notebooks/13-inference.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Inference"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Think Bayes, Second Edition\n",
    "\n",
    "Copyright 2020 Allen B. Downey\n",
    "\n",
    "License: [Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0)](https://creativecommons.org/licenses/by-nc-sa/4.0/)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# If we're running on Colab, install empiricaldist\n",
    "# https://pypi.org/project/empiricaldist/\n",
    "\n",
    "import sys\n",
    "IN_COLAB = 'google.colab' in sys.modules\n",
    "\n",
    "if IN_COLAB:\n",
    "    !pip install empiricaldist"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "# Get utils.py\n",
    "\n",
    "import os\n",
    "\n",
    "if not os.path.exists('utils.py'):\n",
    "    !wget https://github.com/AllenDowney/ThinkBayes2/raw/master/soln/utils.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from utils import set_pyplot_params\n",
    "set_pyplot_params()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Whenever people compare Bayesian inference with conventional approaches, one of the questions that comes up most often is something like, \"What about p-values?\"\n",
    "And one of the most common examples is the comparison of two groups to see if there is a difference in their means.\n",
    "\n",
    "In classical statistical inference, the usual tool for this scenario is a [Student's *t*-test](https://en.wikipedia.org/wiki/Student%27s_t-test), and the result is a [p-value](https://en.wikipedia.org/wiki/P-value).\n",
    "This process is an example of [null hypothesis significance testing](https://en.wikipedia.org/wiki/Statistical_hypothesis_testing).\n",
    "\n",
    "A Bayesian alternative is to compute the posterior distribution of the difference between the groups.\n",
    "Then we can use that distribution to answer whatever questions we are interested in, including the most likely size of the difference, a credible interval that's likely to contain the true difference, the probability of superiority, or the probability that the difference exceeds some threshold.\n",
    "\n",
    "To demonstrate this process, I'll solve a problem borrowed from a statistical textbook: evaluating the effect of an educational \"treatment\" compared to a control."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Improving Reading Ability\n",
    "\n",
    "We'll use data from a [Ph.D. dissertation in educational psychology](https://docs.lib.purdue.edu/dissertations/AAI8807671/) written in 1987, which was used as an example in a [statistics textbook](https://books.google.com/books/about/Introduction_to_the_practice_of_statisti.html?id=pGBNhajABlUC) from 1989 and published on [DASL](https://web.archive.org/web/20000603124754/http://lib.stat.cmu.edu/DASL/Datafiles/DRPScores.html), a web page that collects data stories.  \n",
    "\n",
    "Here's the description from DASL:\n",
    "\n",
    "> An educator conducted an experiment to test whether new directed reading activities in the classroom will help elementary school pupils improve some aspects of their reading ability. She arranged for a third grade class of 21 students to follow these activities for an 8-week period. A control classroom of 23 third graders followed the same curriculum without the activities. At the end of the 8 weeks, all students took a Degree of Reading Power (DRP) test, which measures the aspects of reading ability that the treatment is designed to improve.\n",
    "\n",
    "The [dataset is available here](https://web.archive.org/web/20000603124754/http://lib.stat.cmu.edu/DASL/Datafiles/DRPScores.html)."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The following cell downloads the data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "--2022-08-22 18:41:07--  https://github.com/AllenDowney/ThinkBayes2/raw/master/data/drp_scores.csv\n",
      "Resolving github.com (github.com)... 140.82.121.4\n",
      "Connecting to github.com (github.com)|140.82.121.4|:443... connected.\n",
      "HTTP request sent, awaiting response... 302 Found\n",
      "Location: https://raw.githubusercontent.com/AllenDowney/ThinkBayes2/master/data/drp_scores.csv [following]\n",
      "--2022-08-22 18:41:08--  https://raw.githubusercontent.com/AllenDowney/ThinkBayes2/master/data/drp_scores.csv\n",
      "Resolving raw.githubusercontent.com (raw.githubusercontent.com)... 185.199.111.133, 185.199.110.133, 185.199.109.133, ...\n",
      "Connecting to raw.githubusercontent.com (raw.githubusercontent.com)|185.199.111.133|:443... connected.\n",
      "HTTP request sent, awaiting response... 200 OK\n",
      "Length: 1527 (1.5K) [text/plain]\n",
      "Saving to: ‘drp_scores.csv’\n",
      "\n",
      "drp_scores.csv      100%[===================>]   1.49K  --.-KB/s    in 0s      \n",
      "\n",
      "2022-08-22 18:41:08 (7.98 MB/s) - ‘drp_scores.csv’ saved [1527/1527]\n",
      "\n"
     ]
    }
   ],
   "source": [
    "import os\n",
    "\n",
    "if not os.path.exists('drp_scores.csv'):\n",
    "    !wget https://github.com/AllenDowney/ThinkBayes2/raw/master/data/drp_scores.csv"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll use Pandas to load the data into a `DataFrame`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Treatment</th>\n",
       "      <th>Response</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>Treated</td>\n",
       "      <td>24</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>Treated</td>\n",
       "      <td>43</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>Treated</td>\n",
       "      <td>58</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Treatment  Response\n",
       "0   Treated        24\n",
       "1   Treated        43\n",
       "2   Treated        58"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "df = pd.read_csv('drp_scores.csv', skiprows=21, delimiter='\\t')\n",
    "df.head(3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The `Treatment` column indicates whether each student was in the treated or control group.\n",
    "The `Response` is their score on the test.\n",
    "\n",
    "\n",
    "I'll use `groupby` to separate the data for the `Treated` and `Control` groups:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "grouped = df.groupby('Treatment')\n",
    "responses = {}\n",
    "\n",
    "for name, group in grouped:\n",
    "    responses[name] = group['Response']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are CDFs of the scores for the two groups and summary statistics."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "from empiricaldist import Cdf\n",
    "from utils import decorate\n",
    "\n",
    "for name, response in responses.items():\n",
    "    cdf = Cdf.from_seq(response)\n",
    "    cdf.plot(label=name)\n",
    "    \n",
    "decorate(xlabel='Score', \n",
    "         ylabel='CDF',\n",
    "         title='Distributions of test scores')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is overlap between the distributions, but it looks like the scores are higher in the treated group.\n",
    "The distribution of scores is not exactly normal for either group, but it is close enough that the normal model is a reasonable choice.\n",
    "\n",
    "So I'll assume that in the entire population of students (not just the ones in the experiment), the distribution of scores is well modeled by a normal distribution with unknown mean and standard deviation.\n",
    "I'll use `mu` and `sigma` to denote these unknown parameters,\n",
    "and we'll do a Bayesian update to estimate what they are."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Estimating Parameters\n",
    "\n",
    "As always, we need a prior distribution for the parameters.\n",
    "Since there are two parameters, it will be a joint distribution.\n",
    "I'll construct it by choosing marginal distributions for each parameter and computing their outer product.\n",
    "\n",
    "As a simple starting place, I'll assume that the prior distributions for `mu` and `sigma` are uniform.\n",
    "The following function makes a `Pmf` object that represents a uniform distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "from empiricaldist import Pmf\n",
    "\n",
    "def make_uniform(qs, name=None, **options):\n",
    "    \"\"\"Make a Pmf that represents a uniform distribution.\"\"\"\n",
    "    pmf = Pmf(1.0, qs, **options)\n",
    "    pmf.normalize()\n",
    "    if name:\n",
    "        pmf.index.name = name\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`make_uniform` takes as parameters \n",
    "\n",
    "* An array of quantities, `qs`, and\n",
    "\n",
    "* A string, `name`, which is assigned to the index so it appears when we display the `Pmf`.\n",
    "\n",
    "Here's the prior distribution for `mu`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "\n",
    "qs = np.linspace(20, 80, num=101)\n",
    "prior_mu = make_uniform(qs, name='mean')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I chose the lower and upper bounds by trial and error.\n",
    "I'll explain how when we look at the posterior distribution.\n",
    "\n",
    "Here's the prior distribution for `sigma`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "qs = np.linspace(5, 30, num=101)\n",
    "prior_sigma = make_uniform(qs, name='std')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use `make_joint` to make the joint prior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 114,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import make_joint\n",
    "\n",
    "prior = make_joint(prior_mu, prior_sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we'll start by working with the data from the control group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 211,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(23,)"
      ]
     },
     "execution_count": 211,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = responses['Control']\n",
    "data.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the next section we'll compute the likelihood of this data for each pair of parameters in the prior distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Likelihood\n",
    "\n",
    "We would like to know the probability of each score in the dataset for each hypothetical pair of values, `mu` and `sigma`.\n",
    "I'll do that by making a 3-dimensional grid with values of `mu` on the first axis, values of `sigma` on the second axis, and the scores from the dataset on the third axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 212,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101, 23)"
      ]
     },
     "execution_count": 212,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mu_mesh, sigma_mesh, data_mesh = np.meshgrid(\n",
    "    prior.columns, prior.index, data)\n",
    "\n",
    "mu_mesh.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can use `norm.pdf` to compute the probability density of each score for each hypothetical pair of parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 309,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101, 23)"
      ]
     },
     "execution_count": 309,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import norm\n",
    "\n",
    "densities = norm(mu_mesh, sigma_mesh).pdf(data_mesh)\n",
    "densities.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a 3-D array.  To compute likelihoods, I'll multiply these densities along `axis=2`, which is the axis of the data:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 402,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101)"
      ]
     },
     "execution_count": 402,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "likelihood = densities.prod(axis=2)\n",
    "likelihood.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a 2-D array that contains the likelihood of the entire dataset for each hypothetical pair of parameters.\n",
    "\n",
    "We can use this array to update the prior, like this:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 403,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101)"
      ]
     },
     "execution_count": 403,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from utils import normalize\n",
    "\n",
    "posterior = prior * likelihood\n",
    "normalize(posterior)\n",
    "posterior.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a `DataFrame` that represents the joint posterior distribution.\n",
    "\n",
    "The following function encapsulates these steps."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 404,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_norm(prior, data):\n",
    "    \"\"\"Update the prior based on data.\"\"\"\n",
    "    mu_mesh, sigma_mesh, data_mesh = np.meshgrid(\n",
    "        prior.columns, prior.index, data)\n",
    "    \n",
    "    densities = norm(mu_mesh, sigma_mesh).pdf(data_mesh)\n",
    "    likelihood = densities.prod(axis=2)\n",
    "    \n",
    "    posterior = prior * likelihood\n",
    "    normalize(posterior)\n",
    "\n",
    "    return posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the updates for the control and treatment groups:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 405,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = responses['Control']\n",
    "posterior_control = update_norm(prior, data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 406,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = responses['Treated']\n",
    "posterior_treated = update_norm(prior, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what they look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 407,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "from utils import plot_contour\n",
    "\n",
    "plot_contour(posterior_control, cmap='Blues')\n",
    "plt.text(49.5, 18, 'Control', color='C0')\n",
    "\n",
    "cs = plot_contour(posterior_treated, cmap='Oranges')\n",
    "plt.text(57, 12, 'Treated', color='C1')\n",
    "\n",
    "decorate(xlabel='Mean (mu)', \n",
    "         ylabel='Standard deviation (sigma)',\n",
    "         title='Joint posterior distributions of mu and sigma')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Along the `x` axis, it looks like the mean score for the treated group is higher.\n",
    "Along the `y` axis, it looks like the standard deviation for the treated group is lower.\n",
    "\n",
    "If we think the treatment causes these differences, the data suggest that the treatment increases the mean of the scores and decreases their spread.\n",
    "We can see these differences more clearly by looking at the marginal distributions for `mu` and `sigma`."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Posterior Marginal Distributions\n",
    "\n",
    "I'll use `marginal`, which we saw in <<_MarginalDistributions>>, to extract the posterior marginal distributions for the population means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 408,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import marginal\n",
    "\n",
    "pmf_mean_control = marginal(posterior_control, 0)\n",
    "pmf_mean_treated = marginal(posterior_treated, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what they look like:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 409,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_mean_control.plot(label='Control')\n",
    "pmf_mean_treated.plot(label='Treated')\n",
    "\n",
    "decorate(xlabel='Population mean (mu)', \n",
    "         ylabel='PDF', \n",
    "         title='Posterior distributions of mu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In both cases the posterior probabilities at the ends of the range are near zero, which means that the bounds we chose for the prior distribution are wide enough.\n",
    "\n",
    "Comparing the marginal distributions for the two groups, it looks like the population mean in the treated group is higher.\n",
    "We can use `prob_gt` to compute the probability of superiority:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 410,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.980479025187326"
      ]
     },
     "execution_count": 410,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "Pmf.prob_gt(pmf_mean_treated, pmf_mean_control)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a 98% chance that the mean in the treated group is higher."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Distribution of Differences\n",
    "\n",
    "To quantify the magnitude of the difference between groups, we can use `sub_dist` to compute the distribution of the difference."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 411,
   "metadata": {},
   "outputs": [],
   "source": [
    "pmf_diff = Pmf.sub_dist(pmf_mean_treated, pmf_mean_control)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two things to be careful about when you use methods like `sub_dist`. \n",
    "The first is that the result usually contains more elements than the original `Pmf`.  \n",
    "In this example, the original distributions have the same quantities, so the size increase is moderate."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 412,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101, 879)"
      ]
     },
     "execution_count": 412,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "len(pmf_mean_treated), len(pmf_mean_control), len(pmf_diff)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In the worst case, the size of the result can be the product of the sizes of the originals.\n",
    "\n",
    "The other thing to be careful about is plotting the `Pmf`.\n",
    "In this example, if we plot the distribution of differences, the result is pretty noisy."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 413,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_diff.plot()\n",
    "\n",
    "decorate(xlabel='Difference in population means', \n",
    "         ylabel='PDF', \n",
    "         title='Posterior distribution of difference in mu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two ways to work around that limitation.  One is to plot the CDF, which smooths out the noise:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 414,
   "metadata": {},
   "outputs": [],
   "source": [
    "cdf_diff = pmf_diff.make_cdf()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 415,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf_diff.plot()\n",
    "\n",
    "decorate(xlabel='Difference in population means', \n",
    "         ylabel='CDF', \n",
    "         title='Posterior distribution of difference in mu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The other option is to use kernel density estimation (KDE) to make a smooth approximation of the PDF on an equally-spaced grid, which is what this function does:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 416,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import gaussian_kde\n",
    "\n",
    "def kde_from_pmf(pmf, n=101):\n",
    "    \"\"\"Make a kernel density estimate for a PMF.\"\"\"\n",
    "    kde = gaussian_kde(pmf.qs, weights=pmf.ps)\n",
    "    qs = np.linspace(pmf.qs.min(), pmf.qs.max(), n)\n",
    "    ps = kde.evaluate(qs)\n",
    "    pmf = Pmf(ps, qs)\n",
    "    pmf.normalize()\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "`kde_from_pmf` takes as parameters a `Pmf` and the number of places to evaluate the KDE.\n",
    "\n",
    "It uses `gaussian_kde`, which we saw in <<_KernelDensityEstimation>>, passing the probabilities from the `Pmf` as weights.\n",
    "This makes the estimated densities higher where the probabilities in the `Pmf` are higher.\n",
    "\n",
    "Here's what the kernel density estimate looks like for the `Pmf` of differences between the groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 417,
   "metadata": {},
   "outputs": [],
   "source": [
    "kde_diff = kde_from_pmf(pmf_diff)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 418,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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7k89y5ABlNglERFGSxILZY6tBQXHz4K79h8dVLrOhOECZTQJ7nz1Cd08vANOmtDCtrWXM55o/61hwywY9s3JzgDKbBLIJEmPtfypoz9S+OvZ54kLLjwOU2SSwowwZfAULipr4HKAsPw5QZpNAUf/TOAOUa1A2URygzCaBbAbfeGtQ2QC1Y2+nn4Wy3DhAmU0CO8tYg5o2pZkp6VTx3T29HDjUNa7zmQ3GAcpsEijHOHwFkoqCXIcz+SwnDlBmda6nt4/d6fNKQrTPGl8WH1B0jp3uh7KcOECZ1bmOfYcIkn6iOTOm0NLcOO5zOlHCJoIDlFmdK2f/U0E2QDnV3PLiAGVW58rZ/1TQnu2Dcg3KcuIAZVbn8qhBLZjt4Y4sfw5QZnVuR/YZqHEMEpvlJj6bCA5QZnVux95jU2KUq4lv1rRWmpuSZItDR7rpPOxnoaz8HKDM6tyufcemxGifXZ4AJRWnq3vaDcuDA5RZHevq7mV/5xEAGiTmzijf7LelQx6ZlZsDlFkd233gWM1m7sw2GhvL9yvvZ6Esbw5QZnUsm8AwvwwjSGS1z3GihOXLAcqsju3K1Gzmz24r67kXZPqzPNyR5cEByqyOdWRqNuUYgy+ruInPfVBWfg5QZnUsm11X9iY+90FZzhygzOpYcRNfeQPU3BltNDQkf0IOdB7laFdPWc9v5gBlVsd25djE19Ag5s881q/V4UQJKzMHKLM6FRFFQWP+rPImSUBxM192WnmzcnCAMqtTBw930dXdC0BrcxNTpzSX/RpONbc8OUCZ1alsgkT77KlIKvs1sokXTpSwcnOAMqtT2YDRXuYEiYIFzuSzHDlAmdWpPEeRGOi82WGVzMrBAcqsTuU5isSx8/phXcuPA5RZnerI9kHlVYPKpJnvPnCEvr7I5To2OTlAmdWpbBPfvJwCVGtLEzOmtgLQ19fHvoNHcrmOTU65BihJF0taL2mDpA8MsL9V0k3p/jslrcjse76k2yWtk/SQpPJNZGM2CRQ18eXwDFTBvEwtyqnmVk65BShJjcAngdcAq4A3S1pVctgVwN6IWAlcB3wkfW0T8GXgXRFxBvByoDuvsprVm57ePvY+m9RmhIqCSLkVjcnnmXWtjPKsQZ0HbIiIJyOiC7gRuKTkmEuAL6TLNwMXKXlY49XAgxHxAEBE7I6I3hzLalZX9hw4TJD0B82eMYXmpsbcrpUNULucam5llGeAWgJsyqxvTrcNeExE9AD7gXnAKUBIulXSvZLeP9AFJF0paa2ktR0dHWW/AbNatSvnIY6y3MRneanWJIkm4KXAW9L//7Oki0oPiojrI2J1RKxub2+f6DKaVa08p9koNd81KMtJngFqC7Ass7403TbgMWm/0yxgN0lt62cRsSsiDgG3AC/IsaxmdaVjghIkoDiFfZcf1rUyyjNA3Q2cLOkESS3AZcCakmPWAJeny5cCt0VEALcCZ0qamgaulwG/zrGsZnVlIkaRKJg3y018lo+mvE4cET2S3k0SbBqBGyJinaQPAmsjYg3wWeBLkjYAe0iCGBGxV9JHSYJcALdExHfzKqtZvSkKUDmNw1cwd0YbDRJ9ERzoPEpXdy8tzfklZdjkkVuAAoiIW0ia57Lbrs4sHwHeOMhrv0ySam5mo7RrAkaRKGhoEPNmtfU3K+7af4jF82fkek2bHKo1ScLMxmEia1BQ3Iy4y89CWZk4QJnVmc7DXRw6kjzX3tzUyMypLblf0/1QlgcHKLM6k82kmz+rLZeJCksVZfI5QFmZOECZ1ZniFPP8m/dKr+OJC61cHKDM6syuCZhJt1TRw7quQVmZOECZ1ZmJfAaqINvEt9tJElYmDlBmdWZnpga1YKJqUJkkiY79h0ietzcbHwcoszoz0SnmAFOnNNPanDxW2dXdy8HDXRNyXatvDlBmdWZXBZIkJBVPu+FmPisDByizOtLT28eeA8emXc97oNisookLnclnZeAAZVZHshMVzpnRlutEhaU8L5SVmwOUWR2ZyGk2SmX7u5zJZ+XgAGVWRyqRYl6QTTXvcA3KysAByqyOZAPDRD2kW+CHda3chgxQkr6fWb4q/+KY2Xjs2jdxU72XKuqDcpKElcFwNaj2zPKA8zaZWfXo2NfZvzzRNaj22VMRycC0ew4coae3b0Kvb/VnuADlx8HNakjRRIUTHKCaGhuYM2MKAEG4mc/GbbgZdU+UtAZQZrlfRLw+t5KZ2ahEBDsrWIMCaJ8zlT3PJkGyY98hFs2dPuFlsPoxXIC6JLP8D3kWxMzG5+DhLrq6ewFobW5i2pTmCS/DgtnTWL9xN+CHdW38hgxQEfHTwrKk9nRbR96FMrPR6ygZJHYiJioslR2cdsfeziGONBvecFl8kvTXknYB64HHJHVIunpiimdmI1X0kG4FmvfAwx1ZeQ2XJPGnwEuBcyNibkTMAc4HXiLpT3MvnZmNWEcFJios1T5nWv+yA5SN13AB6m3AmyPiqcKGiHgSeCvw9jwLZmajU8lRJAqKa1Bu4rPxGS5ANUfErtKNaT/UxPfAmtmgOiqYYt5/3ZKZdXv9LJSNw3ABaqhZxzwjmVkVqeRDugUtzY3Mnp48C9UXwe4DHjTWxm64NPOzJB0ACulAhQd3BUzJrVRmNmqVHOYoq332VPYdTOak6th3iAWZfimz0RguzXziJpMxszHr6u5lf2cSFBok5s6o3PfHBXOm8fjmPYATJWx8hgxQkqYA7wJWAg8CN0REz0QUzMxGLpsgMXdmG42NlZuoIPss1E4nStg4DPdT/AVgNfAQ8FvA/829RGY2atWQYj7Q9XfudQ3Kxm64PqhVEXEmgKTPAnflXyQzG61qSDEvaJ/tZ6GsPIarQXUXFty0Z1a9dlZpDcrPQtl4jDSLD5LMvbZMVl9ExMxcS2dmI7IzM+7dggoHqOz1O/Yfpq8vaGiY+HEBrfY5i8+sDmQHZl00r7JTXLS2NDFzWisHOo/S19fHnmcPV7zZ0WpTrqk+ki6WtF7SBkkfGGB/q6Sb0v13SlpRsn+5pIOS/kee5TSrdTv2HAtQC6vguSMPGmvlkFuAktQIfBJ4DbAKeLOkVSWHXQHsjYiVwHXAR0r2fxT4Xl5lNKsHR7p6+h+MbWhoYN7MtgqXKJkXqmCnp92wMcqzBnUesCEinoyILuBGiidAJF3/Qrp8M3CR0klsJL0BeApYl2MZzWrejpL+p0o+A1VQVIPy1O82Rnn+JC8BNmXWN6fbBjwmzRLcD8yTNB34c+BvhrqApCslrZW0tqPD8yja5FRtzXtA0fBGfhbKxqryX7UGdg1wXUQcHOqgiLg+IlZHxOr29vaJKZlZlammBIkCp5pbOQyXZj4eW4BlmfWl6baBjtksqQmYBewmmRTxUkl/D8wG+iQdiYhP5Fhes5pUjTUoJ0lYOeQZoO4GTpZ0Akkgugz4vZJj1gCXA7cDlwK3RUQAFxYOkHQNcNDByWxg2/cca2hYMKc60rmLx+M7RESQdi+bjVhuTXxpn9K7gVuBR4CvR8Q6SR+U9Pr0sM+S9DltAP4MeE4qupkNLVuDOm5udTTxtbU2M72tBYDe3j72PnukwiWyWpRnDYqIuAW4pWTb1ZnlI8AbhznHNbkUzqwO9PUFOzJ9PAvnVkcTHySJEgcPJ/Oa7tzbydwqSH+32lKtSRJmNgJ7nj02rfrMaa20tTZXuETHZPvDtu0eMt/JbEAOUGY1rBoTJAoWZzIKHaBsLBygzGpYcYJEdQWo4zIBaqsDlI2BA5RZDavGBImCxfNn9C+7BmVj4QBlVsO2763OBAkorkFt232Q5AkSs5FzgDKrYdXcBzVjagtTpyRJG0e7e5xqbqPmAGVWw3ZUcQ1K0nNqUWaj4QBlVqMOHenm2UNHAWhqbKyKaTZKOUDZeDhAmdWootrTnKlVOZTQcfOcKGFj5wBlVqOyKebV1rxX4GehbDwcoMxqVHGCRHWlmBf4WSgbDwcosxpVzQkSBdkAtX2PU81tdBygzGpUURNflaWYF0xva+kf1by7p5fdBw5XuERWSxygzGrU9t3VX4MCZ/LZ2DlAmdWgo109/TPVClXdMEdZDlA2Vg5QZjVo6+6DBEl/znHzptPS3FjhEg3OY/LZWDlAmdWgjTv29y8vbZ8xxJGV5xqUjZUDlFkN2tzxbP/ysgUzK1iS4WWfhdq669khjjQr5gBlVoM27TzQv7y0ygNUUar53k76+pxqbiPjAGVWgzZ3HAtQ1V6DamttZta0KQD09vbRsf9QhUtktcIByqzGdHX39qeYC7FkfnX3QYH7oWxsHKDMaszWXc/2Z/AtnDutqjP4ChygbCwcoMxqTDZBotoz+AoWzz8WoLZ0OFHCRsYByqzGZBMkqr3/qWD5wln9y89kUuTNhuIAZVZjailBomDFomMB6unt+zxorI2IA5RZjdm4I5Ni3l4bAWrezDamTmkGkpmAC8M0mQ3FAcqshnT39BaNYr6kRvqgJLFi0ez+9ae3u5nPhucAZVZDtu4+SF/aPLZg9jSmtDRVuEQjV9rMZzYcByizGlJLQxyVygaoZ1yDshFwgDKrIbU0SGwpN/HZaDlAmdWQWq5BLVswkwYJgB17OjnS1VPhElm1c4AyqyGba/AZqIKW5sb+uaGCcDOfDcsByqxG9PT2sXV37WXwZR3vRAkbhVwDlKSLJa2XtEHSBwbY3yrppnT/nZJWpNtfJekeSQ+l/78yz3Ka1YKtuw/S19cHwPxZU2lrba5wiUavOJPPNSgbWm4BSlIj8EngNcAq4M2SVpUcdgWwNyJWAtcBH0m37wJeFxFnApcDX8qrnGa14onNe/qXs3/oa4kTJWw08qxBnQdsiIgnI6ILuBG4pOSYS4AvpMs3AxdJUkTcFxFb0+3rgDZJrTmW1azqrd90LECdvGxuBUsydqWp5h7yyIaSZ4BaAmzKrG9Otw14TET0APuBeSXH/C5wb0QcLb2ApCslrZW0tqOjo2wFN6tGj2VqUKcuK/01qQ1zZkxh5rTku+bR7h627+mscImsmlV1koSkM0ia/d450P6IuD4iVkfE6vb29oktnNkEOtLVw8a0SUyIlUvmVLhEY5MMeeRECRuZPAPUFmBZZn1pum3AYyQ1AbOA3en6UuCbwNsj4okcy2lW9TZs2ds/SeGyhTNrMkGiwP1QNlJ5Bqi7gZMlnSCpBbgMWFNyzBqSJAiAS4HbIiIkzQa+C3wgIn6ZYxnNasJjm3b3L5+ytDb7nwo85JGNVG4BKu1TejdwK/AI8PWIWCfpg5Jenx72WWCepA3AnwGFVPR3AyuBqyXdn/5bkFdZzard45kEiVNqNEGiIFuDenLrXidK2KByHQo5Im4BbinZdnVm+QjwxgFedy1wbZ5lM6sVEVGUIHFyjSZIFCxtn0FrcxNHu3vYfeAwO/cdYuGcaZUullWhqk6SMDPo2HeIfQePANDW2syyGhxBIquxsYFVK+b3r697yhm4NjAHKLMqV1R7WjoHpQOu1rKiAPW0A5QNzAHKrMoV9T8tre3mvYLnnXDssRDXoGwwDlBmVW59JoOvVkeQKHXi4jm0Nidd4B37DrFzrx/YtedygDKrYt09vTy5bV//eq2nmBc0uR/KRsAByqyKPb19P729yQjmi+ZO7x8mqB5kA9TD7oeyAThAmVWx9RszzXt1UnsqcD+UDccByqyK3b9hR//yacvrI0GiwP1QNhwHKLMqdfhoNw8+ubN//QWnLKpgacqvqbGB048/FnRdi7JSDlBmVerex3f09z+tWDSbBXU42sIZmWY+90NZKQcosyp19yNb+5fPPX1xBUuSH/dD2VAcoMyqUE9vH/c8tq1//fw6DVCl/VDb9xyscImsmjhAmVWhXz+9i0NHugGYP2tq0RQV9aSpsYEzTjiWbv6rhzdXsDRWbRygzKrQ3Y9mmvdOW1wX4+8N5qVnHpvX9Kf3b/T0G9bPAcqsykQEd2X7n047roKlyd/5q5bQ0twIwOaOA55l1/o5QJlVmae372fX/kNAMr1GNtOtHk1paeL805f0r//kvmcqWBqrJg5QZlUmW3t6wSmLaGqs/1/Tl529vH/55w9u6k+vt8mt/n/yzWpIRHD7ui396+edVp/Ze6Wef+ICZk+fAsD+ziNFDyjb5OUAZVZFHnhiJ5t2Jn0wzU2NnHPywgqXaGI0NjY8J1nCzAHKrIp86+fr+5dftfoEprW1VLA0E+vl5xzfv3znI1s40tVTwdJYNXCAMqsST2zZy0Np01aDxOsuOLnCJZpYKxbNYln7TAC6unu53c9ETXoOUGZV4puZ2tMFZy6ty7H3hiKJ38gkS9z800fpcbLEpOYAZVYFtu0+yB2Z5Ig3vPTUCpamcl61+gSmTUmaNbfvOch/3PlEhUtkleQAZVYFvv2rxwmSERTOXrmQE46bXdkCVciMqa288RWn96//208e4eDhrgqWyCrJAcqswnbs7eS2e5/uX3/DhZOz9lRw8XknsjBt3jx4uIt//+mjFS6RVYoDlFkF9fT28dGb7qS7pxeAk5bMKZqCYjJqbmrkLa8+s3/9u3ds8Cjnk5QDlFkFfe2H69iwZQ8ADQ0NXPnac+p6YNiRuuCMJZyyLJltt7e3jxu++wB9fR5EdrJxgDKrkPse3863fnEsc++tr3oeK5fOrWCJqock3nHx8/vX73lsGzfc8oBHOp9kHKDMKqBj3yE+/u9396+fc/IiXv+SyfXc03BOXT6P17742HvyvTs38I2frR/iFVZvHKDMJtijz+ziz//lNg50HgVg9vQpvOd3z3XT3gDe8Zrn8+Izlvavf/WHD/Oje56qYIlsIjlAmU2gH93zFFd/7mfs7zwCJP1O733jecya1lrhklUnSfzJpefyvBMW9G/71Lfu4Z+/dQ+dTj+vew5QZhPgiS17+T9fu51Pfeue/qkkpre1cM07LuTMExcM8+rJrbmpkfe/+UUcv2h2/7Yf3vMU7/2nH3D3o1vdL1XHVC8f7urVq2Pt2rWVLoZZv87DXTz0VAe33vUEDz5RPH3E8oWz+MBbLuh/3seGd6DzKJ9ecy93/HpL0fbF82bwsnOW87Kzjqd99tQKlc7GQ9I9EbH6OdvzDFCSLgY+BjQC/xoRHy7Z3wp8EXghsBt4U0Q8ne67CrgC6AX+OCJuHepaDlBWCRFB55Fu9nceZefeTnbs6WTb7oM8snEXT27Z1z86RNZLzlzGf3/DC5nS0lSBEte+Xz28mc98577+PrysRXOnc+LiOZy0eDaL589g3sw25s5sY9a0Vhoa3MdXrQYLULn9hkhqBD4JvArYDNwtaU1E/Dpz2BXA3ohYKeky4CPAmyStAi4DzgAWAz+UdEpE9OZR1tvXbeYXD27K49RWpQrfyyKKQ0hEEAFB8n9vXx99fckDtb19fXT39NHV3UtXTy9HunroPNw9YBAqJcQFZy7ldy48lRWTdBijcrngeUs588R2vvajX/PT+58pmpZj+56DbN9zkF89/Nzf59bmJqZOaaatpYmmpgaamxpobmyksUE0NIgGHftfoihpRfCcJBbntBzzqnNP5OyV5Z+7LM+vcOcBGyLiSQBJNwKXANkAdQlwTbp8M/AJJT8FlwA3RsRR4ClJG9Lz3Z5HQbfsevY5zQZm4yXEiUtmc9ZJC7nohStYNHd6pYtUN2ZMbeXK153D5f/pTO56ZCs/vu8ZHnqqg76+wUc/P9rdw9HuHvZOYDkni+eftACorQC1BMh+jdkMnD/YMRHRI2k/MC/dfkfJa5eUXkDSlcCVAMuXLy/dbTYhprQ0MWNqC+2zp7FwzjQWzZvG8gWzOGPF/Ek14WAltLY0ceFZy7nwrOV0dfeyccd+nti6l6e27WfX/kPsPnCYPQcOe8DZGlXTjeARcT1wPSR9UGM9z/mnL2HxvBllK5dVj5E0w0hCmWWgqKmnsaGBxgbR2CCamxppaU7+TWlpYtqUZpoanQxbDVqaG1m5dO6Ao3H09QWHj3ZzuKuHw0d76Onto7unl+6ePvoi6OsLevuCvrTtt68v+rMDA0acKVgnOWejltfo+3kGqC3Assz60nTbQMdsltQEzCJJlhjJa8tm2YKZLFswM6/Tm1mFNTSIaW0trtHWmDy/+t0NnCzpBEktJEkPa0qOWQNcni5fCtwWyVeVNcBlklolnQCcDNyVY1nNzKzK5FaDSvuU3g3cSpJmfkNErJP0QWBtRKwBPgt8KU2C2EMSxEiP+zpJQkUP8Ed5ZfCZmVl18oO6ZmZWUYM9B+XeXTMzq0oOUGZmVpUcoMzMrCo5QJmZWVWqmyQJSR3AM+M8zXxgVxmKU63q+f7q+d7A91fL6vneoDz3d3xEtJdurJsAVQ6S1g6USVIv6vn+6vnewPdXy+r53iDf+3MTn5mZVSUHKDMzq0oOUMWur3QBclbP91fP9wa+v1pWz/cGOd6f+6DMzKwquQZlZmZVyQHKzMyqkgNUStJ7JD0qaZ2kv89sv0rSBknrJf2nSpZxPCS9T1JImp+uS9LH03t7UNILKl3GsZD0f9LP7UFJ35Q0O7Ov5j87SRen5d8g6QOVLs94SVom6ceSfp3+rv1Jun2upB9Iejz9f06lyzpWkhol3SfpO+n6CZLuTD/Dm9Lph2qSpNmSbk5/5x6R9OI8PzsHKEDSK4BLgLMi4gzgH9Ltq0imADkDuBj4lKTGihV0jCQtA14NbMxsfg3JPFsnA1cC/1yBopXDD4DnRcTzgceAq6A+Pru0vJ8k+axWAW9O76uW9QDvi4hVwIuAP0rv6QPAjyLiZOBH6Xqt+hPgkcz6R4DrImIlsBe4oiKlKo+PAf8REacBZ5HcZ26fnQNU4r8BH46IowARsTPdfglwY0QcjYingA3AeRUq43hcB7yfZPbqgkuAL0biDmC2pOMqUrpxiIjvR0RPunoHyezLUB+f3XnAhoh4MiK6gBtJ7qtmRcS2iLg3XX6W5A/cEpL7+kJ62BeAN1SkgOMkaSnw28C/pusCXgncnB5Sy/c2C/gNknn8iIiuiNhHjp+dA1TiFODCtBr+U0nnptuXAJsyx21Ot9UMSZcAWyLigZJdNX9vA/gD4Hvpcj3cXz3cw6AkrQDOAe4EFkbEtnTXdmBhpco1Tv9I8mWwL12fB+zLfImq5c/wBKAD+FzahPmvkqaR42eX24y61UbSD4FFA+z6S5L3YS5Jk8O5wNclnTiBxRuXYe7tL0ia92rWUPcXEf8vPeYvSZqPvjKRZbOxkTQd+HfgvRFxIKloJCIiJNXc8y+SXgvsjIh7JL28wsXJQxPwAuA9EXGnpI9R0pxX7s9u0gSoiPjNwfZJ+m/ANyJ5KOwuSX0kAyBuAZZlDl2abqsqg92bpDNJvvU8kP4BWArcK+k8auTeYOjPDkDSO4DXAhfFsQf7aub+hlAP9/AckppJgtNXIuIb6eYdko6LiG1pU/POwc9QtV4CvF7SbwFTgJkkfTazJTWltaha/gw3A5sj4s50/WaSAJXbZ+cmvsS3gFcASDoFaCEZnXcNcJmkVkknkCQU3FWpQo5WRDwUEQsiYkVErCD5AXtBRGwnube3p9l8LwL2Z6rpNUPSxSRNKq+PiEOZXTX92aXuBk5Os8BaSJI+1lS4TOOS9sl8FngkIj6a2bUGuDxdvhz4fxNdtvGKiKsiYmn6u3YZcFtEvAX4MXBpelhN3htA+ndjk6RT000XAb8mx89u0tSghnEDcIOkh4Eu4PL0m/g6SV8n+RB6gD+KiN4KlrOcbgF+iyR54BDw+5Utzph9AmgFfpDWEu+IiHdFRM1/dhHRI+ndwK1AI3BDRKyrcLHG6yXA24CHJN2fbvsL4MMkTetXkEyb818qU7xc/Dlwo6RrgftIkwxq1HuAr6RfmJ4k+bvRQE6fnYc6MjOzquQmPjMzq0oOUGZmVpUcoMzMrCo5QJmZWVVygDIzs6rkAGV1TVKvpPvTkbMfUDKqe0O6b7Wkj6fLrZJ+mB77JkkXpq+5X1JbZe9iYJJuUWb0drN64zRzq2uSDkbE9HR5AfBV4JcR8dclx70IuLYwaoWkfwF+ERFfHuF1RPL71DfswWY2Iq5B2aSRjlJ/JfDudASNl0v6Thq4vgycm9aY3knysOHfSvoKgKT/KeluJfNO/U26bYWSuZq+CDwMLBviuEckfSatlX2/UCuTtDKtuT0g6V5JJw12vVKSnpY0f6jzlxz/eUn/LOkOSU+m939D+trPZ457taTb0/L8m5Jx85B0dVqmhyVdnwZlJP1E0kck3SXpMUkXptvPSLfdn97HyWX4GG0ScYCySSUiniQZlWFBZttO4A+Bn0fE2RHxaZLhW/5nRLxF0qtJhko6DzgbeKGk30hffjLwqXQesVOHOe6T6XH7gN9Nt38l3X4WcAGwbZjrDWaw85eaA7wY+NP0Hq8jmTPrTElnK5nQ8q+A34yIFwBrgT9LX/uJiDg3Ip4HtJGMf1jQFBHnAe8FCrXTdwEfi4izgdUkQ22ZjZiHOjIb3qvTf/el69NJAsJG4Jl0Pq3hjnsqIu5Pt98DrJA0A1gSEd8EiIgjkNRgBjnPz4Yo43POP8hx305HnH4I2BERD6XXXJe+ZinJ5Ii/TCtILcDt6WtfIen9wFSS0f/XAd9O9xUGfc1e+3bgL5XMkfSNiHh8iPKbPYcDlE0qSqZR6SUZcfn0kb4M+N9pzSp7rhVA5wiPO5rZ1EtSAxnV9YYx0vMXjusreU0fyd+DXuAHEfHmogJJU4BPAasjYpOka0hG7C49b296HiLiq5LuJJnA7xZJ74yI20ZxTzbJuYnPJg1J7cC/kDRVjSY76FbgDzJ9MUvSfquxHgf0zyi7WdIb0uNbJU0d7XnK7A7gJZJWpteepmSE/0Iw2pWW69LBTlCQfhl4MiI+TjLC9fNzKrPVKdegrN61KRk1u5lkVPMvAR8d8hUlIuL7kk4Hbk+bvQ4CbyWpLYz6uBJvAz4t6YNAN/DGIc6T+xxJEdGhZH6tr0lqTTf/VUQ8JukzJMkg20mmAhnOfwHeJqk7fc2H8iiz1S+nmZuZWVVyE5+ZmVUlBygzM6tKDlBmZlaVHKDMzKwqOUCZmVlVcoAyM7Oq5ABlZmZV6f8D6TmhMu01L6AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "kde_diff.plot()\n",
    "\n",
    "decorate(xlabel='Difference in means', \n",
    "         ylabel='PDF', \n",
    "         title='Posterior distribution of difference in mu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean of this distribution is almost 10 points on a test where the mean is around 45, so the effect of the treatment seems to be substantial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 419,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "9.954413088940848"
      ]
     },
     "execution_count": 419,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf_diff.mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use `credible_interval` to compute a 90% credible interval."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 420,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.4, 17.4])"
      ]
     },
     "execution_count": 420,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf_diff.credible_interval(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on this interval, we are pretty sure the treatment improves test scores by 2 to 17 points."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Using Summary Statistics\n",
    "\n",
    "In this example the dataset is not very big, so it doesn't take too long to compute the probability of every score under every hypothesis.\n",
    "But the result is a 3-D array; for larger datasets, it might be too big to compute practically.\n",
    "\n",
    "Also, with larger datasets the likelihoods get very small, sometimes so small that we can't compute them with floating-point arithmetic.\n",
    "That's because we are computing the probability of a particular dataset; the number of possible datasets is astronomically big, so the probability of any of them is very small.\n",
    "\n",
    "An alternative is to compute a summary of the dataset and compute the likelihood of the summary.\n",
    "For example, if we compute the mean and standard deviation of the data, we can compute the likelihood of those summary statistics under each hypothesis.\n",
    "\n",
    "As an example, suppose we know that the actual mean of the population, $\\mu$,  is 42 and the actual standard deviation, $\\sigma$, is 17."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 421,
   "metadata": {},
   "outputs": [],
   "source": [
    "mu = 42\n",
    "sigma = 17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now suppose we draw a sample from this distribution with sample size `n=20`, and compute the mean of the sample, which I'll call `m`, and the standard deviation of the sample, which I'll call `s`.\n",
    "\n",
    "And suppose it turns out that:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 422,
   "metadata": {},
   "outputs": [],
   "source": [
    "n = 20\n",
    "m = 41\n",
    "s = 18"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The summary statistics, `m` and `s`, are not too far from the parameters $\\mu$ and $\\sigma$, so it seems like they are not too unlikely.\n",
    "\n",
    "To compute their likelihood, we will take advantage of three results from mathematical statistics:\n",
    "\n",
    "* Given $\\mu$ and $\\sigma$, the distribution of `m` is normal with parameters $\\mu$ and $\\sigma/\\sqrt{n}$;\n",
    "\n",
    "* The distribution of $s$ is more complicated, but if we compute the transform $t = n s^2 / \\sigma^2$, the distribution of $t$ is chi-squared with parameter $n-1$; and\n",
    "\n",
    "* According to [Basu's theorem](https://en.wikipedia.org/wiki/Basu%27s_theorem), `m` and `s` are independent.\n",
    "\n",
    "So let's compute the likelihood of `m` and `s` given $\\mu$ and $\\sigma$.\n",
    "\n",
    "First I'll create a `norm` object that represents the distribution of `m`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 423,
   "metadata": {},
   "outputs": [],
   "source": [
    "dist_m = norm(mu, sigma/np.sqrt(n))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This is the \"sampling distribution of the mean\".\n",
    "We can use it to compute the likelihood of the observed value of `m`, which is 41."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 424,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.10137915138497372"
      ]
     },
     "execution_count": 424,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like1 = dist_m.pdf(m)\n",
    "like1"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now let's compute the likelihood of the observed value of `s`, which is 18.\n",
    "First, we compute the transformed value `t`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 425,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "22.422145328719722"
      ]
     },
     "execution_count": 425,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "t = n * s**2 / sigma**2\n",
    "t"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Then we create a `chi2` object to represent the distribution of `t`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 426,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import chi2\n",
    "\n",
    "dist_s = chi2(n-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the likelihood of `t`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 427,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.04736427909437004"
      ]
     },
     "execution_count": 427,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like2 = dist_s.pdf(t)\n",
    "like2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, because `m` and `s` are independent, their joint likelihood is the product of their likelihoods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 428,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.004801750420548287"
      ]
     },
     "execution_count": 428,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like = like1 * like2\n",
    "like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the likelihood of the data for any values of $\\mu$ and $\\sigma$, which we'll use in the next section to do the update."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Update With Summary Statistics\n",
    "\n",
    "Now we're ready to do an update.\n",
    "I'll compute summary statistics for the two groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 429,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'Control': (23, 41.52173913043478, 17.148733229699484),\n",
       " 'Treated': (21, 51.476190476190474, 11.00735684721381)}"
      ]
     },
     "execution_count": 429,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary = {}\n",
    "\n",
    "for name, response in responses.items():\n",
    "    summary[name] = len(response), response.mean(), response.std()\n",
    "    \n",
    "summary"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The result is a dictionary that maps from group name to a tuple that contains the sample size, `n`, the sample mean, `m`, and the sample standard deviation `s`, for each group.\n",
    "\n",
    "I'll demonstrate the update with the summary statistics from the control group."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 430,
   "metadata": {},
   "outputs": [],
   "source": [
    "n, m, s = summary['Control']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll make a mesh with hypothetical values of `mu` on the `x` axis and values of `sigma` on the `y` axis."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 431,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101)"
      ]
     },
     "execution_count": 431,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "mus, sigmas = np.meshgrid(prior.columns, prior.index)\n",
    "mus.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now we can compute the likelihood of seeing the sample mean, `m`, for each pair of parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 432,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101)"
      ]
     },
     "execution_count": 432,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "like1 = norm(mus, sigmas/np.sqrt(n)).pdf(m)\n",
    "like1.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And we can compute the likelihood of the sample standard deviation, `s`, for each pair of parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 433,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(101, 101)"
      ]
     },
     "execution_count": 433,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "ts = n * s**2 / sigmas**2\n",
    "like2 = chi2(n-1).pdf(ts)\n",
    "like2.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, we can do the update with both likelihoods:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 434,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.00030965351017402847"
      ]
     },
     "execution_count": 434,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "posterior_control2 = prior * like1 * like2\n",
    "normalize(posterior_control2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To compute the posterior distribution for the treatment group, I'll put the previous steps in a function:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 435,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update_norm_summary(prior, data):\n",
    "    \"\"\"Update a normal distribution using summary statistics.\"\"\"\n",
    "    n, m, s = data\n",
    "    mu_mesh, sigma_mesh = np.meshgrid(prior.columns, prior.index)\n",
    "    \n",
    "    like1 = norm(mu_mesh, sigma_mesh/np.sqrt(n)).pdf(m)\n",
    "    like2 = chi2(n-1).pdf(n * s**2 / sigma_mesh**2)\n",
    "    \n",
    "    posterior = prior * like1 * like2\n",
    "    normalize(posterior)\n",
    "    \n",
    "    return posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the update for the treatment group:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 436,
   "metadata": {},
   "outputs": [],
   "source": [
    "data = summary['Treated']\n",
    "posterior_treated2 = update_norm_summary(prior, data)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here are the results."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 437,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_contour(posterior_control2, cmap='Blues')\n",
    "plt.text(49.5, 18, 'Control', color='C0')\n",
    "\n",
    "cs = plot_contour(posterior_treated2, cmap='Oranges')\n",
    "plt.text(57, 12, 'Treated', color='C1')\n",
    "\n",
    "decorate(xlabel='Mean (mu)', \n",
    "         ylabel='Standard deviation (sigma)',\n",
    "         title='Joint posterior distributions of mu and sigma')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Visually, these posterior joint distributions are similar to the ones we computed using the entire dataset, not just the summary statistics.\n",
    "But they are not exactly the same, as we can see by comparing the marginal distributions."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Comparing Marginals\n",
    "\n",
    "Again, let's extract the marginal posterior distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 438,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import marginal\n",
    "\n",
    "pmf_mean_control2 = marginal(posterior_control2, 0)\n",
    "pmf_mean_treated2 = marginal(posterior_treated2, 0)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And compare them to results we got using the entire dataset (the dashed lines)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 439,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_mean_control.plot(color='C5', linestyle='dashed')\n",
    "pmf_mean_control2.plot(label='Control')\n",
    "pmf_mean_treated.plot(color='C5', linestyle='dashed')\n",
    "pmf_mean_treated2.plot(label='Treated')\n",
    "\n",
    "decorate(xlabel='Population mean', \n",
    "         ylabel='PDF', \n",
    "         title='Posterior distributions of mu')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distributions based on summary statistics are similar to the posteriors we computed using the entire dataset, but in both cases they are shorter and a little wider.\n",
    "\n",
    "That's because the update with summary statistics is based on the implicit assumption that the distribution of the data is normal.\n",
    "But it's not; as a result, when we replace the dataset with the summary statistics, we lose some information about the true distribution of the data.\n",
    "With less information, we are less certain about the parameters."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Proof By Simulation\n",
    "\n",
    "The update with summary statistics is based on theoretical distributions, and it seems to work, but I think it is useful to test theories like this, for a few reasons:\n",
    "\n",
    "* It confirms that our understanding of the theory is correct,\n",
    "\n",
    "* It confirms that the conditions where we apply the theory are conditions where the theory holds, \n",
    "\n",
    "* It confirms that the implementation details are correct.  For many distributions, there is more than one way to specify the parameters.  If you use the wrong specification, this kind of testing will help you catch the error.\n",
    "\n",
    "In this section I'll use simulations to show that the distribution of the sample mean and standard deviation is as I claimed.\n",
    "But if you want to take my word for it, you can skip this section and the next."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Let's suppose that we know the actual mean and standard deviation of the population:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 440,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "mu = 42\n",
    "sigma = 17"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "I'll create a `norm` object to represent this distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 441,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "dist = norm(mu, sigma)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "`norm` provides `rvs`, which generates random values from the distribution.\n",
    "We can use it to simulate 1000 samples, each with sample size `n=20`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 442,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000, 20)"
      ]
     },
     "execution_count": 442,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "n = 20\n",
    "samples = dist.rvs((1000, n))\n",
    "samples.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The result is an array with 1000 rows, each containing a sample or 20 simulated test scores.\n",
    "\n",
    "If we compute the mean of each row, the result is an array that contains 1000 sample means; that is, each value is the mean of a sample with `n=20`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 443,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 443,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_means = samples.mean(axis=1)\n",
    "sample_means.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Now, let's compare the distribution of these means to `dist_m`.\n",
    "I'll use `pmf_from_dist` to make a discrete approximation of `dist_m`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 444,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def pmf_from_dist(dist, low, high):\n",
    "    \"\"\"Make a discrete approximation of a continuous distribution.\n",
    "    \n",
    "    dist: SciPy dist object\n",
    "    low: low end of range\n",
    "    high: high end of range\n",
    "    \n",
    "    returns: normalized Pmf\n",
    "    \"\"\"\n",
    "    qs = np.linspace(low, high, 101)\n",
    "    ps = dist.pdf(qs)\n",
    "    pmf = Pmf(ps, qs)\n",
    "    pmf.normalize()\n",
    "    return pmf"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "`pmf_from_dist` takes an object representing a continuous distribution, evaluates its probability density function at equally space points between `low` and `high`, and returns a normalized `Pmf` that approximates the distribution.\n",
    "\n",
    "I'll use it to evaluate `dist_m` over a range of six standard deviations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 445,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "low = dist_m.mean() - dist_m.std() * 3\n",
    "high = dist_m.mean() + dist_m.std() * 3\n",
    "\n",
    "pmf_m = pmf_from_dist(dist_m, low, high)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Now let's compare this theoretical distribution to the means of the samples.\n",
    "I'll use `kde_from_sample` to estimate their distribution and evaluate it in the same locations as `pmf_m`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 446,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from utils import kde_from_sample\n",
    "\n",
    "qs = pmf_m.qs\n",
    "pmf_sample_means = kde_from_sample(sample_means, qs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The following figure shows the two distributions."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 447,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_m.plot(label='Theoretical distribution',\n",
    "           style=':', color='C5')\n",
    "pmf_sample_means.plot(label='KDE of sample means')\n",
    "\n",
    "decorate(xlabel='Mean score',\n",
    "         ylabel='PDF',\n",
    "         title='Distribution of the mean')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The theoretical distribution and the distribution of sample means are in accord."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "## Checking Standard Deviation\n",
    "\n",
    "Let's also check that the standard deviations follow the distribution we expect.\n",
    "First I'll compute the standard deviation for each of the 1000 samples.\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 448,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 448,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_stds = samples.std(axis=1)\n",
    "sample_stds.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Now we'll compute the transformed values, $t = n s^2 / \\sigma^2$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 449,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "transformed = n * sample_stds**2 / sigma**2"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "We expect the transformed values to follow a chi-square distribution with parameter $n-1$.\n",
    "SciPy provides `chi2`, which we can use to represent this distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 450,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "from scipy.stats import chi2\n",
    "\n",
    "dist_s = chi2(n-1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "We can use `pmf_from_dist` again to make a discrete approximation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 451,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "low = 0\n",
    "high = dist_s.mean() + dist_s.std() * 4\n",
    "\n",
    "pmf_s = pmf_from_dist(dist_s, low, high)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "And we'll use `kde_from_sample` to estimate the distribution of the sample standard deviations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 452,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "qs = pmf_s.qs\n",
    "pmf_sample_stds = kde_from_sample(transformed, qs)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Now we can compare the theoretical distribution to the distribution of the standard deviations."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 453,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_s.plot(label='Theoretical distribution',\n",
    "           style=':', color='C5')\n",
    "pmf_sample_stds.plot(label='KDE of sample std',\n",
    "                     color='C1')\n",
    "\n",
    "decorate(xlabel='Standard deviation of scores',\n",
    "         ylabel='PDF',\n",
    "         title='Distribution of standard deviation')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The distribution of transformed standard deviations agrees with the theoretical distribution.\n",
    "\n",
    "Finally, to confirm that the sample means and standard deviations are independent, I'll compute their coefficient of correlation:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 454,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.02467498252065539"
      ]
     },
     "execution_count": 454,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.corrcoef(sample_means, sample_stds)[0][1]"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Their correlation is near zero, which is consistent with their being independent.\n",
    "\n",
    "So the simulations confirm the theoretical results we used to do the update with summary statistics."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "We can also use `kdeplot` from Seaborn to see what their joint distribution looks like."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 455,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import seaborn as sns\n",
    "\n",
    "sns.kdeplot(x=sample_means, y=sample_stds)\n",
    "\n",
    "decorate(xlabel='Mean (mu)',\n",
    "         ylabel='Standard deviation (sigma)',\n",
    "         title='Joint distribution of mu and sigma')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "It looks like the axes of the ellipses are aligned with the axes, which indicates that the variables are independent."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Summary\n",
    "\n",
    "In this chapter we used a joint distribution to represent prior probabilities for the parameters of a normal distribution, `mu` and `sigma`.\n",
    "And we updated that distribution two ways: first using the entire dataset and the normal PDF; then using summary statistics, the normal PDF, and the chi-square PDF.\n",
    "Using summary statistics is computationally more efficient, but it loses some information in the process.\n",
    "\n",
    "Normal distributions appear in many domains, so the methods in this chapter are broadly applicable.  The exercises at the end of the chapter will give you a chance to apply them."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercises"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Looking again at the posterior joint distribution of `mu` and `sigma`, it seems like the standard deviation of the treated group might be lower; if so, that would suggest that the treatment is more effective for students with lower scores.\n",
    "\n",
    "But before we speculate too much, we should estimate the size of the difference and see whether it might actually be 0.\n",
    "\n",
    "Extract the marginal posterior distributions of `sigma` for the two groups.\n",
    "What is the probability that the standard deviation is higher in the control group?\n",
    "\n",
    "Compute the distribution of the difference in `sigma` between the two groups.  What is the mean of this difference?  What is the 90% credible interval?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 456,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 457,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 458,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 459,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 460,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 461,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 462,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Exercise\n",
    "\n",
    "An [effect size](http://en.wikipedia.org/wiki/Effect_size) is a statistic intended to quantify the magnitude of a phenomenon.\n",
    "If the phenomenon is a difference in means between two groups, a common way to quantify it is Cohen's effect size, denoted $d$.\n",
    "\n",
    "If the parameters for Group 1 are $(\\mu_1, \\sigma_1)$, and the\n",
    "parameters for Group 2 are $(\\mu_2, \\sigma_2)$, Cohen's\n",
    "effect size is\n",
    "\n",
    "$ d = \\frac{\\mu_1 - \\mu_2}{(\\sigma_1 + \\sigma_2)/2} $\n",
    "\n",
    "Use the joint posterior distributions for the two groups to compute the posterior distribution for Cohen's effect size."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "If we try enumerate all pairs from the two distributions, it takes too\n",
    "long so we'll use random sampling.\n",
    "\n",
    "The following function takes a joint posterior distribution and returns a sample of pairs.\n",
    "It uses some features we have not seen yet, but you can ignore the details for now."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 463,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def sample_joint(joint, size):\n",
    "    \"\"\"Draw a sample from a joint distribution.\n",
    "    \n",
    "    joint: DataFrame representing a joint distribution\n",
    "    size: sample size\n",
    "    \"\"\"\n",
    "    pmf = Pmf(joint.transpose().stack())\n",
    "    return pmf.choice(size)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Here's how we can use it to sample pairs from the posterior distributions for the two groups."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 464,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 464,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_treated = sample_joint(posterior_treated, 1000)\n",
    "sample_treated.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 465,
   "metadata": {
    "tags": []
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(1000,)"
      ]
     },
     "execution_count": 465,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sample_control = sample_joint(posterior_control, 1000)\n",
    "sample_control.shape"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "The result is an array of tuples, where each tuple contains a possible pair of values for $\\mu$ and $\\sigma$.\n",
    "Now you can loop through the samples, compute the Cohen effect size for each, and estimate the distribution of effect sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 466,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 467,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 468,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 469,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 470,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 471,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** This exercise is inspired by [a question that appeared on Reddit](https://www.reddit.com/r/statistics/comments/hcvl2j/q_reverse_empirical_distribution_rule_question/).\n",
    "\n",
    "An instructor announces the results of an exam like this, \"The average score on this exam was 81.  Out of 25 students, 5 got more than 90, and I am happy to report that no one failed (got less than 60).\"\n",
    "\n",
    "Based on this information, what do you think the standard deviation of scores was?\n",
    "\n",
    "You can assume that the distribution of scores is approximately normal.  And let's assume that the sample mean, 81, is actually the population mean, so we only have to estimate `sigma`.\n",
    "\n",
    "Hint: To compute the probability of a score greater than 90, you can use `norm.sf`, which computes the survival function, also known as the complementary CDF, or `1 - cdf(x)`."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 472,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 473,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 474,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 475,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 476,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 477,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 478,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 479,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 480,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 481,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 482,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 483,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** I have a soft spot for crank science, so this exercise is about the [Variability Hypothesis](http://en.wikipedia.org/wiki/Variability_hypothesis), which\n",
    "\n",
    "> \"originated in the early nineteenth century with Johann Meckel, who argued that males have a greater range of ability than females, especially in intelligence. In other words, he believed that most geniuses and most mentally retarded people are men. Because he considered males to be the 'superior animal', Meckel concluded that females' lack of variation was a sign of inferiority.\"\n",
    "\n",
    "I particularly like that last part because I suspect that if it turned out that women were _more_ variable, Meckel would have taken that as a sign of inferiority, too.\n",
    "\n",
    "Nevertheless, the Variability Hypothesis suggests an exercise we can use to practice the methods in this chapter.  Let's look at the distribution of heights for men and women in the U.S. and see who is more variable.\n",
    "\n",
    "I used 2018 data from the CDC’s [Behavioral Risk Factor Surveillance System](https://www.cdc.gov/brfss/annual_data/annual_2018.html) (BRFSS), which includes self-reported heights from 154407 men and 254722 women. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's what I found:\n",
    "\n",
    "* The average height for men is 178 cm; the average height for women is 163 cm. So men are taller on average; no surprise there.\n",
    "\n",
    "* For men the standard deviation is 8.27 cm; for women it is 7.75 cm. So in absolute terms, men's heights are more variable.\n",
    "\n",
    "But to compare variability between groups, it is more meaningful to use the [coefficient of variation](https://en.wikipedia.org/wiki/Coefficient_of_variation) (CV), which is the standard deviation divided by the mean. It is a dimensionless measure of variability relative to scale. \n",
    "\n",
    "For men CV is 0.0465; for women it is 0.0475.\n",
    "The coefficient of variation is higher for women, so this dataset provides evidence against the Variability Hypothesis. But we can use Bayesian methods to make that conclusion more precise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use these summary statistics to compute the posterior distribution of `mu` and `sigma` for the distributions of male and female height.\n",
    "Use `Pmf.div_dist` to compute posterior distributions of CV.\n",
    "Based on this dataset and the assumption that the distribution of height is normal, what is the probability that the coefficient of variation is higher for men?\n",
    "What is the most likely ratio of the CVs and what is the 90% credible interval for that ratio?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": []
   },
   "source": [
    "Hint: Use different prior distributions for the two groups, and chose them so they cover all parameters with non-negligible probability.\n",
    "\n",
    "Also, you might find this function helpful:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 484,
   "metadata": {
    "tags": []
   },
   "outputs": [],
   "source": [
    "def get_posterior_cv(joint):\n",
    "    \"\"\"Get the posterior distribution of CV.\n",
    "    \n",
    "    joint: joint distribution of mu and sigma\n",
    "    \n",
    "    returns: Pmf representing the smoothed posterior distribution\n",
    "    \"\"\"\n",
    "    pmf_mu = marginal(joint, 0)\n",
    "    pmf_sigma = marginal(joint, 1)\n",
    "    pmf_cv = Pmf.div_dist(pmf_sigma, pmf_mu)\n",
    "    return kde_from_pmf(pmf_cv)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 485,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 486,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 487,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 488,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 489,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 490,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 491,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 492,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 493,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
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