cell_type": "markdown", - "id": "8b8c0269", + "id": "fc206fe8", "metadata": {}, "source": [ "## Bayesian Decision Rule\n", @@ -665,7 +665,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b02e6f6b", + "id": "ed918e5d", "metadata": {}, "outputs": [], "source": [ @@ -704,7 +704,7 @@ { "cell_type": "code", "execution_count": null, - "id": "adc19107", + "id": "e6cddff4", "metadata": {}, "outputs": [], "source": [ @@ -736,7 +736,7 @@ { "cell_type": "code", "execution_count": null, - "id": "daa21311", + "id": "6acc6989", "metadata": {}, "outputs": [], "source": [ @@ -746,7 +746,7 @@ { "cell_type": "code", "execution_count": null, - "id": "47f89a54", + "id": "a8a574bd", "metadata": {}, "outputs": [], "source": [ @@ -807,7 +807,7 @@ }, { "cell_type": "markdown", - "id": "a9ffaddf", + "id": "bfee03a8", "metadata": {}, "source": [ "The above figure portrays the value function plotted against the decision\n", @@ -865,7 +865,7 @@ { "cell_type": "code", "execution_count": null, - "id": "98c00d57", + "id": "d9a6608d", "metadata": {}, "outputs": [], "source": [ @@ -906,7 +906,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d869eda3", + "id": "1bdc673f", "metadata": {}, "outputs": [], "source": [ @@ -927,7 +927,7 @@ }, { "cell_type": "markdown", - "id": "a191a386", + "id": "288cee17", "metadata": {}, "source": [ "Given an assumed value for\n", @@ -946,7 +946,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c05b305d", + "id": "202a2842", "metadata": {}, "outputs": [], "source": [ @@ -963,7 +963,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7ba2b46a", + "id": "a8169004", "metadata": {}, "outputs": [], "source": [ @@ -992,7 +992,7 @@ }, { "cell_type": "markdown", - "id": "624792ab", + "id": "af7f2b5e", "metadata": {}, "source": [ "This pattern of outcomes holds more generally.\n", @@ -1005,7 +1005,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a3d7af23", + "id": "fb0a9841", "metadata": {}, "outputs": [], "source": [ @@ -1039,7 +1039,7 @@ }, { "cell_type": "markdown", - "id": "68218f1e", + "id": "06f220da", "metadata": {}, "source": [ "## Was the Navy Captain’s Hunch Correct?\n", @@ -1054,7 +1054,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ee0bb17f", + "id": "38d591e7", "metadata": {}, "outputs": [], "source": [ @@ -1064,7 +1064,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bfa77374", + "id": "a51cfd24", "metadata": {}, "outputs": [], "source": [ @@ -1079,7 +1079,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b491f1d6", + "id": "41ca8000", "metadata": {}, "outputs": [], "source": [ @@ -1093,7 +1093,7 @@ }, { "cell_type": "markdown", - "id": "9e739777", + "id": "5eb77cd3", "metadata": {}, "source": [ "Evidently, there is no sample size $t$ at which the frequentist\n", @@ -1106,7 +1106,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d4c962af", + "id": "5286f30d", "metadata": {}, "outputs": [], "source": [ @@ -1126,7 +1126,7 @@ }, { "cell_type": "markdown", - "id": "b1ef84ac", + "id": "7d837ea2", "metadata": {}, "source": [ "The right panel of the above graph plots the difference\n", @@ -1143,7 +1143,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b95cfe68", + "id": "2ccd5ec8", "metadata": {}, "outputs": [], "source": [ @@ -1152,7 +1152,7 @@ }, { "cell_type": "markdown", - "id": "60f3940b", + "id": "a107aac5", "metadata": {}, "source": [ "Recall that when $\\pi^*=0.5$, the frequentist decision rule sets a\n", @@ -1164,7 +1164,7 @@ { "cell_type": "code", "execution_count": null, - "id": "76b68851", + "id": "e305b35d", "metadata": {}, "outputs": [], "source": [ @@ -1173,7 +1173,7 @@ }, { "cell_type": "markdown", - "id": "2f626788", + "id": "0689b078", "metadata": {}, "source": [ "For convenience, let’s define `t_idx` as the Python array index\n", @@ -1183,7 +1183,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e0faacc0", + "id": "778d0e0c", "metadata": {}, "outputs": [], "source": [ @@ -1192,7 +1192,7 @@ }, { "cell_type": "markdown", - "id": "721c2d95", + "id": "0ee1be99", "metadata": {}, "source": [ "## Distribution of Bayesian Decision Rule’s Time to Decide\n", @@ -1217,7 +1217,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5871ec55", + "id": "da5fea93", "metadata": {}, "outputs": [], "source": [ @@ -1244,7 +1244,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bd63043b", + "id": "107d40b4", "metadata": {}, "outputs": [], "source": [ @@ -1259,7 +1259,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f5650b16", + "id": "9fa7b0ff", "metadata": {}, "outputs": [], "source": [ @@ -1281,7 +1281,7 @@ }, { "cell_type": "markdown", - "id": "822f208e", + "id": "235b5ce8", "metadata": {}, "source": [ "Later we’ll figure out how these distributions ultimately affect\n", @@ -1297,7 +1297,7 @@ { "cell_type": "code", "execution_count": null, - "id": "04046fc9", + "id": "d34d3399", "metadata": {}, "outputs": [], "source": [ @@ -1308,7 +1308,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cf4c8d9e", + "id": "b9587ddb", "metadata": {}, "outputs": [], "source": [ @@ -1333,7 +1333,7 @@ }, { "cell_type": "markdown", - "id": "ab252d41", + "id": "b37b8344", "metadata": {}, "source": [ "The above figures compare averages and variances of updated Bayesian\n", @@ -1362,7 +1362,7 @@ { "cell_type": "code", "execution_count": null, - "id": "385bef74", + "id": "2dd3695a", "metadata": {}, "outputs": [], "source": [ @@ -1381,7 +1381,7 @@ }, { "cell_type": "markdown", - "id": "f7ae337d", + "id": "0238952e", "metadata": {}, "source": [ "## Probability of Making Correct Decision\n", @@ -1402,7 +1402,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16817ab2", + "id": "93d64faf", "metadata": {}, "outputs": [], "source": [ @@ -1413,7 +1413,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6dee25e", + "id": "d63f29c0", "metadata": {}, "outputs": [], "source": [ @@ -1438,7 +1438,7 @@ }, { "cell_type": "markdown", - "id": "ff8a4559", + "id": "4c857777", "metadata": {}, "source": [ "By averaging using $\\pi^{*}$, we also plot the unconditional\n", @@ -1448,7 +1448,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4109ebfa", + "id": "a1e6da3c", "metadata": {}, "outputs": [], "source": [ @@ -1470,7 +1470,7 @@ }, { "cell_type": "markdown", - "id": "88a9cc8c", + "id": "67e33af3", "metadata": {}, "source": [ "## Distribution of Likelihood Ratios at Frequentist’s $t$\n", @@ -1492,7 +1492,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0570055c", + "id": "7d1525fc", "metadata": {}, "outputs": [], "source": [ @@ -1503,7 +1503,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b7794d0a", + "id": "37c3191b", "metadata": {}, "outputs": [], "source": [ @@ -1526,7 +1526,7 @@ }, { "cell_type": "markdown", - "id": "97c0cbb7", + "id": "d695df41", "metadata": {}, "source": [ "The next graph plots the unconditional distribution of Bayesian times to\n", @@ -1537,7 +1537,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2b97b581", + "id": "6ac66f42", "metadata": {}, "outputs": [], "source": [ diff --git a/_sources/ols.ipynb b/_sources/ols.ipynb index daf036f..3acd423 100644 --- a/_sources/ols.ipynb +++ b/_sources/ols.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "3a80930d", + "id": "acad2e94", "metadata": {}, "source": [ "```{raw} html\n", @@ -25,7 +25,7 @@ { "cell_type": "code", "execution_count": null, - "id": "727ac1fd", + "id": "bd11affb", "metadata": { "tags": [ "hide-output" @@ -38,7 +38,7 @@ }, { "cell_type": "markdown", - "id": "11632d55", + "id": "acd0c79b", "metadata": {}, "source": [ "## Overview\n", @@ -70,7 +70,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0bffeb64", + "id": "862ac86f", "metadata": {}, "outputs": [], "source": [ @@ -87,7 +87,7 @@ }, { "cell_type": "markdown", - "id": "54319b60", + "id": "39550010", "metadata": {}, "source": [ "### Prerequisites\n", @@ -116,7 +116,7 @@ { "cell_type": "code", "execution_count": null, - "id": "455e894a", + "id": "d3753bee", "metadata": {}, "outputs": [], "source": [ @@ -126,7 +126,7 @@ }, { "cell_type": "markdown", - "id": "69112a4b", + "id": "a5a4aeac", "metadata": {}, "source": [ "Let's use a scatterplot to see whether any obvious relationship exists\n", @@ -137,7 +137,7 @@ { "cell_type": "code", "execution_count": null, - "id": "489e50ba", + "id": "3c1b4f82", "metadata": {}, "outputs": [], "source": [ @@ -147,7 +147,7 @@ }, { "cell_type": "markdown", - "id": "63a71761", + "id": "1e85d255", "metadata": {}, "source": [ "The plot shows a fairly strong positive relationship between\n", @@ -183,7 +183,7 @@ { "cell_type": "code", "execution_count": null, - "id": "832621a9", + "id": "6451dc4d", "metadata": {}, "outputs": [], "source": [ @@ -220,7 +220,7 @@ }, { "cell_type": "markdown", - "id": "069633da", + "id": "6957b5b5", "metadata": {}, "source": [ "The most common technique to estimate the parameters ($\\beta$'s)\n", @@ -244,7 +244,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fc4cfe2f", + "id": "217a979f", "metadata": {}, "outputs": [], "source": [ @@ -253,7 +253,7 @@ }, { "cell_type": "markdown", - "id": "c22312e5", + "id": "48938bc0", "metadata": {}, "source": [ "Now we can construct our model in `statsmodels` using the OLS function.\n", @@ -264,7 +264,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b233e40e", + "id": "c598c8ac", "metadata": {}, "outputs": [], "source": [ @@ -275,7 +275,7 @@ }, { "cell_type": "markdown", - "id": "69b686f4", + "id": "d18cbed0", "metadata": {}, "source": [ "So far we have simply constructed our model.\n", @@ -287,7 +287,7 @@ { "cell_type": "code", "execution_count": null, - "id": "169ae17a", + "id": "b6ecb079", "metadata": {}, "outputs": [], "source": [ @@ -297,7 +297,7 @@ }, { "cell_type": "markdown", - "id": "7cd94744", + "id": "c2d762d8", "metadata": {}, "source": [ "We now have the fitted regression model stored in `results`.\n", @@ -313,7 +313,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2668191c", + "id": "9269050b", "metadata": {}, "outputs": [], "source": [ @@ -322,7 +322,7 @@ }, { "cell_type": "markdown", - "id": "4d23d53e", + "id": "10414ded", "metadata": {}, "source": [ "From our results, we see that\n", @@ -360,7 +360,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b25c54df", + "id": "11229046", "metadata": {}, "outputs": [], "source": [ @@ -371,7 +371,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d463c10c", + "id": "bf9e108c", "metadata": {}, "outputs": [], "source": [ @@ -381,7 +381,7 @@ }, { "cell_type": "markdown", - "id": "34df081a", + "id": "4ef3691b", "metadata": {}, "source": [ "An easier (and more accurate) way to obtain this result is to use\n", @@ -392,7 +392,7 @@ { "cell_type": "code", "execution_count": null, - "id": "157c6d2c", + "id": "2ca59fc0", "metadata": {}, "outputs": [], "source": [ @@ -401,7 +401,7 @@ }, { "cell_type": "markdown", - "id": "fbfd32f2", + "id": "df03319f", "metadata": {}, "source": [ "We can obtain an array of predicted ${logpgp95}_i$ for every value\n", @@ -418,7 +418,7 @@ { "cell_type": "code", "execution_count": null, - "id": "08a18c34", + "id": "bd22ff5a", "metadata": {}, "outputs": [], "source": [ @@ -446,7 +446,7 @@ }, { "cell_type": "markdown", - "id": "0a8d7f1d", + "id": "1df57dc4", "metadata": {}, "source": [ "## Extending the Linear Regression Model\n", @@ -474,7 +474,7 @@ { "cell_type": "code", "execution_count": null, - "id": "83ad6016", + "id": "e7a9cc3d", "metadata": {}, "outputs": [], "source": [ @@ -496,7 +496,7 @@ }, { "cell_type": "markdown", - "id": "0245b4f6", + "id": "48de12bd", "metadata": {}, "source": [ "Now that we have fitted our model, we will use `summary_col` to\n", @@ -507,7 +507,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7f91691e", + "id": "9fc253bb", "metadata": {}, "outputs": [], "source": [ @@ -534,7 +534,7 @@ }, { "cell_type": "markdown", - "id": "4ad0757c", + "id": "8db43d5b", "metadata": {}, "source": [ "## Endogeneity\n", @@ -584,7 +584,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ff3dc6ae", + "id": "28d7e3cf", "metadata": {}, "outputs": [], "source": [ @@ -618,7 +618,7 @@ }, { "cell_type": "markdown", - "id": "4c6abfe3", + "id": "eb3ac21b", "metadata": {}, "source": [ "The second condition may not be satisfied if settler mortality rates in the 17th to 19th centuries have a direct effect on current GDP (in addition to their indirect effect through institutions).\n", @@ -661,7 +661,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7128c8e8", + "id": "72183a11", "metadata": {}, "outputs": [], "source": [ @@ -681,7 +681,7 @@ }, { "cell_type": "markdown", - "id": "37c0ea05", + "id": "b54898cc", "metadata": {}, "source": [ "**Second stage**\n", @@ -702,7 +702,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d0d34c58", + "id": "a50b19cd", "metadata": {}, "outputs": [], "source": [ @@ -715,7 +715,7 @@ }, { "cell_type": "markdown", - "id": "0e2531a5", + "id": "135514dc", "metadata": {}, "source": [ "The second-stage regression results give us an unbiased and consistent\n", @@ -739,7 +739,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9639016e", + "id": "c5da7f8b", "metadata": {}, "outputs": [], "source": [ @@ -753,7 +753,7 @@ }, { "cell_type": "markdown", - "id": "d7a81949", + "id": "02d5b2f9", "metadata": {}, "source": [ "Given that we now have consistent and unbiased estimates, we can infer\n", @@ -825,7 +825,7 @@ { "cell_type": "code", "execution_count": null, - "id": "131f24d8", + "id": "7740e895", "metadata": {}, "outputs": [], "source": [ @@ -853,7 +853,7 @@ }, { "cell_type": "markdown", - "id": "a228c5fa", + "id": "c74608db", "metadata": {}, "source": [ "The output shows that the coefficient on the residuals is statistically\n", @@ -910,7 +910,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e6a7bae2", + "id": "d5407302", "metadata": {}, "outputs": [], "source": [ @@ -935,7 +935,7 @@ }, { "cell_type": "markdown", - "id": "c40167c1", + "id": "16889a87", "metadata": {}, "source": [ "It is also possible to use `np.linalg.inv(X.T @ X) @ X.T @ y` to solve\n", diff --git a/_sources/pandas_panel.ipynb b/_sources/pandas_panel.ipynb index ca15930..6b64e00 100644 --- a/_sources/pandas_panel.ipynb +++ b/_sources/pandas_panel.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "d355ca03", + "id": "d7b54d1d", "metadata": {}, "source": [ "(ppd)=\n", @@ -62,7 +62,7 @@ { "cell_type": "code", "execution_count": null, - "id": "06572cd7", + "id": "fd6fa711", "metadata": {}, "outputs": [], "source": [ @@ -72,7 +72,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ae29b51c", + "id": "b005edcd", "metadata": {}, "outputs": [], "source": [ @@ -89,7 +89,7 @@ }, { "cell_type": "markdown", - "id": "a665db67", + "id": "9e352dc6", "metadata": {}, "source": [ "Let's have a look at what we've got to work with" @@ -98,7 +98,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7cbb999a", + "id": "d0c744ea", "metadata": {}, "outputs": [], "source": [ @@ -107,7 +107,7 @@ }, { "cell_type": "markdown", - "id": "31bdd8aa", + "id": "7c0e64c8", "metadata": {}, "source": [ "The data is currently in long format, which is difficult to analyze when there are several dimensions to the data.\n", @@ -122,7 +122,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f6e6747c", + "id": "fcea5639", "metadata": {}, "outputs": [], "source": [ @@ -134,7 +134,7 @@ }, { "cell_type": "markdown", - "id": "56e40fcd", + "id": "e134c910", "metadata": {}, "source": [ "To more easily filter our time series data, later on, we will convert the index into a `DateTimeIndex`" @@ -143,7 +143,7 @@ { "cell_type": "code", "execution_count": null, - "id": "46b8a403", + "id": "8a8d1cba", "metadata": {}, "outputs": [], "source": [ @@ -153,7 +153,7 @@ }, { "cell_type": "markdown", - "id": "c9cc90af", + "id": "329f5bbc", "metadata": {}, "source": [ "The columns contain multiple levels of indexing, known as a\n", @@ -167,7 +167,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ac37306d", + "id": "725426e3", "metadata": {}, "outputs": [], "source": [ @@ -177,7 +177,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a6b86801", + "id": "48805517", "metadata": {}, "outputs": [], "source": [ @@ -186,7 +186,7 @@ }, { "cell_type": "markdown", - "id": "d9ba3659", + "id": "1cfb254f", "metadata": {}, "source": [ "Like before, we can select the country (the top level of our\n", @@ -196,7 +196,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7865ba64", + "id": "6c3791cd", "metadata": {}, "outputs": [], "source": [ @@ -205,7 +205,7 @@ }, { "cell_type": "markdown", - "id": "6e10558c", + "id": "bc87395b", "metadata": {}, "source": [ "Stacking and unstacking levels of the `MultiIndex` will be used\n", @@ -219,7 +219,7 @@ { "cell_type": "code", "execution_count": null, - "id": "82f8bcfa", + "id": "d31cee96", "metadata": {}, "outputs": [], "source": [ @@ -228,7 +228,7 @@ }, { "cell_type": "markdown", - "id": "c42618bd", + "id": "21bd36e6", "metadata": {}, "source": [ "We can also pass in an argument to select the level we would like to\n", @@ -238,7 +238,7 @@ { "cell_type": "code", "execution_count": null, - "id": "465bfcee", + "id": "7402ea0e", "metadata": {}, "outputs": [], "source": [ @@ -247,7 +247,7 @@ }, { "cell_type": "markdown", - "id": "80683414", + "id": "cf30a578", "metadata": {}, "source": [ "Using a `DatetimeIndex` makes it easy to select a particular time\n", @@ -260,7 +260,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6c29c509", + "id": "39cdad59", "metadata": {}, "outputs": [], "source": [ @@ -269,7 +269,7 @@ }, { "cell_type": "markdown", - "id": "ab94d0f4", + "id": "828524c3", "metadata": {}, "source": [ "For the rest of lecture, we will work with a dataframe of the hourly\n", @@ -284,7 +284,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3ad0300d", + "id": "25dfeb79", "metadata": {}, "outputs": [], "source": [ @@ -295,7 +295,7 @@ }, { "cell_type": "markdown", - "id": "076e8628", + "id": "88259a2e", "metadata": {}, "source": [ "## Merging Dataframes and Filling NaNs\n", @@ -314,7 +314,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a62185af", + "id": "777827d3", "metadata": {}, "outputs": [], "source": [ @@ -324,7 +324,7 @@ { "cell_type": "code", "execution_count": null, - "id": "23658482", + "id": "4609e637", "metadata": {}, "outputs": [], "source": [ @@ -334,7 +334,7 @@ }, { "cell_type": "markdown", - "id": "a4fbee3a", + "id": "5f92e6e9", "metadata": {}, "source": [ "First, we'll select just the country and continent variables from\n", @@ -344,7 +344,7 @@ { "cell_type": "code", "execution_count": null, - "id": "658f03ab", + "id": "f00651fc", "metadata": {}, "outputs": [], "source": [ @@ -355,7 +355,7 @@ }, { "cell_type": "markdown", - "id": "fe6be643", + "id": "0259d1f9", "metadata": {}, "source": [ "We want to merge our new dataframe, `worlddata`, with `realwage_f`.\n", @@ -371,7 +371,7 @@ { "cell_type": "code", "execution_count": null, - "id": "602046b3", + "id": "235c3964", "metadata": {}, "outputs": [], "source": [ @@ -380,7 +380,7 @@ }, { "cell_type": "markdown", - "id": "34a6ce29", + "id": "dc1631e3", "metadata": {}, "source": [ "We can use either left, right, inner, or outer join to merge our\n", @@ -417,7 +417,7 @@ { "cell_type": "code", "execution_count": null, - "id": "46aa363b", + "id": "acc1ad3c", "metadata": {}, "outputs": [], "source": [ @@ -428,7 +428,7 @@ }, { "cell_type": "markdown", - "id": "78c9999e", + "id": "63f9cd41", "metadata": {}, "source": [ "Countries that appeared in `realwage_f` but not in `worlddata` will\n", @@ -441,7 +441,7 @@ { "cell_type": "code", "execution_count": null, - "id": "90d4ccf4", + "id": "05bcecf5", "metadata": {}, "outputs": [], "source": [ @@ -450,7 +450,7 @@ }, { "cell_type": "markdown", - "id": "ff871cd1", + "id": "a121d30f", "metadata": {}, "source": [ "We have three missing values!\n", @@ -467,7 +467,7 @@ { "cell_type": "code", "execution_count": null, - "id": "815001f4", + "id": "2a0901d9", "metadata": {}, "outputs": [], "source": [ @@ -480,7 +480,7 @@ }, { "cell_type": "markdown", - "id": "44ad9bc0", + "id": "011ce2e5", "metadata": {}, "source": [ "We don't want to overwrite the entire series with this mapping.\n", @@ -492,7 +492,7 @@ { "cell_type": "code", "execution_count": null, - "id": "10294590", + "id": "f373c8e6", "metadata": {}, "outputs": [], "source": [ @@ -505,7 +505,7 @@ }, { "cell_type": "markdown", - "id": "06b73a56", + "id": "80f700d9", "metadata": {}, "source": [ "We will also combine the Americas into a single continent - this will make our visualization nicer later on.\n", @@ -516,7 +516,7 @@ { "cell_type": "code", "execution_count": null, - "id": "091bca8f", + "id": "053cbaf4", "metadata": {}, "outputs": [], "source": [ @@ -530,7 +530,7 @@ }, { "cell_type": "markdown", - "id": "064a7f22", + "id": "1732a9ce", "metadata": {}, "source": [ "Now that we have all the data we want in a single `DataFrame`, we will\n", @@ -545,7 +545,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d6455c6", + "id": "5c1523e4", "metadata": {}, "outputs": [], "source": [ @@ -555,7 +555,7 @@ }, { "cell_type": "markdown", - "id": "77954204", + "id": "033f343c", "metadata": {}, "source": [ "While merging, we lost our `DatetimeIndex`, as we merged columns that\n", @@ -565,7 +565,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b9c62450", + "id": "c4d230f5", "metadata": {}, "outputs": [], "source": [ @@ -574,7 +574,7 @@ }, { "cell_type": "markdown", - "id": "e50ea2bc", + "id": "a5272778", "metadata": {}, "source": [ "Now that we have set the merged columns as the index, we can recreate a\n", @@ -584,7 +584,7 @@ { "cell_type": "code", "execution_count": null, - "id": "446fd5ff", + "id": "8b6a8602", "metadata": {}, "outputs": [], "source": [ @@ -595,7 +595,7 @@ }, { "cell_type": "markdown", - "id": "89e6f39f", + "id": "c1c41b28", "metadata": {}, "source": [ "The `DatetimeIndex` tends to work more smoothly in the row axis, so we\n", @@ -605,7 +605,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d56eee0c", + "id": "865cfa83", "metadata": {}, "outputs": [], "source": [ @@ -615,7 +615,7 @@ }, { "cell_type": "markdown", - "id": "630036b2", + "id": "a87f2bc2", "metadata": {}, "source": [ "## Grouping and Summarizing Data\n", @@ -635,7 +635,7 @@ { "cell_type": "code", "execution_count": null, - "id": "bc3345c8", + "id": "f06ebd5d", "metadata": {}, "outputs": [], "source": [ @@ -644,7 +644,7 @@ }, { "cell_type": "markdown", - "id": "27f82548", + "id": "16d7dcd9", "metadata": {}, "source": [ "Using this series, we can plot the average real minimum wage over the\n", @@ -654,7 +654,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ad37d17a", + "id": "f07f5d6f", "metadata": {}, "outputs": [], "source": [ @@ -666,7 +666,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8b024aa0", + "id": "1d000d3b", "metadata": {}, "outputs": [], "source": [ @@ -683,7 +683,7 @@ }, { "cell_type": "markdown", - "id": "afbd91f7", + "id": "1942214c", "metadata": {}, "source": [ "Passing in `axis=1` to `.mean()` will aggregate over columns (giving\n", @@ -693,7 +693,7 @@ { "cell_type": "code", "execution_count": null, - "id": "714a579e", + "id": "34c2b1f7", "metadata": {}, "outputs": [], "source": [ @@ -702,7 +702,7 @@ }, { "cell_type": "markdown", - "id": "bd381316", + "id": "f99ce830", "metadata": {}, "source": [ "We can plot this time series as a line graph" @@ -711,7 +711,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3b31f210", + "id": "deeb3bc3", "metadata": {}, "outputs": [], "source": [ @@ -724,7 +724,7 @@ }, { "cell_type": "markdown", - "id": "3ba9d123", + "id": "722b99c3", "metadata": {}, "source": [ "We can also specify a level of the `MultiIndex` (in the column axis)\n", @@ -734,7 +734,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f877c64a", + "id": "ea960d3b", "metadata": {}, "outputs": [], "source": [ @@ -743,7 +743,7 @@ }, { "cell_type": "markdown", - "id": "a4609a34", + "id": "af93c94f", "metadata": {}, "source": [ "We can plot the average minimum wages in each continent as a time series" @@ -752,7 +752,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8d93b884", + "id": "694d9657", "metadata": {}, "outputs": [], "source": [ @@ -765,7 +765,7 @@ }, { "cell_type": "markdown", - "id": "67ef626c", + "id": "f87da32e", "metadata": {}, "source": [ "We will drop Australia as a continent for plotting purposes" @@ -774,7 +774,7 @@ { "cell_type": "code", "execution_count": null, - "id": "55809cc2", + "id": "19c73fdd", "metadata": {}, "outputs": [], "source": [ @@ -788,7 +788,7 @@ }, { "cell_type": "markdown", - "id": "b220061f", + "id": "9043ff87", "metadata": {}, "source": [ "`.describe()` is useful for quickly retrieving a number of common\n", @@ -798,7 +798,7 @@ { "cell_type": "code", "execution_count": null, - "id": "81537b55", + "id": "534e906f", "metadata": {}, "outputs": [], "source": [ @@ -807,7 +807,7 @@ }, { "cell_type": "markdown", - "id": "0fd318ec", + "id": "b02157c8", "metadata": {}, "source": [ "This is a simplified way to use `groupby`.\n", @@ -828,7 +828,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fe763e23", + "id": "e3c33d95", "metadata": {}, "outputs": [], "source": [ @@ -838,7 +838,7 @@ }, { "cell_type": "markdown", - "id": "fed8ab37", + "id": "80775022", "metadata": {}, "source": [ "Calling an aggregation method on the object applies the function to each\n", @@ -853,7 +853,7 @@ { "cell_type": "code", "execution_count": null, - "id": "da0276c3", + "id": "97d4be66", "metadata": {}, "outputs": [], "source": [ @@ -862,7 +862,7 @@ }, { "cell_type": "markdown", - "id": "bff6c453", + "id": "ecc33fa7", "metadata": {}, "source": [ "Calling `.get_group()` to return just the countries in a single group,\n", @@ -876,7 +876,7 @@ { "cell_type": "code", "execution_count": null, - "id": "96a88881", + "id": "0c2ece7d", "metadata": {}, "outputs": [], "source": [ @@ -893,7 +893,7 @@ }, { "cell_type": "markdown", - "id": "f80a7327", + "id": "b15052a3", "metadata": {}, "source": [ "## Final Remarks\n", @@ -920,7 +920,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b9b9d6f1", + "id": "d12c0bbd", "metadata": {}, "outputs": [], "source": [ @@ -929,7 +929,7 @@ }, { "cell_type": "markdown", - "id": "3784af2d", + "id": "71927295", "metadata": {}, "source": [ "Reading in the CSV file returns a panel dataset in long format. Use `.pivot_table()` to construct\n", @@ -951,7 +951,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b50c71ef", + "id": "5695b269", "metadata": {}, "outputs": [], "source": [ @@ -965,7 +965,7 @@ }, { "cell_type": "markdown", - "id": "0495266a", + "id": "0ef594c2", "metadata": {}, "source": [ "This is a large dataset so it is useful to explore the levels and\n", @@ -975,7 +975,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a722557a", + "id": "ff3a3efb", "metadata": {}, "outputs": [], "source": [ @@ -984,7 +984,7 @@ }, { "cell_type": "markdown", - "id": "ba4c602c", + "id": "99939cba", "metadata": {}, "source": [ "Variables within levels can be quickly retrieved with a loop" @@ -993,7 +993,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c21ae327", + "id": "79853eda", "metadata": {}, "outputs": [], "source": [ @@ -1003,7 +1003,7 @@ }, { "cell_type": "markdown", - "id": "2d8b8217", + "id": "be0a19c9", "metadata": {}, "source": [ "```{solution-end}\n", @@ -1039,7 +1039,7 @@ { "cell_type": "code", "execution_count": null, - "id": "807331e6", + "id": "d71e9d7a", "metadata": {}, "outputs": [], "source": [ @@ -1049,7 +1049,7 @@ }, { "cell_type": "markdown", - "id": "d312d96f", + "id": "b6ac29c1", "metadata": {}, "source": [ "We need to get rid of a few items in `GEO` which are not countries.\n", @@ -1061,7 +1061,7 @@ { "cell_type": "code", "execution_count": null, - "id": "68b25c1b", + "id": "0d25ce89", "metadata": {}, "outputs": [], "source": [ @@ -1073,7 +1073,7 @@ }, { "cell_type": "markdown", - "id": "eb753146", + "id": "eaac0b59", "metadata": {}, "source": [ "Select only percentage employed in the active population from the\n", @@ -1083,7 +1083,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fa3d31fb", + "id": "13aec29c", "metadata": {}, "outputs": [], "source": [ @@ -1095,7 +1095,7 @@ }, { "cell_type": "markdown", - "id": "5c7cb9b0", + "id": "b9bac149", "metadata": {}, "source": [ "Drop the 'Total' value before creating the grouped boxplot" @@ -1104,7 +1104,7 @@ { "cell_type": "code", "execution_count": null, - "id": "353aa237", + "id": "1b20825b", "metadata": {}, "outputs": [], "source": [ @@ -1114,7 +1114,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a5e8087c", + "id": "c98f429c", "metadata": {}, "outputs": [], "source": [ @@ -1130,7 +1130,7 @@ }, { "cell_type": "markdown", - "id": "e2bd5e7f", + "id": "85ad0ac3", "metadata": {}, "source": [ "```{solution-end}\n", diff --git a/_sources/prob_matrix.ipynb b/_sources/prob_matrix.ipynb index 6c8c5c0..2c21614 100644 --- a/_sources/prob_matrix.ipynb +++ b/_sources/prob_matrix.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "6d0826d3", + "id": "4cc17070", "metadata": {}, "source": [ "# Elementary Probability with Matrices\n", @@ -34,7 +34,7 @@ { "cell_type": "code", "execution_count": null, - "id": "07bf169f", + "id": "a880761a", "metadata": { "tags": [ "hide-output" @@ -47,7 +47,7 @@ }, { "cell_type": "markdown", - "id": "8ed3ab09", + "id": "c929a550", "metadata": {}, "source": [ "As usual, we'll start with some imports" @@ -56,7 +56,7 @@ { "cell_type": "code", "execution_count": null, - "id": "01b3dd6f", + "id": "18b92370", "metadata": {}, "outputs": [], "source": [ @@ -70,7 +70,7 @@ }, { "cell_type": "markdown", - "id": "65a8bc94", + "id": "c9df238f", "metadata": {}, "source": [ "## Sketch of Basic Concepts\n", @@ -579,7 +579,7 @@ { "cell_type": "code", "execution_count": null, - "id": "722ab0d7", + "id": "5cbf7918", "metadata": {}, "outputs": [], "source": [ @@ -602,7 +602,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9f258471", + "id": "bf480800", "metadata": {}, "outputs": [], "source": [ @@ -612,7 +612,7 @@ }, { "cell_type": "markdown", - "id": "534e8ae9", + "id": "efdd2610", "metadata": {}, "source": [ "**Geometric distribution**\n", @@ -673,7 +673,7 @@ { "cell_type": "code", "execution_count": null, - "id": "174a6d43", + "id": "323d5940", "metadata": {}, "outputs": [], "source": [ @@ -696,7 +696,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1b6a7f81", + "id": "a0ca1707", "metadata": {}, "outputs": [], "source": [ @@ -706,7 +706,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6d6e1e76", + "id": "8b976ca3", "metadata": {}, "outputs": [], "source": [ @@ -716,7 +716,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4c56272", + "id": "eb963943", "metadata": {}, "outputs": [], "source": [ @@ -726,7 +726,7 @@ }, { "cell_type": "markdown", - "id": "0a9d72fc", + "id": "53dd0414", "metadata": {}, "source": [ "## Some Discrete Probability Distributions\n", @@ -760,7 +760,7 @@ { "cell_type": "code", "execution_count": null, - "id": "064b0848", + "id": "f9a7c8b3", "metadata": {}, "outputs": [], "source": [ @@ -783,7 +783,7 @@ }, { "cell_type": "markdown", - "id": "d2a0bc81", + "id": "485d9ec3", "metadata": {}, "source": [ "### Newcomb–Benford distribution\n", @@ -822,7 +822,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ca87a87e", + "id": "1db451e2", "metadata": {}, "outputs": [], "source": [ @@ -844,7 +844,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2f1bcc43", + "id": "2c6e4d1d", "metadata": {}, "outputs": [], "source": [ @@ -856,7 +856,7 @@ }, { "cell_type": "markdown", - "id": "f70aafdf", + "id": "2d2d6008", "metadata": {}, "source": [ "### Pascal (negative binomial) distribution\n", @@ -892,7 +892,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4fb8e46", + "id": "2302b5c6", "metadata": {}, "outputs": [], "source": [ @@ -913,7 +913,7 @@ }, { "cell_type": "markdown", - "id": "6454c9c5", + "id": "50f2e8d6", "metadata": {}, "source": [ "## Continuous Random Variables\n", @@ -936,7 +936,7 @@ { "cell_type": "code", "execution_count": null, - "id": "49d84d20", + "id": "5209b758", "metadata": {}, "outputs": [], "source": [ @@ -960,7 +960,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3562003e", + "id": "07100241", "metadata": {}, "outputs": [], "source": [ @@ -971,7 +971,7 @@ }, { "cell_type": "markdown", - "id": "1b4f27a8", + "id": "3ad35d6f", "metadata": {}, "source": [ "### Uniform Distribution\n", @@ -996,7 +996,7 @@ { "cell_type": "code", "execution_count": null, - "id": "867b6609", + "id": "15ebac95", "metadata": {}, "outputs": [], "source": [ @@ -1020,7 +1020,7 @@ }, { "cell_type": "markdown", - "id": "d38246b2", + "id": "b5978b1e", "metadata": {}, "source": [ "## A Mixed Discrete-Continuous Distribution\n", @@ -1052,7 +1052,7 @@ { "cell_type": "code", "execution_count": null, - "id": "908acd74", + "id": "360fbc81", "metadata": {}, "outputs": [], "source": [ @@ -1069,7 +1069,7 @@ }, { "cell_type": "markdown", - "id": "cdf5af94", + "id": "f29c6b34", "metadata": {}, "source": [ "The analytical mean and variance can be computed:\n", @@ -1094,7 +1094,7 @@ { "cell_type": "code", "execution_count": null, - "id": "61aa8501", + "id": "40e940ff", "metadata": {}, "outputs": [], "source": [ @@ -1106,7 +1106,7 @@ }, { "cell_type": "markdown", - "id": "712adcc7", + "id": "317938cb", "metadata": {}, "source": [ "## Matrix Representation of Some Bivariate Distributions\n", @@ -1135,7 +1135,7 @@ { "cell_type": "code", "execution_count": null, - "id": "dd7fa7d6", + "id": "b4e68ec3", "metadata": {}, "outputs": [], "source": [ @@ -1163,7 +1163,7 @@ }, { "cell_type": "markdown", - "id": "eb0bdadf", + "id": "dc29c398", "metadata": {}, "source": [ "Here, we use exactly the inverse CDF technique to generate sample from the joint distribution $F$." @@ -1172,7 +1172,7 @@ { "cell_type": "code", "execution_count": null, - "id": "74463b26", + "id": "beb9bc6d", "metadata": {}, "outputs": [], "source": [ @@ -1199,7 +1199,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b48b21a8", + "id": "ade81452", "metadata": {}, "outputs": [], "source": [ @@ -1232,7 +1232,7 @@ }, { "cell_type": "markdown", - "id": "6c635ef6", + "id": "2944e9f8", "metadata": {}, "source": [ "Let's calculate population marginal and conditional probabilities using matrix algebra.\n", @@ -1292,7 +1292,7 @@ { "cell_type": "code", "execution_count": null, - "id": "388bc455", + "id": "a6676d1f", "metadata": {}, "outputs": [], "source": [ @@ -1410,7 +1410,7 @@ }, { "cell_type": "markdown", - "id": "c0be2fb7", + "id": "615aa249", "metadata": {}, "source": [ "Let's apply our code to some examples.\n", @@ -1421,7 +1421,7 @@ { "cell_type": "code", "execution_count": null, - "id": "867f4727", + "id": "d79b7730", "metadata": {}, "outputs": [], "source": [ @@ -1433,7 +1433,7 @@ { "cell_type": "code", "execution_count": null, - "id": "684ba33f", + "id": "669672d1", "metadata": {}, "outputs": [], "source": [ @@ -1445,7 +1445,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2fa1d887", + "id": "51f5c8be", "metadata": {}, "outputs": [], "source": [ @@ -1455,7 +1455,7 @@ }, { "cell_type": "markdown", - "id": "435a7a4a", + "id": "c19cb842", "metadata": {}, "source": [ "**Example 2**" @@ -1464,7 +1464,7 @@ { "cell_type": "code", "execution_count": null, - "id": "96ae125e", + "id": "3cb3f4de", "metadata": {}, "outputs": [], "source": [ @@ -1478,7 +1478,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c502a905", + "id": "e2f53e6c", "metadata": {}, "outputs": [], "source": [ @@ -1489,7 +1489,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a4718b21", + "id": "6f57b2f5", "metadata": {}, "outputs": [], "source": [ @@ -1498,7 +1498,7 @@ }, { "cell_type": "markdown", - "id": "54138871", + "id": "ff322622", "metadata": {}, "source": [ "## A Continuous Bivariate Random Vector\n", @@ -1531,7 +1531,7 @@ { "cell_type": "code", "execution_count": null, - "id": "d72e7e1b", + "id": "07347b1d", "metadata": {}, "outputs": [], "source": [ @@ -1548,7 +1548,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4b10a66f", + "id": "63f31e63", "metadata": {}, "outputs": [], "source": [ @@ -1562,7 +1562,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1dff6397", + "id": "3fdf7379", "metadata": {}, "outputs": [], "source": [ @@ -1573,7 +1573,7 @@ }, { "cell_type": "markdown", - "id": "d33f36d2", + "id": "806626dc", "metadata": {}, "source": [ "**Joint Distribution**\n", @@ -1584,7 +1584,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7c8a82c2", + "id": "714ca04e", "metadata": {}, "outputs": [], "source": [ @@ -1600,7 +1600,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6b946290", + "id": "117adb10", "metadata": {}, "outputs": [], "source": [ @@ -1618,7 +1618,7 @@ }, { "cell_type": "markdown", - "id": "ec96eb42", + "id": "77f21660", "metadata": {}, "source": [ "Next we can simulate from a built-in `numpy` function and calculate a **sample** marginal distribution from the sample mean and variance." @@ -1627,7 +1627,7 @@ { "cell_type": "code", "execution_count": null, - "id": "88d135e0", + "id": "f1d8ed79", "metadata": {}, "outputs": [], "source": [ @@ -1641,7 +1641,7 @@ }, { "cell_type": "markdown", - "id": "df19bbfe", + "id": "db02753f", "metadata": {}, "source": [ "**Marginal distribution**" @@ -1650,7 +1650,7 @@ { "cell_type": "code", "execution_count": null, - "id": "3d35ae99", + "id": "b95d828e", "metadata": {}, "outputs": [], "source": [ @@ -1665,7 +1665,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e0647226", + "id": "05641ec5", "metadata": {}, "outputs": [], "source": [ @@ -1679,7 +1679,7 @@ }, { "cell_type": "markdown", - "id": "e9c0eb5d", + "id": "5cc6a596", "metadata": {}, "source": [ "**Conditional distribution**\n", @@ -1707,7 +1707,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b2b52d58", + "id": "8b1d1125", "metadata": {}, "outputs": [], "source": [ @@ -1720,7 +1720,7 @@ }, { "cell_type": "markdown", - "id": "dda972ff", + "id": "a8b916b5", "metadata": {}, "source": [ "The mean and variance are computed by\n", @@ -1738,7 +1738,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c2314002", + "id": "b69ae7ef", "metadata": {}, "outputs": [], "source": [ @@ -1756,7 +1756,7 @@ }, { "cell_type": "markdown", - "id": "41601547", + "id": "0a40494a", "metadata": {}, "source": [ "Fix $x=1$." @@ -1765,7 +1765,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a0d5d4ec", + "id": "7127798a", "metadata": {}, "outputs": [], "source": [ @@ -1778,7 +1778,7 @@ { "cell_type": "code", "execution_count": null, - "id": "640e36d0", + "id": "246b8d59", "metadata": {}, "outputs": [], "source": [ @@ -1794,7 +1794,7 @@ }, { "cell_type": "markdown", - "id": "a67448eb", + "id": "8063515c", "metadata": {}, "source": [ "We compare with the analytically computed parameters and note that they are close." @@ -1803,7 +1803,7 @@ { "cell_type": "code", "execution_count": null, - "id": "01f5da8c", + "id": "b156e378", "metadata": {}, "outputs": [], "source": [ @@ -1816,7 +1816,7 @@ }, { "cell_type": "markdown", - "id": "72ccc37d", + "id": "e64fa3e4", "metadata": {}, "source": [ "## Sum of Two Independently Distributed Random Variables\n", @@ -2075,7 +2075,7 @@ { "cell_type": "code", "execution_count": null, - "id": "95ce945c", + "id": "4cd82866", "metadata": {}, "outputs": [], "source": [ @@ -2101,7 +2101,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cb33a992", + "id": "1b53676f", "metadata": {}, "outputs": [], "source": [ @@ -2127,7 +2127,7 @@ }, { "cell_type": "markdown", - "id": "4ffbce04", + "id": "a32b9923", "metadata": {}, "source": [ "Let's now take our two marginal distributions, one for $X$, the other for $Y$, and construct two distinct couplings.\n", @@ -2153,7 +2153,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6edb8aa7", + "id": "f0f109cd", "metadata": {}, "outputs": [], "source": [ @@ -2186,7 +2186,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fcbff450", + "id": "172f8720", "metadata": {}, "outputs": [], "source": [ @@ -2210,7 +2210,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6463a385", + "id": "72c852a9", "metadata": {}, "outputs": [], "source": [ @@ -2236,7 +2236,7 @@ }, { "cell_type": "markdown", - "id": "f0c1c610", + "id": "c4268fb2", "metadata": {}, "source": [ "Now, let's construct another joint distribution that is also a coupling of $X$ and $Y$\n", @@ -2252,7 +2252,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9b13477a", + "id": "4855ddb6", "metadata": {}, "outputs": [], "source": [ @@ -2285,7 +2285,7 @@ { "cell_type": "code", "execution_count": null, - "id": "9cf85b85", + "id": "bee7954e", "metadata": {}, "outputs": [], "source": [ @@ -2309,7 +2309,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e4b5ec74", + "id": "c4aa0f6b", "metadata": {}, "outputs": [], "source": [ @@ -2335,7 +2335,7 @@ }, { "cell_type": "markdown", - "id": "b5f9bf90", + "id": "c323b916", "metadata": {}, "source": [ "We have verified that both joint distributions, $c_1$ and $c_2$, have identical marginal distributions of $X$ and $Y$, respectively.\n", diff --git a/_sources/prob_meaning.ipynb b/_sources/prob_meaning.ipynb index 6c10450..cc1b696 100644 --- a/_sources/prob_meaning.ipynb +++ b/_sources/prob_meaning.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "0a52a36d", + "id": "3b5ec395", "metadata": {}, "source": [ "# Two Meanings of Probability\n", @@ -49,7 +49,7 @@ { "cell_type": "code", "execution_count": null, - "id": "085f13d5", + "id": "601284ab", "metadata": { "tags": [ "hide-output" @@ -62,7 +62,7 @@ }, { "cell_type": "markdown", - "id": "d4612ec2", + "id": "091efcf1", "metadata": {}, "source": [ "To answer our coding questions, we'll start with some imports" @@ -71,7 +71,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b21e2b2c", + "id": "e3d37086", "metadata": {}, "outputs": [], "source": [ @@ -85,7 +85,7 @@ }, { "cell_type": "markdown", - "id": "d9a07de9", + "id": "98504f43", "metadata": {}, "source": [ "Empowered with these Python tools, we'll now explore the two meanings described above.\n", @@ -162,7 +162,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7689e2f0", + "id": "7dc1e78c", "metadata": {}, "outputs": [], "source": [ @@ -227,7 +227,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4753e99d", + "id": "ab0881d3", "metadata": {}, "outputs": [], "source": [ @@ -240,7 +240,7 @@ }, { "cell_type": "markdown", - "id": "d1e565ba", + "id": "c25f3ad1", "metadata": {}, "source": [ "From the table above, can you see the law of large numbers at work?\n", @@ -264,7 +264,7 @@ { "cell_type": "code", "execution_count": null, - "id": "86c05241", + "id": "2258e88b", "metadata": {}, "outputs": [], "source": [ @@ -284,7 +284,7 @@ { "cell_type": "code", "execution_count": null, - "id": "68862fdf", + "id": "bd2f9341", "metadata": {}, "outputs": [], "source": [ @@ -302,7 +302,7 @@ }, { "cell_type": "markdown", - "id": "67b6bad2", + "id": "457d5c61", "metadata": {}, "source": [ "**Comparison with different $n$**\n", @@ -315,7 +315,7 @@ { "cell_type": "code", "execution_count": null, - "id": "abb36969", + "id": "acc0534b", "metadata": {}, "outputs": [], "source": [ @@ -335,7 +335,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2525714a", + "id": "b6adb60f", "metadata": {}, "outputs": [], "source": [ @@ -353,7 +353,7 @@ }, { "cell_type": "markdown", - "id": "6de23a53", + "id": "df95cb3d", "metadata": {}, "source": [ "**Comparison with different $I$**\n", @@ -364,7 +364,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fdf28e20", + "id": "bf6fc48a", "metadata": {}, "outputs": [], "source": [ @@ -385,7 +385,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a2a63c31", + "id": "9f60613e", "metadata": {}, "outputs": [], "source": [ @@ -403,7 +403,7 @@ }, { "cell_type": "markdown", - "id": "74a7b8b5", + "id": "bd9fa39d", "metadata": {}, "source": [ "From the above graphs, we can see that **$I$, the number of independent sequences,** plays an important role.\n", @@ -523,7 +523,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fd17027c", + "id": "610c12b6", "metadata": {}, "outputs": [], "source": [ @@ -590,7 +590,7 @@ }, { "cell_type": "markdown", - "id": "7689cf9f", + "id": "67aa7ae1", "metadata": {}, "source": [ "**d)** Please plot the posterior distribution for $\\theta$ as a function of $\\theta$ as $n$ grows from $1, 2, \\ldots$." @@ -599,7 +599,7 @@ { "cell_type": "code", "execution_count": null, - "id": "4f1a7061", + "id": "c31284f9", "metadata": {}, "outputs": [], "source": [ @@ -629,7 +629,7 @@ }, { "cell_type": "markdown", - "id": "dc961c25", + "id": "7c26ebe1", "metadata": {}, "source": [ "**e)** For various $n$'s, please describe and compute $.05$ and $.95$ quantiles for posterior probabilities." @@ -638,7 +638,7 @@ { "cell_type": "code", "execution_count": null, - "id": "029ae36e", + "id": "e1be8595", "metadata": {}, "outputs": [], "source": [ @@ -655,7 +655,7 @@ }, { "cell_type": "markdown", - "id": "23208af4", + "id": "eee7dcc4", "metadata": {}, "source": [ "As $n$ increases, we can see that Bayesian coverage intervals narrow and move toward $0.4$.\n", @@ -678,7 +678,7 @@ { "cell_type": "code", "execution_count": null, - "id": "17ebdb82", + "id": "c1618738", "metadata": {}, "outputs": [], "source": [ @@ -699,7 +699,7 @@ }, { "cell_type": "markdown", - "id": "d74bf3e0", + "id": "a9606188", "metadata": {}, "source": [ "Notice that in the graph above the posterior probabililty that $\\theta \\in [.45, .55]$ typically exhibits a hump shape as $n$ increases.\n", @@ -726,7 +726,7 @@ { "cell_type": "code", "execution_count": null, - "id": "750f601e", + "id": "6ee7bc69", "metadata": {}, "outputs": [], "source": [ @@ -747,7 +747,7 @@ }, { "cell_type": "markdown", - "id": "4641a3ba", + "id": "6759bb8a", "metadata": {}, "source": [ "As $n$ increases, we can see that the probability density functions _concentrate_ on $0.4$, the true value of $\\theta$.\n", @@ -760,7 +760,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cbdd6f00", + "id": "1478c344", "metadata": {}, "outputs": [], "source": [ @@ -786,7 +786,7 @@ }, { "cell_type": "markdown", - "id": "d3d63da1", + "id": "6175d81e", "metadata": {}, "source": [ "```{solution-end}\n", @@ -837,7 +837,7 @@ { "cell_type": "code", "execution_count": null, - "id": "df79f37f", + "id": "f571a3ac", "metadata": {}, "outputs": [], "source": [ @@ -859,7 +859,7 @@ }, { "cell_type": "markdown", - "id": "468cbfe2", + "id": "b68618f8", "metadata": {}, "source": [ "After observing a large number of outcomes, the posterior distribution collapses around $0.4$.\n", diff --git a/_sources/rand_resp.ipynb b/_sources/rand_resp.ipynb index bcc0d81..c7b3153 100644 --- a/_sources/rand_resp.ipynb +++ b/_sources/rand_resp.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "94c3448e", + "id": "14301ec7", "metadata": {}, "source": [ "# Randomized Response Surveys\n", @@ -39,7 +39,7 @@ { "cell_type": "code", "execution_count": null, - "id": "5e8c4fab", + "id": "7aea5379", "metadata": {}, "outputs": [], "source": [ @@ -49,7 +49,7 @@ }, { "cell_type": "markdown", - "id": "28ac7a8b", + "id": "dd578665", "metadata": {}, "source": [ "Suppose that every person in population either belongs to Group A or Group B. \n", @@ -206,7 +206,7 @@ { "cell_type": "code", "execution_count": null, - "id": "8001fd13", + "id": "54896fb2", "metadata": {}, "outputs": [], "source": [ @@ -265,7 +265,7 @@ }, { "cell_type": "markdown", - "id": "1400e86e", + "id": "de715ec0", "metadata": {}, "source": [ "Let's put the code to work for parameter values\n", @@ -281,7 +281,7 @@ { "cell_type": "code", "execution_count": null, - "id": "a31858e3", + "id": "4136457e", "metadata": {}, "outputs": [], "source": [ @@ -293,7 +293,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ddc4c39f", + "id": "2ecf818b", "metadata": {}, "outputs": [], "source": [ @@ -303,7 +303,7 @@ }, { "cell_type": "markdown", - "id": "bba67104", + "id": "0b500935", "metadata": {}, "source": [ "The theoretical calculations do a good job of predicting Monte Carlo results.\n", @@ -325,7 +325,7 @@ { "cell_type": "code", "execution_count": null, - "id": "12258200", + "id": "10c9e647", "metadata": {}, "outputs": [], "source": [ @@ -337,7 +337,7 @@ { "cell_type": "code", "execution_count": null, - "id": "942149a1", + "id": "8ddb3678", "metadata": {}, "outputs": [], "source": [ @@ -347,7 +347,7 @@ }, { "cell_type": "markdown", - "id": "4f8d1ca1", + "id": "b2840604", "metadata": {}, "source": [ "We can also revisit a calculation in the concluding section of Warner {cite}`warner1965randomized` in which \n", @@ -361,7 +361,7 @@ { "cell_type": "code", "execution_count": null, - "id": "7db353ea", + "id": "2a5006ce", "metadata": {}, "outputs": [], "source": [ @@ -373,7 +373,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1a7b1a8e", + "id": "2b46e7c4", "metadata": {}, "outputs": [], "source": [ @@ -383,7 +383,7 @@ }, { "cell_type": "markdown", - "id": "5ed4dc0c", + "id": "bc9c7bbd", "metadata": {}, "source": [ "Evidently, as $n$ increases, the randomized response method does better performance in more situations.\n", diff --git a/_sources/status.ipynb b/_sources/status.ipynb index c390dc8..1fa027e 100644 --- a/_sources/status.ipynb +++ b/_sources/status.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "f2f2329e", + "id": "ccd29ac3", "metadata": {}, "source": [ "# Execution Statistics\n", diff --git a/_sources/troubleshooting.ipynb b/_sources/troubleshooting.ipynb index ca0245b..149192b 100644 --- a/_sources/troubleshooting.ipynb +++ b/_sources/troubleshooting.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "17023089", + "id": "3e6422b0", "metadata": {}, "source": [ "(troubleshooting)=\n", diff --git a/_sources/util_rand_resp.ipynb b/_sources/util_rand_resp.ipynb index b26af1e..a29744e 100644 --- a/_sources/util_rand_resp.ipynb +++ b/_sources/util_rand_resp.ipynb @@ -3,7 +3,7 @@ { "cell_type": "code", "execution_count": null, - "id": "2c6f03b8", + "id": "917522f2", "metadata": {}, "outputs": [], "source": [ @@ -13,7 +13,7 @@ }, { "cell_type": "markdown", - "id": "b13416f9", + "id": "0eb8766f", "metadata": {}, "source": [ "# Expected Utilities of Random Responses\n", @@ -279,7 +279,7 @@ { "cell_type": "code", "execution_count": null, - "id": "37d9a79f", + "id": "d6dc0c93", "metadata": {}, "outputs": [], "source": [ @@ -312,7 +312,7 @@ }, { "cell_type": "markdown", - "id": "91aa9319", + "id": "868e5861", "metadata": {}, "source": [ "Figure 1.1 three types of truth border.\n", @@ -330,7 +330,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e9a9b197", + "id": "e4a53842", "metadata": {}, "outputs": [], "source": [ @@ -358,7 +358,7 @@ }, { "cell_type": "markdown", - "id": "173f1b5f", + "id": "4491cd25", "metadata": {}, "source": [ "## Utilitarian View of Survey Design\n", @@ -414,7 +414,7 @@ { "cell_type": "code", "execution_count": null, - "id": "1908e665", + "id": "d3810074", "metadata": {}, "outputs": [], "source": [ @@ -456,7 +456,7 @@ }, { "cell_type": "markdown", - "id": "f64d9b21", + "id": "a3353017", "metadata": {}, "source": [ "Properties of iso-variance curves are:\n", @@ -477,7 +477,7 @@ { "cell_type": "code", "execution_count": null, - "id": "cc6f9ef3", + "id": "71d67680", "metadata": {}, "outputs": [], "source": [ @@ -487,7 +487,7 @@ }, { "cell_type": "markdown", - "id": "b109866e", + "id": "5921cdb4", "metadata": {}, "source": [ "### Optimal Survey\n", @@ -542,7 +542,7 @@ { "cell_type": "code", "execution_count": null, - "id": "e69395f4", + "id": "20686c12", "metadata": {}, "outputs": [], "source": [ @@ -585,7 +585,7 @@ }, { "cell_type": "markdown", - "id": "dac4d8b6", + "id": "dcc89f0a", "metadata": {}, "source": [ "### Method of Leysieffer and Warner (1976)\n", @@ -637,7 +637,7 @@ { "cell_type": "code", "execution_count": null, - "id": "ce63db72", + "id": "7a93e709", "metadata": {}, "outputs": [], "source": [ @@ -651,7 +651,7 @@ { "cell_type": "code", "execution_count": null, - "id": "6dd5d05d", + "id": "fefd81ce", "metadata": {}, "outputs": [], "source": [ @@ -693,7 +693,7 @@ }, { "cell_type": "markdown", - "id": "04138928", + "id": "325d96c1", "metadata": {}, "source": [ "### Method of Greenberg et al. (1977)\n", diff --git a/_sources/wald_friedman.ipynb b/_sources/wald_friedman.ipynb index ff517e4..4761f11 100644 --- a/_sources/wald_friedman.ipynb +++ b/_sources/wald_friedman.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "7c0d04df", + "id": "72aaf421", "metadata": {}, "source": [ "(wald_friedman)=\n", @@ -31,7 +31,7 @@ { "cell_type": "code", "execution_count": null, - "id": "08d715e9", + "id": "2bc152b0", "metadata": { "tags": [ "hide-output" @@ -44,7 +44,7 @@ }, { "cell_type": "markdown", - "id": "09d9b77b", + "id": "d8151bf4", "metadata": {}, "source": [ "## Overview\n", @@ -76,7 +76,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f75e03b8", + "id": "c272cca1", "metadata": {}, "outputs": [], "source": [ @@ -90,7 +90,7 @@ }, { "cell_type": "markdown", - "id": "df9cff92", + "id": "90fc8687", "metadata": {}, "source": [ "This lecture uses ideas studied in {doc}`this lecture `, {doc}`this lecture `.\n", @@ -103,6 +103,11 @@ "during World War II, when they worked at the US Government's\n", "Statistical Research Group at Columbia University.\n", "\n", + "```{note}\n", + "See pages 25 and 26 of Allen Wallis's 1980 article {cite}`wallis1980statistical` about the Statistical Research Group at Columbia University during World War II for his account of the episode and for important contributions that Harold Hotelling made to formulating the problem. Also see chapter 5 of Jennifer Burns book about\n", + "Milton Friedman {cite}`Burns_2023`.\n", + "```\n", + "\n", "Let's listen to Milton Friedman tell us what happened\n", "\n", "> In order to understand the story, it is necessary to have an idea of a\n", @@ -213,7 +218,7 @@ { "cell_type": "code", "execution_count": null, - "id": "db2df142", + "id": "30c11bc6", "metadata": {}, "outputs": [], "source": [ @@ -247,7 +252,7 @@ }, { "cell_type": "markdown", - "id": "3caa5eda", + "id": "0d642308", "metadata": {}, "source": [ "### Losses and Costs\n", @@ -432,7 +437,7 @@ { "cell_type": "code", "execution_count": null, - "id": "c3526d62", + "id": "84e4495d", "metadata": {}, "outputs": [], "source": [ @@ -453,7 +458,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f22aa0ef", + "id": "31622b5a", "metadata": {}, "outputs": [], "source": [ @@ -510,7 +515,7 @@ }, { "cell_type": "markdown", - "id": "6a3a8721", + "id": "76ebd371", "metadata": {}, "source": [ "As in the {doc}`optimal growth lecture `, to approximate a continuous value function\n", @@ -524,7 +529,7 @@ { "cell_type": "code", "execution_count": null, - "id": "f665cb6f", + "id": "390abcf0", "metadata": {}, "outputs": [], "source": [ @@ -562,7 +567,7 @@ }, { "cell_type": "markdown", - "id": "bbf38eb8", + "id": "68e2d88f", "metadata": {}, "source": [ "To solve the key functional equation, we will iterate using `Q` to find the fixed point" @@ -571,7 +576,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b4b513c7", + "id": "c44c0e8d", "metadata": {}, "outputs": [], "source": [ @@ -602,7 +607,7 @@ }, { "cell_type": "markdown", - "id": "796f5a53", + "id": "0c8dcec1", "metadata": {}, "source": [ "## Analysis\n", @@ -615,7 +620,7 @@ { "cell_type": "code", "execution_count": null, - "id": "b75f8e62", + "id": "c1dd16aa", "metadata": {}, "outputs": [], "source": [ @@ -632,7 +637,7 @@ }, { "cell_type": "markdown", - "id": "f9fb6376", + "id": "1165f227", "metadata": {}, "source": [ "### Value Function\n", @@ -643,7 +648,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0c6b9971", + "id": "9123dafb", "metadata": {}, "outputs": [], "source": [ @@ -652,7 +657,7 @@ }, { "cell_type": "markdown", - "id": "6e1fba0c", + "id": "589ea7b3", "metadata": {}, "source": [ "We will also set up a function to compute the cutoffs $\\alpha$ and $\\beta$\n", @@ -662,7 +667,7 @@ { "cell_type": "code", "execution_count": null, - "id": "16238e1d", + "id": "81287d71", "metadata": {}, "outputs": [], "source": [ @@ -723,7 +728,7 @@ }, { "cell_type": "markdown", - "id": "e100cb50", + "id": "917aaa8c", "metadata": {}, "source": [ "The cost function $J$ equals $\\pi L_1$ for $\\pi \\leq \\beta$, and $(1-\\pi )L_0$ for $\\pi\n", @@ -754,7 +759,7 @@ { "cell_type": "code", "execution_count": null, - "id": "fbf585a4", + "id": "e768a922", "metadata": {}, "outputs": [], "source": [ @@ -852,7 +857,7 @@ }, { "cell_type": "markdown", - "id": "18e4e660", + "id": "f6bc2946", "metadata": {}, "source": [ "### Comparative Statics\n", @@ -870,7 +875,7 @@ { "cell_type": "code", "execution_count": null, - "id": "0e8dd71c", + "id": "22f3a2c0", "metadata": {}, "outputs": [], "source": [ @@ -880,7 +885,7 @@ }, { "cell_type": "markdown", - "id": "9e3332ce", + "id": "e7707a44", "metadata": {}, "source": [ "Increased cost per draw has induced the decision-maker to take fewer draws before deciding.\n", @@ -1101,25 +1106,25 @@ 40, 67, 74, - 192, - 219, - 399, - 414, - 464, - 473, - 504, - 508, - 532, - 540, - 550, - 556, - 558, + 197, + 224, + 404, + 419, + 469, + 478, + 509, + 513, + 537, + 545, + 555, + 561, 563, - 617, - 643, - 734, - 747, - 750 + 568, + 622, + 648, + 739, + 752, + 755 ] }, "nbformat": 4, diff --git a/_sources/wald_friedman.md b/_sources/wald_friedman.md index 31517b4..f5c4f85 100644 --- a/_sources/wald_friedman.md +++ b/_sources/wald_friedman.md @@ -83,6 +83,11 @@ Milton Friedman described a problem presented to him and Allen Wallis during World War II, when they worked at the US Government's Statistical Research Group at Columbia University. +```{note} +See pages 25 and 26 of Allen Wallis's 1980 article {cite}`wallis1980statistical` about the Statistical Research Group at Columbia University during World War II for his account of the episode and for important contributions that Harold Hotelling made to formulating the problem. Also see chapter 5 of Jennifer Burns book about +Milton Friedman {cite}`Burns_2023`. +``` + Let's listen to Milton Friedman tell us what happened > In order to understand the story, it is necessary to have an idea of a diff --git a/_sources/zreferences.ipynb b/_sources/zreferences.ipynb index 113c364..0102ffb 100644 --- a/_sources/zreferences.ipynb +++ b/_sources/zreferences.ipynb @@ -2,7 +2,7 @@ "cells": [ { "cell_type": "markdown", - "id": "ff72bcf2", + "id": "6b4e7595", "metadata": {}, "source": [ "(references)=\n", diff --git a/_static/quant-econ.bib b/_static/quant-econ.bib index 1c32e7f..fa2b46a 100644 --- a/_static/quant-econ.bib +++ b/_static/quant-econ.bib @@ -2369,6 +2369,25 @@ @article{Jacobson_73 pages = "124-131" } +@article{wallis1980statistical, + author = "Wallis, W Allen", + title = "The statistical research group, 1942--1945", + journal = "Journal of the American Statistical Association", + volume = "75", + number = "370", + pages = "320--330", + year = "1980", + publisher = "Taylor \\& Francis" +} + +@book{Burns_2023, + author = "Burns, Jennifer", + title = "Milton Friedman: The Last Conservative by Jennifer Burns", + year = "2023", + publisher = "Farrar, Straus, and Giroux", + address = "New York" +} + @article{Orcutt_Winokur_69, author = "Orcutt, Guy H. and Winokur, Herbert S.", issn = "00129682, 14680262", diff --git a/ar1_bayes.html b/ar1_bayes.html index a91481e..3020531 100644 --- a/ar1_bayes.html +++ b/ar1_bayes.html @@ -243,20 +243,20 @@

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   Stored in directory: /github/home/.cache/pip/wheels/95/8f/45/fe0a5b5e232401da571d514eb545833fbe220993ac8336c94e
 

 

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9. Posterior Distributions for  AR(1) Pa
 

 

 
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9. Posterior Distributions for  AR(1) Pa
 

 

 
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9. Posterior Distributions for  AR(1) Pa
 

 

 
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+?25h  Created wheel for miniKanren: filename=miniKanren-1.0.3-py3-none-any.whl size=23910 sha256=05600c8294b2b1a3e6dd5e9db5bb4a33b1363135664eefcadb441600d5040321
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Successfully built cons logical-unification etuples miniKanren
 

 

 
Installing collected packages: fastprogress, cachetools, logical-unification, numpyro, cons, etuples, miniKanren, pytensor, pymc
@@ -623,12 +623,12 @@ 
9.1. PyMC Implementation
-_images/ed7e93ad31cef42467c2222a55ebb72c10495b392826b90950aaf99e3109332d.png
+_images/dffc9b951c10799013b93dd468464bdfe4fbca76cd94d44cd9700f33c376935a.png
 

 

 
Evidently, the posteriors aren’t centered on the true values of \(.5, 1\) that we used to generate the data.

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This is a symptom of the classic Hurwicz bias for first order autoregressive processes (see Leonid Hurwicz [Hur50].)

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The Hurwicz bias is worse the smaller is the sample (see [OW69]).

+
This is a symptom of the classic Hurwicz bias for first order autoregressive processes (see Leonid Hurwicz [Hur50].)

+
The Hurwicz bias is worse the smaller is the sample (see [OW69]).

 
Be that as it may, here is more information about the posterior.

 

 

@@ -673,25 +673,25 @@ 
9.1. PyMC Implementation9.1. PyMC Implementation
     

       
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@@ -767,7 +767,7 @@ 
9.1. PyMC Implementation
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9.1. PyMC Implementation10. Forecasting  an AR(1) Process
 
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10. Forecasting  an AR(1) Process

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10. Forecasting  an AR(1) Process
sample path properties that are defined as non-linear functions of future values \(\{y_{t+j}\}_{j \geq 1}\) at time \(t\)

 
 
Sample path properties are things like “time to next turning point” or “time to next recession”.

-
To investigate sample path properties we’ll use a simulation procedure recommended by Wecker [Wec79].

+
To investigate sample path properties we’ll use a simulation procedure recommended by Wecker [Wec79].

 
To acknowledge uncertainty about parameters, we’ll deploy pymc to construct a Bayesian joint posterior distribution for unknown parameters.

 
Let’s start with some imports.

 

@@ -366,7 +366,7 @@ 
10.1. A Univariate First-Order Autoregre
 
  • “severe recession”, and
    • 
 
  • the time until the next turning point (positive or negative).
    • 
 
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    To accomplish that for situations in which we are uncertain about parameter values, we shall extend Wecker’s [Wec79] approach in the following way.
    
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    To accomplish that for situations in which we are uncertain about parameter values, we shall extend Wecker’s [Wec79] approach in the following way.
    
 
      
 
    • first simulate an initial path of length \(T_0\);
      • 
 
    • for a given prior, draw a sample of size \(N\) from the posterior joint distribution of parameters \(\left(\rho,\sigma\right)\) after observing the initial path;
      • 
@@ -451,7 +451,7 @@ 
      10.2. Implementation
 
      10.3. Predictive Distributions of Path Properties#
      
-
      Wecker [Wec79] proposed using simulation techniques to characterize  predictive distribution of some statistics that are  non-linear functions of \(y\).
      
+
      Wecker [Wec79] proposed using simulation techniques to characterize  predictive distribution of some statistics that are  non-linear functions of \(y\).
      
 
      He called these functions “path properties” to contrast them with properties of single data points.
      
 
      He studied two special  prospective path properties of a given series \(\{y_t\}\).
      
 
      The first was time until the next turning point.
      
@@ -479,7 +479,7 @@ 
      10.3. Predictive Distributions of Path P
 \[
 W_t(\omega):= \inf \{ k\geq 1 \mid Z_{t+k}(\omega) = 1\}
 \]
    
-
    Wecker  [Wec79] also studied the minimum value of \(Y\) over the next 8 quarters
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    Wecker  [Wec79] also studied the minimum value of \(Y\) over the next 8 quarters
 which can be defined as the random variable.
    
 
    
 \[ 
@@ -525,7 +525,7 @@ 
    10.3. Predictive Distributions of Path P
 
      
 
    • ``after one or two decrease(s), \(Y\) will grow for two consecutive quarters’’
      • 
 
    
-
    Following [Wec79], we can use simulations to calculate  probabilities of \(P_t\) and \(N_t\) for each period \(t\).
    
+
    Following [Wec79], we can use simulations to calculate  probabilities of \(P_t\) and \(N_t\) for each period \(t\).
    
 
 
    
 
    10.4. A Wecker-Like Algorithm#
    
@@ -609,9 +609,9 @@ 
    10.5. Using Simulations to Approximate a
 
    
     
    
       
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    _images/31e035fc186caebe56272ace4f382ac75abc250ca2b0bddec0637a2defb4a777.png
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    _images/e2a1637b9d7209531689690c35003275f453d4b677cd92b345b5fac733784eb9.png
 
    
 
    
 
    The graphs on the left portray posterior marginal distributions.
    
@@ -812,7 +812,7 @@ 
    10.8. Extended Wecker Method
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    @@ -831,7 +831,7 @@

    10.9. Comparison

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    20. Introduction to Artificial Neural Ne
 
 
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    20. Introduction to Artificial Neural Ne
 
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    20.6. Example 1
 
    
 
    
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    8. Non-Conjugate Priors
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         ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 144.3/410.6 MB 137.3 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 149.2/410.6 MB 137.2 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━ 154.0/410.6 MB 137.2 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 158.7/410.6 MB 136.0 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━ 163.6/410.6 MB 136.0 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 168.4/410.6 MB 137.0 MB/s eta 0:00:02
 
    
 
    
-
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 173.2/410.6 MB 136.7 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 178.1/410.6 MB 137.5 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 182.8/410.6 MB 136.8 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━ 187.6/410.6 MB 135.6 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 192.4/410.6 MB 135.5 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━ 197.1/410.6 MB 135.5 MB/s eta 0:00:02
 
    
 
    
-
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 201.9/410.6 MB 135.0 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 206.6/410.6 MB 134.8 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 211.4/410.6 MB 135.5 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 216.1/410.6 MB 135.3 MB/s eta 0:00:02
 
    
 
    
-
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━ 220.9/410.6 MB 134.9 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 225.6/410.6 MB 134.5 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━ 230.4/410.6 MB 135.1 MB/s eta 0:00:02
 
    
 
    
-
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 235.1/410.6 MB 135.2 MB/s eta 0:00:02
 
    
 
    
-
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 240.0/410.6 MB 136.9 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 244.7/410.6 MB 136.8 MB/s eta 0:00:02
 
    
 
    
-
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 249.5/410.6 MB 135.2 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 254.2/410.6 MB 135.3 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 259.0/410.6 MB 135.9 MB/s eta 0:00:02
 
    
 
    
-
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 263.9/410.6 MB 136.8 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 268.7/410.6 MB 136.5 MB/s eta 0:00:02
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 273.4/410.6 MB 136.2 MB/s eta 0:00:02
+     ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 278.2/410.6 MB 136.8 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 283.0/410.6 MB 136.3 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 287.6/410.6 MB 133.9 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 292.5/410.6 MB 134.8 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 297.1/410.6 MB 134.5 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
+
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 306.6/410.6 MB 135.4 MB/s eta 0:00:01
 
    
 
    
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+
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 325.7/410.6 MB 135.4 MB/s eta 0:00:01
 
    
 
    
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 340.1/410.6 MB 137.8 MB/s eta 0:00:01
 
    
 
    
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 354.5/410.6 MB 136.0 MB/s eta 0:00:01
 
    
 
    
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 368.7/410.6 MB 133.5 MB/s eta 0:00:01
 
    
 
    
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 387.6/410.6 MB 134.6 MB/s eta 0:00:01
 
    
 
    
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 401.7/410.6 MB 134.3 MB/s eta 0:00:01
 
    
 
    
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 410.6/410.6 MB 139.5 MB/s eta 0:00:01
 
    
 
    
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-     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 133.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 410.6/410.6 MB 139.5 MB/s eta 0:00:01
 
    
 
    
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 410.6/410.6 MB 139.5 MB/s eta 0:00:01
 
    
 
    
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 410.6/410.6 MB 139.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 424.7/670.2 MB 125.2 MB/s eta 0:00:02
+
         ━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 24.4/121.6 MB 139.5 MB/s eta 0:00:01
+     ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 29.3/121.6 MB 140.1 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 429.0/670.2 MB 123.2 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 433.4/670.2 MB 124.4 MB/s eta 0:00:02
+
         ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 34.3/121.6 MB 139.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 437.8/670.2 MB 126.0 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━ 39.2/121.6 MB 140.2 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 44.1/121.6 MB 139.3 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 442.1/670.2 MB 124.6 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 446.5/670.2 MB 124.9 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 49.1/121.6 MB 140.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 451.0/670.2 MB 127.1 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 53.9/121.6 MB 139.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 58.8/121.6 MB 137.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 455.3/670.2 MB 125.4 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 459.6/670.2 MB 124.4 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 63.7/121.6 MB 139.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 464.0/670.2 MB 123.5 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 68.6/121.6 MB 139.8 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 468.3/670.2 MB 123.5 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 73.7/121.6 MB 141.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 78.6/121.6 MB 140.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 472.8/670.2 MB 126.2 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 477.3/670.2 MB 126.9 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 83.5/121.6 MB 138.3 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 481.7/670.2 MB 128.1 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 88.4/121.6 MB 139.1 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 93.4/121.6 MB 140.9 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 486.1/670.2 MB 126.9 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 490.4/670.2 MB 125.2 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 98.4/121.6 MB 142.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 494.9/670.2 MB 125.8 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 103.3/121.6 MB 140.8 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 108.3/121.6 MB 140.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 499.3/670.2 MB 127.4 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 503.7/670.2 MB 127.9 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 113.2/121.6 MB 140.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 508.2/670.2 MB 126.5 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 118.1/121.6 MB 139.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 512.6/670.2 MB 126.8 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 517.0/670.2 MB 126.9 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 521.4/670.2 MB 125.4 MB/s eta 0:00:02
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 525.8/670.2 MB 125.4 MB/s eta 0:00:02
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 530.1/670.2 MB 124.9 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 534.4/670.2 MB 123.7 MB/s eta 0:00:02
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 547.4/670.2 MB 125.0 MB/s eta 0:00:01
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 560.3/670.2 MB 124.5 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 121.6/121.6 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 573.5/670.2 MB 127.0 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 121.6/121.6 MB 16.9 MB/s eta 0:00:00
+?25h
 
    
 
    
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    Collecting nvidia-curand-cu12==10.3.2.106 (from torch)
 
    
 
    
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      Downloading nvidia_curand_cu12-10.3.2.106-py3-none-manylinux1_x86_64.whl (56.5 MB)
+?25l     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0/56.5 MB ? eta -:--:--
+     ━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 4.9/56.5 MB 147.0 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 9.8/56.5 MB 143.9 MB/s eta 0:00:01
 
    
 
    
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+
         ━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 14.8/56.5 MB 140.7 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 19.7/56.5 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 599.6/670.2 MB 124.1 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 603.9/670.2 MB 124.7 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 24.7/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 608.2/670.2 MB 123.8 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 29.6/56.5 MB 139.7 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 34.4/56.5 MB 138.2 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 612.6/670.2 MB 125.2 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 617.0/670.2 MB 125.6 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 39.4/56.5 MB 140.2 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 621.5/670.2 MB 126.3 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 44.4/56.5 MB 141.2 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 625.9/670.2 MB 126.5 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 630.3/670.2 MB 128.6 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 634.7/670.2 MB 127.1 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 639.0/670.2 MB 124.7 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 643.2/670.2 MB 123.8 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 647.6/670.2 MB 124.7 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 652.0/670.2 MB 125.5 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 656.3/670.2 MB 124.0 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 660.6/670.2 MB 122.7 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 664.9/670.2 MB 123.2 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 669.5/670.2 MB 127.0 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 47.2/56.5 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 51.8/56.5 MB 17.6 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 56.5/56.5 MB 17.6 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 56.5/56.5 MB 17.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 56.5/56.5 MB 17.6 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 56.5/56.5 MB 12.0 MB/s eta 0:00:00
+?25h
 
    
 
    
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+
    Collecting nvidia-cusolver-cu12==11.4.5.107 (from torch)
+  Downloading nvidia_cusolver_cu12-11.4.5.107-py3-none-manylinux1_x86_64.whl (124.2 MB)
+?25l     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0/124.2 MB ? eta -:--:--
 
    
 
    
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         ━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 24.5/124.2 MB 138.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 29.4/124.2 MB 139.8 MB/s eta 0:00:01
+     ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 34.3/124.2 MB 140.3 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━ 39.3/124.2 MB 140.5 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 44.3/124.2 MB 141.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 49.2/124.2 MB 141.2 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 54.2/124.2 MB 141.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 59.2/124.2 MB 142.7 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 64.1/124.2 MB 141.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 69.0/124.2 MB 139.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 73.9/124.2 MB 138.9 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 78.9/124.2 MB 140.0 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 83.8/124.2 MB 140.1 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 88.8/124.2 MB 140.3 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 93.8/124.2 MB 141.6 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 98.7/124.2 MB 140.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 103.6/124.2 MB 139.1 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━ 108.5/124.2 MB 139.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 113.4/124.2 MB 140.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 118.4/124.2 MB 141.1 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 123.4/124.2 MB 141.9 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 124.2/124.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 124.2/124.2 MB 15.9 MB/s eta 0:00:00
+?25h
 
    
 
    
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    Collecting nvidia-cusparse-cu12==12.1.0.106 (from torch)
+  Downloading nvidia_cusparse_cu12-12.1.0.106-py3-none-manylinux1_x86_64.whl (196.0 MB)
+?25l     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0/196.0 MB ? eta -:--:--
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 7.1/196.0 MB 104.4 MB/s eta 0:00:02
+     ━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 12.1/196.0 MB 138.6 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 17.0/196.0 MB 139.4 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 21.9/196.0 MB 139.6 MB/s eta 0:00:02
+     ━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 26.8/196.0 MB 140.7 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 31.8/196.0 MB 141.5 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 36.9/196.0 MB 143.0 MB/s eta 0:00:02
+     ━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 41.9/196.0 MB 142.5 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 46.8/196.0 MB 140.6 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━ 51.8/196.0 MB 141.8 MB/s eta 0:00:02
+     ━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━ 56.8/196.0 MB 142.3 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 61.9/196.0 MB 142.4 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 66.8/196.0 MB 142.4 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 71.7/196.0 MB 139.5 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━ 76.6/196.0 MB 139.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━ 80.0/196.0 MB 121.4 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 84.9/196.0 MB 122.6 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 89.9/196.0 MB 140.3 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 94.7/196.0 MB 139.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 99.7/196.0 MB 140.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━ 104.7/196.0 MB 141.4 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━ 109.8/196.0 MB 116.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 114.9/196.0 MB 116.3 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 119.9/196.0 MB 142.7 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 124.9/196.0 MB 142.2 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 129.9/196.0 MB 141.3 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 134.9/196.0 MB 142.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 139.9/196.0 MB 141.2 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 144.8/196.0 MB 140.7 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 149.8/196.0 MB 141.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 154.8/196.0 MB 142.9 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━ 159.7/196.0 MB 140.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 164.7/196.0 MB 140.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━ 169.6/196.0 MB 140.8 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 174.7/196.0 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 179.5/196.0 MB 140.8 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 184.6/196.0 MB 140.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 189.6/196.0 MB 143.0 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 194.7/196.0 MB 142.1 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 196.0/196.0 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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    Collecting nvidia-nccl-cu12==2.18.1 (from torch)
+  Downloading nvidia_nccl_cu12-2.18.1-py3-none-manylinux1_x86_64.whl (209.8 MB)
+?25l     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 0.0/209.8 MB ? eta -:--:--
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 59.4/209.8 MB 140.6 MB/s eta 0:00:02
+     ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 64.5/209.8 MB 141.1 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 69.4/209.8 MB 141.1 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━ 74.4/209.8 MB 142.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 79.4/209.8 MB 142.8 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 84.4/209.8 MB 141.8 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 89.5/209.8 MB 142.4 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 94.4/209.8 MB 142.1 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 99.4/209.8 MB 141.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 104.5/209.8 MB 143.2 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 109.6/209.8 MB 143.1 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 114.5/209.8 MB 141.8 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 119.4/209.8 MB 140.9 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 124.6/209.8 MB 142.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 129.6/209.8 MB 144.3 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 134.7/209.8 MB 143.1 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 139.7/209.8 MB 142.1 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 144.6/209.8 MB 141.6 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 149.6/209.8 MB 140.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 154.5/209.8 MB 139.7 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 159.4/209.8 MB 140.2 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 164.4/209.8 MB 141.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 169.3/209.8 MB 140.1 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 174.4/209.8 MB 140.5 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 179.3/209.8 MB 141.5 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 184.3/209.8 MB 141.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 189.3/209.8 MB 141.4 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 194.4/209.8 MB 142.5 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 199.5/209.8 MB 143.9 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 204.5/209.8 MB 143.8 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.7/209.8 MB 145.1 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 145.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 145.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 145.5 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 145.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 145.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
         ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 145.5 MB/s eta 0:00:01
+     ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 209.8/209.8 MB 145.5 MB/s eta 0:00:01
 
    
 
    
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+  Downloading nvidia_nvtx_cu12-12.1.105-py3-none-manylinux1_x86_64.whl (99 kB)
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+  Obtaining dependency information for triton==2.1.0 from https://files.pythonhosted.org/packages/5c/c1/54fffb2eb13d293d9a429fead3646752ea190de0229bcf3d591ba2481263/triton-2.1.0-0-cp311-cp311-manylinux2014_x86_64.manylinux_2_17_x86_64.whl.metadata
 
    
 
    
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+Requirement already satisfied: nvidia-nvjitlink-cu12 in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from nvidia-cusolver-cu12==11.4.5.107->torch) (12.3.101)
 
    
 
    
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+Requirement already satisfied: six in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from multipledispatch->numpyro) (1.16.0)
+Requirement already satisfied: mpmath>=0.19 in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from sympy->torch) (1.3.0)
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 40.2/670.2 MB 144.9 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 45.1/670.2 MB 143.8 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 50.2/670.2 MB 143.0 MB/s eta 0:00:05
+   ━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 55.2/670.2 MB 144.3 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 60.3/670.2 MB 144.9 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 65.3/670.2 MB 144.0 MB/s eta 0:00:05
+   ━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 70.4/670.2 MB 144.0 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 75.4/670.2 MB 143.9 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 80.4/670.2 MB 143.0 MB/s eta 0:00:05
+   ━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 85.4/670.2 MB 142.9 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 90.4/670.2 MB 142.6 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 95.4/670.2 MB 142.2 MB/s eta 0:00:05
+   ━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 100.4/670.2 MB 142.4 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 105.4/670.2 MB 142.6 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 110.4/670.2 MB 142.4 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 115.5/670.2 MB 142.7 MB/s eta 0:00:04
+   ━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 120.5/670.2 MB 142.0 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 125.6/670.2 MB 142.6 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 130.6/670.2 MB 144.1 MB/s eta 0:00:04
+   ━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 135.7/670.2 MB 143.0 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 140.7/670.2 MB 142.5 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 145.6/670.2 MB 142.1 MB/s eta 0:00:04
+   ━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 150.6/670.2 MB 142.0 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 155.7/670.2 MB 142.6 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 160.7/670.2 MB 143.2 MB/s eta 0:00:04
+   ━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 165.8/670.2 MB 143.6 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 170.9/670.2 MB 143.3 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 176.0/670.2 MB 144.0 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 181.0/670.2 MB 143.4 MB/s eta 0:00:04
+   ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 186.0/670.2 MB 141.8 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━ 191.1/670.2 MB 142.9 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━ 196.1/670.2 MB 143.8 MB/s eta 0:00:04
+   ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 201.1/670.2 MB 143.0 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 206.2/670.2 MB 142.8 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━ 211.2/670.2 MB 143.2 MB/s eta 0:00:04
+   ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 216.3/670.2 MB 144.5 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 221.4/670.2 MB 144.9 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━ 226.5/670.2 MB 144.2 MB/s eta 0:00:04
+   ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━ 231.5/670.2 MB 144.1 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 236.6/670.2 MB 145.0 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━ 241.7/670.2 MB 143.9 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━ 246.7/670.2 MB 142.3 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 251.7/670.2 MB 142.4 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 256.7/670.2 MB 142.0 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 261.8/670.2 MB 142.7 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━ 266.9/670.2 MB 144.2 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━ 271.8/670.2 MB 142.8 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 276.9/670.2 MB 142.5 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 281.9/670.2 MB 142.8 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━ 287.0/670.2 MB 143.5 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 292.2/670.2 MB 149.5 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 297.2/670.2 MB 149.5 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 302.3/670.2 MB 144.9 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 307.4/670.2 MB 145.0 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 312.4/670.2 MB 142.8 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 317.5/670.2 MB 142.8 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━ 322.5/670.2 MB 143.1 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 327.4/670.2 MB 141.2 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 332.5/670.2 MB 142.2 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━ 337.6/670.2 MB 143.9 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━ 342.7/670.2 MB 143.7 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 347.8/670.2 MB 144.8 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 352.9/670.2 MB 145.1 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 358.0/670.2 MB 145.1 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 363.1/670.2 MB 143.4 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 368.2/670.2 MB 142.5 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━ 373.2/670.2 MB 143.0 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 378.2/670.2 MB 141.8 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 383.3/670.2 MB 142.5 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━ 388.3/670.2 MB 143.0 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━ 393.4/670.2 MB 143.4 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 398.4/670.2 MB 143.4 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 403.3/670.2 MB 141.6 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 408.4/670.2 MB 141.5 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 413.5/670.2 MB 143.1 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 418.4/670.2 MB 142.1 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 423.5/670.2 MB 142.7 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 428.5/670.2 MB 142.9 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 433.5/670.2 MB 142.4 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 438.6/670.2 MB 144.0 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 443.5/670.2 MB 142.6 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 448.4/670.2 MB 139.9 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 453.4/670.2 MB 140.2 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 458.4/670.2 MB 141.4 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 463.5/670.2 MB 142.9 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 468.5/670.2 MB 142.4 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 473.6/670.2 MB 142.6 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 478.5/670.2 MB 142.8 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 483.6/670.2 MB 141.5 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 488.6/670.2 MB 141.5 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 493.6/670.2 MB 142.1 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 498.7/670.2 MB 143.2 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 503.6/670.2 MB 141.6 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 508.7/670.2 MB 141.3 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 513.7/670.2 MB 142.1 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 518.6/670.2 MB 141.2 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 523.6/670.2 MB 141.6 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 528.5/670.2 MB 141.0 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 533.6/670.2 MB 140.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 538.5/670.2 MB 140.2 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 543.4/670.2 MB 140.1 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 548.4/670.2 MB 140.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━ 553.4/670.2 MB 140.8 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━ 558.4/670.2 MB 143.1 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 563.6/670.2 MB 144.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 568.5/670.2 MB 143.1 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 573.5/670.2 MB 140.9 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 578.5/670.2 MB 141.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 583.6/670.2 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━ 588.6/670.2 MB 142.5 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 593.6/670.2 MB 142.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 598.6/670.2 MB 142.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 603.6/670.2 MB 141.9 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 608.7/670.2 MB 143.0 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 613.7/670.2 MB 142.9 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 618.8/670.2 MB 142.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 623.8/670.2 MB 142.4 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 628.7/670.2 MB 141.0 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 633.7/670.2 MB 141.2 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 638.8/670.2 MB 142.3 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 643.8/670.2 MB 142.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 648.8/670.2 MB 142.1 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 653.8/670.2 MB 142.9 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 658.7/670.2 MB 142.0 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 663.7/670.2 MB 139.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 668.7/670.2 MB 139.9 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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+
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
+
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 142.6 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 670.2/670.2 MB 125.9 MB/s eta 0:00:01
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+   ━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 125.6/731.7 MB 143.5 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 77.8/731.7 MB 140.2 MB/s eta 0:00:05
-   ━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 82.7/731.7 MB 140.6 MB/s eta 0:00:05
+
       ━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 130.7/731.7 MB 143.5 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 87.7/731.7 MB 141.9 MB/s eta 0:00:05
+
       ━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 135.8/731.7 MB 144.2 MB/s eta 0:00:05
+   ━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 140.8/731.7 MB 143.0 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 92.6/731.7 MB 141.5 MB/s eta 0:00:05
-   ━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 97.4/731.7 MB 140.9 MB/s eta 0:00:05
+
       ━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 146.0/731.7 MB 143.6 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 102.2/731.7 MB 138.1 MB/s eta 0:00:05
+
       ━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 151.0/731.7 MB 144.3 MB/s eta 0:00:05
 
    
 
    
-
       ━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 107.0/731.7 MB 137.5 MB/s eta 0:00:05
+
       ━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 156.0/731.7 MB 142.7 MB/s eta 0:00:05
+   ━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 161.1/731.7 MB 143.4 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 112.0/731.7 MB 138.6 MB/s eta 0:00:05
-   ━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 117.2/731.7 MB 145.3 MB/s eta 0:00:05
+
       ━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 166.0/731.7 MB 142.7 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 122.5/731.7 MB 154.2 MB/s eta 0:00:04
+
       ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 171.1/731.7 MB 142.7 MB/s eta 0:00:04
+   ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 176.2/731.7 MB 144.8 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 127.7/731.7 MB 152.7 MB/s eta 0:00:04
-   ━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 133.0/731.7 MB 153.6 MB/s eta 0:00:04
+
       ━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 181.2/731.7 MB 144.2 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 138.2/731.7 MB 153.5 MB/s eta 0:00:04
+
       ━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 186.3/731.7 MB 143.7 MB/s eta 0:00:04
+   ━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 191.4/731.7 MB 143.7 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 143.5/731.7 MB 151.8 MB/s eta 0:00:04
-   ━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 148.6/731.7 MB 151.9 MB/s eta 0:00:04
+
       ━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 196.5/731.7 MB 143.0 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 153.8/731.7 MB 151.4 MB/s eta 0:00:04
+
       ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 201.6/731.7 MB 142.4 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 159.0/731.7 MB 151.0 MB/s eta 0:00:04
-   ━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 164.2/731.7 MB 151.9 MB/s eta 0:00:04
+
       ━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━ 206.6/731.7 MB 141.2 MB/s eta 0:00:04
+   ━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━ 211.7/731.7 MB 140.8 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 169.5/731.7 MB 153.2 MB/s eta 0:00:04
+
       ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 216.7/731.7 MB 140.0 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 174.6/731.7 MB 152.0 MB/s eta 0:00:04
-   ━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 179.9/731.7 MB 152.0 MB/s eta 0:00:04
+
       ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 221.7/731.7 MB 140.7 MB/s eta 0:00:04
+   ━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━ 226.8/731.7 MB 141.6 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 185.2/731.7 MB 153.9 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━ 231.9/731.7 MB 142.1 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 190.4/731.7 MB 153.2 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 236.9/731.7 MB 141.3 MB/s eta 0:00:04
+   ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 242.0/731.7 MB 142.7 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 195.6/731.7 MB 152.1 MB/s eta 0:00:04
-   ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 200.8/731.7 MB 152.7 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━ 247.1/731.7 MB 142.6 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 206.0/731.7 MB 152.3 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━ 252.1/731.7 MB 141.5 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━━ 211.2/731.7 MB 151.8 MB/s eta 0:00:04
-   ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 216.5/731.7 MB 153.7 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 257.2/731.7 MB 142.4 MB/s eta 0:00:04
+   ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 262.3/731.7 MB 143.0 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━━ 221.9/731.7 MB 154.8 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━ 267.4/731.7 MB 143.7 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━ 227.1/731.7 MB 153.9 MB/s eta 0:00:04
-   ━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━━ 232.4/731.7 MB 153.2 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 272.3/731.7 MB 141.3 MB/s eta 0:00:04
+   ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 277.3/731.7 MB 140.1 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 237.7/731.7 MB 155.3 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 282.3/731.7 MB 141.3 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━━ 242.9/731.7 MB 153.0 MB/s eta 0:00:04
-   ━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━━ 248.1/731.7 MB 151.9 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 287.4/731.7 MB 141.8 MB/s eta 0:00:04
+   ━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━ 292.4/731.7 MB 140.4 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 253.3/731.7 MB 152.4 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━ 297.5/731.7 MB 140.4 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━━ 258.6/731.7 MB 153.7 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 302.5/731.7 MB 140.7 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━ 263.8/731.7 MB 152.9 MB/s eta 0:00:04
-   ━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━━ 269.1/731.7 MB 152.7 MB/s eta 0:00:04
+
       ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 307.6/731.7 MB 141.3 MB/s eta 0:00:04
+   ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━ 312.7/731.7 MB 147.9 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 274.3/731.7 MB 154.4 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━ 317.7/731.7 MB 141.4 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━━ 279.5/731.7 MB 151.9 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 284.8/731.7 MB 152.2 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 322.1/731.7 MB 133.0 MB/s eta 0:00:04
+   ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 326.0/731.7 MB 121.5 MB/s eta 0:00:04
 
    
 
    
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       ━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━━ 290.1/731.7 MB 154.2 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 330.1/731.7 MB 113.5 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━━ 295.3/731.7 MB 153.8 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 300.7/731.7 MB 154.5 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 334.9/731.7 MB 122.8 MB/s eta 0:00:04
 
    
 
    
-
       ━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━━ 306.0/731.7 MB 155.6 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 339.6/731.7 MB 131.2 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 344.3/731.7 MB 131.5 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━ 311.3/731.7 MB 155.3 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━━ 316.7/731.7 MB 155.3 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━ 349.0/731.7 MB 130.3 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 322.0/731.7 MB 154.9 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━ 353.7/731.7 MB 129.8 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 358.3/731.7 MB 129.8 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━━ 327.2/731.7 MB 154.5 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 362.9/731.7 MB 128.8 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━━ 332.6/731.7 MB 154.6 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 337.8/731.7 MB 153.6 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━ 367.7/731.7 MB 131.1 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━ 372.5/731.7 MB 134.2 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━━ 342.9/731.7 MB 151.3 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 377.5/731.7 MB 137.3 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━ 348.2/731.7 MB 152.1 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━━ 353.4/731.7 MB 153.3 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 382.5/731.7 MB 137.7 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 358.7/731.7 MB 152.9 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 387.4/731.7 MB 138.0 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 392.4/731.7 MB 138.4 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━━ 363.9/731.7 MB 152.3 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━ 369.2/731.7 MB 153.3 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 397.2/731.7 MB 136.8 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━━ 374.4/731.7 MB 153.6 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 402.1/731.7 MB 136.4 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━ 407.1/731.7 MB 137.8 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━━ 379.7/731.7 MB 153.2 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 385.0/731.7 MB 154.2 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━ 412.0/731.7 MB 138.5 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━━ 390.2/731.7 MB 152.8 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 416.9/731.7 MB 137.5 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 395.2/731.7 MB 149.3 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 421.8/731.7 MB 135.9 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━ 426.8/731.7 MB 136.6 MB/s eta 0:00:03
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━━ 400.5/731.7 MB 150.1 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━ 405.7/731.7 MB 152.5 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 431.7/731.7 MB 137.7 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━━ 411.0/731.7 MB 152.9 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 436.6/731.7 MB 138.8 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 441.5/731.7 MB 138.4 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 416.3/731.7 MB 154.4 MB/s eta 0:00:03
-   ━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━━ 421.4/731.7 MB 152.3 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 446.6/731.7 MB 138.6 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━━ 426.6/731.7 MB 150.5 MB/s eta 0:00:03
+
       ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 451.5/731.7 MB 138.2 MB/s eta 0:00:03
+   ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 456.5/731.7 MB 136.2 MB/s eta 0:00:03
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 431.8/731.7 MB 151.7 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━━ 437.0/731.7 MB 151.1 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 461.5/731.7 MB 138.5 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 442.2/731.7 MB 150.3 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 466.4/731.7 MB 139.0 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━━ 447.4/731.7 MB 151.4 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 452.5/731.7 MB 151.2 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 471.3/731.7 MB 137.5 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 476.4/731.7 MB 138.8 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━━ 457.8/731.7 MB 151.8 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 481.4/731.7 MB 140.2 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 463.1/731.7 MB 153.0 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━━ 468.3/731.7 MB 153.1 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 486.4/731.7 MB 138.5 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 491.4/731.7 MB 138.4 MB/s eta 0:00:02
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━━ 473.6/731.7 MB 153.1 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 496.4/731.7 MB 140.1 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 478.8/731.7 MB 152.6 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 501.3/731.7 MB 138.7 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━━ 484.1/731.7 MB 153.1 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 489.3/731.7 MB 153.0 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 506.2/731.7 MB 138.9 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 511.1/731.7 MB 138.6 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━━ 494.5/731.7 MB 151.5 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 516.1/731.7 MB 138.7 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 499.7/731.7 MB 152.2 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━━ 504.9/731.7 MB 153.2 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 521.0/731.7 MB 139.7 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 526.0/731.7 MB 140.7 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 510.1/731.7 MB 151.9 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 530.9/731.7 MB 140.9 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━━ 515.3/731.7 MB 150.7 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━━ 520.5/731.7 MB 150.7 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 535.8/731.7 MB 140.4 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 540.8/731.7 MB 139.7 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 525.7/731.7 MB 152.7 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 545.7/731.7 MB 139.4 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━━ 531.0/731.7 MB 153.3 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 536.2/731.7 MB 152.5 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 550.6/731.7 MB 139.4 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 555.5/731.7 MB 139.3 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━━ 541.2/731.7 MB 149.4 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 560.4/731.7 MB 139.1 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 546.4/731.7 MB 149.6 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━━ 551.7/731.7 MB 152.3 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 565.3/731.7 MB 138.7 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 556.8/731.7 MB 151.7 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 570.3/731.7 MB 139.8 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 575.2/731.7 MB 138.1 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━━ 562.0/731.7 MB 150.4 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 580.1/731.7 MB 137.9 MB/s eta 0:00:02
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━━ 567.1/731.7 MB 150.7 MB/s eta 0:00:02
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 572.4/731.7 MB 150.9 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 585.0/731.7 MB 139.8 MB/s eta 0:00:02
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 590.0/731.7 MB 141.8 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━━ 577.5/731.7 MB 150.3 MB/s eta 0:00:02
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 595.0/731.7 MB 141.6 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 582.7/731.7 MB 150.2 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━━ 587.9/731.7 MB 151.0 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 599.9/731.7 MB 139.3 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━ 604.8/731.7 MB 138.3 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 593.1/731.7 MB 152.1 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━ 609.6/731.7 MB 138.8 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━━ 598.3/731.7 MB 151.0 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━ 603.4/731.7 MB 149.6 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 614.6/731.7 MB 139.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━━ 608.6/731.7 MB 149.4 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 619.5/731.7 MB 140.2 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 624.5/731.7 MB 139.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 613.8/731.7 MB 149.5 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 629.3/731.7 MB 138.8 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━━ 619.1/731.7 MB 153.3 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━━ 624.3/731.7 MB 153.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 634.3/731.7 MB 139.5 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━ 639.3/731.7 MB 140.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 629.4/731.7 MB 150.2 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━ 644.2/731.7 MB 140.6 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━━ 634.6/731.7 MB 149.2 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━ 639.7/731.7 MB 148.7 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 649.3/731.7 MB 142.3 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 654.3/731.7 MB 142.9 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━━ 644.7/731.7 MB 143.4 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 659.4/731.7 MB 143.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 649.8/731.7 MB 143.5 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━━ 655.1/731.7 MB 149.8 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 664.4/731.7 MB 143.8 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 669.5/731.7 MB 143.2 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 660.1/731.7 MB 149.1 MB/s eta 0:00:01
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 674.6/731.7 MB 144.1 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━━ 665.2/731.7 MB 142.8 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 670.3/731.7 MB 144.0 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 679.6/731.7 MB 143.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━━ 675.3/731.7 MB 143.2 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 684.6/731.7 MB 142.1 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 689.6/731.7 MB 140.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━━ 680.4/731.7 MB 142.4 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 694.7/731.7 MB 141.0 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 685.6/731.7 MB 143.8 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━━ 690.8/731.7 MB 151.4 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 699.8/731.7 MB 143.4 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 704.8/731.7 MB 144.2 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 696.0/731.7 MB 151.5 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 709.9/731.7 MB 143.3 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺━ 701.1/731.7 MB 148.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 706.4/731.7 MB 150.1 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 714.9/731.7 MB 143.4 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 719.8/731.7 MB 141.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸━ 711.5/731.7 MB 150.6 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 724.9/731.7 MB 141.4 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 716.7/731.7 MB 150.9 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╺ 722.1/731.7 MB 153.0 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 730.0/731.7 MB 143.5 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 727.2/731.7 MB 152.0 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
+
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 145.7 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 731.7/731.7 MB 147.3 MB/s eta 0:00:01
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    Downloading triton-2.1.0-0-cp311-cp311-manylinux2014_x86_64.manylinux_2_17_x86_64.whl (89.2 MB)
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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+
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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+
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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+
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
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-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
+
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-
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
+
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 141.3 MB/s eta 0:00:01
 
    
 
    
-
       ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
-
    
-
    
-
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-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━╸ 89.2/89.2 MB 150.5 MB/s eta 0:00:01
-   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 89.2/89.2 MB 6.1 MB/s eta 0:00:00
+
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+   ━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━━ 89.2/89.2 MB 6.4 MB/s eta 0:00:00
 ?25h
 
    
 
    
@@ -4398,9 +3103,7 @@ 
    8. Non-Conjugate Priors
        Found existing installation: nvidia-cufft-cu12 11.0.12.1
-
    
-
    
-
        Uninstalling nvidia-cufft-cu12-11.0.12.1:
+    Uninstalling nvidia-cufft-cu12-11.0.12.1:
 
    
 
    
 
          Successfully uninstalled nvidia-cufft-cu12-11.0.12.1
@@ -4420,7 +3123,9 @@ 
    8. Non-Conjugate Priors
        Found existing installation: nvidia-cuda-nvrtc-cu12 12.3.103
-    Uninstalling nvidia-cuda-nvrtc-cu12-12.3.103:
+
    
+
    
+
        Uninstalling nvidia-cuda-nvrtc-cu12-12.3.103:
 
    
 
    
 
          Successfully uninstalled nvidia-cuda-nvrtc-cu12-12.3.103
@@ -4450,7 +3155,9 @@ 
    8. Non-Conjugate Priors
        Found existing installation: nvidia-cusolver-cu12 11.5.4.101
-    Uninstalling nvidia-cusolver-cu12-11.5.4.101:
+
    
+
    
+
        Uninstalling nvidia-cusolver-cu12-11.5.4.101:
 
    
 
    
 
          Successfully uninstalled nvidia-cusolver-cu12-11.5.4.101
@@ -5148,7 +3855,7 @@ 
    8.4. Alternative Prior Distributions
    
 
    
-_images/5fdd4013eada9d4301670592315c2fb8d01611c25d10e9d7174435378936eb65.png
+_images/e49b1ec0d769199f5cc527c2584ad35d002ad8e29d4da225fb3d5c6fb7e2bf79.png
 
    
 
    
 
    These graphs look good too.
    
@@ -5367,7 +4074,7 @@ 
    8.5.1. Beta Prior and Posteriors:
 
    
 
    
-_images/0f2ca2d9da25f6335370f5162ff45f5d09e5c328faeef2287defe5729c496343.png
+_images/8b0c228f10916566aa1ced06fb231d932aae7f14526610ee720d924481b9831c.png
 
    
 
    
 
    Now let’s use MCMC while still using a beta prior.
    
@@ -5380,8 +4087,8 @@ 
    8.5.1. Beta Prior and Posteriors:
 
    
 
    
-_images/74113456e317327df3fdd4e11db95576a1c29fa0ac98e1943ccef5d5f78e34f4.png
-_images/9b4b83052732181ee068666e3d7663fa6e6a4db8700f8223871248e5552c570a.png
+_images/e30d24fbf244702e4829e01de9a1961910582eb9fab622d7f420858939fa8ebd.png
+_images/b1109e399aff49d72716078a6638921d3b27074f291b07995e12c3f8e4fc2d11.png
 
    
 
    
 
    Here the MCMC approximation looks good.
    
@@ -5400,7 +4107,7 @@ 
    8.5.1. Beta Prior and Posteriors:
 
    
 
    
-_images/c821ff8131e59b24f3d042f9b23e92b56549568f6be8635453cb954793485c83.png
+_images/fce448a7181ee78af3ecfd8794585c16d06ff04f174804ee0efe1b7f8af1674b.png
 
    
 
    
 
@@ -5457,14 +4164,14 @@ 
    8.6.1. MCMC
+_images/e524b046f875dea7a9581a195652bb8918939cfc8e40fa0d456ab1ca08653176.png
 
    =======INFO=======
 Parameters: (0.2, 0.7)
 Prior Dist: uniform
 Solver: numpyro
 
    
 
    
-_images/53eaf6240cd70fea57eb5af89a93edb4a63a80c4476259cfa18db62d627ab442.png
+_images/f6a494e5a10f92a3404b3fac9980e21cd46ef433262e6d4e2bac5b62e6eb81d1.png
 
    
 
    
 
    In the situation depicted above, we have assumed a  \(Uniform(\underline{\theta}, \overline{\theta})\) prior that puts zero probability   outside a bounded support that excludes the true value.
    
@@ -5490,14 +4197,14 @@ 
    8.6.1. MCMC
+_images/91d73adab48642b7b3ab7929a0a031c5b761e0851bf31da2e5d8d6b6a84a9a67.png
 
    =======INFO=======
 Parameters: (0, 2)
 Prior Dist: lognormal
 Solver: pyro
 
    
 
    
-_images/1ace320adca9746d3e57f49a02e4df936391d1daa417cddaba99a223dfca322b.png
+_images/9e06442ca0349f05ba3f1a1b86f392948a6960d67a5bac819f30a236d0a6277c.png
 
    
 
    
 
    
@@ -5524,7 +4231,7 @@ 
    8.6.1. MCMC
+_images/a6b71263be9190312161bcf31722783996c1c3f176fab64b3b9774ff0094c34f.png
 
    =======INFO=======
 Parameters: 40
 Prior Dist: vonMises
@@ -5533,7 +4240,7 @@ 
    8.6.1. MCMC
+_images/3ac560e67fdaf3a8eb61e51a0c49aa6824ff4dc885b652e702a896bd7c563650.png
 
    
 
    
 
    
@@ -5552,7 +4259,7 @@ 
    8.6.1. MCMC
+_images/e1cb5b6731f846b6ae68d5c0093f22279045f52df2685722c51955d7d320bfa5.png
 
    
 
    
 
    To get more accuracy we will now increase the number of steps for Variational Inference (VI)
    
@@ -5581,7 +4288,7 @@ 
    8.6.1.1. VI with a  Truncated Normal Gui
 Solver: numpyro
 
    
 
    
-_images/f6747ece611790d26d9ba5d135b1183ebbf3380deaf13e44101c6ee7efabf374.png
+_images/b7cfc18c94f0fdc3de7ffe2b18674ea8e93c59327459af82d8883005f6c40286.png
 
    
 
    
 
    
@@ -5600,7 +4307,7 @@ 
    8.6.1.1. VI with a  Truncated Normal Gui
 Solver: numpyro
 
    
 
    
-_images/fc5200c359609d36d7fa5a1e4dc18373140054184bcf68aa4cb313d8230894e3.png
+_images/a87e00e6dcec8e8e7638ac4e94e024195b9c62962c0c0c64588e68a39b59b530.png
 
    
 
    
 
    
@@ -5622,7 +4329,7 @@ 
    8.6.1.1. VI with a  Truncated Normal Gui
 NB: Shifted von Mises
 
    
 
    
-_images/e6bd30834e31bdacf25360190a89b5064eb2c1aee8a230685720bec695e4a4ed.png
+_images/dbfa9bf1efc5f217b3e1f1729e186e5fe5a3fa883f79f7e09128cdf66b5efae8.png
 
    
 
    
 
    
@@ -5641,7 +4348,7 @@ 
    8.6.1.1. VI with a  Truncated Normal Gui
 Solver: numpyro
 
    
 
    
-_images/90ddb265ffd471ddd3a7e9f273981a6a57a21ed4ba3774af3b9cb5d03a88eca4.png
+_images/7fa574a08ab780fb8a550b18d23b3637248b4b8d86dbb37c859e2f37a1837e77.png
 
    
 
    
 
@@ -5663,7 +4370,7 @@ 
    8.6.1.2. Variational Inference with a  B
 Solver: pyro
 
    
 
    
-_images/75ddc66975f66b6d6f28b98b8843e75f02826240909455d5748d8545e7ab9e38.png
+_images/5ee3a8847923ea85f18460bdd0ca2a440eab32e32ba4bbf878aa082e6f99433b.png
 
    
 
    
 
    
@@ -5686,14 +4393,14 @@ 
    8.6.1.2. Variational Inference with a  B
 Solver: numpyro
 
    
 
    
-_images/669c20da42b48d36f95ecb8f484d8496de56fad3c731fee3cea8fa8fa05fdab2.png
+_images/c56e7b2ff16151d834a99715ca1c0f5f1792005d496c26cf6c108e760e0f5ca7.png
 
    =======INFO=======
 Parameters: (0, 2)
 Prior Dist: lognormal
 Solver: pyro
 
    
 
    
-_images/2c75009cdbde09606a47c554f7e7db584405e52342ce60114485f84ad81efa9c.png
+_images/080a83a17e79b3a4f322644af6c8f84ac6f3d25aeb272e33d901660621a404d0.png
 
    
 
    
 
    
@@ -5720,7 +4427,7 @@ 
    8.6.1.2. Variational Inference with a  B
 NB: Shifted von Mises
 
    
 
    
-_images/bf9bca88953f2a128b98efa3801d7f10a20ad5c9b682708c9cf60d332ebb9c38.png
+_images/3185fc8f2e3e141b6c88a667af4733c9c4542094e60cd22ec8e7536de4cbb8e7.png
 
    =======INFO=======
 Parameters: 40
 Prior Dist: vonMises
@@ -5729,7 +4436,7 @@ 
    8.6.1.2. Variational Inference with a  B
 NB: Truncated von Mises
 
    
 
    
-_images/6342b300ede148355dd00021febcc57dc655a5c1912be449285a3b0644895fc2.png
+_images/24bdc3fc27058fd63a12cc336f32427582c03ddfb3890293aebb27f5e272b2fe.png
 
    
 
    
 
    
@@ -5748,7 +4455,7 @@ 
    8.6.1.2. Variational Inference with a  B
 Solver: numpyro
 
    
 
    
-_images/daf9953d767194eb6ac8c55316a117246de1d5f35052743d719fedbdd8f8c4fc.png
+_images/2edbb86a6066f40dd85be46467890c0ce68125d9b61ded305d21c09853d3b2a1.png
 
    
 
    
 
diff --git a/exchangeable.html b/exchangeable.html
index 9c6d260..98b8556 100644
--- a/exchangeable.html
+++ b/exchangeable.html
@@ -781,7 +781,7 @@ 
    14.8.1. Sample Paths of 
-_images/4027f03d5748f4402de609f00b22f705eeb8d59b4035a7e94728516c7adc6963.png
+_images/cb76852f4ec53574e12dddb69f39c2d1185a2c1643fbdc036747a9b217c75247.png
 
    
 
    
 
    In the above example,  for most paths \(\pi_t \rightarrow 1\).
    
@@ -797,7 +797,7 @@ 
    14.8.1. Sample Paths of 
-_images/eb00aa9a9982ab27b8ddbf3a03d9ae51ce96b38d0de7d2908fc7a68dfab3440b.png
+_images/0a4d2ce2034090dfb504019d2394c0d69bf12d91eb1bc47abaecb7ef3497a5e4.png
 
    
 
    
 
    In the above graph we observe that now  most paths \(\pi_t \rightarrow 0\).
    
@@ -820,7 +820,7 @@ 
    14.8.2. Rates of convergence
-_images/2b9290f51596731eddecd5b92cf888d2c978ff5ddaeb06903a0b713d71d248bb.png
+_images/b6a72a79b8292e60ebfc335542d53436712b925a31c74fc4c71f86ab0e300c68.png
 
    
 
    
 
    From the above graph, rates of convergence appear not to depend on whether \(F\) or \(G\) generates the data.
    
diff --git a/hoist_failure.html b/hoist_failure.html
index e340c12..6793103 100644
--- a/hoist_failure.html
+++ b/hoist_failure.html
@@ -246,8 +246,8 @@ 
    19.1. Overview
 
    For more about Fourier transforms see this quantecon lecture Circulant Matrices
 as well as these  lecture  Covariance Stationary Processes and Estimation of Spectra.
    
-
    El-Shanawany, Ardron,  and Walker [ESAW18] and Greenfield and Sargent [GS93]  used some of the methods described here  to approximate probabilities of failures of safety systems in nuclear facilities.
    
-
    These methods respond to some of the recommendations made by Apostolakis  [Apo90] for constructing procedures for quantifying
+
    El-Shanawany, Ardron,  and Walker [ESAW18] and Greenfield and Sargent [GS93]  used some of the methods described here  to approximate probabilities of failures of safety systems in nuclear facilities.
    
+
    These methods respond to some of the recommendations made by Apostolakis  [Apo90] for constructing procedures for quantifying
 uncertainty about the reliability of a safety system.
    
 
    We’ll start by bringing in some Python machinery.
    
 
    
@@ -421,7 +421,7 @@ 
    19.4. Approximating Distributions
 
    
 
    
-_images/c6ba9dfeff66756cd4a460f8a4635bbabe7db2198af463e16a2294f259ef8ded.png
+_images/fcf1c69964dc74498b813aa9df7038ec98aa088045a4f2a0090a3204a772c53b.png
 
    
 
    
 
    
@@ -431,7 +431,7 @@ 
    19.4. Approximating Distributions
 
    
 
    
-_images/4713a3481187655b71de953b84911d8a172306124dd2f6dfc0cf329e70618016.png
+_images/842adeb62974e77e3c6ba9217a79d664e2b128b132867e65adff7d34ee567cc2.png
 
    
 
    
 
    
@@ -441,7 +441,7 @@ 
    19.4. Approximating Distributions
 
    
 
    
-_images/a4966bfb298fbc5e267147f2d30e6ec5a01d9256e0dd629fd4b36de28c07ddbc.png
+_images/a629f134d1795d157ee0cdc6944c3efe6dc273d0e48b7c143a355e082abdc7c8.png
 
    
 
    
 
    
@@ -454,7 +454,7 @@ 
    19.4. Approximating Distributions
 
    
 
    
-
    (244.69193226422038, 246.1058233152007, 5.0, 1.0)
+
    (244.69193226422038, 243.62625549695608, 5.0, 1.0)
 
    
 
    
 
    
@@ -514,7 +514,7 @@ 
    19.4. Approximating Distributions
 
    
 
    
-_images/93442fd0cd55e4ab9f3ef4e18079873c2af36f89648df53811054a5492273bd2.png
+_images/d033d9166126d9a9d1dfc8830d5c184a4b8654de5986f5b37f796b6e15b2b7f9.png
 
    
 
    
 
    
@@ -601,7 +601,7 @@ 
    19.5. Convolving Probability Mass Functi
 
    
 
    
 
    
-
    time with np.convolve =  47.28964252100013 ; time with fftconvolve =  0.1614581720004935
+
    time with np.convolve =  45.46649831200011 ; time with fftconvolve =  0.17207892199985508
 
    
 
    
 
    
@@ -625,7 +625,7 @@ 
    19.5. Convolving Probability Mass Functi
 
    
 
    
 
    
-_images/6ef098185a13e1025c7f96b3d64a03ed92e03166a81ba5d2996ef9463e12f2f7.png
+_images/0c8224806e3743ffcee7c554a12231d17e2c985e4b778867c2a34e1688367dba.png
 
    
 
    
 
    
@@ -644,7 +644,7 @@ 
    19.5. Convolving Probability Mass Functi
 
    
 
    
 
    
-_images/5d8757826d5eb2fd7b5101cdd3f0e5f18dc925fa1620245ae7138e63da8659a4.png
+_images/a6ebb695fce8f01bad902eda852146fe3db9e64d944140b4706b27a462c03a09.png
 
    
 
    
 
    
@@ -684,7 +684,7 @@ 
    19.6. Failure Tree Analysis[ESAW18].
    
+
    The model is an example of the widely used  failure tree analysis described by  El-Shanawany, Ardron,  and Walker [ESAW18].
    
 
    To construct the statistical model, we repeatedly use  what is called the rare event approximation.
    
 
    We want to compute the probabilty of an event \(A \cup B\).
    
 
    
 
    
-
    0.9670522129335177
+
    1.008712475303812
 
    
 
    
 
    
@@ -466,7 +466,7 @@ 
    12.5. 
 
    
 
    
-
    0.9980822451622499
+
    0.9993505959783151
 
    
 
    
 
    
@@ -482,7 +482,7 @@ 
    12.5. 
 
    
 
    
-
    0.8885005292861006
+
    0.4328772088957214
 
    
 
    
 
    
@@ -494,7 +494,7 @@ 
    12.5. 
 
    
 
    
-
    1.0128354768900691
+
    0.9439802877697646
 
    
 
    
 
    
@@ -539,7 +539,7 @@ 
    12.6. 
 
    
 
    
-
    (1.0000617381821493, 0.06060259893116859)
+
    (1.0085436308519349, 0.038984632424601734)
 
    
 
    
 
    
@@ -552,7 +552,7 @@ 
    12.6. 
 
    
 
    
-
    (1.0000644410358084, 2.3910075177394037e-05)
+
    (0.9999539740995881, 2.3606191148093092e-05)
 
    
 
    
 
    
@@ -590,7 +590,7 @@ 
    12.6. 
 
    
 
    
-_images/465539a092a95876eef3fded9607468ed523c6c79115c14465516f3de20ff2b8.png
+_images/705e140b9b9e5bac4ea209454509ef0b738e8ce73c60843b33f265ac4746f38a.png
 
    
 
    
 
    The simulation exercises above show that the importance sampling estimates are unbiased under all \(T\)
@@ -700,7 +700,7 @@ 
    12.7. 
 
    
 
    
-_images/f9e7437539da4919cc7149854dad671d4d6b33cc55fc1fd7e04cab3d7148e0bf.png
+_images/9eb184dd15266baa4d145c0a2732d226d6f26f5f07f09b8642ce44bbfd8e0e1d.png
 
    
 
    
 
    Our simulations suggest that indeed \(h_2\) is a quite  good importance sampling distribution for our problem.
    
@@ -738,7 +738,7 @@ 
    12.7. 
 
    
 
    
-_images/07092f92f5e19ae9bc172adde38c16d3d7d831b51a361136a4ef1324e0a4fd81.png
+_images/276fdc6d68ecc672a2a90662c08f4118ea2f81bb9f66537ab5d39e67194f40db.png
 
    
 
    
 
    However, \(h_3\) is evidently a poor importance sampling distribution forpir problem,
diff --git a/likelihood_bayes.html b/likelihood_bayes.html
index ac26a6b..1580fc6 100644
--- a/likelihood_bayes.html
+++ b/likelihood_bayes.html
@@ -316,7 +316,7 @@ 
    15.2. The Setting
 
    The likelihood ratio and its logarithm are key tools for making
 inferences using a classic frequentist approach due to Neyman and
-Pearson [NP33].
    
+Pearson [NP33].
    
 
    We’ll again deploy the following Python code from this lecture that
 evaluates \(f\) and \(g\) as two different
 beta distributions, then computes and simulates an associated likelihood
diff --git a/likelihood_ratio_process.html b/likelihood_ratio_process.html
index aad6f40..4521a12 100644
--- a/likelihood_ratio_process.html
+++ b/likelihood_ratio_process.html
@@ -319,7 +319,7 @@ 
    11.2. 
 
    The likelihood ratio and its logarithm are key tools for making
 inferences using a classic frequentist approach due to Neyman and
-Pearson [NP33].
    
+Pearson [NP33].
    
 
    To help us appreciate how things work, the following Python code evaluates \(f\) and \(g\) as two different
 beta distributions, then computes and simulates an associated likelihood
 ratio process by generating a sequence \(w^t\) from one of the two
@@ -392,7 +392,7 @@ 
    11.3. 
 
    
 
    
-_images/a9f1ad23f9e9dc7de47e12c9773874db29d7a5290f2756f2e1b6245a6332a01b.png
+_images/37bb995f6737bbab94edbe4a068064027d776bc63960b9a1490a7224f08c4ef8.png
 
    
 
    
 
    Evidently, as sample length \(T\) grows, most probability mass
@@ -407,10 +407,10 @@ 
    11.3. 
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x7f4b29ed6650>]
+
    [<matplotlib.lines.Line2D at 0x7f82edbe3e90>]
 
    
 
    
-_images/9bdeb83296344a6b688174d70f3a5017e502177127fcd8ff4766b1b7792d53a7.png
+_images/fe0b5b520f0424e7a74bec171826bc7b4d6603795326daa6a38702ec85100bb6.png
 
    
 
    
 
    Despite the evident convergence of most probability mass to a
@@ -519,10 +519,10 @@ 
    11.5. 
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x7f4b29ed5cd0>]
+
    [<matplotlib.lines.Line2D at 0x7f82ede6b410>]
 
    
 
    
-_images/6c54665c78b1c0e589c295fe04292b8fcef138397f50ab0f7c7e23101cd9ca38.png
+_images/9de7cb0ff00260fa82ba2244eeada6831941d089854836c257aa442809df4348.png
 
    
 
    
 
    We also plot the probability that \(L\left(w^t\right)\) falls into
@@ -535,17 +535,17 @@ 
    11.5. 
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x7f4b29efcfd0>]
+
    [<matplotlib.lines.Line2D at 0x7f82ede79510>]
 
    
 
    
-_images/0dc861bf04d5dfcdf8d00b70c75bdab027f1c4881ab90cc492decd0e9181ae09.png
+_images/bb3b8ab76440743979c018df395a9f07b7deaeb61105a879f9831088939089e8.png
 
    
 
    
 
 
    
 
    11.6. Likelihood Ratio Test#
    
 
    We now describe how to employ the machinery
-of Neyman and Pearson [NP33] to test the hypothesis that  history \(w^t\) is generated by repeated
+of Neyman and Pearson [NP33] to test the hypothesis that  history \(w^t\) is generated by repeated
 IID draws from density \(g\).
    
 
    Denote \(q\) as the data generating process, so that
 \(q=f \text{ or } g\).
    
@@ -657,7 +657,7 @@ 
    11.6. 
 
    
 
    
-_images/47261abad162c48b093ce781b2dd7a3a63362cf6758744e38b681fa6189999d1.png
+_images/9cf0f79380f694c59f83068a5c703de5aa57c5ed49964d477cacab714257b632.png
 
    
 
    
 
    The graph below shows more clearly that, when we hold the threshold
@@ -682,7 +682,7 @@ 
    11.6. 
 
    
 
    
-_images/1a7ab6510a099bb5351402a1eb79ae1fe15d71033725f568eb987d4c806f01fc.png
+_images/a4139710999224acc00d731d59aff15ececfed6379ef49b1820ae94a3bcf0003.png
 
    
 
    
 
    For a given sample size \(t\),  the threshold \(c\) uniquely pins down  probabilities
@@ -717,7 +717,7 @@ 
    11.6. 
 
    
 
    
-_images/6f8228431333bce26ad4f6e2b45ce94a01eb65453d65ef63b89a69ee0562c3c4.png
+_images/6f9f86237eb22afa7ef3be68ba30e60c27452e537c6ac3a159695cf7e2b5ec63.png
 
    
 
    
 
    Notice that as \(t\) increases, we are assured a larger probability
@@ -758,7 +758,7 @@ 
    11.6. 
 
    
 
    
-_images/97c3d8bf9d3ae189544e271be9413fcf6c6e388080a65ff7fe65070bd8df1548.png
+_images/97d30d64c83bd5ebd30f87cab017696f8912bc12fb96e40f4c74efb60ee7fe52.png
 
    
 
    
 
    The United States Navy evidently used a procedure like this to select a sample size \(t\) for doing quality
@@ -896,10 +896,10 @@ 
    11.7. 
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x7f4b29da5f50>]
+
    [<matplotlib.lines.Line2D at 0x7f82ed976390>]
 
    
 
    
-_images/e5372ce198f485b36d9732e107f18a12298b747520d30ef32698769ef54cb251.png
+_images/5a69cd29bde74089fcc28ad7ad3ad1e682e014da5cc0dc4cbe8d2b76e2952587.png
 
    
 
    
 
    We can also try an \(h\) that is closer to \(f\) than is
@@ -943,10 +943,10 @@ 
    11.7. 
 
    
 
    
-
    [<matplotlib.lines.Line2D at 0x7f4b2ac56390>]
+
    [<matplotlib.lines.Line2D at 0x7f82ed9b6390>]
 
    
 
    
-_images/216b1668416530f48e33cee160276900cbbe5ec882fccfcf1edd62ea2b507925.png
+_images/ef4f2e094da8d1ac10c128bb7654467834c68f167bc6ea43ca8cd8a9b002b0e3.png
 
    
 
    
 
diff --git a/lln_clt.html b/lln_clt.html
index f2087ff..8329499 100644
--- a/lln_clt.html
+++ b/lln_clt.html
@@ -437,7 +437,7 @@ 
    5.3.3. Illustration
 
    
 
    
-_images/47d136ee64c2ec948c02dcf852092064b0ccfa39e73e383b61ade460b30b3fe4.png
+_images/7ae5b1e179fad98334943915c89def9699460676ee1473e0d088d291253bb605.png
 
    
 
    
 
    The three distributions are chosen at random from a selection stored in the dictionary distributions.
    
@@ -554,7 +554,7 @@ 
    5.4.3. Simulation 1
 
    
 
    
-_images/9daf2cbdd1184a8770403f125c9a7952678c1ca64cb58b67548efb4287fb60aa.png
+_images/d27faa0a991bbd92e8585f89a57e62832d073e9f9070ef5d090af282ea8169e7.png
 
    
 
    
 
    Notice the absence of for loops — every operation is vectorized, meaning that the major calculations are all shifted to highly optimized C code.
    
@@ -640,7 +640,7 @@ 
    5.4.4. Simulation 2
 
    
 
    
-_images/7c3c8fa91ba5d3067af44e8a6506e6f70080f964c675bb17aa0ae8f1109cd3d8.png
+_images/328059d3d0a6f180cc953561f66472e56398932348ebc68c989e6d3a4e531fa0.png
 
    
 
    
 
    As expected, the distribution smooths out into a bell curve as \(n\)
@@ -797,7 +797,7 @@ 
    5.5. 
 
    
 
    
 
    
-_images/ae30b85f983c89953fce17f2a422175d25bf64cf4078e1835bd4f184aca6b4df.png
+_images/67d2baf1cbe2e664d9c3ce0e1e84f28f01e9f663d8eb87e606536683d0518e1b.png
 
    
 
    
 
    What happens when you replace \([0, \pi / 2]\) with
@@ -982,7 +982,7 @@ 
    5.5. 
 
    
 
    
 
    
-_images/4d1ea53635a263121cb9c09872b18d3f09f3ecf1e4bb4c52dd50e7fa313ab0b4.png
+_images/7e701ebbe171feb3870f4110209f83a22891f11e9c756a2fccfd3f349426f4eb.png
 
    
 
    
 
diff --git a/mix_model.html b/mix_model.html
index 1a7e3ca..6cb941c 100644
--- a/mix_model.html
+++ b/mix_model.html
@@ -242,12 +242,12 @@
 
    
 
    Requirement already satisfied: numpyro in /opt/conda/envs/quantecon/lib/python3.11/site-packages (0.13.2)
 Requirement already satisfied: jax in /opt/conda/envs/quantecon/lib/python3.11/site-packages (0.4.23)
-Requirement already satisfied: jaxlib>=0.4.14 in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (0.4.23+cuda12.cudnn89)
-Requirement already satisfied: multipledispatch in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (0.6.0)
-Requirement already satisfied: numpy in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (1.24.3)
 
    
 
    
-
    Requirement already satisfied: tqdm in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (4.65.0)
+
    Requirement already satisfied: jaxlib>=0.4.14 in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (0.4.23+cuda12.cudnn89)
+Requirement already satisfied: multipledispatch in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (0.6.0)
+Requirement already satisfied: numpy in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (1.24.3)
+Requirement already satisfied: tqdm in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from numpyro) (4.65.0)
 
    
 
    
 
    Requirement already satisfied: ml-dtypes>=0.2.0 in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from jax) (0.3.1)
diff --git a/mle.html b/mle.html
index 0bcb391..8a98e5a 100644
--- a/mle.html
+++ b/mle.html
@@ -988,8 +988,8 @@ 
    3.6. 
 Dep. Variable:                      y   No. Observations:                    5
 Model:                        Poisson   Df Residuals:                        2
 Method:                           MLE   Df Model:                            2
-Date:                Wed, 24 Jan 2024   Pseudo R-squ.:                  0.2546
-Time:                        02:09:17   Log-Likelihood:                -3.3784
+Date:                Mon, 29 Jan 2024   Pseudo R-squ.:                  0.2546
+Time:                        01:45:32   Log-Likelihood:                -3.3784
 converged:                       True   LL-Null:                       -4.5325
 Covariance Type:            nonrobust   LLR p-value:                    0.3153
 ==============================================================================
@@ -1055,8 +1055,8 @@ 
    3.6. 
 Dep. Variable:                numbil0   No. Observations:                  197
 Model:                        Poisson   Df Residuals:                      193
 Method:                           MLE   Df Model:                            3
-Date:                Wed, 24 Jan 2024   Pseudo R-squ.:                  0.8574
-Time:                        02:09:17   Log-Likelihood:                -438.54
+Date:                Mon, 29 Jan 2024   Pseudo R-squ.:                  0.8574
+Time:                        01:45:32   Log-Likelihood:                -438.54
 converged:                       True   LL-Null:                       -3074.7
 Covariance Type:                  HC0   LLR p-value:                     0.000
 ==============================================================================
@@ -1414,8 +1414,8 @@ 
    3.8. 18.3.2. Back to The Administrator’s Pr
 
    
 
    
 
    
-
    array([3.9573438, 0.2773919, 1.1597726, 0.6054917])
+
    array([3.9581672, 0.2774228, 1.15951  , 0.6049   ])
 
    
 
    
 
    
@@ -647,10 +647,10 @@ 
    18.3.2. Back to The Administrator’s Pr
 
    
 
    
 
    
-
    array([[ 1.31940498, -0.17935783, -0.74882188, -0.39122526],
-       [-0.17935783,  0.25896886, -0.05232443, -0.0272866 ],
-       [-0.74882188, -0.05232443,  0.91530181, -0.11415549],
-       [-0.39122526, -0.0272866 , -0.11415549,  0.53266735]])
+
    array([[ 1.31893595, -0.17924375, -0.74939483, -0.39029738],
+       [-0.17924375,  0.25897962, -0.05229222, -0.02744365],
+       [-0.74939483, -0.05229222,  0.91596525, -0.11427821],
+       [-0.39029738, -0.02744365, -0.11427821,  0.53201924]])
 
    
 
    
 
    
@@ -736,7 +736,7 @@ 
    18.3.3. Quality of Normal Approximation<
 
    
 
    
 
    
-_images/cec4741775ee7fe04523e841dd1e8dd3d9cda711b3aa0e6ecdf14d40ede54932.png
+_images/1a21c3e906f8c8702468ca900194b97995e577d0dd7d88350454fcc9d4604657.png
 
    
 
    
 
    The diagonal graphs plot the marginal distributions of \(k_i\) for
@@ -775,7 +775,7 @@ 
    18.3.3. Quality of Normal Approximation<
 
    
 
    
 
    
-
    array([3.62974711e-04, 5.38823513e-01, 2.94429715e-01, 1.38236939e-01])
+
    array([0.51603198, 0.90659528, 0.93141439, 0.55497686])
 
    
 
    
 
    
diff --git a/multivariate_normal.html b/multivariate_normal.html
index d40ac6e..fba92ad 100644
--- a/multivariate_normal.html
+++ b/multivariate_normal.html
@@ -764,7 +764,7 @@ 
    6.3. 
 
    
 
    
 
    
-
    (array([[0.5]]), array([0.50054302]))
+
    (array([[0.5]]), array([0.50043162]))
 
    
 
    
 
    
@@ -778,7 +778,7 @@ 
    6.3. 
 
    
 
    
 
    
-
    (array([[0.75]]), 0.7514252098660497)
+
    (array([[0.75]]), 0.7488549611211766)
 
    
 
    
 
    
@@ -792,7 +792,7 @@ 
    6.3. 
 
    
 
    
 
    
-
    (array([2.5]), array([2.50217209]))
+
    (array([2.5]), array([2.50172648]))
 
    
 
    
 
    
@@ -824,10 +824,10 @@ 
    6.4. 
 
    
 
    
 
    
-
    (array([0.84308772, 0.75783934, 0.2418833 ]),
- array([[1.09639042, 0.25126988, 0.8116043 ],
-        [0.25126988, 0.19917535, 0.33166667],
-        [0.8116043 , 0.33166667, 0.93819647]]))
+
    (array([0.10680857, 0.58578642, 0.28217415]),
+ array([[0.20050523, 0.63309   , 0.60323981],
+        [0.63309   , 2.31957698, 2.04569305],
+        [0.60323981, 2.04569305, 1.91250494]]))
 
    
 
    
 
    
@@ -880,7 +880,7 @@ 
    6.4. 
 
    
 
    
 
    
-
    (array([[-0.43508125,  1.01887641]]), array([-0.43549909,  1.01885402]))
+
    (array([[-0.09252613,  0.41438841]]), array([-0.09285127,  0.41458393]))
 
    
 
    
 
    
@@ -892,7 +892,7 @@ 
    6.4. 
 
    
 
    
 
    
-
    (array([[0.37878877]]), 0.3795689629335765)
+
    (array([[0.00910702]]), 0.009115458143038832)
 
    
 
    
 
    
@@ -904,7 +904,7 @@ 
    6.4. 
 
    
 
    
 
    
-
    (array([5.15057975]), array([5.14995422]))
+
    (array([1.93096921]), array([1.93143183]))
 
    
 
    
 
    
@@ -1082,7 +1082,7 @@ 
    6.5. 
 
    
 
    
 
    
-
    94.78457351068239
+
    95.92381126606453
 
    
 
    
 
    
@@ -1100,7 +1100,7 @@ 
    6.5. 
 
    
 
    
 
    
-
    (array([96.00140348]), array([[1.96078431]]))
+
    (array([94.86707972]), array([[1.96078431]]))
 
    
 
    
 
    
@@ -1161,7 +1161,7 @@ 
    6.5. 
 
    
 
    
 
    
-_images/0c1d7615fe53419b82afb978197bdf02deab68decf4211312e70b631c41eae16.png
+_images/7d662dcfafc335623b0766578e071238b44eca53c5a1f387118bd90e8fa3ce7e.png
 
    
 
    
 
    The solid blue line in the plot above shows \(\hat{\mu}_{\theta}\)
@@ -1434,7 +1434,7 @@ 
    6.8. 
 
    
 
    
 
    
-
    (91.01454417025573, 100.31422830271013)
+
    (102.70095792247895, 101.13231180591593)
 
    
 
    
 
    
@@ -1453,7 +1453,7 @@ 
    6.8. 
 
    
 
    
 
    
-
    (array([ 94.06701229, 100.4715653 ]),
+
    (array([100.52856538,  95.74714986]),
  array([[33.33333333,  0.        ],
         [ 0.        , 33.33333333]]))
 
    
@@ -1496,12 +1496,12 @@ 
    6.8. 
 
    
 
    
 
    
-
    The mean and variance of θ conditional on y1, y2, y3, y4  are 94.07 and 33.33 respectively
-The mean and variance of θ conditional on y1, y2          are 94.07 and 33.33 respectively
+
    The mean and variance of θ conditional on y1, y2, y3, y4  are 100.53 and 33.33 respectively
+The mean and variance of θ conditional on y1, y2          are 100.53 and 33.33 respectively
 The mean and variance of θ conditional on y3, y4          are 100.00 and 100.00 respectively
-The mean and variance of η conditional on y1, y2, y3, y4  are 100.47 and 33.33 respectively
+The mean and variance of η conditional on y1, y2, y3, y4  are 95.75 and 33.33 respectively
 The mean and variance of η conditional on y1, y2          are 100.00 and 100.00 respectively
-The mean and variance of η conditional on y3, y4          are 100.47 and 33.33 respectively
+The mean and variance of η conditional on y3, y4          are 95.75 and 33.33 respectively
 
    
 
    
 
    
@@ -1757,12 +1757,12 @@ 
    6.9.1. Smoothing Example
-
    X =  [0.95243558 1.09047684 1.50208752 0.70245538]
-Y =  [0.88958073 1.04073463 1.42410312 0.64297361]
+
    X =  [0.41420076 0.84605636 1.02995885 0.24857123]
+Y =  [0.43081146 0.8680004  1.07296077 0.22667393]
  E [ X | Y] = 
 
    
 
    
-
    (array([0.8879057 , 1.04121919, 1.421464  , 0.6445605 ]),
+
    (array([0.4308138 , 0.86745331, 1.07058231, 0.22851146]),
  array([[2.48875094e-03, 5.57449314e-06, 1.24861729e-08, 2.80236945e-11],
         [5.57449314e-06, 2.48876343e-03, 5.57452116e-06, 1.25113944e-08],
         [1.24861728e-08, 5.57452116e-06, 2.48876346e-03, 5.58575339e-06],
@@ -1835,7 +1835,7 @@ 
    6.9.2. Filtering Exercise
-
    (array([1.28059978]), array([[1.00201996]]))
+
    (array([0.96500878]), array([[1.00201996]]))
 
    
 
    
 
    
@@ -1900,7 +1900,7 @@ 
    6.9.3. Prediction Exercise
-
    (array([0.84250698]), array([[1.81413617]]))
+
    (array([0.7021102]), array([[1.81413617]]))
 
    
 
    
 
    
@@ -1945,7 +1945,7 @@ 
    6.9.4. Constructing a Wold Representatio
 
    
 
    
 
    
-
    array([ 0.88847083,  0.24156323,  0.48688513, -0.63619001])
+
    array([ 0.43027396,  0.48015308,  0.29217875, -0.73667186])
 
    
 
    
 
    
@@ -1957,7 +1957,7 @@ 
    6.9.4. Constructing a Wold Representatio
 
    
 
    
 
    
-
    array([0.88958073, 1.04073463, 1.42410312, 0.64297361])
+
    array([0.43081146, 0.8680004 , 1.07296077, 0.22667393])
 
    
 
    
 
    
@@ -2254,7 +2254,7 @@ 
    6.11. 
 
    
 
    
-_images/c577db4dd75556c0f01c0a3bab42b82666652f366d4280f97d6dc0555cbaf7a8.png
+_images/8462fe542bc6b35b8d0aa059eab3a81f468e24a467c779398f2232d62653dbee.png
 
    
 
    
 
    In the above graph, the green line is what the price of the stock would
@@ -2708,7 +2708,7 @@ 
    6.13. 
 
    
 
    
-
    (array([-0.66020949,  0.36056727]),
+
    (array([-2.66759188, -0.07854034]),
  array([[0.04761905, 0.        ],
         [0.        , 0.04761905]]))
 
    
@@ -2727,7 +2727,7 @@ 
    6.13. 
 
    
 
    
-
    array([-0.66020949,  0.36056727])
+
    array([-2.66759188, -0.07854034])
 
    
 
    
 
    
@@ -2740,8 +2740,8 @@ 
    6.13. 
 
    
 
    
-
    (array([-0.5959297 , -0.5959297 , -0.5959297 , -0.5959297 , -0.5959297 ,
-         0.14201974,  0.14201974,  0.14201974,  0.14201974,  0.14201974]),
+
    (array([-2.91933291, -2.91933291, -2.91933291, -2.91933291, -2.91933291,
+         0.01516719,  0.01516719,  0.01516719,  0.01516719,  0.01516719]),
  array([[0.25, 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],
         [0.  , 0.25, 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],
         [0.  , 0.  , 0.25, 0.  , 0.  , 0.  , 0.  , 0.  , 0.  , 0.  ],
@@ -2765,8 +2765,8 @@ 
    6.13. 
 
    
 
    
-
    array([-0.5959297 , -0.5959297 , -0.5959297 , -0.5959297 , -0.5959297 ,
-        0.14201974,  0.14201974,  0.14201974,  0.14201974,  0.14201974])
+
    array([-2.91933291, -2.91933291, -2.91933291, -2.91933291, -2.91933291,
+        0.01516719,  0.01516719,  0.01516719,  0.01516719,  0.01516719])
 
    
 
    
 
    
@@ -2868,8 +2868,9 @@ 
    6.14. 
 
    
 
    
-
    ε =  [ 0.84656557 -1.55008696  0.6512519  -0.07484045 -0.25961836 -0.0072204
- -0.19973887  0.13112262 -0.15425939 -0.71370551]
+
    ε =  [-1.84402614e-01 -6.26316262e+00 -5.50358461e-01 -7.21373647e-01
+ -6.40530477e-01 -4.20463776e-01  1.69595229e-01 -3.99981810e-01
+ -4.79474556e-03 -2.66155410e-01]
 
    
 
    
 
    
@@ -2883,7 +2884,7 @@ 
    6.14. 
 
    
 
    
-
    f =  [-0.5959297   0.14201974]
+
    f =  [-2.91933291  0.01516719]
 
    
 
    
 
    
@@ -2912,7 +2913,7 @@ 
    6.14. 
 
    
 
    
-_images/88187e9523e3e67fb8bd4da1de55e3d73dfa9a277f264a02ef19112f2917d870.png
+_images/fe30aac9519fd5e8e2f5cb9122683f55fc56e645a1346c5b1c1112e809ead0c5.png
 
    
 
    
 
    Consequently, the first two \(\epsilon_{j}\) correspond to the
@@ -2925,7 +2926,7 @@ 
    6.14. 
 
    
 
    
-
    array([ 0.84656557, -1.55008696])
+
    array([-0.18440261, -6.26316262])
 
    
 
    
 
    
@@ -2938,7 +2939,7 @@ 
    6.14. 
 
    
 
    
-
    array([-0.66020949,  0.36056727])
+
    array([-2.66759188, -0.07854034])
 
    
 
    
 
    
@@ -2994,7 +2995,7 @@ 
    6.14. 
 
    
 
    
-_images/366513170497aa946b6791673775dd1de71ef76537198a0af4f8810fbda159f8.png
+_images/531b57e40e9c621ac10f321cddb95490bc58e988ea094e140348e30c40842395.png
 
    
 
    
 
    The covariance matrix of \(\hat{Y}\) can be computed by first
diff --git a/navy_captain.html b/navy_captain.html
index e4817be..2693531 100644
--- a/navy_captain.html
+++ b/navy_captain.html
@@ -269,14 +269,16 @@ 
    17. B
 
    
 
      Downloading interpolation-2.2.1-py3-none-any.whl (56 kB)
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    17.3. 
 
    
 
    
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    We can compute sequences of likelihood ratios using simulated samples.
    
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    17.3. 
 
    
 
    
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    Our frequentist minimizes the expected total loss presented in equation
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    17.3. 
 
    
 
    
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    17.3. 
 
    
 
    
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    The following shows how optimal sample size \(t\) and targeted
@@ -778,7 +780,7 @@ 
    17.3. 
 
    
 
    
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@@ -925,7 +927,7 @@ 
    17.4. 
 
    
 
    
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    The above figure portrays the value function plotted against the decision
@@ -1031,7 +1033,7 @@ 
    17.4. 
 
    
 
    
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    Given an assumed value for
@@ -1083,7 +1085,7 @@ 
    17.4. 
 
    
 
    
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    This pattern of outcomes holds more generally.
    
@@ -1163,7 +1165,7 @@ 
    17.5. 
 
    
 
    
-_images/6edf40b1b3509c6684df2de47caf6c6df3c265dbda927cf7cbeabe3237573852.png
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    Evidently, there is no sample size \(t\) at which the frequentist
@@ -1188,7 +1190,7 @@ 
    17.5. 
 
    
 
    
-_images/92835edc4afa76b88b479ecd4cae5d64bc6b6276c1dc724bf4e83c0c463b905c.png
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    The right panel of the above graph plots the difference
@@ -1301,7 +1303,7 @@ 
    17.7. 
 
    
 
    
-_images/a42a5a62beba27abea63968ae5b6502945ef402f787381aafe3d3babfc4576af.png
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    Later we’ll figure out how these distributions ultimately affect
@@ -1341,7 +1343,7 @@ 
    17.7. 
 
    
 
    
-_images/852b19c54255f3f41dbaafcb451ac233b0b0a7ce3bf0a00e1aea17a978fdfb79.png
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    The above figures compare averages and variances of updated Bayesian
@@ -1377,7 +1379,7 @@ 
    17.7. 
 
    
 
    
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@@ -1423,7 +1425,7 @@ 
    17.8. 
 
    
 
    
-_images/9088b57f62e60431008410840149675251e2a0ac598f74064d81b01e30257c22.png
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    By averaging using \(\pi^{*}\), we also plot the unconditional
@@ -1448,7 +1450,7 @@ 
    17.8. 
 
    
 
    
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@@ -1492,7 +1494,7 @@ 
    17.9. 
 
    
 
    
-_images/5b20862d3d338dcd8026945f7e6079556e8c1f1f66472c6dd1baad69347495d6.png
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    The next graph plots the unconditional distribution of Bayesian times to
@@ -1515,7 +1517,7 @@ 
    17.9. 
 
    
 
    
-_images/f6f14832d0d521729261d4f6ac8649cee3233b17d1c805bc469e762a8f23f2fe.png
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    4.10. Generating Random Numbers
 
    
 
    
-_images/6a1a7fb16409106a1f7d70af5c7659774a268fcddf84851b153d1399d2ae6f73.png
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@@ -750,7 +750,7 @@ 
    4.10. Generating Random Numbers
 
    
 
    
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    Geometric distribution
    
@@ -817,7 +817,7 @@ 
    4.10. Generating Random Numbers
 
    
 
    
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    4.10. Generating Random Numbers
 
    
 
    
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    67
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    4.10. Generating Random Numbers
 
    
 
    
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@@ -901,8 +901,8 @@ 
    4.12. Geometric distribution
-
    The sample mean is:  3.330922 
-The sample variance is:  7.746850629916
+
    The sample mean is:  3.335851 
+The sample variance is:  7.794655105799005
 
 The population mean is:  3.3333333333333335
 The population variance is:  7.777777777777778
@@ -1016,8 +1016,8 @@ 
    4.12.2. Pascal (negative binomial) distr
 
    
 
    
 
    
-
    The sample mean is:  23.319227 
-The sample variance is:  77.73253912247104
+
    The sample mean is:  23.33843 
+The sample variance is:  77.8551591351
 
 The population mean is:  23.333333333333336
 The population variance is:  77.77777777777779
@@ -1061,8 +1061,8 @@ 
    4.13.1. Univariate Gaussian distribution
 
    
 
    
 
    
-
    The sample mean is:  9.636478246143661e-06
-The sample standard deviation is:  0.10000523925464563
+
    The sample mean is:  9.608895325681954e-05
+The sample standard deviation is:  0.10009814368839606
 
    
 
    
 
    
@@ -1122,8 +1122,8 @@ 
    4.13.2. Uniform Distribution
-
    The sample mean is:  15.001536794231042 
-The sample variance is:  8.336328987868342
+
    The sample mean is:  14.999499889014206 
+The sample variance is:  8.335783207735261
 
 The population mean is:  15.0
 The population variance is:  8.333333333333334
@@ -1167,8 +1167,8 @@ 
    4.14. A Mixed Discrete-Continuous Distri
 
    
 
    
 
    
-
    The sample mean is:  17.476148753558295 
-The sample variance is:  5851.348691429288
+
    The sample mean is:  17.53292902964758 
+The sample variance is:  5875.127696851872
 
    
 
    
 
    
@@ -1251,8 +1251,8 @@ 
    4.15. Matrix Representation of Some Biva
 
    
 
    
 
    
-
    [[ 1.  0.  0. ...  0.  1.  0.]
- [10. 10. 20. ... 10. 20. 10.]]
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+ [20. 20. 20. ... 20. 20. 20.]]
 
    
 
    
 
    
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    4.15. Matrix Representation of Some Biva
 
    
 
    
 
    marginal distribution for x
-+---------+---------------------+
-| x_value |        x_prob       |
-+---------+---------------------+
-|    0    |       0.500821      |
-|    1    | 0.49917900000000004 |
-+---------+---------------------+
++---------+----------+
+| x_value |  x_prob  |
++---------+----------+
+|    0    | 0.500833 |
+|    1    | 0.499167 |
++---------+----------+
 
 marginal distribution for y
-+---------+--------+
-| y_value | y_prob |
-+---------+--------+
-|    10   | 0.4009 |
-|    20   | 0.5991 |
-+---------+--------+
++---------+----------+
+| y_value |  y_prob  |
++---------+----------+
+|    10   | 0.399922 |
+|    20   | 0.600078 |
++---------+----------+
 
    
 
    
 
    
@@ -1333,20 +1333,20 @@ 
    4.15. Matrix Representation of Some Biva
 
    
 
    
 
    conditional distribution for x
-+---------+---------------------+--------------------+
-| y_value |      prob(x=0)      |     prob(x=1)      |
-+---------+---------------------+--------------------+
-|    10   |  0.7512671489149414 | 0.2487328510850586 |
-|    20   | 0.33322984476715073 | 0.6667701552328493 |
-+---------+---------------------+--------------------+
++---------+---------------------+---------------------+
+| y_value |      prob(x=0)      |      prob(x=1)      |
++---------+---------------------+---------------------+
+|    10   |  0.7500087517065828 | 0.24999124829341723 |
+|    20   | 0.33476981325760985 |  0.6652301867423902 |
++---------+---------------------+---------------------+
 
 conditional distribution for y
-+---------+---------------------+--------------------+
-| x_value |      prob(y=10)     |     prob(y=20)     |
-+---------+---------------------+--------------------+
-|    0    |  0.6013785364431603 | 0.3986214635568397 |
-|    1    | 0.19976200921913784 | 0.8002379907808621 |
-+---------+---------------------+--------------------+
++---------+---------------------+---------------------+
+| x_value |      prob(y=10)     |      prob(y=20)     |
++---------+---------------------+---------------------+
+|    0    |  0.5988922455189654 | 0.40110775448103464 |
+|    1    | 0.20028767927366994 |   0.79971232072633  |
++---------+---------------------+---------------------+
 
    
 
    
 
    
@@ -1550,8 +1550,8 @@ 
    4.15. Matrix Representation of Some Biva
  +---------+----------+
 | x_value |  x_prob  |
 +---------+----------+
-|    0    | 0.500416 |
-|    1    | 0.499584 |
+|    0    | 0.500002 |
+|    1    | 0.499998 |
 |   sum   |   1.0    |
 +---------+----------+
 
@@ -1559,8 +1559,8 @@ 
    4.15. Matrix Representation of Some Biva
  +---------+----------+
 | y_value |  y_prob  |
 +---------+----------+
-|    10   | 0.400367 |
-|    20   | 0.599633 |
+|    10   | 0.400105 |
+|    20   | 0.599895 |
 |   sum   |   1.0    |
 +---------+----------+
 
    
@@ -1576,19 +1576,19 @@ 
    4.15. Matrix Representation of Some Biva
 
    
 
    
 
    conditional distribution for x
- +---------+---------------------+--------------------+-----+
-| x_value |          0          |         1          | sum |
-+---------+---------------------+--------------------+-----+
-|    10   |  0.7517852370450112 | 0.2482147629549888 | 1.0 |
-|    20   | 0.33258009482466777 | 0.6674199051753322 | 1.0 |
-+---------+---------------------+--------------------+-----+
+ +---------+--------------------+---------------------+-----+
+| x_value |         0          |          1          | sum |
++---------+--------------------+---------------------+-----+
+|    10   | 0.7495232501468364 | 0.25047674985316354 | 1.0 |
+|    20   | 0.3335817101326065 |  0.6664182898673935 | 1.0 |
++---------+--------------------+---------------------+-----+
 
 conditional distribution for y
  +---------+---------------------+--------------------+-----+
 | y_value |          10         |         20         | sum |
 +---------+---------------------+--------------------+-----+
-|    0    |  0.6014795689985931 | 0.3985204310014068 | 1.0 |
-|    1    | 0.19891950102485267 | 0.8010804989751473 | 1.0 |
+|    0    |  0.5997736009055964 | 0.4002263990944036 | 1.0 |
+|    1    | 0.20043480173920697 | 0.7995651982607931 | 1.0 |
 +---------+---------------------+--------------------+-----+
 
    
 
    
@@ -1631,9 +1631,9 @@ 
    4.15. Matrix Representation of Some Biva
  +---------+----------+
 | x_value |  x_prob  |
 +---------+----------+
-|    10   | 0.299775 |
-|    20   | 0.399669 |
-|    30   | 0.300556 |
+|    10   | 0.300108 |
+|    20   | 0.399395 |
+|    30   | 0.300497 |
 |   sum   |   1.0    |
 +---------+----------+
 
@@ -1641,8 +1641,8 @@ 
    4.15. Matrix Representation of Some Biva
  +---------+----------+
 | y_value |  y_prob  |
 +---------+----------+
-|    1    | 0.450522 |
-|    2    | 0.549478 |
+|    1    | 0.451167 |
+|    2    | 0.548833 |
 |   sum   |   1.0    |
 +---------+----------+
 
    
@@ -1660,18 +1660,18 @@ 
    4.15. Matrix Representation of Some Biva
  +---------+---------------------+---------------------+---------------------+-----+
 | x_value |          10         |          20         |          30         | sum |
 +---------+---------------------+---------------------+---------------------+-----+
-|    1    | 0.44336569579288027 | 0.22271276430451786 | 0.33392153990260187 | 1.0 |
-|    2    | 0.18204368509749252 |  0.544757023939084  |  0.2731992909634235 | 1.0 |
+|    1    |  0.4437026644235948 | 0.22223699871666147 | 0.33406033685974373 | 1.0 |
+|    2    | 0.18206631161027126 |  0.5450273580488054 |  0.2729063303409234 | 1.0 |
 +---------+---------------------+---------------------+---------------------+-----+
 
 conditional distribution for y
- +---------+--------------------+---------------------+-----+
-| y_value |         1          |          2          | sum |
-+---------+--------------------+---------------------+-----+
-|    10   | 0.6663197398048536 | 0.33368026019514635 | 1.0 |
-|    20   | 0.2510502440769737 |  0.7489497559230263 | 1.0 |
-|    30   | 0.5005356738844009 |  0.4994643261155991 | 1.0 |
-+---------+--------------------+---------------------+-----+
+ +---------+--------------------+--------------------+-----+
+| y_value |         1          |         2          | sum |
++---------+--------------------+--------------------+-----+
+|    10   | 0.6670398656483666 | 0.3329601343516334 | 1.0 |
+|    20   | 0.2510447051164887 | 0.7489552948835113 | 1.0 |
+|    30   | 0.5015590837845303 | 0.4984409162154697 | 1.0 |
++---------+--------------------+--------------------+-----+
 
    
 
    
 
    
@@ -1796,10 +1796,10 @@ 
    4.16. A Continuous Bivariate Random Vect
 
    
 
    
 
    
-
    -0.002411765363199629 2.237559077223067
+
    0.0032480593471459394 2.2354098871665107
 
    
 
    
-_images/b53d6756caada07da19391897251f777bdfc20076bee25aec52b379514665cca.png
+_images/d1b7f1c58540a6de418725dfbdd7c06aef1a2d1df4a869381606ab92800cf369.png
 
    
 
    
 
    
@@ -1814,10 +1814,10 @@ 
    4.16. A Continuous Bivariate Random Vect
 
    
 
    
 
    
-
    5.001308753910631 1.0001803340799973
+
    5.000450929226026 0.9990968176580851
 
    
 
    
-_images/7f3e268b97bf5cf71b6fdbdc208ef857c1997495fb5bab797b84a97a31c8a8fe.png
+_images/a1cc90a49f8238de0a5d1ee8b5b0431be73599e2455212dd4159e58d0130b12e.png
 
    
 
    
 
    Conditional distribution
    
@@ -1875,7 +1875,7 @@ 
    4.16. A Continuous Bivariate Random Vect
 
    
 
    
 
    
-_images/61afba31d38f78cb208482ad14a7ebeb0e8cd9295cb20053f264d16850b41258.png
+_images/2de054a7495bca17a640a6d7de56f4f617dd82b12660e96ab2a4a9a6e8ae23d1.png
 
    
 
    
 
    Fix \(x=1\).
    
@@ -1906,7 +1906,7 @@ 
    4.16. A Continuous Bivariate Random Vect
 
    
 
    
 
    
-_images/b57504942226fa8c850beb8132d83d1e31931552d045247e246cefc20c78abdd.png
+_images/8a7a1b6ddba1a3d5a8289c38aee8ea7b2ec6ebe2083bb28241055d85291f802a.png
 
    
 
    
 
    We compare  with the analytically computed parameters and note that they are close.
    
@@ -2191,15 +2191,15 @@ 
    4.20. Copula Functions4.20. Copula Functions4.20. Copula Functions4.20. Copula Functions4.20. Copula Functions7.1. Overview
 
    
 
    Requirement already satisfied: prettytable in /opt/conda/envs/quantecon/lib/python3.11/site-packages (3.9.0)
-Requirement already satisfied: wcwidth in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from prettytable) (0.2.5)
+
    
+
    
+
    Requirement already satisfied: wcwidth in /opt/conda/envs/quantecon/lib/python3.11/site-packages (from prettytable) (0.2.5)
 
    
 
    
 
    WARNING: Running pip as the 'root' user can result in broken permissions and conflicting behaviour with the system package manager. It is recommended to use a virtual environment instead: https://pip.pypa.io/warnings/venv
@@ -422,24 +424,24 @@ 
    7.2. Frequentist Interpretation
    
 
    
@@ -489,7 +491,7 @@ 
    7.2. Frequentist Interpretation
 
    
 
    
-_images/042687b62982e880e5b68616fcaa9ec0fe47c18d784518bd6bc15e4a5d8e068c.png
+_images/83a6a56fbc12de62823ee139d1c98f59d66dd7badebbd71bd600e0b88f6ce08b.png
 
    
 
    
 
    Comparison with different \(n\)
    
@@ -528,7 +530,7 @@ 
    7.2. Frequentist Interpretation
 
    
 
    
-_images/5a9743313175bdd64ae5f2507fd175659255b2f8884594abf4d63ebbf963c681.png
+_images/4bb1d7c565690ab1304c973c8d68546668798fca503611880371ed0b53f908f7.png
 
    
 
    
 
    Comparison with different \(I\)
    
@@ -567,7 +569,7 @@ 
    7.2. Frequentist Interpretation
 
    
 
    
-_images/7e58dd700f3c9bfef1a8a1823336cf5e851e302330d3dd711d295ecde44fb7ac.png
+_images/2cc7bb5e6e181b01c132d2cd4057383b00b19aa8d82719dc303897470af47897.png
 
    
 
    
 
    From the above graphs, we can see that \(I\), the number of independent sequences, plays an important role.
    
@@ -747,7 +749,7 @@ 
    7.3. Bayesian Interpretation
-_images/576a6603c052cb0c4cdd512496ff249530bc7256dfaf34b15d8d2d62beb46277.png
+_images/3bb5f589685941d8eae90c94a1cef6467b10ccaf95c4520594fc751f17bc016d.png
 
    
 
    
 
    e) For various \(n\)’s, please describe and compute  \(.05\) and \(.95\) quantiles for  posterior probabilities.
    
@@ -804,36 +806,36 @@ 
    7.3. Bayesian Interpretation7.3. Bayesian Interpretation
-_images/c73e464707d27eb3215f6c4485ba5961bc0cb68313ed3c84b6fb6db8a69e86b4.png
+_images/d0e95f43f0d51eeee47820a41d2eb960acd0db3b079fe8947163fa18cef670cf.png
 
    
 
    
 
    Notice that in the graph above the posterior probabililty that \(\theta \in [.45, .55]\) typically exhibits a hump shape as \(n\) increases.
    
@@ -900,7 +902,7 @@ 
    7.3. Bayesian Interpretation
-_images/28686568e8d75867968147792a3f8f446262b4d81b6ee83435b8b025fa2e2b37.png
+_images/46a5d8bc079823e9e7c38f4982e7c172eb4893955d918f20294e82cfc3a264ba.png
 
    
 
    
 
    As \(n\) increases, we can see that the probability density functions concentrate on \(0.4\), the true value of \(\theta\).
    
@@ -930,7 +932,7 @@ 
    7.3. Bayesian Interpretation
-_images/b2ab30ff98e5b167d27cc43c5d5f621b3ee713626b801354c5313da3bc183c4c.png
+_images/81fd826451b75fda8b85b07ec0cd04e9b1d8364d7999ce9dbc9a530cb3332c6b.png
 
    
 
    
 
@@ -985,7 +987,7 @@ 
    7.3. Bayesian Interpretation
-_images/5bc62da97739d8e3aff73c006dcd836e2efc919a19b7a45493e35efe65a289e9.png
+_images/5b980c197bd3d772fe67ef4e7244b390455b488e5c6cec00a3adb6c87fdf10f1.png
 
    
 
    
 
    After observing a large number of outcomes, the  posterior distribution collapses around \(0.4\).
    
diff --git a/rand_resp.html b/rand_resp.html
index 90cc867..aa488ee 100644
--- a/rand_resp.html
+++ b/rand_resp.html
@@ -229,7 +229,7 @@ 
    21.1. OverviewSocial stigmas can inhibit people from confessing potentially embarrassing activities or opinions.
    
 
    When people are reluctant to participate a sample survey about personally  sensitive issues, they  might decline  to participate, and even if they do participate, they might choose to provide incorrect answers to  sensitive questions.
    
 
    These problems induce  selection  biases that present challenges to interpreting and designing surveys.
    
-
    To illustrate how social scientists have thought about estimating the prevalence of such embarrassing activities and opinions, this lecture describes a classic approach  of S. L. Warner [War65].
    
+
    To illustrate how social scientists have thought about estimating the prevalence of such embarrassing activities and opinions, this lecture describes a classic approach  of S. L. Warner [War65].
    
 
    Warner  used elementary  probability to construct a  way to protect the privacy  of individual respondents to surveys while still    estimating  the fraction of a collection of individuals   who have a socially stigmatized characteristic or who engage in  a socially stigmatized activity.
    
 
    Warner’s idea was to  add noise between the respondent’s answer and the signal about that answer that the  survey maker ultimately receives.
    
 
    Knowing about the structure of the noise assures the respondent that the survey maker does not observe his answer.
    
@@ -250,7 +250,7 @@ 
    21.2. Warner’s Strategy\(\pi\) who belong to Group A while protecting individual respondents’ privacy.
    
-
    Warner [War65] proposed and analyzed the following procedure.
    
+
    Warner [War65] proposed and analyzed the following procedure.
    
 
    
 
    
-
    We can also revisit a calculation in the  concluding section of Warner [War65] in which
    
+
    We can also revisit a calculation in the  concluding section of Warner [War65] in which
    
 
      
 
    • \(\pi_A=0.6\)
      • 
 
    • \(n=2000\)
      • 
@@ -1379,7 +1379,7 @@ 
      21.3. Comparing Two Survey Designs21.4. Concluding Remarks#
      
 
      This QuantEcon lecture  describes some alternative randomized response surveys.
      
 
      That lecture presents a utilitarian analysis of those alternatives conducted by Lars Ljungqvist
-[Lju93].
      
+[Lju93].
      
 
 
 
diff --git a/searchindex.js b/searchindex.js
index b2df6e2..87d7f3f 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
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\ No newline at end of file
diff --git a/status.html b/status.html
index 04c4d64..063df63 100644
--- a/status.html
+++ b/status.html
@@ -225,159 +225,159 @@ 
      25. Execution Statistics
      ar1_bayes
      
-
      2024-01-24 00:50
      
+
      2024-01-29 00:22
      
 
      cache
      
-
      572.23
      
+
      598.32
      
 
      ✅
      
 
 
      ar1_turningpts
      
-
      2024-01-24 00:51
      
+
      2024-01-29 00:23
      
 
      cache
      
-
      60.45
      
+
      62.53
      
 
      ✅
      
 
 
      back_prop
      
-
      2024-01-24 00:54
      
+
      2024-01-29 00:26
      
 
      cache
      
-
      133.16
      
+
      136.09
      
 
      ✅
      
 
 
      bayes_nonconj
      
-
      2024-01-24 02:01
      
+
      2024-01-29 01:37
      
 
      cache
      
-
      4027.08
      
+
      4279.22
      
 
      ✅
      
 
 
      exchangeable
      
-
      2024-01-24 02:01
      
+
      2024-01-29 01:37
      
 
      cache
      
-
      9.97
      
+
      10.17
      
 
      ✅
      
 
 
      hoist_failure
      
-
      2024-01-24 02:02
      
+
      2024-01-29 01:38
      
 
      cache
      
-
      76.49
      
+
      75.62
      
 
      ✅
      
 
 
      imp_sample
      
-
      2024-01-24 02:07
      
+
      2024-01-29 01:43
      
 
      cache
      
-
      277.73
      
+
      275.9
      
 
      ✅
      
 
 
      intro
      
-
      2024-01-24 02:07
      
+
      2024-01-29 01:43
      
 
      cache
      
-
      1.14
      
+
      4.02
      
 
      ✅
      
 
 
      likelihood_bayes
      
-
      2024-01-24 02:08
      
+
      2024-01-29 01:44
      
 
      cache
      
-
      49.06
      
+
      49.22
      
 
      ✅
      
 
 
      likelihood_ratio_process
      
-
      2024-01-24 02:08
      
+
      2024-01-29 01:44
      
 
      cache
      
-
      10.38
      
+
      10.98
      
 
      ✅
      
 
 
      lln_clt
      
-
      2024-01-24 02:08
      
+
      2024-01-29 01:44
      
 
      cache
      
-
      14.75
      
+
      15.36
      
 
      ✅
      
 
 
      mix_model
      
-
      2024-01-24 02:09
      
+
      2024-01-29 01:45
      
 
      cache
      
-
      38.99
      
+
      39.68
      
 
      ✅
      
 
 
      mle
      
-
      2024-01-24 02:09
      
+
      2024-01-29 01:45
      
 
      cache
      
-
      6.04
      
+
      6.2
      
 
      ✅
      
 
 
      multi_hyper
      
-
      2024-01-24 02:09
      
+
      2024-01-29 01:45
      
 
      cache
      
-
      25.55
      
+
      26.26
      
 
      ✅
      
 
 
      multivariate_normal
      
-
      2024-01-24 02:09
      
+
      2024-01-29 01:46
      
 
      cache
      
-
      5.39
      
+
      5.87
      
 
      ✅
      
 
 
      navy_captain
      
-
      2024-01-24 02:10
      
+
      2024-01-29 01:46
      
 
      cache
      
-
      37.81
      
+
      39.27
      
 
      ✅
      
 
 
      ols
      
-
      2024-01-24 02:10
      
+
      2024-01-29 01:47
      
 
      cache
      
-
      17.24
      
+
      17.47
      
 
      ✅
      
 
 
      pandas_panel
      
-
      2024-01-24 02:10
      
+
      2024-01-29 01:47
      
 
      cache
      
-
      5.86
      
+
      5.98
      
 
      ✅
      
 
 
      prob_matrix
      
-
      2024-01-24 02:11
      
+
      2024-01-29 01:47
      
 
      cache
      
-
      18.06
      
+
      18.14
      
 
      ✅
      
 
 
      prob_meaning
      
-
      2024-01-24 02:12
      
+
      2024-01-29 01:48
      
 
      cache
      
-
      76.02
      
+
      76.77
      
 
      ✅
      
 
 
      rand_resp
      
-
      2024-01-24 02:12
      
+
      2024-01-29 01:48
      
 
      cache
      
-
      3.02
      
+
      3.08
      
 
      ✅
      
 
 
      status
      
-
      2024-01-24 02:07
      
+
      2024-01-29 01:43
      
 
      cache
      
-
      1.14
      
+
      4.02
      
 
      ✅
      
 
 
      troubleshooting
      
-
      2024-01-24 02:07
      
+
      2024-01-29 01:43
      
 
      cache
      
-
      1.14
      
+
      4.02
      
 
      ✅
      
 
 
      util_rand_resp
      
-
      2024-01-24 02:12
      
+
      2024-01-29 01:48
      
 
      cache
      
-
      3.73
      
+
      3.54
      
 
      ✅
      
 
 
      wald_friedman
      
-
      2024-01-24 02:12
      
+
      2024-01-29 01:49
      
 
      cache
      
-
      20.09
      
+
      20.53
      
 
      ✅
      
 
 
      zreferences
      
-
      2024-01-24 02:07
      
+
      2024-01-29 01:43
      
 
      cache
      
-
      1.14
      
+
      4.02
      
 
      ✅
      
 
 
diff --git a/util_rand_resp.html b/util_rand_resp.html
index 1fb7d49..5d20185 100644
--- a/util_rand_resp.html
+++ b/util_rand_resp.html
@@ -258,12 +258,12 @@
 
      22. Expected Utilities of Random Responses#
      
 
      
 
      22.1. Overview#
      
-
      This QuantEcon lecture describes randomized response surveys in the tradition of Warner [War65] that are designed  to protect  respondents’ privacy.
      
-
      Lars Ljungqvist [Lju93]  analyzed how a respondent’s decision about whether to answer truthfully depends on  expected utility.
      
+
      This QuantEcon lecture describes randomized response surveys in the tradition of Warner [War65] that are designed  to protect  respondents’ privacy.
      
+
      Lars Ljungqvist [Lju93]  analyzed how a respondent’s decision about whether to answer truthfully depends on  expected utility.
      
 
      The lecture tells how Ljungqvist  used his  framework to shed light on alternative randomized response survey techniques
-proposed, for example, by [Lan75], [Lan76], [LW76],
-[And76], [FPS77], [GKAH77],
-[GAESH69].
      
+proposed, for example, by [Lan75], [Lan76], [LW76],
+[And76], [FPS77], [GKAH77],
+[GAESH69].
      
 
      
 
      
 
      22.2. Privacy Measures#
      
@@ -335,8 +335,8 @@ 
      22.3.1. Leysieffer and Warner(1976)
 
      
 
      22.3.2. Lanke(1976)#
      
-
      Lanke (1975) [Lan75] argued that “it is membership in Group A that people may want to hide, not membership in the complementary Group A’.”
      
-
      For that reason, Lanke (1976) [Lan76] argued  that an appropriate measure of protection is to minimize
      
+
      Lanke (1975) [Lan75] argued that “it is membership in Group A that people may want to hide, not membership in the complementary Group A’.”
      
+
      For that reason, Lanke (1976) [Lan76] argued  that an appropriate measure of protection is to minimize
      
 
      
 (22.5)#\[
 \max \left\{ \text{Pr}(A|\text{yes}) , \text{Pr}(A|\text{no}) \right\}
@@ -345,7 +345,7 @@ 
      22.3.2. Lanke(1976)
 
      
 
      22.3.3. 2.3 Fligner, Policello, and Singh#
      
-
      Fligner, Policello, and Singh reached similar conclusion as Lanke (1976). [FPS77]
      
+
      Fligner, Policello, and Singh reached similar conclusion as Lanke (1976). [FPS77]
      
 
      They measured “private protection” as
      
 
      
 (22.6)#\[
@@ -354,7 +354,7 @@ 
      22.3.3. 2.3 Fligner, Policello, and Sing
 
      
 
      
 
      22.3.4. 2.4 Greenberg, Kuebler, Abernathy, and Horvitz (1977)#
      
-
      [GKAH77]
      
+
      [GKAH77]
      
 
      Greenberg, Kuebler, Abernathy, and Horvitz (1977) stressed the importance of examining the risk to respondents who do not belong to \(A\) as well as the risk to those who do belong to the sensitive group.
      
 
      They defined the hazard for an individual in \(A\) as the probability that he or she is perceived as belonging to \(A\):
      
 
    
-
    Given a design that ensures truthful answers by all respondents, Anderson(1976, Theorem 1) [And76] showed that the minimum variance estimate in the two-response model has variance
    
+
    Given a design that ensures truthful answers by all respondents, Anderson(1976, Theorem 1) [And76] showed that the minimum variance estimate in the two-response model has variance
    
 
    
 (22.17)#\[
 \begin{aligned}
@@ -617,7 +617,7 @@ 
    22.5.2. Drawing  Iso-variance Curves
    All points on one iso-variance curve share the same variance
    
 
  • From \(V_1\) to \(V_9\), the variance of the iso-variance curve increase monotonically, as colors  brighten monotonically
    • 
 
-
    Suppose the parameters of the iso-variance model follow those in Ljungqvist [Lju93], which are:
    
+
    Suppose the parameters of the iso-variance model follow those in Ljungqvist [Lju93], which are:
    
 
-
    A practical implication of the  analysis of [Lju93] is that uncertainty about respondents’ demands for privacy can be acknowledged by choosing \(\text{Pr}(A|\text{yes})\) and \(\text{Pr}(A|\text{no})\) sufficiently close to each other.
    
+
    A practical implication of the  analysis of [Lju93] is that uncertainty about respondents’ demands for privacy can be acknowledged by choosing \(\text{Pr}(A|\text{yes})\) and \(\text{Pr}(A|\text{no})\) sufficiently close to each other.
    
 
 
 
diff --git a/wald_friedman.html b/wald_friedman.html
index 535cedc..fa4e7b3 100644
--- a/wald_friedman.html
+++ b/wald_friedman.html
@@ -242,20 +242,20 @@
                 QuantEcon
         
 
    
-
    13. A Problem that Stumped Milton Friedman#
    
+
    13. A Problem that Stumped Milton Friedman#
    
 
    (and that Abraham Wald solved by inventing sequential analysis)
    
 
 
    
-
    13.1. Overview#
    
+
    13.1. Overview#
    
 
    This lecture describes a statistical decision problem presented to Milton
 Friedman and W. Allen Wallis during World War II when they were analysts at
 the U.S. Government’s  Statistical Research Group at Columbia University.
    
@@ -334,11 +334,16 @@ 
    13.1. this lecture.
    
 
    
 
    
-
    13.2. Origin of the Problem#
    
+
    13.2. Origin of the Problem#
    
 
    On pages 137-139 of his 1998 book Two Lucky People with Rose Friedman [FF98],
 Milton Friedman described a problem presented to him and Allen Wallis
 during World War II, when they worked at the US Government’s
 Statistical Research Group at Columbia University.
    
+
    
+
    Note
    
+
    See pages 25 and 26  of Allen Wallis’s 1980 article [Wal80]  about the Statistical Research Group at Columbia University during World War II for his account of the episode and  for important contributions  that Harold Hotelling made to formulating the problem.   Also see  chapter 5 of Jennifer Burns book about
+Milton Friedman [Bur23].
    
+
    
 
    Let’s listen to Milton Friedman tell us what happened
    
 
    
 
    In order to understand the story, it is necessary to have an idea of a
@@ -371,13 +376,13 @@ 
    13.2. 
    
 
    Friedman and Wallis struggled with the problem but, after realizing that
 they were not able to solve it,  described the problem to  Abraham Wald.
    
-
    That started Wald on the path that led him  to Sequential Analysis [Wal47].
    
+
    That started Wald on the path that led him  to Sequential Analysis [Wal47].
    
 
    We’ll formulate the problem using dynamic programming.
    
 
    
 
    
-
    13.3. A Dynamic Programming Approach#
    
+
    13.3. A Dynamic Programming Approach#
    
 
    The following presentation of the problem closely follows Dmitri
-Berskekas’s treatment in Dynamic Programming and Stochastic Control [Ber75].
    
+Berskekas’s treatment in Dynamic Programming and Stochastic Control [Ber75].
    
 
    A decision-maker can observe a sequence of draws of a random variable \(z\).
    
 
    He (or she) wants to know which of two probability distributions \(f_0\) or \(f_1\) governs \(z\).
    
 
    Conditional on knowing that successive observations are drawn from distribution \(f_0\), the sequence of
@@ -415,7 +420,7 @@ 
    13.3. 
 
    which  is a mixture of distributions \(f_0\) and \(f_1\), with the weight
-on \(f_0\) being the posterior probability that \(f = f_0\) 1.
    
+on \(f_0\) being the posterior probability that \(f = f_0\) 1.
    
 
    To  illustrate such a distribution, let’s inspect some mixtures of beta distributions.
    
 
    The density of a beta probability distribution with parameters \(a\) and \(b\) is
    
 
    
@@ -600,7 +605,7 @@ 
    13.3.4. A Bellman Equation
-
    13.4. Implementation#
    
+
    13.4. Implementation#
    
 
    First, we will construct a jitclass to store the parameters of the model
    
 
    
 
    
@@ -749,7 +754,7 @@ 
    13.4. 
 
    
 
    
-
    13.5. Analysis#
    
+
    13.5. Analysis#
    
 
    Let’s inspect outcomes.
    
 
    We will be using the default parameterization with distributions like so
    
 
    
@@ -841,7 +846,7 @@ 
    13.5.1. Value Function
-_images/ec0bf5edcd4175d6d0667474cdbcb535b664ca43bed6b582da2546729fbeba81.png
+_images/d5fe5613bd01cc37d192e001f30a709000942bd18a0c41152f4ec069bb8f9f04.png
 
    
 
    
 
    The cost function \(J\) equals \(\pi L_1\) for \(\pi \leq \beta\), and \((1-\pi )L_0\) for \(\pi
@@ -956,7 +961,7 @@ 
    13.5.2. Simulations
 
    
 
    
-_images/374280a8447fb7387de5a4bc00e57a38623d9b884e3da53764bce5fe23e7a797.png
+_images/50ab8fb2f8f032e131b5f4900c97deebf589082812ca026b35a9e9620d320316.png
 
    
 
    
 
@@ -977,7 +982,7 @@ 
    13.5.3. Comparative Statics
-_images/ce64e51c29cd5a50d9e9ea1eb297398325a6fdd3cb9512cf8cfd50ae156aa11f.png
+_images/690f05a0c249e34e31971ddfd7f1a19c089191e229969566f1c6d66a93ed43d9.png
 
    
 
    
 
    Increased cost per draw has induced the decision-maker to take fewer draws before deciding.
    
@@ -1002,7 +1007,7 @@ 
    13.5.4. A Notebook Implementation
 
 
    
-
    13.6. Comparison with Neyman-Pearson Formulation#
    
+
    13.6. Comparison with Neyman-Pearson Formulation#
    
 
    For several reasons, it is useful to describe the theory underlying the test
 that Navy Captain G. S. Schuyler had been told to use and that led him
 to approach Milton Friedman and Allan Wallis to convey his conjecture
@@ -1010,7 +1015,7 @@ 
    13.6. Evidently, the Navy had told
 Captail Schuyler to use what it knew to be a state-of-the-art
 Neyman-Pearson test.
    
-
    We’ll rely on Abraham Wald’s [Wal47] elegant summary of Neyman-Pearson theory.
    
+
    We’ll rely on Abraham Wald’s [Wal47] elegant summary of Neyman-Pearson theory.
    
 
    For our purposes, watch for there features of the setup:
    
 
-
    In chapter 1 of Sequential Analysis [Wal47] Abraham Wald summarizes the
+
    In chapter 1 of Sequential Analysis [Wal47] Abraham Wald summarizes the
 Neyman-Pearson approach to hypothesis testing.
    
 
    Wald frames the problem as making a decision about a probability
 distribution that is partially known.
    
@@ -1154,7 +1159,7 @@ 
    13.6. 
 
    
 
    
-
    13.7. Sequels#
    
+
    13.7. Sequels#
    
 
    We’ll dig deeper into some of the ideas used here in the following lectures:
    
 
      
 
    • this lecture discusses the key concept of exchangeability that rationalizes statistical learning
      • 
@@ -1165,10 +1170,10 @@ 
      13.7. 
 
      
 
      
-
      1
      
+
      1
      
 
      The decision maker acts as if he believes that the sequence of random variables
 \([z_{0}, z_{1}, \ldots]\) is exchangeable.  See Exchangeability and Bayesian Updating and
-[Kre88] chapter 11, for  discussions of exchangeability.
      
+[Kre88] chapter 11, for  discussions of exchangeability.
      
 
      
 
      
 
    
diff --git a/zreferences.html b/zreferences.html
index d2f2914..5c9645c 100644
--- a/zreferences.html
+++ b/zreferences.html
@@ -219,16 +219,19 @@
 
    AJR01
    
 
    Daron Acemoglu, Simon Johnson, and James A Robinson. The colonial origins of comparative development: an empirical investigation. The American Economic Review, 91(5):1369–1401, 2001.
    
 
    
-
    And76
    
+
    And76
    
 
    Harald Anderson. Estimation of a proportion through randomized response. International Statistical Review/Revue Internationale de Statistique, pages 213–217, 1976.
    
 
    
-
    Apo90
    
+
    Apo90
    
 
    George Apostolakis. The concept of probability in safety assessments of technological systems. Science, 250(4986):1359–1364, 1990.
    
 
    
 
    Ber75
    
 
    Dmitri Bertsekas. Dynamic Programming and Stochastic Control. Academic Press, New York, 1975.
    
 
    
-
    CM88
    
+
    Bur23
    
+
    Jennifer Burns. Milton Friedman: The Last Conservative by Jennifer Burns. Farrar, Straus, and Giroux, New York, 2023.
    
+
    
+
    CM88
    
 
    A Chadhuri and R Mukerjee. Randomized Response: Theory and Technique. Marcel Dekker, New York, 1988.
    
 
    
 
    dF37
    
@@ -237,49 +240,49 @@
 
    Dud02
    
 
    R M Dudley. Real Analysis and Probability. Cambridge Studies in Advanced Mathematics. Cambridge University Press, 2002.
    
 
    
-
    ESAW18
    
+
    ESAW18
    
 
    Ashraf Ben El-Shanawany, Keith H Ardron, and Simon P Walker. Lognormal approximations of fault tree uncertainty distributions. Risk Analysis, 38(8):1576–1584, 2018.
    
 
    
-
    FPS77
    
+
    FPS77
    
 
    Michael A Fligner, George E Policello, and Jagbir Singh. A comparison of two randomized response survey methods with consideration for the level of respondent protection. Communications in Statistics-Theory and Methods, 6(15):1511–1524, 1977.
    
 
    
 
    FF98
    
 
    Milton Friedman and Rose D Friedman. Two Lucky People. University of Chicago Press, 1998.
    
 
    
-
    GAESH69
    
+
    GAESH69
    
 
    Bernard G Greenberg, Abdel-Latif A Abul-Ela, Walt R Simmons, and Daniel G Horvitz. The unrelated question randomized response model: theoretical framework. Journal of the American Statistical Association, 64(326):520–539, 1969.
    
 
    
-
    GKAH77
    
+
    GKAH77
    
 
    Bernard G Greenberg, Roy R Kuebler, James R Abernathy, and Daniel G Horvitz. Respondent hazards in the unrelated question randomized response model. Journal of Statistical Planning and Inference, 1(1):53–60, 1977.
    
 
    
-
    GS93
    
+
    GS93
    
 
    Moses A Greenfield and Thomas J Sargent. A probabilistic analysis of a catastrophic transuranic waste hoise accident at the wipp. Environmental Evaluation Group, Albuquerque, New Mexico, June 1993. URL: http://www.tomsargent.com/research/EEG-53.pdf.
    
 
    
-
    Hur50
    
+
    Hur50
    
 
    Leonid Hurwicz. Least squares bias in time series. Statistical inference in dynamic economic models, 10:365–383, 1950.
    
 
    
 
    Kre88
    
 
    David M. Kreps. Notes on the Theory of Choice. Westview Press, Boulder, Colorado, 1988.
    
 
    
-
    Lan75
    
+
    Lan75
    
 
    Jan Lanke. On the choice of the unrelated question in simmons' version of randomized response. Journal of the American Statistical Association, 70(349):80–83, 1975.
    
 
    
-
    Lan76
    
+
    Lan76
    
 
    Jan Lanke. On the degree of protection in randomized interviews. International Statistical Review/Revue Internationale de Statistique, pages 197–203, 1976.
    
 
    
-
    LW76
    
+
    LW76
    
 
    Frederick W Leysieffer and Stanley L Warner. Respondent jeopardy and optimal designs in randomized response models. Journal of the American Statistical Association, 71(355):649–656, 1976.
    
 
    
-
    Lju93
    
+
    Lju93
    
 
    Lars Ljungqvist. A unified approach to measures of privacy in randomized response models: a utilitarian perspective. Journal of the American Statistical Association, 88(421):97–103, 1993.
    
 
    
 
    McC70
    
 
    J J McCall. Economics of Information and Job Search. The Quarterly Journal of Economics, 84(1):113–126, 1970.
    
 
    
-
    NP33
    
+
    NP33
    
 
    J. Neyman and E. S Pearson. On the problem of the most efficient tests of statistical hypotheses. Phil. Trans. R. Soc. Lond. A. 231 (694–706), pages 289–337, 1933.
    
 
    
-
    OW69
    
+
    OW69
    
 
    Guy H. Orcutt and Herbert S. Winokur. First order autoregression: inference, estimation, and prediction. Econometrica, 37(1):1–14, 1969.
    
 
    
 
    Tre16
    
@@ -288,10 +291,13 @@
 
    Wal47
    
 
    Abraham Wald. Sequential Analysis. John Wiley and Sons, New York, 1947.
    
 
    
-
    War65
    
+
    Wal80
    
+
    W Allen Wallis. The statistical research group, 1942–1945. Journal of the American Statistical Association, 75(370):320–330, 1980.
    
+
    
+
    War65
    
 
    Stanley L Warner. Randomized response: a survey technique for eliminating evasive answer bias. Journal of the American Statistical Association, 60(309):63–69, 1965.
    
 
    
-
    Wec79
    
+
    Wec79
    
 
    William E Wecker. Predicting the turning points of a time series. Journal of business, pages 35–50, 1979.
    
 
    
 
    Woo15