diff --git a/_sources/ar1_bayes.ipynb b/_sources/ar1_bayes.ipynb
index 6d206f1..1ce9e52 100644
--- a/_sources/ar1_bayes.ipynb
+++ b/_sources/ar1_bayes.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "6013ae77",
+   "id": "c10d71ae",
    "metadata": {},
    "source": [
     "# Posterior Distributions for  AR(1) Parameters\n",
@@ -13,7 +13,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47810a32",
+   "id": "c35ed4c0",
    "metadata": {
     "tags": [
      "hide-output"
@@ -27,7 +27,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "67b516d9",
+   "id": "0e69bbed",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -51,7 +51,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b9cfb0da",
+   "id": "a6787ce2",
    "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",
@@ -151,7 +151,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "adf685b2",
+   "id": "93be6790",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -179,7 +179,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6c2cd2ae",
+   "id": "2474928c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -189,7 +189,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d6051fe",
+   "id": "697bbd31",
    "metadata": {},
    "source": [
     "Now we shall use Bayes' law to construct a posterior distribution, conditioning on the initial value of $y_0$.\n",
@@ -207,7 +207,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0c363eef",
+   "id": "a990e832",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -228,7 +228,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d012b3b3",
+   "id": "09b81bea",
    "metadata": {},
    "source": [
     "[pmc.sample](https://www.pymc.io/projects/docs/en/latest/api/generated/pymc.sample.html?highlight=sample#pymc.sample) by default uses the NUTS samplers to generate samples as shown in the below cell:"
@@ -237,7 +237,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e35861a5",
+   "id": "7cf090ae",
    "metadata": {
     "tag": [
      "hide-output"
@@ -252,7 +252,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3cf2578c",
+   "id": "e4213657",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -262,7 +262,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e732852d",
+   "id": "cc38cb31",
    "metadata": {},
    "source": [
     "Evidently, the posteriors aren't centered on the true values of $.5, 1$ that we used to generate the data.\n",
@@ -278,7 +278,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "77d718a3",
+   "id": "3916f902",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -290,7 +290,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c0f469a",
+   "id": "4923a1a6",
    "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",
@@ -307,7 +307,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3c3e105f",
+   "id": "8c729b82",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -331,7 +331,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "06b2bb89",
+   "id": "72dec655",
    "metadata": {
     "tag": [
      "hide-output"
@@ -348,7 +348,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bb6c6194",
+   "id": "b65286b0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -359,7 +359,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5698c3f5",
+   "id": "b97c5a83",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -371,7 +371,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f08b887e",
+   "id": "fb857ef1",
    "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",
@@ -393,7 +393,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ba67d93f",
+   "id": "9731b733",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -427,7 +427,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b8e53fba",
+   "id": "34eac730",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -446,7 +446,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d458bd18",
+   "id": "6efe88a6",
    "metadata": {
     "tag": [
      "hide-output"
@@ -468,7 +468,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1ecdaa52",
+   "id": "13ac5f54",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -478,7 +478,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5dc0b1db",
+   "id": "55357b0c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -487,7 +487,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "333854a4",
+   "id": "a7585d5b",
    "metadata": {},
    "source": [
     "Next, we again compute the posterior under the assumption that $y_0$ is drawn from the stationary distribution, so that\n",
@@ -502,7 +502,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7177f488",
+   "id": "c3ed0cef",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -525,7 +525,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1c055d7c",
+   "id": "d6331c3c",
    "metadata": {
     "tag": [
      "hide-output"
@@ -547,7 +547,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ebd11acb",
+   "id": "544e9719",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -557,7 +557,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ad2ebb99",
+   "id": "3c766b4f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -566,7 +566,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d6bc153e",
+   "id": "a03d726f",
    "metadata": {},
    "source": [
     "Look what happened to the posterior!\n",
diff --git a/_sources/ar1_turningpts.ipynb b/_sources/ar1_turningpts.ipynb
index afffe18..d98ab28 100644
--- a/_sources/ar1_turningpts.ipynb
+++ b/_sources/ar1_turningpts.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d2a17147",
+   "id": "115e8385",
    "metadata": {},
    "source": [
     "# Forecasting  an AR(1) Process"
@@ -11,7 +11,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "60c15dea",
+   "id": "5bf0fee4",
    "metadata": {
     "tags": [
      "hide-output"
@@ -24,7 +24,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67df34fd",
+   "id": "9fccdc91",
    "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": "a8138203",
+   "id": "078cc1bc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -74,7 +74,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc01e34d",
+   "id": "96f3c2c3",
    "metadata": {},
    "source": [
     "## A Univariate First-Order Autoregressive Process\n",
@@ -146,7 +146,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "74b34ac1",
+   "id": "95db2652",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -210,7 +210,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ad6d2294",
+   "id": "99b1e43a",
    "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": "5fa0f545",
+   "id": "aa5acd55",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -384,7 +384,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b849ae5",
+   "id": "66756d7d",
    "metadata": {},
    "source": [
     "The graphs on the left portray posterior marginal distributions.\n",
@@ -397,7 +397,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7795c30d",
+   "id": "e78cf7fb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48d51ebc",
+   "id": "efa03397",
    "metadata": {},
    "source": [
     "## Original Wecker Method\n",
@@ -469,7 +469,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a59c434d",
+   "id": "9556a4bd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -535,7 +535,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c5a17d9",
+   "id": "729b82dd",
    "metadata": {},
    "source": [
     "## Extended Wecker Method\n",
@@ -549,7 +549,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bea3dbe3",
+   "id": "34f69e5e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -608,7 +608,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ac48489",
+   "id": "0b60d5e5",
    "metadata": {},
    "source": [
     "## Comparison\n",
@@ -619,7 +619,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cf692bcc",
+   "id": "c4312cae",
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/_sources/back_prop.ipynb b/_sources/back_prop.ipynb
index 2ef5fba..6cd0dcf 100644
--- a/_sources/back_prop.ipynb
+++ b/_sources/back_prop.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "1f60d3b5",
+   "id": "66d8c071",
    "metadata": {},
    "source": [
     "# Introduction to Artificial Neural Networks"
@@ -11,7 +11,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "397e785c",
+   "id": "8ef2f18e",
    "metadata": {
     "tags": [
      "hide-output"
@@ -25,7 +25,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6b41904d",
+   "id": "5cb66da4",
    "metadata": {},
    "source": [
     "```{note}\n",
@@ -315,7 +315,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2387ac73",
+   "id": "91e785b9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -330,7 +330,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b95d6ecb",
+   "id": "9b9b2d29",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -349,7 +349,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b4649d59",
+   "id": "797eef0c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -395,7 +395,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8fc04500",
+   "id": "4f1c9530",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -410,7 +410,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ddb37559",
+   "id": "6e1050bb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -422,7 +422,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b9a06505",
+   "id": "4c23a2f2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -433,7 +433,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3833ebc8",
+   "id": "21aa58f9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -443,7 +443,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "abfe9268",
+   "id": "a4ac8598",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -458,7 +458,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bb5370ef",
+   "id": "e3b38a68",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -470,7 +470,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b509dd7a",
+   "id": "30c52ee5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -480,7 +480,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "447a79a5",
+   "id": "3190cc06",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -491,7 +491,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6a02be66",
+   "id": "d5d48453",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -522,7 +522,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b6cd8d36",
+   "id": "50264df9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -533,7 +533,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "459c2ba1",
+   "id": "76b911eb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -542,7 +542,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65d02577",
+   "id": "f4197105",
    "metadata": {},
    "source": [
     "## Example 1\n",
@@ -565,7 +565,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ca3fc421",
+   "id": "920f2f27",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -580,7 +580,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fd868585",
+   "id": "bc9e0c40",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -600,7 +600,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "978f39ae",
+   "id": "f1cc32b8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -613,7 +613,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6e1f6f6b",
+   "id": "cdfe613b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -624,7 +624,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d4069487",
+   "id": "fbd9d5d1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -634,7 +634,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0b6bbd04",
+   "id": "018b9a4a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -650,7 +650,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6df4261f",
+   "id": "425c7675",
    "metadata": {},
    "source": [
     "## How Deep? \n",
@@ -677,7 +677,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b9d252ee",
+   "id": "2315881c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -691,7 +691,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3696c23c",
+   "id": "90c76f5f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -704,7 +704,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c51ca866",
+   "id": "2df0bd03",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -717,7 +717,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a945c71e",
+   "id": "c7a38392",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -730,7 +730,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9e0c6c9d",
+   "id": "b6677734",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -740,7 +740,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ffbe6965",
+   "id": "b4ef0a04",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -750,7 +750,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fbf0ecf2",
+   "id": "2119a388",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -760,7 +760,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0f7df1f5",
+   "id": "27b95ee1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -772,7 +772,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e4c1c982",
+   "id": "d06489be",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -791,7 +791,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "855c6d4a",
+   "id": "1f7bb7bb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -803,7 +803,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d07f0067",
+   "id": "3d00dce3",
    "metadata": {},
    "source": [
     "```{note}\n",
diff --git a/_sources/bayes_nonconj.ipynb b/_sources/bayes_nonconj.ipynb
index 2e69b63..1c491df 100644
--- a/_sources/bayes_nonconj.ipynb
+++ b/_sources/bayes_nonconj.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "9e74b5d1",
+   "id": "7d9a5fc5",
    "metadata": {},
    "source": [
     "# Non-Conjugate Priors\n",
@@ -41,7 +41,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9e2f34de",
+   "id": "75f5cb2b",
    "metadata": {
     "tags": [
      "hide-output"
@@ -56,7 +56,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3117dd7f",
+   "id": "b22ebb03",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -95,7 +95,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c8ea2c62",
+   "id": "29bd2957",
    "metadata": {},
    "source": [
     "## Unleashing MCMC on a  Binomial Likelihood\n",
@@ -170,7 +170,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ba2de3b3",
+   "id": "78dd5505",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -207,7 +207,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82bc5c93",
+   "id": "c40ab855",
    "metadata": {},
    "source": [
     "### Two Ways to Approximate Posteriors\n",
@@ -282,7 +282,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17669bb1",
+   "id": "a6932d8b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -359,7 +359,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "36575a0d",
+   "id": "5597884c",
    "metadata": {},
    "source": [
     "### Variational Inference\n",
@@ -482,7 +482,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "be5ed875",
+   "id": "b41fafa9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -731,7 +731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77785cf5",
+   "id": "ba2d24b2",
    "metadata": {},
    "source": [
     "## Alternative Prior Distributions\n",
@@ -749,7 +749,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e97ec366",
+   "id": "4cec6b21",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -764,7 +764,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25a86a4c",
+   "id": "188041dd",
    "metadata": {},
    "source": [
     "The above graphs show that sampling seems to work well with both distributions.\n",
@@ -776,7 +776,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d2132a0d",
+   "id": "6c7fc9e6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -791,7 +791,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f55a3876",
+   "id": "77b7e3f5",
    "metadata": {},
    "source": [
     "These graphs look good too.\n",
@@ -802,7 +802,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ebd0caa4",
+   "id": "1aa97b19",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -813,7 +813,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "588bba03",
+   "id": "d3b832fe",
    "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",
@@ -834,7 +834,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b0a65c92",
+   "id": "a1c7ca32",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -965,7 +965,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "155f6bb1",
+   "id": "eea25315",
    "metadata": {},
    "source": [
     "Let's set some parameters that we'll use in all of the examples  below.\n",
@@ -978,7 +978,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "018cdc17",
+   "id": "6929faf8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -992,7 +992,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54f1b2e2",
+   "id": "59b58fe0",
    "metadata": {},
    "source": [
     "### Beta Prior and Posteriors:\n",
@@ -1011,7 +1011,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3c11024c",
+   "id": "c9976527",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1046,7 +1046,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73ed0145",
+   "id": "0d7632ea",
    "metadata": {},
    "source": [
     "Now let's use MCMC while still using a beta prior.  \n",
@@ -1057,7 +1057,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d2752103",
+   "id": "75882eea",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1067,7 +1067,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "123702ec",
+   "id": "2d8646bf",
    "metadata": {},
    "source": [
     "Here the MCMC approximation looks good.\n",
@@ -1088,7 +1088,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "46917076",
+   "id": "44994f41",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1097,7 +1097,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9769a249",
+   "id": "325e1955",
    "metadata": {},
    "source": [
     "## Non-conjugate Prior Distributions\n",
@@ -1117,7 +1117,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e8764b0e",
+   "id": "3c0e8d36",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1143,7 +1143,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a8e83e15",
+   "id": "30d1b409",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1159,7 +1159,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a5b2f61f",
+   "id": "9f80a886",
    "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",
@@ -1172,7 +1172,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7dfdaae7",
+   "id": "932063f2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1189,7 +1189,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "db448e2d",
+   "id": "0fde4779",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1208,7 +1208,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "db1812ba",
+   "id": "17f51e0f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1220,7 +1220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d51c9fb2",
+   "id": "b909dfe2",
    "metadata": {},
    "source": [
     "To get more accuracy we will now increase the number of steps for Variational Inference (VI)"
@@ -1229,7 +1229,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83367ca5",
+   "id": "35921668",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1238,7 +1238,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "df0e5202",
+   "id": "fbae5ad2",
    "metadata": {},
    "source": [
     "#### VI with a  Truncated Normal Guide"
@@ -1247,7 +1247,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7dc10c46",
+   "id": "091d0fbd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1260,7 +1260,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c66088ab",
+   "id": "76bd3d4c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1273,7 +1273,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f1f40398",
+   "id": "1607132a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1287,7 +1287,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e7868fd7",
+   "id": "cdadb83a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1299,7 +1299,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7fa8cd95",
+   "id": "b737e7b7",
    "metadata": {},
    "source": [
     "#### Variational Inference with a  Beta Guide Distribution"
@@ -1308,7 +1308,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "aded7b68",
+   "id": "3bac3d58",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1321,7 +1321,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47357982",
+   "id": "f1041e8c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1338,7 +1338,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fd83cd98",
+   "id": "83f81552",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1357,7 +1357,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f76e4d97",
+   "id": "dc4e19fe",
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/_sources/exchangeable.ipynb b/_sources/exchangeable.ipynb
index b4f74d5..5dd22b0 100644
--- a/_sources/exchangeable.ipynb
+++ b/_sources/exchangeable.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "2e88dd9b",
+   "id": "3ab308d6",
    "metadata": {},
    "source": [
     "(odu_v3)=\n",
@@ -66,7 +66,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4a9d5220",
+   "id": "dbdb93b7",
    "metadata": {
     "tags": [
      "hide-output"
@@ -86,7 +86,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c98d9ad",
+   "id": "d7905076",
    "metadata": {},
    "source": [
     "## Independently and Identically Distributed\n",
@@ -417,7 +417,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9a63307b",
+   "id": "a3df6e2b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -506,7 +506,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e2cfed2f",
+   "id": "df047cbb",
    "metadata": {},
    "source": [
     "Now we'll create a group of graphs that illustrate  dynamics induced by Bayes' Law.\n",
@@ -517,7 +517,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "650c9c0c",
+   "id": "28ec2b31",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -526,7 +526,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5f430d2",
+   "id": "eb2c4cf2",
    "metadata": {},
    "source": [
     "Please look at the three graphs above created for an instance in which $f$ is a uniform distribution on $[0,1]$\n",
@@ -570,7 +570,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "09115a72",
+   "id": "4a49bf29",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -579,7 +579,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7eca44c5",
+   "id": "33b839b1",
    "metadata": {},
    "source": [
     "Notice how the likelihood ratio, the middle graph, and the arrows compare with the previous instance of our example.\n",
@@ -603,7 +603,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "299cf35a",
+   "id": "01adec49",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -662,7 +662,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bc6ce124",
+   "id": "8bb2eecd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -671,7 +671,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab73e19d",
+   "id": "0c7a9267",
    "metadata": {},
    "source": [
     "We begin by generating $N$ simulated $\\{\\pi_t\\}$ paths with $T$\n",
@@ -681,7 +681,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b3315e8d",
+   "id": "78eca2d4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -691,7 +691,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5f0fcaff",
+   "id": "a9e19e3d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -701,7 +701,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7bd08442",
+   "id": "bc3f45c8",
    "metadata": {},
    "source": [
     "In the above example,  for most paths $\\pi_t \\rightarrow 1$. \n",
@@ -716,7 +716,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9fb4dfbd",
+   "id": "d0c41164",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -726,7 +726,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2fc649d1",
+   "id": "d5782fd2",
    "metadata": {},
    "source": [
     "In the above graph we observe that now  most paths $\\pi_t \\rightarrow 0$.\n",
@@ -746,7 +746,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ee09b756",
+   "id": "e2a7b6ad",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -758,7 +758,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43d95d93",
+   "id": "ce55c9a4",
    "metadata": {},
    "source": [
     "From the above graph, rates of convergence appear not to depend on whether $F$ or $G$ generates the data.\n",
@@ -784,7 +784,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4ce0bce3",
+   "id": "0cb9ec70",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -816,7 +816,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ce625cee",
+   "id": "8fad7e69",
    "metadata": {},
    "source": [
     "First, consider the case where $F_a=F_b=1$ and\n",
@@ -826,7 +826,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "92b872eb",
+   "id": "95888db6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -835,7 +835,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72fc7e56",
+   "id": "d03c6707",
    "metadata": {},
    "source": [
     "The above graphs shows that when $F$ generates the data, $\\pi_t$ on average always heads north, while\n",
@@ -851,7 +851,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "afa3864a",
+   "id": "54b31ca9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -860,7 +860,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "852391a6",
+   "id": "f1cbc640",
    "metadata": {},
    "source": [
     "The above graph says that $\\pi_t$ is inert and  remains at its initial value.\n",
@@ -873,7 +873,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0cd3521f",
+   "id": "24e451ce",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -882,7 +882,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7571b0fd",
+   "id": "baed7481",
    "metadata": {},
    "source": [
     "## Sequels\n",
diff --git a/_sources/hoist_failure.ipynb b/_sources/hoist_failure.ipynb
index b0fdf73..3a35f13 100644
--- a/_sources/hoist_failure.ipynb
+++ b/_sources/hoist_failure.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "125e6fe3",
+   "id": "363219a2",
    "metadata": {},
    "source": [
     "# Fault Tree Uncertainties\n",
@@ -43,7 +43,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f5e1e96d",
+   "id": "d7c612df",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -53,7 +53,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "82d8cb27",
+   "id": "c62984f5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -68,7 +68,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a01807d1",
+   "id": "f72ddc64",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -77,7 +77,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7d75343",
+   "id": "0699f865",
    "metadata": {},
    "source": [
     "<!-- #region -->\n",
@@ -203,7 +203,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "99996b1d",
+   "id": "83d42501",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -220,7 +220,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f243476d",
+   "id": "c6575104",
    "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",
@@ -243,7 +243,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ea84e3f6",
+   "id": "1c2aa94d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -270,7 +270,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "90dc6f82",
+   "id": "e7a443b7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -280,7 +280,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "70d752d7",
+   "id": "6237091f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -290,7 +290,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8b346a39",
+   "id": "a33f91f4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -302,7 +302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f25d4a5",
+   "id": "5a962348",
    "metadata": {},
    "source": [
     "Here are helper functions that create a discretized version of a log normal\n",
@@ -312,7 +312,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c87dfad8",
+   "id": "46514578",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -329,7 +329,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8c5e354d",
+   "id": "9ae2183e",
    "metadata": {},
    "source": [
     "<!-- #region -->\n",
@@ -350,7 +350,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4682631a",
+   "id": "ba2cdd81",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -362,7 +362,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7d4e8858",
+   "id": "a2dbf8bd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -385,7 +385,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "68e4699d",
+   "id": "95f0d93e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -398,7 +398,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5261d9d8",
+   "id": "77f026c8",
    "metadata": {},
    "source": [
     "## Convolving Probability Mass Functions\n",
@@ -460,7 +460,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dd01524b",
+   "id": "4abd7a40",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -495,7 +495,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2859663",
+   "id": "f40ae1af",
    "metadata": {},
    "source": [
     "The fast Fourier transform is two orders of magnitude faster than `numpy.convolve`\n",
@@ -507,7 +507,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4b34d0a4",
+   "id": "659712db",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -527,7 +527,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c3502408",
+   "id": "2e3b9624",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -546,7 +546,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "368eea95",
+   "id": "532ddfa1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -559,7 +559,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "66878cc4",
+   "id": "f88dd9a6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -571,7 +571,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3a422c7",
+   "id": "1423be91",
    "metadata": {},
    "source": [
     "<!-- #region -->\n",
@@ -696,7 +696,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4de6f538",
+   "id": "abb906aa",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -711,7 +711,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c981d52b",
+   "id": "cde7aa1b",
    "metadata": {},
    "source": [
     "```{note}\n",
@@ -728,7 +728,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6b9139b7",
+   "id": "fe660334",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -740,7 +740,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "da8da26d",
+   "id": "0441e85d",
    "metadata": {},
    "source": [
     "We compute the required thirteen convolutions in the following code.\n",
@@ -755,7 +755,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ab13fa79",
+   "id": "24c26611",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -807,7 +807,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4c15faaf",
+   "id": "f823d0d7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -852,7 +852,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "476dfad4",
+   "id": "7541edba",
    "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 00bb2c7..3ae3600 100644
--- a/_sources/imp_sample.ipynb
+++ b/_sources/imp_sample.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "8f0423ac",
+   "id": "7ca79ce7",
    "metadata": {},
    "source": [
     "# Computing Mean of a Likelihood Ratio Process\n",
@@ -27,7 +27,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1cd5a146",
+   "id": "f7827823",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -40,7 +40,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68f7716d",
+   "id": "00975b3b",
    "metadata": {},
    "source": [
     "## Mathematical Expectation of Likelihood Ratio\n",
@@ -81,7 +81,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9a2671f6",
+   "id": "98325437",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -102,7 +102,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fb7eb0dc",
+   "id": "c949919b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -118,7 +118,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "642d36b4",
+   "id": "6b5bcb41",
    "metadata": {},
    "source": [
     "The likelihood ratio is `l(w)=f(w)/g(w)`."
@@ -127,7 +127,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "940797bd",
+   "id": "7b759e83",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -137,7 +137,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cd1d5505",
+   "id": "5af039a6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -149,7 +149,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "236e1a4d",
+   "id": "914e833d",
    "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",
@@ -209,7 +209,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "782e4835",
+   "id": "bb24c687",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -220,7 +220,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "96af7c64",
+   "id": "78f522f2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -236,7 +236,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea905806",
+   "id": "1b09f11e",
    "metadata": {},
    "source": [
     "## Approximating a cumulative likelihood ratio\n",
@@ -261,7 +261,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "244aeef8",
+   "id": "43bbf7fe",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -289,7 +289,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a180ec03",
+   "id": "b94e7b73",
    "metadata": {},
    "source": [
     "Consider the case when $T=1$, which amounts  to approximating $E_0\\left[\\ell\\left(\\omega\\right)\\right]$\n",
@@ -300,7 +300,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47b8c5d4",
+   "id": "145b4283",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -309,7 +309,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "786a2dbf",
+   "id": "9e1b3dfe",
    "metadata": {},
    "source": [
     "For our importance sampling estimate, we set $q = h$."
@@ -318,7 +318,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "94c956e1",
+   "id": "f24579e4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -327,7 +327,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2788c158",
+   "id": "41a79bb2",
    "metadata": {},
    "source": [
     "Evidently, even at T=1, our importance sampling  estimate is closer to $1$ than is the Monte Carlo estimate.\n",
@@ -341,7 +341,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f75b50e7",
+   "id": "c18b77bc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -351,7 +351,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fedb5200",
+   "id": "a717cb05",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -360,7 +360,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1a65ef8b",
+   "id": "67ed8f18",
    "metadata": {},
    "source": [
     "## Distribution of  Sample Mean\n",
@@ -373,7 +373,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3fa0e0ec",
+   "id": "66c94b87",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -392,7 +392,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9934e241",
+   "id": "9de9bc2a",
    "metadata": {},
    "source": [
     "Again, we first consider estimating ${E} \\left[\\ell\\left(\\omega\\right)\\right]$ by setting T=1.\n",
@@ -403,7 +403,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0a664591",
+   "id": "beaee7bb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -414,7 +414,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "931de44a",
+   "id": "82c7b531",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -425,7 +425,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6577a168",
+   "id": "20ecefb6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -435,7 +435,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d5f0aac",
+   "id": "bad92f20",
    "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",
@@ -446,7 +446,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57c6ac2e",
+   "id": "e94c8cd8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -479,7 +479,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9008b1d",
+   "id": "bfdfed4c",
    "metadata": {},
    "source": [
     "The simulation exercises above show that the importance sampling estimates are unbiased under all $T$\n",
@@ -492,7 +492,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "34cc7560",
+   "id": "04974444",
    "metadata": {},
    "source": [
     "Above, we arbitraily chose $h = Beta(0.5,0.5)$ as the importance distribution.\n",
@@ -515,7 +515,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "76319083",
+   "id": "504b9db5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -525,7 +525,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2a8872b0",
+   "id": "1f47da91",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -535,7 +535,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0dd9f43",
+   "id": "4c9a8a7a",
    "metadata": {},
    "source": [
     "We could also use other distributions as our importance distribution.\n",
@@ -546,7 +546,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2c7a3649",
+   "id": "1ae8d532",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -557,7 +557,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6983a1a6",
+   "id": "7858b304",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -575,7 +575,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "66103dd1",
+   "id": "31874730",
    "metadata": {},
    "source": [
     "We consider two additonal distributions.\n",
@@ -601,7 +601,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "72a894c6",
+   "id": "389108b1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -636,7 +636,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f1018ef",
+   "id": "3104f386",
    "metadata": {},
    "source": [
     "Our simulations suggest that indeed $h_2$ is a quite  good importance sampling distribution for our problem.\n",
@@ -647,7 +647,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9c1eb2d8",
+   "id": "274c7bc2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -682,7 +682,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b638b7f",
+   "id": "2e374ed5",
    "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 da8670e..b7b2d0a 100644
--- a/_sources/intro.ipynb
+++ b/_sources/intro.ipynb
@@ -2,11 +2,10 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "5b0ae0e6",
+   "id": "3c983194",
    "metadata": {},
    "source": [
     "# Statistics for Computational Economics\n",
-    "**Authors:** [Thomas J. Sargent](http://www.tomsargent.com/) and [John Stachurski](http://johnstachurski.net/)\n",
     "\n",
     "This website presents a set of lectures on statistics for computational economics.\n",
     "\n",
diff --git a/_sources/intro.md b/_sources/intro.md
index 04b4641..4c971d1 100644
--- a/_sources/intro.md
+++ b/_sources/intro.md
@@ -10,7 +10,6 @@ kernelspec:
 ---
 
 # Statistics for Computational Economics
-**Authors:** [Thomas J. Sargent](http://www.tomsargent.com/) and [John Stachurski](http://johnstachurski.net/)
 
 This website presents a set of lectures on statistics for computational economics.
 
diff --git a/_sources/likelihood_bayes.ipynb b/_sources/likelihood_bayes.ipynb
index 9413650..52b80d3 100644
--- a/_sources/likelihood_bayes.ipynb
+++ b/_sources/likelihood_bayes.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "afaceaf9",
+   "id": "8dc938f5",
    "metadata": {},
    "source": [
     "(likelihood_ratio_process)=\n",
@@ -46,7 +46,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8318b612",
+   "id": "23e3dc93",
    "metadata": {
     "hide-output": false
    },
@@ -71,7 +71,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a3debec",
+   "id": "f6493f2d",
    "metadata": {},
    "source": [
     "## The Setting\n",
@@ -149,7 +149,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "79b6d983",
+   "id": "e3e11022",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -170,7 +170,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "173e5c14",
+   "id": "21c8cd22",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -195,7 +195,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9a6309c4",
+   "id": "0ea2f311",
    "metadata": {},
    "source": [
     "We'll also use the following Python code to prepare some informative simulations"
@@ -204,7 +204,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9163909f",
+   "id": "456ba1b6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -215,7 +215,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "583d56f8",
+   "id": "595ccc0f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -225,7 +225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "80a3f524",
+   "id": "091bbb38",
    "metadata": {},
    "source": [
     "## Likelihood Ratio Process and Bayes’ Law\n",
@@ -257,7 +257,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "94928c17",
+   "id": "959695ea",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -273,7 +273,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9562693c",
+   "id": "acc159f5",
    "metadata": {},
    "source": [
     "Formula {eq}`eq_recur1` can be generalized  by iterating on it and thereby deriving an\n",
@@ -354,7 +354,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "393f9d29",
+   "id": "2b8dd337",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -363,7 +363,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e8decab2",
+   "id": "076bb608",
    "metadata": {},
    "source": [
     "Next we generate paths of the likelihood ratio process $L_t$ and the posterior $\\pi_t$ for a\n",
@@ -373,7 +373,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9c498af0",
+   "id": "32534b23",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -389,7 +389,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6060c333",
+   "id": "a27882ea",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -412,7 +412,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fbb56776",
+   "id": "6ae5e178",
    "metadata": {},
    "source": [
     "The dotted line in the graph above records the logarithm of the  likelihood ratio process $\\log L(w^t)$.\n",
@@ -425,7 +425,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da5b83b1",
+   "id": "d6f008b2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -441,7 +441,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dd4a38ab",
+   "id": "7c529672",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -464,7 +464,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2e4efd17",
+   "id": "dc649526",
    "metadata": {},
    "source": [
     "Below we offer Python code that verifies that nature chose permanently to draw from density $f$."
@@ -473,7 +473,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "96fc0b38",
+   "id": "6bb1f6ed",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -488,7 +488,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eb4a4ca1",
+   "id": "f3f3b9eb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -497,7 +497,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "578d423d",
+   "id": "a1250e1a",
    "metadata": {},
    "source": [
     "We thus conclude that  the likelihood ratio process is a key ingredient of the formula {eq}`eq_Bayeslaw103` for\n",
@@ -717,7 +717,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c30c6e9e",
+   "id": "c8a67978",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -771,7 +771,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "18a73310",
+   "id": "488756fb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -786,7 +786,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f9a83fd8",
+   "id": "02da8e11",
    "metadata": {},
    "source": [
     "The above graph indicates that \n",
@@ -805,7 +805,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8f9a62f2",
+   "id": "6bc71fa1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -821,7 +821,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4d755a37",
+   "id": "81bf2120",
    "metadata": {},
    "source": [
     "Evidently, by $t = 199$, $\\pi_t$ has converged to either $0$ or $1$.\n",
@@ -842,7 +842,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e775d465",
+   "id": "28c8d97a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -856,7 +856,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0edd05a1",
+   "id": "6cb7d4ff",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -872,7 +872,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e7d1b5db",
+   "id": "6a57936f",
    "metadata": {},
    "source": [
     "For the preceding ensemble that assumed $\\pi_0 = .5$, the following graph shows two  paths of\n",
@@ -887,7 +887,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f5331652",
+   "id": "66b26f9c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -906,7 +906,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "73e5b82a",
+   "id": "e93aa844",
    "metadata": {},
    "source": [
     "##  Initial Prior is Verified by Paths Drawn from Subjective Conditional Densities\n",
@@ -928,7 +928,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "63066efb",
+   "id": "5429a62a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -939,7 +939,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dd646b8f",
+   "id": "85e2670b",
    "metadata": {},
    "source": [
     "The fraction of simulations for which $\\pi_{t}$  had converged to $1$ is indeed always  close  to $\\pi_{-1}$, as anticipated.\n",
@@ -966,7 +966,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c2993bfa",
+   "id": "0e63da65",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -999,7 +999,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dc710a43",
+   "id": "125d161f",
    "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 42159a5..befef12 100644
--- a/_sources/likelihood_ratio_process.ipynb
+++ b/_sources/likelihood_ratio_process.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "33f80d7d",
+   "id": "31068a4d",
    "metadata": {},
    "source": [
     "(likelihood_ratio_process)=\n",
@@ -41,7 +41,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7cbd2601",
+   "id": "664caf20",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -56,7 +56,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e35eb85c",
+   "id": "425753ec",
    "metadata": {},
    "source": [
     "## Likelihood Ratio Process\n",
@@ -132,7 +132,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "13ddec51",
+   "id": "8632c8a9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -153,7 +153,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d524474f",
+   "id": "4e6258aa",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -178,7 +178,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c75a5bd",
+   "id": "bce6a577",
    "metadata": {},
    "source": [
     "## Nature Permanently Draws from Density g\n",
@@ -190,7 +190,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7f019e98",
+   "id": "b3a5ea7a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -201,7 +201,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "67972508",
+   "id": "331a6cee",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -217,7 +217,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7a6a836b",
+   "id": "b5c6d380",
    "metadata": {},
    "source": [
     "Evidently, as sample length $T$ grows, most probability mass\n",
@@ -231,7 +231,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cc2a3dbb",
+   "id": "c49a5689",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -240,7 +240,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b98af8d9",
+   "id": "4aaf84f0",
    "metadata": {},
    "source": [
     "Despite the evident convergence of most probability mass to a\n",
@@ -307,7 +307,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9482d09f",
+   "id": "ec60b9ad",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -317,7 +317,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0eb83b3c",
+   "id": "ccea43a3",
    "metadata": {},
    "source": [
     "It would be useful to use simulations to verify that  unconditional means\n",
@@ -366,7 +366,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "020dc334",
+   "id": "57c11a3d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -377,7 +377,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3f4ce7f9",
+   "id": "88f0981d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -387,7 +387,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55f1a644",
+   "id": "7f6f5696",
    "metadata": {},
    "source": [
     "We also plot the probability that $L\\left(w^t\\right)$ falls into\n",
@@ -398,7 +398,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27eed9e2",
+   "id": "64555910",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -407,7 +407,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dbb82eeb",
+   "id": "3ff8eae2",
    "metadata": {},
    "source": [
     "## Likelihood Ratio Test\n",
@@ -495,7 +495,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10baf494",
+   "id": "2d502171",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -504,7 +504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2253e6a5",
+   "id": "e796fe2f",
    "metadata": {},
    "source": [
     "Below we plot empirical distributions of logarithms of the cumulative\n",
@@ -530,7 +530,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3fe919c6",
+   "id": "81b07730",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -561,7 +561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5debe0c3",
+   "id": "bc7b26d0",
    "metadata": {},
    "source": [
     "The graph below shows more clearly that, when we hold the threshold\n",
@@ -572,7 +572,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "46fbdff5",
+   "id": "3352a25e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -593,7 +593,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2118223c",
+   "id": "a5994e6c",
    "metadata": {},
    "source": [
     "For a given sample size $t$,  the threshold $c$ uniquely pins down  probabilities\n",
@@ -612,7 +612,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0411189a",
+   "id": "3aa2d1d0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -638,7 +638,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5f47202",
+   "id": "884525d3",
    "metadata": {},
    "source": [
     "Notice that as $t$ increases, we are assured a larger probability\n",
@@ -670,7 +670,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "adc2318a",
+   "id": "8ce46786",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -693,7 +693,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7bf3bcc",
+   "id": "c842ef94",
    "metadata": {},
    "source": [
     "The United States Navy evidently used a procedure like this to select a sample size $t$ for doing quality\n",
@@ -760,7 +760,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ba848317",
+   "id": "0901aa95",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -772,7 +772,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fbe95d33",
+   "id": "0ddb549c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -787,7 +787,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70903f62",
+   "id": "90329138",
    "metadata": {},
    "source": [
     "Let’s compute the Kullback–Leibler discrepancies by quadrature\n",
@@ -797,7 +797,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "56eb3660",
+   "id": "30177123",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -811,7 +811,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f29a8355",
+   "id": "b1e6acc2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -826,7 +826,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "61863029",
+   "id": "104bf4ed",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -836,7 +836,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2063e6cd",
+   "id": "1780866d",
    "metadata": {},
    "source": [
     "We have $K_g < K_f$.\n",
@@ -848,7 +848,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58ed0db7",
+   "id": "b807aba2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -858,7 +858,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3982f4c2",
+   "id": "56540d80",
    "metadata": {},
    "source": [
     "The figure below plots over time the fraction of paths\n",
@@ -871,7 +871,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a1f1e0fa",
+   "id": "c1746dd1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -881,7 +881,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "70446cfd",
+   "id": "09b60292",
    "metadata": {},
    "source": [
     "We can also try an $h$ that is closer to $f$ than is\n",
@@ -891,7 +891,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3d422968",
+   "id": "2d1bb64f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -902,7 +902,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11a2e233",
+   "id": "7169b86d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -913,7 +913,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fca77286",
+   "id": "cf6f078d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -923,7 +923,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7d38a55",
+   "id": "58ef3016",
    "metadata": {},
    "source": [
     "Now probability mass of $L\\left(w^t\\right)$ falling above\n",
@@ -933,7 +933,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4541a76c",
+   "id": "ba7a1cb7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -943,7 +943,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b7d3b6ea",
+   "id": "f8adce66",
    "metadata": {},
    "source": [
     "## Sequels\n",
diff --git a/_sources/lln_clt.ipynb b/_sources/lln_clt.ipynb
index 8166f85..b141a2a 100644
--- a/_sources/lln_clt.ipynb
+++ b/_sources/lln_clt.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "f45eab88",
+   "id": "cf6da0e4",
    "metadata": {},
    "source": [
     "(lln_clt)=\n",
@@ -50,7 +50,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a0b4b0c8",
+   "id": "c24ceeb2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -68,7 +68,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8bf3479f",
+   "id": "432d3b5c",
    "metadata": {},
    "source": [
     "## Relationships\n",
@@ -237,7 +237,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6bda4a27",
+   "id": "2679cb0a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -290,7 +290,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6c2a0251",
+   "id": "4c162ce9",
    "metadata": {},
    "source": [
     "The three distributions are chosen at random from a selection stored in the dictionary `distributions`.\n",
@@ -354,7 +354,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "62e7c2ee",
+   "id": "ea9fc92b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -376,7 +376,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e45c665f",
+   "id": "c4915e18",
    "metadata": {},
    "source": [
     "When $n = 1$, the distribution is flat --- one success or no successes\n",
@@ -426,7 +426,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5ed10d13",
+   "id": "e3dc5641",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -457,7 +457,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed293bf8",
+   "id": "58099070",
    "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",
@@ -492,7 +492,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e0ff9a3e",
+   "id": "b9883e62",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -559,7 +559,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a7188ca1",
+   "id": "f266e55b",
    "metadata": {},
    "source": [
     "As expected, the distribution smooths out into a bell curve as $n$\n",
@@ -734,7 +734,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a2b6a645",
+   "id": "80ef0502",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -772,7 +772,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d98cc5a1",
+   "id": "57c71ac9",
    "metadata": {},
    "source": [
     "What happens when you replace $[0, \\pi / 2]$ with\n",
@@ -954,7 +954,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eefde615",
+   "id": "c9f89f54",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1002,7 +1002,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fe351234",
+   "id": "b6ad44be",
    "metadata": {},
    "source": [
     "```{solution-end}\n",
diff --git a/_sources/mix_model.ipynb b/_sources/mix_model.ipynb
index 4c9d990..3011334 100644
--- a/_sources/mix_model.ipynb
+++ b/_sources/mix_model.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "a34780c1",
+   "id": "3491b786",
    "metadata": {},
    "source": [
     "(likelihood-ratio-process)=\n",
@@ -109,7 +109,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a36129d1",
+   "id": "ebab5368",
    "metadata": {
     "hide-output": false
    },
@@ -145,7 +145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca0b3ce3",
+   "id": "6078b261",
    "metadata": {},
    "source": [
     "Let's use Python to generate two beta distributions"
@@ -154,7 +154,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ffdaa0bf",
+   "id": "52675d0d",
    "metadata": {
     "hide-output": false
    },
@@ -177,7 +177,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "82311fbe",
+   "id": "fd4d0af7",
    "metadata": {
     "hide-output": false
    },
@@ -204,7 +204,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39cdd6ec",
+   "id": "507d9815",
    "metadata": {},
    "source": [
     "We’ll also use the following Python code to prepare some informative simulations"
@@ -213,7 +213,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9362f305",
+   "id": "261c0a9d",
    "metadata": {
     "hide-output": false
    },
@@ -226,7 +226,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ca5c1d5f",
+   "id": "cd9f0ee0",
    "metadata": {
     "hide-output": false
    },
@@ -238,7 +238,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b8821efa",
+   "id": "e9d0e900",
    "metadata": {},
    "source": [
     "## Sampling from  Compound Lottery $H$\n",
@@ -287,7 +287,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6824340c",
+   "id": "a34a3277",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -318,7 +318,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bad70c71",
+   "id": "154ac4b5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -343,7 +343,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "879bc73b",
+   "id": "9c3cdbb8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -354,7 +354,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fda56af8",
+   "id": "d8759be8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -364,7 +364,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fffa3c25",
+   "id": "bfb6772e",
    "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",
@@ -404,7 +404,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cac49e2b",
+   "id": "5d556018",
    "metadata": {
     "hide-output": false
    },
@@ -422,7 +422,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "72d593d3",
+   "id": "14f8beee",
    "metadata": {},
    "source": [
     "Formula {eq}`equation-eq-recur1` can be generalized  by iterating on it and thereby deriving an\n",
@@ -503,7 +503,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "12e67df2",
+   "id": "11ddfba6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -556,7 +556,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f7626684",
+   "id": "ea7ad51f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -565,7 +565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e597299e",
+   "id": "04d31919",
    "metadata": {},
    "source": [
     "The above graph shows a sample path of the log likelihood ratio process as the blue dotted line, together with\n",
@@ -578,7 +578,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "304faf2f",
+   "id": "55823034",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -587,7 +587,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f52f684b",
+   "id": "3a3a2338",
    "metadata": {},
    "source": [
     "Evidently, $\\alpha$ is having a big effect on the destination of $\\pi_t$ as $t \\rightarrow + \\infty$\n",
@@ -625,7 +625,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0210cfdd",
+   "id": "8f7a675b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -680,7 +680,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "219a23c6",
+   "id": "bdcf9918",
    "metadata": {},
    "source": [
     "Let us first plot the KL divergences $KL_g\\left(\\alpha\\right), KL_f\\left(\\alpha\\right)$ for each $\\alpha$."
@@ -689,7 +689,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a5361366",
+   "id": "abf4c5fe",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -711,7 +711,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33ae0c11",
+   "id": "d0a36a9f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -733,7 +733,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7089182d",
+   "id": "62dad854",
    "metadata": {},
    "source": [
     "Let's compute an $\\alpha$ for which  the KL divergence  between $h$ and $g$ is the same as that between $h$ and $f$."
@@ -742,7 +742,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1b94ac0e",
+   "id": "1b1a863c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -752,7 +752,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6c7e138",
+   "id": "f107aff5",
    "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",
@@ -766,7 +766,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cb3a3249",
+   "id": "7703205d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -794,7 +794,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "631650aa",
+   "id": "150eb05b",
    "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",
@@ -845,7 +845,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "69e4c470",
+   "id": "fb155cc9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -874,7 +874,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d0d32893",
+   "id": "74937960",
    "metadata": {},
    "source": [
     "The following code generates the graph below that displays Bayesian posteriors for $\\alpha$ at various history lengths."
@@ -883,7 +883,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16c3b086",
+   "id": "29db1d41",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -903,7 +903,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3eecb57b",
+   "id": "ebffad8f",
    "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 c47e008..0631232 100644
--- a/_sources/mle.ipynb
+++ b/_sources/mle.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "66e1595a",
+   "id": "e25d6124",
    "metadata": {},
    "source": [
     "```{raw} html\n",
@@ -42,7 +42,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5cbdf9b6",
+   "id": "6fc4c9e9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86060685",
+   "id": "58d22111",
    "metadata": {},
    "source": [
     "### Prerequisites\n",
@@ -114,7 +114,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fcf56bcf",
+   "id": "fe52c954",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -145,7 +145,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "713bc699",
+   "id": "769746fd",
    "metadata": {},
    "source": [
     "Notice that the Poisson distribution begins to resemble a normal distribution as the mean of $y$ increases.\n",
@@ -161,7 +161,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6bee294f",
+   "id": "93da7513",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -174,7 +174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf421da5",
+   "id": "be269559",
    "metadata": {},
    "source": [
     "Using a histogram, we can view the distribution of the number of\n",
@@ -185,7 +185,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7b8ddf0f",
+   "id": "b7a774a9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -203,7 +203,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cc9d0b8a",
+   "id": "06420955",
    "metadata": {},
    "source": [
     "From the histogram, it appears that the Poisson assumption is not unreasonable (albeit with a very low $\\mu$ and some outliers).\n",
@@ -238,7 +238,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0c95200e",
+   "id": "76d3652b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -278,7 +278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8e540110",
+   "id": "bbb03347",
    "metadata": {},
    "source": [
     "We can see that the distribution of $y_i$ is conditional on\n",
@@ -320,7 +320,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "80c68ace",
+   "id": "37bbc121",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -346,7 +346,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ecaf429",
+   "id": "1ea4fcbd",
    "metadata": {},
    "source": [
     "Similarly, the joint pmf of our data (which is distributed as a\n",
@@ -441,7 +441,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0a017f41",
+   "id": "a7682fec",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -470,7 +470,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3713a29",
+   "id": "75a28540",
    "metadata": {},
    "source": [
     "The plot shows that the maximum likelihood value (the top plot) occurs\n",
@@ -526,7 +526,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b5bddd7d",
+   "id": "bcd7d8d9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -561,7 +561,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "043ed777",
+   "id": "2b4302e2",
    "metadata": {},
    "source": [
     "Our function `newton_raphson` will take a `PoissonRegression` object\n",
@@ -584,7 +584,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c551806f",
+   "id": "1707113b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -624,7 +624,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7e2f0ca7",
+   "id": "f33a9a6e",
    "metadata": {},
    "source": [
     "Let's try out our algorithm with a small dataset of 5 observations and 3\n",
@@ -634,7 +634,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "69c1327b",
+   "id": "d5c6f684",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -658,7 +658,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6546e5e6",
+   "id": "0521a438",
    "metadata": {},
    "source": [
     "As this was a simple model with few observations, the algorithm achieved\n",
@@ -681,7 +681,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5355b130",
+   "id": "547a79c7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -690,7 +690,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e969221f",
+   "id": "bbeefd98",
    "metadata": {},
    "source": [
     "The iterative process can be visualized in the following diagram, where\n",
@@ -700,7 +700,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cde4f69d",
+   "id": "be9e0fed",
    "metadata": {
     "tags": [
      "output_scroll"
@@ -742,7 +742,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3278bdf7",
+   "id": "6db2e5b8",
    "metadata": {},
    "source": [
     "Note that our implementation of the Newton-Raphson algorithm is rather\n",
@@ -766,7 +766,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1707ba92",
+   "id": "e5d36f26",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -784,7 +784,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a4cc2e7e",
+   "id": "24cb8e58",
    "metadata": {},
    "source": [
     "Now let's replicate results from Daniel Treisman's paper, [Russia's\n",
@@ -807,7 +807,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6723dd78",
+   "id": "67970ca8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -827,7 +827,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77a98060",
+   "id": "bba3cf4a",
    "metadata": {},
    "source": [
     "Then we can use the `Poisson` function from `statsmodels` to fit the\n",
@@ -839,7 +839,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1cd92b98",
+   "id": "f420fbec",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -851,7 +851,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7136128a",
+   "id": "cd34af56",
    "metadata": {},
    "source": [
     "Success! The algorithm was able to achieve convergence in 9 iterations.\n",
@@ -868,7 +868,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d00e1b3c",
+   "id": "d56056e7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -906,7 +906,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ebccb22d",
+   "id": "7216c186",
    "metadata": {},
    "source": [
     "The output suggests that the frequency of billionaires is positively\n",
@@ -922,7 +922,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fa5dec9a",
+   "id": "43b7f7ef",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -949,7 +949,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "107628bc",
+   "id": "f56aec5f",
    "metadata": {},
    "source": [
     "As we can see, Russia has by far the highest number of billionaires in\n",
@@ -1060,7 +1060,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "037395b0",
+   "id": "6ab1dced",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1098,7 +1098,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6ef44ca8",
+   "id": "2e248ece",
    "metadata": {},
    "source": [
     "```{solution-end}\n",
@@ -1146,7 +1146,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b9a8ead1",
+   "id": "e36f9637",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1155,7 +1155,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14dc8e1a",
+   "id": "d85efe70",
    "metadata": {},
    "source": [
     "Note that the simple Newton-Raphson algorithm developed in this lecture\n",
@@ -1175,7 +1175,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "886c9299",
+   "id": "c45a138f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1200,7 +1200,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cb5e55e0",
+   "id": "c4288f80",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1211,7 +1211,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "94dc6f9f",
+   "id": "5d7aecc6",
    "metadata": {},
    "source": [
     "```{solution-end}\n",
diff --git a/_sources/multi_hyper.ipynb b/_sources/multi_hyper.ipynb
index 2ff7338..d3ddac3 100644
--- a/_sources/multi_hyper.ipynb
+++ b/_sources/multi_hyper.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d13b0c1a",
+   "id": "8f30777c",
    "metadata": {},
    "source": [
     "(multi_hyper_v7)=\n",
@@ -110,7 +110,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b16fd514",
+   "id": "ab85292a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -125,7 +125,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab67259a",
+   "id": "7596e038",
    "metadata": {},
    "source": [
     "To recapitulate, we assume there are in total $c$ types of objects in an urn.\n",
@@ -173,7 +173,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b959db06",
+   "id": "e62bb39d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -269,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f7e5142d",
+   "id": "ea5103c8",
    "metadata": {},
    "source": [
     "## Usage\n",
@@ -291,7 +291,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b763c330",
+   "id": "c95f87d6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -302,7 +302,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bc2ca239",
+   "id": "32f00f78",
    "metadata": {},
    "source": [
     "Now use the Urn Class method `pmf` to compute the probability of the outcome $X = \\begin{pmatrix} 2 & 2 & 2 \\end{pmatrix}$"
@@ -311,7 +311,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3cd02387",
+   "id": "5affee14",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -321,7 +321,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2100c67c",
+   "id": "13aa09c9",
    "metadata": {},
    "source": [
     "We can use the code to compute probabilities of a list of possible outcomes by\n",
@@ -333,7 +333,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b04ef1fa",
+   "id": "363feb3c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -343,7 +343,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd2bcfb7",
+   "id": "f7a95178",
    "metadata": {},
    "source": [
     "Now let's compute the mean vector and variance-covariance matrix."
@@ -352,7 +352,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8980c3c5",
+   "id": "8386b403",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -363,7 +363,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e25054c6",
+   "id": "089b383a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -373,7 +373,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "238a856e",
+   "id": "8db8c33c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -382,7 +382,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "be1f9c54",
+   "id": "d4649f62",
    "metadata": {},
    "source": [
     "### Back to The Administrator's Problem\n",
@@ -397,7 +397,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da43e804",
+   "id": "b39c3abf",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -407,7 +407,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eebd76a2",
+   "id": "9e81e957",
    "metadata": {},
    "source": [
     "Let's compute the probability of the outcome $\\left(10, 1, 4, 0 \\right)$."
@@ -416,7 +416,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f42f7706",
+   "id": "ed190aaa",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -426,7 +426,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2b41d32b",
+   "id": "1fe46e9f",
    "metadata": {},
    "source": [
     "We can compute probabilities of three possible outcomes by constructing a 3-dimensional\n",
@@ -436,7 +436,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1bcb6e1a",
+   "id": "a7915a3e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -446,7 +446,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba273dbf",
+   "id": "d94122b3",
    "metadata": {},
    "source": [
     "Now let's compute the mean and variance-covariance matrix of $X$ when $n=6$."
@@ -455,7 +455,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "420d4ec6",
+   "id": "cb8d09f2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -466,7 +466,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ca0592e6",
+   "id": "714531cb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -477,7 +477,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0b9df512",
+   "id": "f94524ea",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -487,7 +487,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c855cad0",
+   "id": "834e9299",
    "metadata": {},
    "source": [
     "We can simulate a large sample and verify that sample means and covariances closely approximate the population means and covariances."
@@ -496,7 +496,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "74dc7d9e",
+   "id": "494f0cc7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -507,7 +507,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d974548f",
+   "id": "02db7b73",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -518,7 +518,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1d285d46",
+   "id": "e484bcd7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -528,7 +528,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c8c2b7aa",
+   "id": "c554ab95",
    "metadata": {},
    "source": [
     "Evidently, the sample means and covariances approximate their population counterparts well.\n",
@@ -541,7 +541,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d1386433",
+   "id": "598c67ad",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -551,7 +551,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ab7ab289",
+   "id": "f8339c34",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -574,7 +574,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a4aa4a80",
+   "id": "1d16287f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -592,7 +592,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c4977f97",
+   "id": "a4618a8e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -628,7 +628,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "22e6dcab",
+   "id": "0fec454d",
    "metadata": {},
    "source": [
     "The diagonal graphs plot the marginal distributions of $k_i$ for\n",
@@ -654,7 +654,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c2dada96",
+   "id": "bd2e93c3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -664,7 +664,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e26b5451",
+   "id": "f2446a8e",
    "metadata": {},
    "source": [
     "As we can see, all the p-values are almost $0$ and the null hypothesis is soundly rejected.\n",
@@ -675,7 +675,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8e15b54f",
+   "id": "409e0b25",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -685,7 +685,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b53946a6",
+   "id": "4eedb953",
    "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 63fb8ad..b003edc 100644
--- a/_sources/multivariate_normal.ipynb
+++ b/_sources/multivariate_normal.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "3d0cb836",
+   "id": "c8e751ec",
    "metadata": {},
    "source": [
     "(multivariate_normal_v11)=\n",
@@ -60,7 +60,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6153d76b",
+   "id": "5cc02d6f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -74,7 +74,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c33de5a1",
+   "id": "031718db",
    "metadata": {},
    "source": [
     "Assume that an $N \\times 1$ random vector $z$ has a\n",
@@ -96,7 +96,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "86c1f8bc",
+   "id": "7eca339d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -129,7 +129,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8052ca22",
+   "id": "c0e399cd",
    "metadata": {},
    "source": [
     "For some integer $k\\in \\{1,\\dots, N-1\\}$, partition\n",
@@ -202,7 +202,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e068bb82",
+   "id": "bca1adfd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -278,7 +278,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74400201",
+   "id": "4139d415",
    "metadata": {},
    "source": [
     "Let’s put this code to work on a suite of examples.\n",
@@ -314,7 +314,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5fcd3cf5",
+   "id": "0f6c0c8a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -328,7 +328,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3938b70a",
+   "id": "d8dc3e72",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -341,7 +341,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "db79b2a3",
+   "id": "188491c9",
    "metadata": {},
    "source": [
     "Let's illustrate the fact that you _can regress anything on anything else_.\n",
@@ -378,7 +378,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7f471d2f",
+   "id": "caa9b52a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -393,7 +393,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1acf7fba",
+   "id": "ab806fe4",
    "metadata": {},
    "source": [
     "Let's print out the intercepts and slopes.\n",
@@ -405,7 +405,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "de19385e",
+   "id": "896ec5ad",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -415,7 +415,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "24a4d86b",
+   "id": "cf7bd8d7",
    "metadata": {},
    "source": [
     "For the regression of $z_2$ on $z_1$ we have"
@@ -424,7 +424,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d54538f4",
+   "id": "c8967ce5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -434,7 +434,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9e2a2fc3",
+   "id": "b36f085f",
    "metadata": {},
    "source": [
     "Now let's plot the two regression lines and stare at them."
@@ -443,7 +443,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c7ab75fe",
+   "id": "01784f8d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -482,7 +482,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5eea6bb5",
+   "id": "f31e9f5d",
    "metadata": {},
    "source": [
     "The red line is the  expectation of $z_1$ conditional on $z_2$.\n",
@@ -493,7 +493,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6e4e9f0f",
+   "id": "79b802fb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -503,7 +503,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8a1b761c",
+   "id": "76e0b0ad",
    "metadata": {},
    "source": [
     "The blue line is the expectation of $z_2$ conditional on $z_1$.  \n",
@@ -514,7 +514,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "89e9b927",
+   "id": "ffb5008c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -524,7 +524,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c27c8e27",
+   "id": "e5216c24",
    "metadata": {},
    "source": [
     "We can use these regression lines or our code to compute conditional expectations.\n",
@@ -538,7 +538,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "70a9732c",
+   "id": "8cd83b3b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -552,7 +552,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "729e3420",
+   "id": "cb0b5ce4",
    "metadata": {},
    "source": [
     "Now let’s compute the mean and variance of the distribution of $z_1$\n",
@@ -562,7 +562,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d02f7381",
+   "id": "4b8d6544",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -576,7 +576,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "86c0de99",
+   "id": "96d32d05",
    "metadata": {},
    "source": [
     "Let’s compare the preceding population mean and variance with outcomes\n",
@@ -603,7 +603,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8b73324d",
+   "id": "301fc517",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -621,7 +621,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "52fb0f25",
+   "id": "26b7806e",
    "metadata": {},
    "source": [
     "Let’s compare the preceding population $\\beta$ with the OLS sample\n",
@@ -631,7 +631,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27b07712",
+   "id": "b1b19984",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -640,7 +640,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "322cdab0",
+   "id": "c1796711",
    "metadata": {},
    "source": [
     "Let’s compare our population $\\hat{\\Sigma}_1$ with the\n",
@@ -650,7 +650,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a45d0408",
+   "id": "7f553fb6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -659,7 +659,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ff794dd3",
+   "id": "31bfce15",
    "metadata": {},
    "source": [
     "Lastly, let’s compute the estimate of $\\hat{E z_1 | z_2}$ and\n",
@@ -669,7 +669,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "90491e60",
+   "id": "ee487812",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -678,7 +678,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "913b22fb",
+   "id": "ed0833fa",
    "metadata": {},
    "source": [
     "Thus, in each case, for our very large sample size, the sample analogues\n",
@@ -697,7 +697,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7dfe0f88",
+   "id": "0bbed2c5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -711,7 +711,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b2fedda9",
+   "id": "ba415432",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -721,7 +721,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "83320893",
+   "id": "7294f25e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -731,7 +731,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "abe172fb",
+   "id": "c4a2508b",
    "metadata": {},
    "source": [
     "Let’s compute the distribution of $z_1$ conditional on\n",
@@ -741,7 +741,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d7ec8718",
+   "id": "0064d1d6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -754,7 +754,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dd63742b",
+   "id": "2f48d705",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -767,7 +767,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10ab4a03",
+   "id": "e6f25e99",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -777,7 +777,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fadf4372",
+   "id": "1ba9682e",
    "metadata": {},
    "source": [
     "As above, we compare population and sample regression coefficients, the\n",
@@ -788,7 +788,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "53425b8a",
+   "id": "4fee86d1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -798,7 +798,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "06b8f289",
+   "id": "f0e44958",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -808,7 +808,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "397668b3",
+   "id": "4a930bc7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -817,7 +817,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dff724a5",
+   "id": "bdbf43dc",
    "metadata": {},
    "source": [
     "Once again, sample analogues do a good job of approximating their\n",
@@ -914,7 +914,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "653974c2",
+   "id": "5c7a06f7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -933,7 +933,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ea303c2b",
+   "id": "e35c6a4e",
    "metadata": {},
    "source": [
     "Now let’s consider a specific instance of this model.\n",
@@ -949,7 +949,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5cbbb8e3",
+   "id": "b87bae88",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -962,7 +962,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "31f47676",
+   "id": "8be4a7f1",
    "metadata": {},
    "source": [
     "We can now use our `MultivariateNormal` class to construct an\n",
@@ -977,7 +977,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5ae4fe8a",
+   "id": "0f98e5cc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -989,7 +989,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45cf5acc",
+   "id": "79c37672",
    "metadata": {},
    "source": [
     "Using the generator `multivariate_normal`, we can make one draw of the\n",
@@ -1002,7 +1002,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f36933bb",
+   "id": "002b7df2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1014,7 +1014,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dfc68362",
+   "id": "fc8527bb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1024,7 +1024,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "69cf0a2c",
+   "id": "deeaa466",
    "metadata": {},
    "source": [
     "The method `cond_dist` takes test scores $y$ as input and returns the\n",
@@ -1039,7 +1039,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0c9928cd",
+   "id": "707f4d1a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1049,7 +1049,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bbc72f33",
+   "id": "b63320fe",
    "metadata": {},
    "source": [
     "The first number is the conditional mean $\\hat{\\mu}_{\\theta}$ and\n",
@@ -1068,7 +1068,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ca433fdd",
+   "id": "f5123498",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1098,7 +1098,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "31d2a238",
+   "id": "d95e7f81",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1121,7 +1121,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3fe8d82f",
+   "id": "36e431a8",
    "metadata": {},
    "source": [
     "The solid blue line in the plot above shows $\\hat{\\mu}_{\\theta}$\n",
@@ -1237,7 +1237,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b47dfdab",
+   "id": "15fc7fb8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1250,7 +1250,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3a1e5c08",
+   "id": "112c0d78",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1263,7 +1263,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2fbb5237",
+   "id": "5e224436",
    "metadata": {},
    "source": [
     "To confirm that these formulas give the same answers that we computed\n",
@@ -1277,7 +1277,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c28bbf7b",
+   "id": "73101318",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1288,7 +1288,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b09f6e6e",
+   "id": "8244b3a1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1298,7 +1298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "683a878f",
+   "id": "08554ee2",
    "metadata": {},
    "source": [
     "## Cholesky Factor Magic\n",
@@ -1382,7 +1382,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1896e897",
+   "id": "3fa7f673",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1409,7 +1409,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c38ab239",
+   "id": "62dd5b83",
    "metadata": {},
    "source": [
     "Let’s put the function to work."
@@ -1418,7 +1418,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "98932ab6",
+   "id": "ec21fa2d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1433,7 +1433,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2c5e5f35",
+   "id": "652f46c5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1450,7 +1450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1506e6bf",
+   "id": "04f204a0",
    "metadata": {},
    "source": [
     "We first compute the joint normal distribution of\n",
@@ -1460,7 +1460,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c5fa1927",
+   "id": "c875160e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1474,7 +1474,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2104a01",
+   "id": "f37d83a6",
    "metadata": {},
    "source": [
     "Now let’s compute distributions of $\\theta$ and $\\mu$\n",
@@ -1487,7 +1487,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ab742606",
+   "id": "c7002a73",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1504,7 +1504,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fb1ee723",
+   "id": "fd270a92",
    "metadata": {},
    "source": [
     "Let’s see how things work for an example."
@@ -1513,7 +1513,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "49f40e0d",
+   "id": "be87a6b7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1531,7 +1531,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ed283f4",
+   "id": "a03d327c",
    "metadata": {},
    "source": [
     "Evidently, math tests provide no information about $\\mu$ and\n",
@@ -1634,7 +1634,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "caf4bd44",
+   "id": "12cbf380",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1645,7 +1645,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c167f9ce",
+   "id": "6949b70e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1662,7 +1662,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1dd05d99",
+   "id": "cdcf3469",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1680,7 +1680,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1a3b33d1",
+   "id": "e0d593f6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1690,7 +1690,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "929d0db9",
+   "id": "fec435dc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1704,7 +1704,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "56c19b05",
+   "id": "238db6b8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1720,7 +1720,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "58e2c551",
+   "id": "a77d91cd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1730,7 +1730,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3eedf2ab",
+   "id": "262a0431",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1740,7 +1740,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b842762a",
+   "id": "339a023d",
    "metadata": {},
    "source": [
     "The following Python code lets us sample random vectors $X$ and\n",
@@ -1753,7 +1753,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7d4e9628",
+   "id": "d9338671",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1765,7 +1765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "10d3f278",
+   "id": "b8ee0ae5",
    "metadata": {},
    "source": [
     "### Smoothing Example\n",
@@ -1784,7 +1784,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "40ad3077",
+   "id": "3be4496f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1797,7 +1797,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dd7c4980",
+   "id": "40660afb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1808,7 +1808,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0a5d624a",
+   "id": "64406621",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1823,7 +1823,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a907d234",
+   "id": "26977143",
    "metadata": {},
    "source": [
     "### Filtering Exercise\n",
@@ -1841,7 +1841,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e3215332",
+   "id": "57bbfd99",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1851,7 +1851,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3a4518bb",
+   "id": "4339f601",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1870,7 +1870,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d56bb798",
+   "id": "bc937a4a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1880,7 +1880,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1a38df1c",
+   "id": "9e86eedd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1891,7 +1891,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9e098d92",
+   "id": "434000f3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1902,7 +1902,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b270322d",
+   "id": "8d6e47cc",
    "metadata": {},
    "source": [
     "### Prediction Exercise\n",
@@ -1919,7 +1919,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37b0ad4e",
+   "id": "c6586b65",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1930,7 +1930,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8f2dcf19",
+   "id": "19856933",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1946,7 +1946,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "80125b8b",
+   "id": "b4c05422",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1956,7 +1956,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cf6987e3",
+   "id": "2cee5e2d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1967,7 +1967,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "82dd47e0",
+   "id": "3e46752f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1978,7 +1978,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82aab1e5",
+   "id": "0956e614",
    "metadata": {},
    "source": [
     "### Constructing a Wold Representation\n",
@@ -2000,7 +2000,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a7ecb459",
+   "id": "202e1761",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2012,7 +2012,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da194d47",
+   "id": "cd629874",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2024,7 +2024,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fd6fd3cc",
+   "id": "51532486",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2033,7 +2033,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a009fa0f",
+   "id": "ba804472",
    "metadata": {},
    "source": [
     "This example is an instance of what is known as a **Wold representation** in time series analysis.\n",
@@ -2134,7 +2134,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "25a2cc2f",
+   "id": "a150842f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2158,7 +2158,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d6605b00",
+   "id": "4f4f26a5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2180,7 +2180,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8faf8e9f",
+   "id": "79149400",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2195,7 +2195,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a6961a04",
+   "id": "703a5b1b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2212,7 +2212,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bd116f91",
+   "id": "dd27c180",
    "metadata": {},
    "source": [
     "## Application to Stock Price Model\n",
@@ -2260,7 +2260,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0c3d1b00",
+   "id": "1a2a339f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2270,7 +2270,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "77d9e1bb",
+   "id": "beaf34f7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2283,7 +2283,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d1a53747",
+   "id": "2c996849",
    "metadata": {},
    "source": [
     "Denote\n",
@@ -2314,7 +2314,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a3a0b2fc",
+   "id": "79bf247a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2324,7 +2324,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "587a0cca",
+   "id": "d5fb6712",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2334,7 +2334,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "653a7e75",
+   "id": "657087e1",
    "metadata": {},
    "source": [
     "We can simulate paths of $y_{t}$ and $p_{t}$ and compute the\n",
@@ -2345,7 +2345,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a25126f3",
+   "id": "a8a3ba06",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2356,7 +2356,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8c53d0af",
+   "id": "72e7f8aa",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2377,7 +2377,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "96c4fdde",
+   "id": "453b96cc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2393,7 +2393,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45cb160b",
+   "id": "977acd4f",
    "metadata": {},
    "source": [
     "In the above graph, the green line is what the price of the stock would\n",
@@ -2604,7 +2604,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6eab0d35",
+   "id": "5b90550c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2621,7 +2621,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6c914973",
+   "id": "a3725905",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2632,7 +2632,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0aeefec5",
+   "id": "1711d4a1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2642,7 +2642,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f6dd113f",
+   "id": "40d41c78",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2657,7 +2657,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37de59ad",
+   "id": "9d28c1a7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2672,7 +2672,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a06ae47f",
+   "id": "e205dcab",
    "metadata": {},
    "source": [
     "### Code for Iterating\n",
@@ -2684,7 +2684,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b5fa9648",
+   "id": "f88b4f13",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2720,7 +2720,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cde49658",
+   "id": "d8bdd04b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2729,7 +2729,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2d818614",
+   "id": "869fa4ba",
    "metadata": {},
    "source": [
     "The iterative algorithm just described is a version of the celebrated **Kalman filter**.\n",
@@ -2801,7 +2801,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "76ad5e85",
+   "id": "d3ffa567",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2811,7 +2811,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "92197f92",
+   "id": "e7e5fcdb",
    "metadata": {},
    "source": [
     "We set the coefficient matrix $\\Lambda$ and the covariance matrix\n",
@@ -2844,7 +2844,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8d30067f",
+   "id": "b98496d4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2859,7 +2859,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ce268151",
+   "id": "70117966",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2869,7 +2869,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ae503ba0",
+   "id": "36343f5d",
    "metadata": {},
    "source": [
     "We can now construct the mean vector and the covariance matrix for\n",
@@ -2879,7 +2879,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0801fce9",
+   "id": "e315a57f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2896,7 +2896,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b00b3a7b",
+   "id": "a5179d40",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2909,7 +2909,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a53c0fde",
+   "id": "271f2597",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2919,7 +2919,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "592baac5",
+   "id": "b835ce3a",
    "metadata": {},
    "source": [
     "Let’s compute the conditional distribution of the hidden factor\n",
@@ -2929,7 +2929,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f8a20508",
+   "id": "6bea3262",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2938,7 +2938,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "17f708fa",
+   "id": "c09b4a08",
    "metadata": {},
    "source": [
     "We can verify that the conditional mean\n",
@@ -2949,7 +2949,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5998288f",
+   "id": "25817abb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2960,7 +2960,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd4a4750",
+   "id": "f31c2c45",
    "metadata": {},
    "source": [
     "Similarly, we can compute the conditional distribution $Y \\mid f$."
@@ -2969,7 +2969,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "36846a28",
+   "id": "c7cdfd56",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2978,7 +2978,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "68722b9f",
+   "id": "076af3a7",
    "metadata": {},
    "source": [
     "It can be verified that the mean is\n",
@@ -2988,7 +2988,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3e4464ce",
+   "id": "c91d0bcf",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2997,7 +2997,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "46220ebc",
+   "id": "43273318",
    "metadata": {},
    "source": [
     "## PCA and Factor Analysis\n",
@@ -3046,7 +3046,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c7842ca2",
+   "id": "f58b410c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3065,7 +3065,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fcf1ce55",
+   "id": "5578d9b1",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3076,7 +3076,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d60837e6",
+   "id": "159d6672",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3087,7 +3087,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "edc105a3",
+   "id": "60e1b47b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3099,7 +3099,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b380cb3d",
+   "id": "432f093a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3110,7 +3110,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "50793291",
+   "id": "8afa3a88",
    "metadata": {},
    "source": [
     "Below we’ll plot several things\n",
@@ -3128,7 +3128,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da00379c",
+   "id": "20db6652",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3143,7 +3143,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5f1a0b91",
+   "id": "965c6307",
    "metadata": {},
    "source": [
     "Consequently, the first two $\\epsilon_{j}$ correspond to the\n",
@@ -3155,7 +3155,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2c46770c",
+   "id": "ecfb5de4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3165,7 +3165,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2b145ba6",
+   "id": "c0d7255b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3175,7 +3175,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c53c7fe7",
+   "id": "0b8f6c2d",
    "metadata": {},
    "source": [
     "The fraction of variance in $y_{t}$ explained by the first two\n",
@@ -3185,7 +3185,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ed3b3ea1",
+   "id": "8321defc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3194,7 +3194,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bf8b3151",
+   "id": "4c1f1d48",
    "metadata": {},
    "source": [
     "Compute\n",
@@ -3210,7 +3210,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4997df6d",
+   "id": "229ca563",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3219,7 +3219,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "62005f6c",
+   "id": "1fccfa18",
    "metadata": {},
    "source": [
     "In this example, it turns out that the projection $\\hat{Y}$ of\n",
@@ -3234,7 +3234,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e9fca130",
+   "id": "9d63784b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -3253,7 +3253,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd015041",
+   "id": "c356b548",
    "metadata": {},
    "source": [
     "The covariance matrix of $\\hat{Y}$ can be computed by first\n",
@@ -3264,7 +3264,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "841eca75",
+   "id": "e55686c1",
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/_sources/navy_captain.ipynb b/_sources/navy_captain.ipynb
index 53e8334..052cb98 100644
--- a/_sources/navy_captain.ipynb
+++ b/_sources/navy_captain.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "02131f92",
+   "id": "7f202244",
    "metadata": {},
    "source": [
     "(bayesian_vs_frequentist__v1)=\n",
@@ -26,7 +26,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9fe7afcf",
+   "id": "9f077ae8",
    "metadata": {
     "tags": [
      "hide-output"
@@ -40,7 +40,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b3f53c17",
+   "id": "ba8fc8a5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -57,7 +57,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "842ca0c4",
+   "id": "50790e60",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -139,7 +139,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11b1b94c",
+   "id": "477e7f74",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -154,7 +154,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25fa874e",
+   "id": "c8449823",
    "metadata": {},
    "source": [
     "We start with defining a `jitclass` that stores parameters and\n",
@@ -165,7 +165,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "591a6f3c",
+   "id": "859f51fa",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -188,7 +188,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "30a1d30c",
+   "id": "387bfeb3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -239,7 +239,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4eeba3d0",
+   "id": "dddc5cbe",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -263,7 +263,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ae5e6b8",
+   "id": "91723098",
    "metadata": {},
    "source": [
     "Above, we plot the two possible probability densities $f_0$ and\n",
@@ -336,7 +336,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "cb38e5a4",
+   "id": "794cb614",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -347,7 +347,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e4867528",
+   "id": "2f50883e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -358,7 +358,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0aa09fbe",
+   "id": "9be534b7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -370,7 +370,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55e719d5",
+   "id": "dce1c2b9",
    "metadata": {},
    "source": [
     "We can compute sequences of likelihood ratios using simulated samples."
@@ -379,7 +379,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff49c00f",
+   "id": "cafa3991",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -389,7 +389,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6f3bdd71",
+   "id": "5c06916d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "274a3716",
+   "id": "9e4a1fc8",
    "metadata": {},
    "source": [
     "With an empirical distribution of likelihood ratios in hand, we can draw\n",
@@ -413,7 +413,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "18c27206",
+   "id": "f49dd0b4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -439,7 +439,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ab27991b",
+   "id": "7d4c4e78",
    "metadata": {},
    "source": [
     "Our frequentist minimizes the expected total loss presented in equation\n",
@@ -465,7 +465,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7786e24b",
+   "id": "f33acb0d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -485,7 +485,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1a11cd4c",
+   "id": "7e57a1e7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -504,7 +504,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c0a79201",
+   "id": "24e4f645",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -528,7 +528,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6181603c",
+   "id": "76b68918",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -545,7 +545,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "98cc4ad0",
+   "id": "f319f168",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -555,7 +555,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e8c698e8",
+   "id": "72bfbda3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -565,7 +565,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "550be3ab",
+   "id": "c0581ec7",
    "metadata": {},
    "source": [
     "Let’s now change the value of $\\pi^{*}$ and watch how the decision\n",
@@ -575,7 +575,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "28510ff2",
+   "id": "32d0dc20",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -600,7 +600,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d5a56103",
+   "id": "39dec7b9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -613,7 +613,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "75a08fd4",
+   "id": "fcb7c5ce",
    "metadata": {},
    "source": [
     "The following shows how optimal sample size $t$ and targeted\n",
@@ -623,7 +623,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9fcb65e6",
+   "id": "933cebf7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -644,7 +644,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d13640ad",
+   "id": "0431e04a",
    "metadata": {},
    "source": [
     "## Bayesian Decision Rule\n",
@@ -666,7 +666,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8f565e33",
+   "id": "2f651e3a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -705,7 +705,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6aeb7076",
+   "id": "c1f682dc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -737,7 +737,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "05348c01",
+   "id": "dd3a36be",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -747,7 +747,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "11e04ac8",
+   "id": "6c429ef6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -808,7 +808,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed795f75",
+   "id": "3679c798",
    "metadata": {},
    "source": [
     "The above figure portrays the value function plotted against the decision\n",
@@ -866,7 +866,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39b78c5c",
+   "id": "54af1478",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -907,7 +907,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19153ce8",
+   "id": "24da5967",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -928,7 +928,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca635ce0",
+   "id": "11fda91c",
    "metadata": {},
    "source": [
     "Given an assumed value for\n",
@@ -947,7 +947,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "539453cd",
+   "id": "ccd028c3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -964,7 +964,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "65e7e7e6",
+   "id": "d4e9329d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -993,7 +993,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c855b7a2",
+   "id": "257204fd",
    "metadata": {},
    "source": [
     "This pattern of outcomes holds more generally.\n",
@@ -1006,7 +1006,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e38eee2d",
+   "id": "f1a021d4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1040,7 +1040,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "82a4d2f1",
+   "id": "f9cc7f7f",
    "metadata": {},
    "source": [
     "## Was the Navy Captain’s Hunch Correct?\n",
@@ -1055,7 +1055,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "26ba2784",
+   "id": "8f2de166",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1065,7 +1065,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "66dc7d91",
+   "id": "e2501001",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1080,7 +1080,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6eb37ba4",
+   "id": "23c7645b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1094,7 +1094,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5c19e445",
+   "id": "aa20706a",
    "metadata": {},
    "source": [
     "Evidently, there is no sample size $t$ at which the frequentist\n",
@@ -1107,7 +1107,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "42bba95a",
+   "id": "b856f53d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1127,7 +1127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "293be788",
+   "id": "3981c53f",
    "metadata": {},
    "source": [
     "The right panel of the above graph plots the difference\n",
@@ -1144,7 +1144,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "da79a29c",
+   "id": "6517d4d4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1153,7 +1153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8ecea6b8",
+   "id": "33a9bc42",
    "metadata": {},
    "source": [
     "Recall that when $\\pi^*=0.5$, the frequentist decision rule sets a\n",
@@ -1165,7 +1165,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a3539523",
+   "id": "057949cc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1174,7 +1174,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "edbf11c5",
+   "id": "0ae0f97f",
    "metadata": {},
    "source": [
     "For convenience, let’s define `t_idx` as the Python array index\n",
@@ -1184,7 +1184,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3119b1c8",
+   "id": "7f7a75d4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1193,7 +1193,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1b56ab01",
+   "id": "5c24f7c6",
    "metadata": {},
    "source": [
     "## Distribution of Bayesian Decision Rule’s Time to Decide\n",
@@ -1218,7 +1218,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d54e41e5",
+   "id": "25d14b63",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1245,7 +1245,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d0ddb53b",
+   "id": "61a778eb",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1260,7 +1260,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e0d040d8",
+   "id": "1a89549a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1282,7 +1282,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "901896dd",
+   "id": "f239929d",
    "metadata": {},
    "source": [
     "Later we’ll figure out how these distributions ultimately affect\n",
@@ -1298,7 +1298,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "942cbbdd",
+   "id": "ff3d39ee",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1309,7 +1309,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "67e17d7c",
+   "id": "d3698494",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1334,7 +1334,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3284ba90",
+   "id": "35ec883a",
    "metadata": {},
    "source": [
     "The above figures compare averages and variances of updated Bayesian\n",
@@ -1363,7 +1363,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16a0439e",
+   "id": "6d717783",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1382,7 +1382,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2fa7d3cf",
+   "id": "c97474ab",
    "metadata": {},
    "source": [
     "## Probability of Making Correct Decision\n",
@@ -1403,7 +1403,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e3b89537",
+   "id": "7facd4e8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1414,7 +1414,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2af101d0",
+   "id": "1af0fe87",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1439,7 +1439,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c22bca7e",
+   "id": "7f2a6968",
    "metadata": {},
    "source": [
     "By averaging using $\\pi^{*}$, we also plot the unconditional\n",
@@ -1449,7 +1449,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e903a7f6",
+   "id": "9cf6c23c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1471,7 +1471,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f4c9088f",
+   "id": "7c77047d",
    "metadata": {},
    "source": [
     "## Distribution of Likelihood Ratios at Frequentist’s $t$\n",
@@ -1493,7 +1493,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "deb9a5ac",
+   "id": "14d213a0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1504,7 +1504,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d295b1d5",
+   "id": "f0a40d5a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1527,7 +1527,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "4451fba4",
+   "id": "aa06286a",
    "metadata": {},
    "source": [
     "The next graph plots the unconditional distribution of Bayesian times to\n",
@@ -1538,7 +1538,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "962fa7f1",
+   "id": "d8c7cdfd",
    "metadata": {},
    "outputs": [],
    "source": [
diff --git a/_sources/ols.ipynb b/_sources/ols.ipynb
index 0863946..b7dd8fe 100644
--- a/_sources/ols.ipynb
+++ b/_sources/ols.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "6006b2bd",
+   "id": "4419873a",
    "metadata": {},
    "source": [
     "```{raw} html\n",
@@ -25,7 +25,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a5c0eee5",
+   "id": "998160ce",
    "metadata": {
     "tags": [
      "hide-output"
@@ -38,7 +38,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "99b6b1d7",
+   "id": "f2e8a65d",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -70,7 +70,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2dba43eb",
+   "id": "800ad5d3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -88,7 +88,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "06cef4d4",
+   "id": "b902d70e",
    "metadata": {},
    "source": [
     "### Prerequisites\n",
@@ -117,7 +117,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "16f59a18",
+   "id": "c66f7574",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -127,7 +127,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e9651ec0",
+   "id": "401e3ca6",
    "metadata": {},
    "source": [
     "Let's use a scatterplot to see whether any obvious relationship exists\n",
@@ -138,7 +138,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fed439a8",
+   "id": "e1c5d084",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -148,7 +148,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32a58f01",
+   "id": "1acc3291",
    "metadata": {},
    "source": [
     "The plot shows a fairly strong positive relationship between\n",
@@ -184,7 +184,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ba09faa9",
+   "id": "d35bb615",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -221,7 +221,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f95b9803",
+   "id": "565ba473",
    "metadata": {},
    "source": [
     "The most common technique to estimate the parameters ($\\beta$'s)\n",
@@ -245,7 +245,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c2a632ef",
+   "id": "14c77966",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -254,7 +254,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "67fce7fd",
+   "id": "ede586b0",
    "metadata": {},
    "source": [
     "Now we can construct our model in `statsmodels` using the OLS function.\n",
@@ -265,7 +265,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5743fdc6",
+   "id": "1e885a11",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -276,7 +276,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6db60a42",
+   "id": "e60ade90",
    "metadata": {},
    "source": [
     "So far we have simply constructed our model.\n",
@@ -288,7 +288,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6d0484ae",
+   "id": "ffa99289",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -298,7 +298,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "39639460",
+   "id": "5590ecc1",
    "metadata": {},
    "source": [
     "We now have the fitted regression model stored in `results`.\n",
@@ -314,7 +314,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "644c7a34",
+   "id": "8365aca7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -323,7 +323,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "77e20a70",
+   "id": "36600f71",
    "metadata": {},
    "source": [
     "From our results, we see that\n",
@@ -361,7 +361,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "94559138",
+   "id": "24d9d04e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -372,7 +372,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "59268209",
+   "id": "e59dc5cf",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -382,7 +382,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3f3873c5",
+   "id": "fc01e624",
    "metadata": {},
    "source": [
     "An easier (and more accurate) way to obtain this result is to use\n",
@@ -393,7 +393,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "17aefe80",
+   "id": "145c76f2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bcb80da3",
+   "id": "74eb500c",
    "metadata": {},
    "source": [
     "We can obtain an array of predicted ${logpgp95}_i$ for every value\n",
@@ -419,7 +419,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2fa708c0",
+   "id": "b84cf1ac",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -447,7 +447,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d49b541e",
+   "id": "23faa975",
    "metadata": {},
    "source": [
     "## Extending the Linear Regression Model\n",
@@ -475,7 +475,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fa31434a",
+   "id": "c42fb65e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -497,7 +497,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "58c22ef2",
+   "id": "a170f1e4",
    "metadata": {},
    "source": [
     "Now that we have fitted our model, we will use `summary_col` to\n",
@@ -508,7 +508,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6ae24b35",
+   "id": "831a3a29",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -535,7 +535,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "23cb562a",
+   "id": "3c2d15ed",
    "metadata": {},
    "source": [
     "## Endogeneity\n",
@@ -585,7 +585,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "27d26dac",
+   "id": "41d88e60",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -619,7 +619,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e922ccd7",
+   "id": "fc184c74",
    "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",
@@ -662,7 +662,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b5a8326f",
+   "id": "25a8dd11",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -682,7 +682,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aa73d9ef",
+   "id": "8f43836a",
    "metadata": {},
    "source": [
     "**Second stage**\n",
@@ -703,7 +703,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8676d0a9",
+   "id": "ff6e2603",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -716,7 +716,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65632dea",
+   "id": "9dd3f663",
    "metadata": {},
    "source": [
     "The second-stage regression results give us an unbiased and consistent\n",
@@ -740,7 +740,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c474c0db",
+   "id": "fdcf4d09",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -754,7 +754,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "8b37475c",
+   "id": "9689c28e",
    "metadata": {},
    "source": [
     "Given that we now have consistent and unbiased estimates, we can infer\n",
@@ -826,7 +826,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a072228b",
+   "id": "437a22d8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -854,7 +854,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f378faa2",
+   "id": "74f6c818",
    "metadata": {},
    "source": [
     "The output shows that the coefficient on the residuals is statistically\n",
@@ -911,7 +911,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d4ab451a",
+   "id": "721ffec9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -936,7 +936,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1e93240b",
+   "id": "4a637ab4",
    "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 406cfda..f6284ee 100644
--- a/_sources/pandas_panel.ipynb
+++ b/_sources/pandas_panel.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "e46d1103",
+   "id": "bc5bb386",
    "metadata": {},
    "source": [
     "(ppd)=\n",
@@ -62,7 +62,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dea770eb",
+   "id": "3d5d1e9b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -72,7 +72,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "eea94ade",
+   "id": "0ab0209a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -89,7 +89,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7c07e9de",
+   "id": "12b36687",
    "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": "ebdb637b",
+   "id": "9414dab5",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -107,7 +107,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd07c7f9",
+   "id": "0fc0aaee",
    "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": "cc3cc360",
+   "id": "0ab4baa3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -134,7 +134,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "697e1d00",
+   "id": "d2ed0f48",
    "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": "6a09242d",
+   "id": "3dd6ae53",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -153,7 +153,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "89e63a05",
+   "id": "52012631",
    "metadata": {},
    "source": [
     "The columns contain multiple levels of indexing, known as a\n",
@@ -167,7 +167,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ff5779e3",
+   "id": "4978f241",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -177,7 +177,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "278ea411",
+   "id": "91011176",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -186,7 +186,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5a9efc70",
+   "id": "c7b740bf",
    "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": "f04cbe79",
+   "id": "a8d6310f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -205,7 +205,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1587db7b",
+   "id": "763be615",
    "metadata": {},
    "source": [
     "Stacking and unstacking levels of the `MultiIndex` will be used\n",
@@ -219,7 +219,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1c3d424b",
+   "id": "1ae9b80d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -228,7 +228,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d36f81df",
+   "id": "eb149398",
    "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": "085469cc",
+   "id": "b252a12e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -247,7 +247,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ca5cd9ca",
+   "id": "03240a30",
    "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": "65aa2406",
+   "id": "ca18cb09",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -269,7 +269,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "01a8ed6d",
+   "id": "1b6bec84",
    "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": "d83e3eff",
+   "id": "63d52c4f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -295,7 +295,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f77ed0f2",
+   "id": "4ecabba5",
    "metadata": {},
    "source": [
     "## Merging Dataframes and Filling NaNs\n",
@@ -314,7 +314,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1b07fec2",
+   "id": "84ca2164",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -324,7 +324,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f206e979",
+   "id": "f53258fd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -334,7 +334,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f87df1c0",
+   "id": "011243cb",
    "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": "c1079d1a",
+   "id": "347f1e43",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -355,7 +355,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eaa2a025",
+   "id": "43b7cc38",
    "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": "4ed38214",
+   "id": "c8836e56",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -380,7 +380,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "08b8ac34",
+   "id": "e4e696e7",
    "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": "762a402c",
+   "id": "c9249e3a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -428,7 +428,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c24d6b8a",
+   "id": "8d8bffa3",
    "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": "32c787b9",
+   "id": "0e319839",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -450,7 +450,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "669a0d73",
+   "id": "42e97946",
    "metadata": {},
    "source": [
     "We have three missing values!\n",
@@ -467,7 +467,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f8b2d0af",
+   "id": "1ea5737d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -480,7 +480,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9b799f2b",
+   "id": "b03d1cde",
    "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": "5d1c7f06",
+   "id": "cae5301c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -505,7 +505,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "60584e46",
+   "id": "14e3f3d8",
    "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": "a58b50a4",
+   "id": "a8e18d92",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -530,7 +530,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "16b6bc09",
+   "id": "ca477dbe",
    "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": "ee1b8cf6",
+   "id": "7373a00f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -555,7 +555,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "43597abf",
+   "id": "3eff2ad3",
    "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": "18082dbb",
+   "id": "b95f50e2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -574,7 +574,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "74249541",
+   "id": "674f5e55",
    "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": "7a746f6a",
+   "id": "9c1e5d24",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -595,7 +595,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0a79d03f",
+   "id": "81aef8c6",
    "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": "66fa97bd",
+   "id": "2a125fc9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -615,7 +615,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6dacbaac",
+   "id": "7b69bdf5",
    "metadata": {},
    "source": [
     "## Grouping and Summarizing Data\n",
@@ -635,7 +635,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "39f89e16",
+   "id": "1450ba0c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -644,7 +644,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "658038d6",
+   "id": "f3aaac11",
    "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": "55c6e046",
+   "id": "80180180",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -666,7 +666,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d5d69ec8",
+   "id": "49bed80d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -683,7 +683,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "122d5b43",
+   "id": "9c4837f5",
    "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": "c527011d",
+   "id": "2b364f6e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -702,7 +702,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "923f5a2e",
+   "id": "e72b6899",
    "metadata": {},
    "source": [
     "We can plot this time series as a line graph"
@@ -711,7 +711,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b12ad99c",
+   "id": "338362fd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -724,7 +724,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "55bccb4a",
+   "id": "c290996c",
    "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": "9c4b722a",
+   "id": "b2c38c5b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -743,7 +743,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b1782834",
+   "id": "a7dcbc11",
    "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": "8fa8e33c",
+   "id": "5c8c9435",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -765,7 +765,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3322a9de",
+   "id": "5f2871fb",
    "metadata": {},
    "source": [
     "We will drop Australia as a continent for plotting purposes"
@@ -774,7 +774,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5728bab5",
+   "id": "a19814ce",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -788,7 +788,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e5a75cf0",
+   "id": "005cc325",
    "metadata": {},
    "source": [
     "`.describe()` is useful for quickly retrieving a number of common\n",
@@ -798,7 +798,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4aafd2ba",
+   "id": "f59ce4b9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -807,7 +807,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d9bc62ed",
+   "id": "6b37eeeb",
    "metadata": {},
    "source": [
     "This is a simplified way to use `groupby`.\n",
@@ -828,7 +828,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "972790a0",
+   "id": "ad390d9a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -838,7 +838,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a68903c3",
+   "id": "1bd068d5",
    "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": "8ca07261",
+   "id": "d53a5204",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -862,7 +862,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bae04471",
+   "id": "56874832",
    "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": "88f1ad93",
+   "id": "67490932",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -893,7 +893,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "bfda698f",
+   "id": "0c68b013",
    "metadata": {},
    "source": [
     "## Final Remarks\n",
@@ -920,7 +920,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "46d8c10b",
+   "id": "ec878e09",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -929,7 +929,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "679401bf",
+   "id": "10d7d943",
    "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": "0001632a",
+   "id": "7c5ca1d8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -965,7 +965,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7d7b27ba",
+   "id": "5894ae1d",
    "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": "82d83008",
+   "id": "86e9bdde",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -984,7 +984,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d2d673b1",
+   "id": "c6e2711a",
    "metadata": {},
    "source": [
     "Variables within levels can be quickly retrieved with a loop"
@@ -993,7 +993,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "189390a4",
+   "id": "d76c1784",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1003,7 +1003,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "298bced6",
+   "id": "b39835f1",
    "metadata": {},
    "source": [
     "```{solution-end}\n",
@@ -1039,7 +1039,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4d31c3df",
+   "id": "fa21c4ac",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1049,7 +1049,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a26fa68f",
+   "id": "c0da0bdf",
    "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": "e32394e3",
+   "id": "ef9f1f54",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1073,7 +1073,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d9ada98",
+   "id": "7e646af6",
    "metadata": {},
    "source": [
     "Select only percentage employed in the active population from the\n",
@@ -1083,7 +1083,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "869cd315",
+   "id": "5c92392a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1095,7 +1095,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "28c98bec",
+   "id": "b24a7a06",
    "metadata": {},
    "source": [
     "Drop the 'Total' value before creating the grouped boxplot"
@@ -1104,7 +1104,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6abf3060",
+   "id": "8459718c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1114,7 +1114,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0d171a97",
+   "id": "3e532b56",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1130,7 +1130,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d14d53e1",
+   "id": "3da0b818",
    "metadata": {},
    "source": [
     "```{solution-end}\n",
diff --git a/_sources/prob_matrix.ipynb b/_sources/prob_matrix.ipynb
index 288d39d..5038f9f 100644
--- a/_sources/prob_matrix.ipynb
+++ b/_sources/prob_matrix.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "0882d74e",
+   "id": "62472898",
    "metadata": {},
    "source": [
     "# Elementary Probability with Matrices\n",
@@ -34,7 +34,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "56587a9f",
+   "id": "c8f197d9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -44,7 +44,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d3c24cf1",
+   "id": "f1408b0a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -59,7 +59,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "565c3230",
+   "id": "f7b62be6",
    "metadata": {},
    "source": [
     "## Sketch of Basic Concepts\n",
@@ -568,7 +568,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5f05881d",
+   "id": "d7458879",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -591,7 +591,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d896f999",
+   "id": "22108acd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -601,7 +601,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "7fd3304c",
+   "id": "f4a0cf8c",
    "metadata": {},
    "source": [
     "**Geometric distribution**\n",
@@ -662,7 +662,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d3e48524",
+   "id": "a385fe8b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -685,7 +685,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c3d35b4c",
+   "id": "245b0471",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -695,7 +695,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dbe8bb08",
+   "id": "46b17802",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -705,7 +705,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dab3fe5b",
+   "id": "07a40033",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -715,7 +715,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "65bedf57",
+   "id": "6d956bb6",
    "metadata": {},
    "source": [
     "## Some Discrete Probability Distributions\n",
@@ -749,7 +749,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c7cb65e7",
+   "id": "90f36ba4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -772,7 +772,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2997c9ac",
+   "id": "c773add4",
    "metadata": {},
    "source": [
     "### Newcomb–Benford distribution\n",
@@ -811,7 +811,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9173de44",
+   "id": "eff0abda",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -833,7 +833,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "69d27b03",
+   "id": "00f48120",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -845,7 +845,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9c4096e6",
+   "id": "a69ddb75",
    "metadata": {},
    "source": [
     "### Pascal (negative binomial) distribution \n",
@@ -881,7 +881,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "98f178e0",
+   "id": "cb3ba8e3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -902,7 +902,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "32962379",
+   "id": "8954199f",
    "metadata": {},
    "source": [
     "## Continuous Random Variables\n",
@@ -925,7 +925,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c263d1cb",
+   "id": "f5d7bdbc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -949,7 +949,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "25fc67e3",
+   "id": "cce9839b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -960,7 +960,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3d26b55",
+   "id": "909309a9",
    "metadata": {},
    "source": [
     "### Uniform Distribution\n",
@@ -985,7 +985,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c8308cd3",
+   "id": "c3f533c9",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1009,7 +1009,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ba7eb14b",
+   "id": "8a5367d3",
    "metadata": {},
    "source": [
     "##  A Mixed Discrete-Continuous Distribution\n",
@@ -1041,7 +1041,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "2c91b304",
+   "id": "147e84e2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1058,7 +1058,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ac66de69",
+   "id": "80c84886",
    "metadata": {},
    "source": [
     "The analytical mean and variance can be computed:\n",
@@ -1083,7 +1083,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f6ee6fd1",
+   "id": "b69f624f",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1095,7 +1095,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "e3ee9c0b",
+   "id": "85b99923",
    "metadata": {},
    "source": [
     "## Matrix Representation of Some Bivariate Distributions\n",
@@ -1124,7 +1124,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "baa52a83",
+   "id": "1c157f44",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1152,7 +1152,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a31eeb3f",
+   "id": "1caf161e",
    "metadata": {},
    "source": [
     "Here, we use exactly the inverse CDF technique to generate sample from the joint distribution $F$."
@@ -1161,7 +1161,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c37d8e4a",
+   "id": "ef088c09",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1188,7 +1188,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "89a74f2e",
+   "id": "5891709b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1221,7 +1221,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c9c5139b",
+   "id": "30843ea0",
    "metadata": {},
    "source": [
     "Let's  calculate population  marginal and conditional probabilities  using matrix algebra.\n",
@@ -1281,7 +1281,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8713c403",
+   "id": "7dc07234",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1399,7 +1399,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b4fc7ee8",
+   "id": "8fe8f453",
    "metadata": {},
    "source": [
     "Let's apply our code to some examples.\n",
@@ -1410,7 +1410,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5b7604c9",
+   "id": "a8de8277",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1422,7 +1422,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5fcc2a62",
+   "id": "952c74e8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1434,7 +1434,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ee816021",
+   "id": "270e52ba",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1444,7 +1444,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "14a5c8e7",
+   "id": "8f059896",
    "metadata": {},
    "source": [
     "**Example 2**"
@@ -1453,7 +1453,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "049726d8",
+   "id": "dc9a4c3a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1467,7 +1467,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a62995d1",
+   "id": "a30a51da",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1478,7 +1478,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8326ed16",
+   "id": "f2786997",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1487,7 +1487,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "48f177d5",
+   "id": "6c85d43c",
    "metadata": {},
    "source": [
     "## A Continuous Bivariate Random Vector \n",
@@ -1520,7 +1520,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "10515dce",
+   "id": "a8f927fe",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1537,7 +1537,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "20917bb7",
+   "id": "ea97cbb4",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1551,7 +1551,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c1838686",
+   "id": "7c490c41",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1562,7 +1562,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "3cd8a381",
+   "id": "fe733eab",
    "metadata": {},
    "source": [
     "**Joint Distribution**\n",
@@ -1573,7 +1573,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "4b91d690",
+   "id": "7801247d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1589,7 +1589,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "b922df48",
+   "id": "8a6a072b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1607,7 +1607,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6354640a",
+   "id": "d426efaf",
    "metadata": {},
    "source": [
     "Next  we can simulate from  a built-in `numpy` function  and calculate a **sample** marginal distribution from the sample mean and variance."
@@ -1616,7 +1616,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "15670706",
+   "id": "abebd46c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1630,7 +1630,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "774390d8",
+   "id": "b91ecebe",
    "metadata": {},
    "source": [
     "**Marginal distribution**"
@@ -1639,7 +1639,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a784feff",
+   "id": "18442624",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1654,7 +1654,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "bb1c04e4",
+   "id": "b7619214",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1668,7 +1668,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "504ff7a3",
+   "id": "c735a4f0",
    "metadata": {},
    "source": [
     "**Conditional distribution**\n",
@@ -1696,7 +1696,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a259bf97",
+   "id": "c0b9e5ea",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1709,7 +1709,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "761a5e3d",
+   "id": "d164bba8",
    "metadata": {},
    "source": [
     "The mean and variance are computed by\n",
@@ -1727,7 +1727,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1d88d796",
+   "id": "1742c8c7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1745,7 +1745,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa72c53c",
+   "id": "4cd733bc",
    "metadata": {},
    "source": [
     "Fix $x=1$."
@@ -1754,7 +1754,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dece79c3",
+   "id": "613c8c81",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1767,7 +1767,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "273b2434",
+   "id": "d7839b90",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1783,7 +1783,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "dce4be52",
+   "id": "a78ff68b",
    "metadata": {},
    "source": [
     "We compare  with the analytically computed parameters and note that they are close."
@@ -1792,7 +1792,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33b655a7",
+   "id": "19129ac3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -1805,7 +1805,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6cfc162f",
+   "id": "eeb63ef7",
    "metadata": {},
    "source": [
     "## Sum of Two Independently Distributed Random Variables\n",
@@ -2064,7 +2064,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9f41136c",
+   "id": "a1497daf",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2090,7 +2090,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "6fcf0a9f",
+   "id": "465b635c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2116,7 +2116,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "9ba4048c",
+   "id": "82142d30",
    "metadata": {},
    "source": [
     "Let's now take our two marginal  distributions, one for $X$, the other for  $Y$, and construct  two distinct couplings.\n",
@@ -2142,7 +2142,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3361e667",
+   "id": "467e5cae",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2175,7 +2175,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f7f732e0",
+   "id": "91772d4e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2199,7 +2199,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "9972b474",
+   "id": "9b7fc177",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2225,7 +2225,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b487ed5e",
+   "id": "cb87422a",
    "metadata": {},
    "source": [
     "Now, let's construct another  joint distribution that is  also a coupling of $X$ and $Y$\n",
@@ -2241,7 +2241,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ba31c53d",
+   "id": "1c8fc13b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2274,7 +2274,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ad4a97c8",
+   "id": "f3b4e58c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2298,7 +2298,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0f508a77",
+   "id": "15fcf82b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -2324,7 +2324,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "45582c3d",
+   "id": "7af37dfa",
    "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 c1ec957..c48fe35 100644
--- a/_sources/prob_meaning.ipynb
+++ b/_sources/prob_meaning.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "e495974b",
+   "id": "21c0a449",
    "metadata": {},
    "source": [
     "# Two Meanings of Probability\n",
@@ -49,7 +49,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "33bd45ca",
+   "id": "c0736a0e",
    "metadata": {
     "tags": [
      "hide-output"
@@ -62,7 +62,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d98833f",
+   "id": "61e9863f",
    "metadata": {},
    "source": [
     "To answer our coding questions, we'll start with some imports"
@@ -71,7 +71,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "013cb776",
+   "id": "6e60cff6",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -86,7 +86,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c79cf9a7",
+   "id": "0b204701",
    "metadata": {},
    "source": [
     "Empowered with these Python tools, we'll now  explore the two meanings described above.\n",
@@ -163,7 +163,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ebbb0dd6",
+   "id": "40eb5a17",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -228,7 +228,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a951040a",
+   "id": "72cf44d8",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -241,7 +241,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0988a1ba",
+   "id": "29a77411",
    "metadata": {},
    "source": [
     "From the table above, can you see the law of large numbers at work?\n",
@@ -265,7 +265,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a76b7d53",
+   "id": "f4a03cfc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -285,7 +285,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "50a89832",
+   "id": "801f2564",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -303,7 +303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "5077736d",
+   "id": "8ea327d2",
    "metadata": {},
    "source": [
     "**Comparison with different $n$**\n",
@@ -316,7 +316,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "ddf09c41",
+   "id": "a4b042b3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -336,7 +336,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "a7b8afe7",
+   "id": "e2be3dd3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -354,7 +354,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0295be79",
+   "id": "2372c72a",
    "metadata": {},
    "source": [
     "**Comparison with different $I$**\n",
@@ -365,7 +365,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e3d373c3",
+   "id": "bea55e5d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -386,7 +386,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "fcebdf03",
+   "id": "54c093c0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -404,7 +404,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c0fe91be",
+   "id": "a3887166",
    "metadata": {},
    "source": [
     "From the above graphs, we can see that **$I$, the number of independent sequences,** plays an important role.\n",
@@ -524,7 +524,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "01a90070",
+   "id": "a472433b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -591,7 +591,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "fa757827",
+   "id": "e300a1c2",
    "metadata": {},
    "source": [
     "**d)** Please plot the posterior distribution for $\\theta$ as a function of $\\theta$ as $n$ grows from $1, 2, \\ldots$."
@@ -600,7 +600,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "1e7c434b",
+   "id": "f4d21934",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -630,7 +630,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "54cb88e7",
+   "id": "78200f3b",
    "metadata": {},
    "source": [
     "**e)** For various $n$'s, please describe and compute  $.05$ and $.95$ quantiles for  posterior probabilities."
@@ -639,7 +639,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c65e9f4f",
+   "id": "d89e733e",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -656,7 +656,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "c7ec79a6",
+   "id": "0f2847fe",
    "metadata": {},
    "source": [
     "As $n$ increases, we can see that Bayesian coverage intervals narrow and move toward $0.4$.\n",
@@ -679,7 +679,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f92ff06a",
+   "id": "d76489dc",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -700,7 +700,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f17a23a",
+   "id": "82073aff",
    "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",
@@ -727,7 +727,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "514d2045",
+   "id": "d37529cd",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -748,7 +748,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "632bce4d",
+   "id": "22868f6e",
    "metadata": {},
    "source": [
     "As $n$ increases, we can see that the probability density functions _concentrate_ on $0.4$, the true value of $\\theta$.\n",
@@ -761,7 +761,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "0ea90dfe",
+   "id": "ebfb9af0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -787,7 +787,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a55c838d",
+   "id": "c1432aae",
    "metadata": {},
    "source": [
     "```{solution-end}\n",
@@ -838,7 +838,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "86ca0cd5",
+   "id": "fe068fe0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -860,7 +860,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1f6a1181",
+   "id": "283f7cfb",
    "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 2e503c1..78abc00 100644
--- a/_sources/rand_resp.ipynb
+++ b/_sources/rand_resp.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "3d3b1ce7",
+   "id": "315d0810",
    "metadata": {},
    "source": [
     "# Randomized Response Surveys\n",
@@ -39,7 +39,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "e5c47abf",
+   "id": "08c0f20a",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -49,7 +49,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "ed3c9178",
+   "id": "7f726378",
    "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": "5b9d0897",
+   "id": "94eeb234",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -265,7 +265,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b08e59cf",
+   "id": "3ecfd9fe",
    "metadata": {},
    "source": [
     "Let's put the code to work for parameter values\n",
@@ -281,7 +281,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "159665c0",
+   "id": "c3c40ecf",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -293,7 +293,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8019e451",
+   "id": "6783fb2c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -303,7 +303,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "aba8df78",
+   "id": "79da20de",
    "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": "115e1e0b",
+   "id": "19cf8fc3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -337,7 +337,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "47576adb",
+   "id": "7755c4e3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -347,7 +347,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "f1842702",
+   "id": "96d6f009",
    "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": "a0ad1990",
+   "id": "3aaee31b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -373,7 +373,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "65e682dc",
+   "id": "2a4adc19",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -383,7 +383,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "d3224ae5",
+   "id": "53beecaf",
    "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 9f44e3f..6966124 100644
--- a/_sources/status.ipynb
+++ b/_sources/status.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "cd6efb98",
+   "id": "7789a45a",
    "metadata": {},
    "source": [
     "# Execution Statistics\n",
diff --git a/_sources/troubleshooting.ipynb b/_sources/troubleshooting.ipynb
index 4fbaa86..a6dc594 100644
--- a/_sources/troubleshooting.ipynb
+++ b/_sources/troubleshooting.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "d08577d7",
+   "id": "73d81091",
    "metadata": {},
    "source": [
     "(troubleshooting)=\n",
diff --git a/_sources/util_rand_resp.ipynb b/_sources/util_rand_resp.ipynb
index 3c7c230..1addb8b 100644
--- a/_sources/util_rand_resp.ipynb
+++ b/_sources/util_rand_resp.ipynb
@@ -3,7 +3,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "57000d05",
+   "id": "67d49b53",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -13,7 +13,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "24f2bb4e",
+   "id": "8af3f3eb",
    "metadata": {},
    "source": [
     "# Expected Utilities of Random Responses\n",
@@ -279,7 +279,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "09a0d7b6",
+   "id": "fc0b9574",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -312,7 +312,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "25e42ed3",
+   "id": "61fafbf3",
    "metadata": {},
    "source": [
     "Figure 1.1 three types of truth border.\n",
@@ -330,7 +330,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "19da6457",
+   "id": "f0f7bba3",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -358,7 +358,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0ec89dfc",
+   "id": "e2cd3092",
    "metadata": {},
    "source": [
     "## Utilitarian View of Survey Design\n",
@@ -414,7 +414,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d6dd39d6",
+   "id": "6797584d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -456,7 +456,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d4a0da0",
+   "id": "0f806858",
    "metadata": {},
    "source": [
     "Properties of  iso-variance curves  are:\n",
@@ -477,7 +477,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "5f1f200a",
+   "id": "a47b6a29",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -487,7 +487,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b3417422",
+   "id": "778859df",
    "metadata": {},
    "source": [
     "### Optimal Survey\n",
@@ -542,7 +542,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "8570c474",
+   "id": "d9d84f36",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -585,7 +585,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "a2800d88",
+   "id": "4e316e46",
    "metadata": {},
    "source": [
     "### Method of Leysieffer and Warner (1976)\n",
@@ -637,7 +637,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d09d5223",
+   "id": "3738bd3c",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -651,7 +651,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "54836ad1",
+   "id": "144f0567",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -693,7 +693,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd978f0c",
+   "id": "a47a7f9b",
    "metadata": {},
    "source": [
     "### Method of Greenberg et al. (1977)\n",
diff --git a/_sources/wald_friedman.ipynb b/_sources/wald_friedman.ipynb
index 2fc9f94..3d9eb43 100644
--- a/_sources/wald_friedman.ipynb
+++ b/_sources/wald_friedman.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "5352ed0e",
+   "id": "4ec9c046",
    "metadata": {},
    "source": [
     "(wald_friedman)=\n",
@@ -31,7 +31,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "3fc8f7d7",
+   "id": "784127c7",
    "metadata": {
     "tags": [
      "hide-output"
@@ -45,7 +45,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d87fb86",
+   "id": "c6b5d8b1",
    "metadata": {},
    "source": [
     "## Overview\n",
@@ -77,7 +77,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "f93357fe",
+   "id": "3980ded2",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -91,7 +91,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "71fe1c53",
+   "id": "3eefb917",
    "metadata": {},
    "source": [
     "This lecture uses ideas studied in {doc}`this lecture <likelihood_ratio_process>`, {doc}`this lecture <likelihood_bayes>`.\n",
@@ -214,7 +214,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "c205653b",
+   "id": "f640a601",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -248,7 +248,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "1d0c9583",
+   "id": "ca4465f2",
    "metadata": {},
    "source": [
     "### Losses and Costs\n",
@@ -433,7 +433,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "dcab7007",
+   "id": "00fd2083",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -454,7 +454,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "08b32e33",
+   "id": "00f8658d",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -511,7 +511,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "59ba2981",
+   "id": "81dfffbf",
    "metadata": {},
    "source": [
     "As in the {doc}`optimal growth lecture <optgrowth>`, to approximate a continuous value function\n",
@@ -525,7 +525,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "646e8af1",
+   "id": "598f8df0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -563,7 +563,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "eb8ae633",
+   "id": "3a489885",
    "metadata": {},
    "source": [
     "To solve the key functional equation, we will iterate using `Q` to find the fixed point"
@@ -572,7 +572,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "effc01ef",
+   "id": "d3ba20c7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -603,7 +603,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "866dd792",
+   "id": "a7e94f07",
    "metadata": {},
    "source": [
     "## Analysis\n",
@@ -616,7 +616,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "438c0df2",
+   "id": "a8d3cfd0",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -633,7 +633,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "0cf5dedb",
+   "id": "30ec25bb",
    "metadata": {},
    "source": [
     "### Value Function\n",
@@ -644,7 +644,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "7b53dfdf",
+   "id": "9421518b",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -653,7 +653,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "cd56cd78",
+   "id": "528c9803",
    "metadata": {},
    "source": [
     "We will also set up a function to compute the cutoffs $\\alpha$ and $\\beta$\n",
@@ -663,7 +663,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "81ecf8d5",
+   "id": "41e5d832",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -724,7 +724,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "2c41d284",
+   "id": "8959c7aa",
    "metadata": {},
    "source": [
     "The cost function $J$ equals $\\pi L_1$ for $\\pi \\leq \\beta$, and $(1-\\pi )L_0$ for $\\pi\n",
@@ -755,7 +755,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "37e9b010",
+   "id": "7b644764",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -853,7 +853,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "6d4dfb37",
+   "id": "310036a3",
    "metadata": {},
    "source": [
     "### Comparative Statics\n",
@@ -871,7 +871,7 @@
   {
    "cell_type": "code",
    "execution_count": null,
-   "id": "d86968af",
+   "id": "8065d6f7",
    "metadata": {},
    "outputs": [],
    "source": [
@@ -881,7 +881,7 @@
   },
   {
    "cell_type": "markdown",
-   "id": "b6a66e85",
+   "id": "9e480ffb",
    "metadata": {},
    "source": [
     "Increased cost per draw has induced the decision-maker to take fewer draws before deciding.\n",
diff --git a/_sources/zreferences.ipynb b/_sources/zreferences.ipynb
index 1c16ba0..2929a04 100644
--- a/_sources/zreferences.ipynb
+++ b/_sources/zreferences.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "markdown",
-   "id": "50344f46",
+   "id": "d129aa9c",
    "metadata": {},
    "source": [
     "(references)=\n",
diff --git a/intro.html b/intro.html
index 9e2bacc..9e374b8 100644
--- a/intro.html
+++ b/intro.html
@@ -220,7 +220,6 @@
                         
   <section class="tex2jax_ignore mathjax_ignore" id="statistics-for-computational-economics">
 <h1>Statistics for Computational Economics<a class="headerlink" href="#statistics-for-computational-economics" title="Permalink to this heading">#</a></h1>
-<p><strong>Authors:</strong> <a class="reference external" href="http://www.tomsargent.com/">Thomas J. Sargent</a> and <a class="reference external" href="http://johnstachurski.net/">John Stachurski</a></p>
 <p>This website presents a set of lectures on statistics for computational economics.</p>
 <p>For an overview of the series, see <a class="reference external" href="https://quantecon.org/python-lectures/">this page</a></p>
 <div class="toctree-wrapper compound">
diff --git a/searchindex.js b/searchindex.js
index 99f3f7d..92c06d6 100644
--- a/searchindex.js
+++ b/searchindex.js
@@ -1 +1 @@
-Search.setIndex({"docnames": ["ar1_bayes", "ar1_turningpts", "back_prop", "bayes_nonconj", "exchangeable", "hoist_failure", "imp_sample", "intro", "likelihood_bayes", "likelihood_ratio_process", "lln_clt", "mix_model", "mle", "multi_hyper", "multivariate_normal", "navy_captain", "ols", "pandas_panel", "prob_matrix", "prob_meaning", "rand_resp", "status", "troubleshooting", "util_rand_resp", "wald_friedman", "zreferences"], "filenames": ["ar1_bayes.md", "ar1_turningpts.md", "back_prop.md", "bayes_nonconj.md", "exchangeable.md", "hoist_failure.md", "imp_sample.md", "intro.md", "likelihood_bayes.md", "likelihood_ratio_process.md", "lln_clt.md", "mix_model.md", "mle.md", "multi_hyper.md", "multivariate_normal.md", "navy_captain.md", "ols.md", "pandas_panel.md", "prob_matrix.md", "prob_meaning.md", "rand_resp.md", "status.md", "troubleshooting.md", "util_rand_resp.md", "wald_friedman.md", "zreferences.md"], "titles": ["<span class=\"section-number\">9. </span>Posterior Distributions for  AR(1) Parameters", "<span class=\"section-number\">10. </span>Forecasting  an AR(1) Process", "<span class=\"section-number\">20. </span>Introduction to Artificial Neural Networks", "<span class=\"section-number\">8. </span>Non-Conjugate Priors", "<span class=\"section-number\">14. </span>Exchangeability and Bayesian Updating", "<span class=\"section-number\">19. </span>Fault Tree Uncertainties", "<span class=\"section-number\">12. </span>Computing Mean of a Likelihood Ratio Process", "Statistics for Computational Economics", "<span class=\"section-number\">15. </span>Likelihood Ratio Processes and Bayesian Learning", "<span class=\"section-number\">11. </span>Likelihood Ratio Processes", "<span class=\"section-number\">5. </span>LLN and CLT", "<span class=\"section-number\">16. </span>Incorrect Models", "<span class=\"section-number\">3. </span>Maximum Likelihood Estimation", "<span class=\"section-number\">18. </span>Multivariate Hypergeometric Distribution", "<span class=\"section-number\">6. </span>Multivariate Normal Distribution", "<span class=\"section-number\">17. </span>Bayesian versus Frequentist Decision Rules", "<span class=\"section-number\">2. </span>Linear Regression in Python", "<span class=\"section-number\">1. </span>Pandas for Panel Data", "<span class=\"section-number\">4. </span>Elementary Probability with Matrices", "<span class=\"section-number\">7. </span>Two Meanings of Probability", "<span class=\"section-number\">21. </span>Randomized Response Surveys", "<span class=\"section-number\">25. </span>Execution Statistics", "<span class=\"section-number\">23. </span>Troubleshooting", "<span class=\"section-number\">22. </span>Expected Utilities of Random Responses", "<span class=\"section-number\">13. </span>A Problem that Stumped Milton Friedman", "<span class=\"section-number\">24. </span>References"], "terms": {"we": [0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "ll": [0, 1, 2, 3, 4, 5, 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+Search.setIndex({"docnames": ["ar1_bayes", "ar1_turningpts", "back_prop", "bayes_nonconj", "exchangeable", "hoist_failure", "imp_sample", "intro", "likelihood_bayes", "likelihood_ratio_process", "lln_clt", "mix_model", "mle", "multi_hyper", "multivariate_normal", "navy_captain", "ols", "pandas_panel", "prob_matrix", "prob_meaning", "rand_resp", "status", "troubleshooting", "util_rand_resp", "wald_friedman", "zreferences"], "filenames": ["ar1_bayes.md", "ar1_turningpts.md", "back_prop.md", "bayes_nonconj.md", "exchangeable.md", "hoist_failure.md", "imp_sample.md", "intro.md", "likelihood_bayes.md", "likelihood_ratio_process.md", "lln_clt.md", "mix_model.md", "mle.md", "multi_hyper.md", "multivariate_normal.md", "navy_captain.md", "ols.md", "pandas_panel.md", "prob_matrix.md", "prob_meaning.md", "rand_resp.md", "status.md", "troubleshooting.md", "util_rand_resp.md", "wald_friedman.md", "zreferences.md"], "titles": ["<span class=\"section-number\">9. </span>Posterior Distributions for  AR(1) Parameters", "<span class=\"section-number\">10. </span>Forecasting  an AR(1) Process", "<span class=\"section-number\">20. </span>Introduction to Artificial Neural Networks", "<span class=\"section-number\">8. </span>Non-Conjugate Priors", "<span class=\"section-number\">14. </span>Exchangeability and Bayesian Updating", "<span class=\"section-number\">19. </span>Fault Tree Uncertainties", "<span class=\"section-number\">12. </span>Computing Mean of a Likelihood Ratio Process", "Statistics for Computational Economics", "<span class=\"section-number\">15. </span>Likelihood Ratio Processes and Bayesian Learning", "<span class=\"section-number\">11. </span>Likelihood Ratio Processes", "<span class=\"section-number\">5. </span>LLN and CLT", "<span class=\"section-number\">16. </span>Incorrect Models", "<span class=\"section-number\">3. </span>Maximum Likelihood Estimation", "<span class=\"section-number\">18. </span>Multivariate Hypergeometric Distribution", "<span class=\"section-number\">6. </span>Multivariate Normal Distribution", "<span class=\"section-number\">17. </span>Bayesian versus Frequentist Decision Rules", "<span class=\"section-number\">2. </span>Linear Regression in Python", "<span class=\"section-number\">1. </span>Pandas for Panel Data", "<span class=\"section-number\">4. </span>Elementary Probability with Matrices", "<span class=\"section-number\">7. </span>Two Meanings of Probability", "<span class=\"section-number\">21. </span>Randomized Response Surveys", "<span class=\"section-number\">25. </span>Execution Statistics", "<span class=\"section-number\">23. </span>Troubleshooting", "<span class=\"section-number\">22. </span>Expected Utilities of Random Responses", "<span class=\"section-number\">13. </span>A Problem that Stumped Milton Friedman", "<span class=\"section-number\">24. </span>References"], "terms": {"we": [0, 1, 2, 3, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 22, 23, 24], "ll": [0, 1, 2, 3, 4, 5, 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