{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian analysis of the Curtis Flowers trials\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": 1,
   "metadata": {},
   "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": 2,
   "metadata": {},
   "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/code/soln/utils.py"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "\n",
    "from empiricaldist import Pmf\n",
    "from utils import decorate, savefig"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "On September 5, 2020, prosecutors in Mississippi dropped charges against [Curtis Flowers](https://en.wikipedia.org/wiki/Curtis_Flowers), freeing him after 23 years of incarceration.\n",
    "\n",
    "Flowers had been tried six times for a 1996 multiple murder.  Two trials ended in a mistrial due to a hung jury; four trials ended in convictions.  \n",
    "\n",
    "According to [this NPR report](https://www.npr.org/2020/09/05/910061573/after-6-trials-prosecutors-drop-charges-against-curtis-flowers)\n",
    "\n",
    "> After each conviction, a higher court struck down the initial ruling. The latest ruling invalidating Flowers' conviction, and death sentence, came from the U.S. Supreme Court in June of last year. The justices noted the Mississippi Supreme Court had found that in three prior convictions the prosecution had misrepresented evidence and deliberately eliminated Black jurors.\n",
    "\n",
    "Since the racial composition of the juries was the noted reason the last conviction was invalidated, the purpose of this article is to explore the relationship between the composition of the juries and the outcome of the trials.\n",
    "\n",
    "Flowers' trials were the subject of the [In the Dark](https://www.apmreports.org/episode/2018/05/01/in-the-dark-s2e1) podcast, which reported the racial composition of the juries and the outcomes:\n",
    "\n",
    "```\n",
    "Trial         Jury                     Outcome\n",
    "  1           All white                Guilty\n",
    "  2           11 white, 1 black        Guilty\n",
    "  3           11 white, 1 black        Guilty\n",
    "  4           7 white, 5 black         Hung jury\n",
    "  5           9 white, 3 black         Hung jury\n",
    "  6           11 white, 1 black        Guilty\n",
    "```\n",
    "\n",
    "We can use this data to estimate the probability that white and black jurors would vote to convict, and then use those estimates to compute the probability of a guilty verdict.\n",
    "\n",
    "As a modeling simplification, I'll assume:\n",
    "\n",
    "* The six juries were presented with essentially the same evidence, prosecution case, and defense;\n",
    "\n",
    "* The probabilities of conviction did not change over the years of the trials (from 1997 to 2010); and\n",
    "\n",
    "* Each juror votes independently of the others; that is, I ignore interactions between jurors.\n",
    "\n",
    "I'll use the same prior distribution for white and black jurors, a uniform distribution from 0 to 1."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "ps = np.linspace(0, 1, 101)\n",
    "prior_p1 = Pmf(1.0, ps)\n",
    "prior_p1.index.name = 'p1'"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior_p2 = Pmf(1.0, ps)\n",
    "prior_p2.index.name = 'p2'"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "To prepare for the updates, I'll form a joint distribution of the two probabilities."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import make_joint\n",
    "\n",
    "joint = make_joint(prior_p2, prior_p1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "p1   p2  \n",
       "0.0  0.00    1.0\n",
       "     0.01    1.0\n",
       "     0.02    1.0\n",
       "     0.03    1.0\n",
       "     0.04    1.0\n",
       "dtype: float64"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "prior_pmf = Pmf(joint.stack())\n",
    "prior_pmf.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's how we compute the update.\n",
    "\n",
    "Assuming that a guilty verdict must be unanimous, the probability of conviction is\n",
    "\n",
    "$ p = p_1^{n_1} ~ p_2^{n_2}$\n",
    "\n",
    "where\n",
    "\n",
    "* $p_1$ is the probability a white juror votes to convict\n",
    "* $p_2$ is the probability a black juror votes to convict\n",
    "* $n_1$ is the number of white jurors\n",
    "* $n_2$ is the number of black jurors\n",
    "\n",
    "The probability of an acquittal or hung jury is the complement of $p$.\n",
    "\n",
    "The following function performs a Bayesian update given the composition of the jury and the outcome, either `'guilty'` or `'hung'`.  We could also do an update for an acquittal, but since that didn't happen, I didn't implement it."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def update(prior, data):\n",
    "    n1, n2, outcome = data\n",
    "    likelihood = prior.copy()\n",
    "\n",
    "    for p1, p2 in prior.index:\n",
    "        like = p1**n1 * p2**n2\n",
    "        if outcome == 'guilty':\n",
    "            likelihood.loc[p1, p2] = like\n",
    "        elif outcome == 'hung':\n",
    "            likelihood.loc[p1, p2] = 1-like\n",
    "        else:\n",
    "            raise ValueError()\n",
    "            \n",
    "    posterior = prior * likelihood\n",
    "    posterior.normalize()\n",
    "    return posterior"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "I'll use the following function to plot the marginal posterior distributions after each update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "from utils import pmf_marginal\n",
    "\n",
    "def plot_marginals(posterior):\n",
    "    marginal0 = pmf_marginal(posterior, 0)\n",
    "    marginal0.plot(label='white')\n",
    "    \n",
    "    marginal1 = pmf_marginal(posterior, 1)\n",
    "    marginal1.plot(label='black')\n",
    "\n",
    "    decorate(xlabel='Probability of voting to convict',\n",
    "             ylabel='PDF',\n",
    "             title='Marginal posterior distributions')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the update for the first trial."
   ]
  },
  {
   "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": [
    "data1 = 12, 0, 'guilty'\n",
    "posterior1 = update(prior_pmf, data1)\n",
    "plot_marginals(posterior1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since there were no black jurors for the first trial, we learn nothing about their probability of conviction, so the posterior distribution is the same as the prior.\n",
    "\n",
    "The posterior distribution for white voters reflects the data that 12 of them voted to convict.\n",
    "\n",
    "Here are the posterior distributions after the second trial."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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Zs2YNv/xlcivYwQcfzKpVq1i8eDEAmzdv3v6sqH322Ye7776bCy64wI/aMLOia9rSzriaSuqqKwu6HyeoIpg7dy633norRxxxBOvXr+fyyy/fvmzevHkceeSRHHrooVx88cXbmwJrampYuHAhn/zkJ5k3bx5nnHEGbW1t29c76KCDuO222/jIRz7Cyy+/XPRjMrPRa0Nre0Ef9d7Dj9sYwUb78ZtZYVxwy5/Y1NrOT684qf/CefDjNszMbEisb9lW8OtP4ARlZmYDtH5L4cfhg1GQoEZKE+ZAjdbjNrPCW9/aztQiXIMa0Qmqrq6OpqamUfdlHRE0NTVRV1dX6lDMbIRpbe+kraObyWMLn6BG9H1QM2fOpLGxkdH4KI66ujpmzpzZf0EzswHoGUWi0OPwwQhPUNXV1cyZM6fUYZiZjRjFukkXRngTn5mZDa31PcMc+RqUmZmVk/U9A8UW4RqUE5SZmeVtexOfa1BmZlZOmlraqa4U42sL34XBCcrMzPK2oaWdKeNqen3awlBygjIzs7w1tbQX5R4ocIIyM7MBWN+yrSijSIATlJmZDcD6luKMwwdOUGZmNgDrW9qLMooEOEGZmVmeOrq6aW7r9DUoMzMrLxuKeA8UOEGZmVmemlqKN1AsOEGZmVme1m7eBsDuE9xJwszMysia5jYAdhtfnGfNOUGZmVle1vYkKNegzMysnKxp3saksdXUVlUWZX9OUGZmlpc1zW3sXqTmPXCCMjOzPK3ZvK1ozXvgBGVmZnla29zG7hNcgzIzszLS3R2s3bytaF3MwQnKzMzy0NTSTld3uAZlZmblpdj3QIETlJmZ5WFdkUeRACcoMzPLQ08Nyk18ZmZWVtY0JzWo6eNdgzIzszKyZnMb0+prqK4sXtoo6J4knSlpmaTlkj6fY/kpkp6Q1CnpnKxlXZKeSl+LChmnmZn1bW1zW1E7SABUFWrDkiqBbwNnAI3AYkmLIuL5jGKvAxcBn8mxia0RMb9Q8ZmZWf7WNBf3HigobA3qGGB5RKyIiHbgDuDszAIR8WpEPAN0FzAOMzPbRWtKUIMqZIKaAbyR8b4xnZevOklLJD0q6cNDG5qZmeWrs6ubt7YUvwZVsCY+QDnmxQDW3zsiVknaF/i1pGcj4uUddiBdClwKsPfeew8+UjMz61VTSzvdAbsVsYs5FLYG1QjMyng/E1iV78oRsSr9uwJ4GDgyR5mbIqIhIhqmT5++a9GamVlOpbgHCgqboBYDB0iaI6kGOA/IqzeepMmSatPpacCJwPN9r2VmZoXQcw/UiOkkERGdwBXAfcCfgTsjYqmkayWdBSDpaEmNwEeA70pamq4+F1gi6WngIeArWb3/zMysSEpVgyrkNSgi4l7g3qx5X8qYXkzS9Je93h+BwwsZm5mZ5WdtcxsVgqnjaoq6X48kYWZmfVq7eRvT6mupKuIoEuAEZWZm/VhT5Cfp9nCCMjOzPpViFAlwgjIzs36s3dxW9HugwAnKzMz60NHVzVtb2tm9yMMcgROUmZn1oRRP0u3hBGVmZr3quQdqNycoMzMrJz2jSBR7JHNwgjIzsz6s3VyaUSTACcrMzPrw5qY2qipU9FEkwAnKzMz60LhhK3tNGkNFRa4nKBWWE5SZmfWqcUMrMyePKcm+naDMzKxXb2zYyqzJY0uybycoMzPLqa2ji3Wbt7kGZWZm5aVxw1YAZk1xDcrMzMpI44ZWANegzMysvLzhGpSZmZWjxg2t1FRWML2++MMcgROUmZn1onH9VmZMLs09UOAEZWZmvSjlPVDgBGVmZr1o3LCVmSW6BwqcoMzMLIeWbZ00tbQza4prUGZmVkZWbkx68LkGZWZmZeWN9ck9ULN8DcrMzMpJzygSrkGZmVlZeWN9K3XVFUyrL/5zoHo4QZmZ2U56evBJpbkHCpygzMwshzdKfA8UOEGZmVkOjSV8DlSPPhOUpPszpv+x8OGYmVmpNbd1sGlrR9nXoKZnTH+kkIGYmVl5aFxf2lHMe/SXoKIoUZiZWdko9XOgelT1s3xfSYsAZUxvFxFnFSwyMzMrie3PgSrxNaj+EtTZGdPXFzIQMzMrD40bWhlXU8mksdUljaPPBBURv+mZljQ9nbeu0EGZmVnpvLF+K7OmlPYeKOi/F58kXS3pLeAF4EVJ6yR9qTjhmZlZsTVuaGXGpNJef4L+O0l8CjgJODoipkbEZOBY4ERJny54dGZmVlTd3cGrTS3MmTau1KH0m6AuAD4aEa/0zIiIFcD56TIzMxtBVm7cSltHN/vvVl/qUPpNUNUR8Vb2zPQ6VL9XzySdKWmZpOWSPp9j+SmSnpDUKemcrGUXSnopfV3Y377MzGzXLV+7BYD9hkGCah/kMiRVAt8G3gccAnxU0iFZxV4HLgJ+nLXuFOBqkubEY4CrJU3uJ1YzM9tFL69LEtT+00ufoPrrZj5PUjPJfVDw9o27Aur6WfcYYHnaJIikO0i6rT/fUyAiXk2XdWet+17ggYhYny5/ADgTuL2ffZqZ2S5YvnYLU8fVMHlc6R6z0aO/buaVu7DtGcAbGe8bSWpEg113RnYhSZcClwLsvffeg4vSzMy2W752S1k070H/3czrJH1K0rckXSqpvxrXDqvnmJfv0El5rRsRN0VEQ0Q0TJ8+PccqZmaWr4hg+bot7FcGzXvQ/zWoW4EG4Fng/cA3BrDtRmBWxvuZwKoirGtmZoOwvqWdja0dZdGDD/q/BnVIRBwOIOlm4E8D2PZi4ABJc4CVwHnAx/Jc9z7gf2d0jHgP4Md9mJkVUE8PvnJJUP3VoDp6JiKicyAbTstfQZJs/gzcGRFLJV0r6SwASUdLaiR5lMd3JS1N110P/DNJklsMXNvTYcLMzApjedqDb7/ppb9JF/LvxQfJdaExGb36IiIm9LVyRNwL3Js170sZ04tJmu9yrXsLcEs/8ZmZ2RBZvnYLY6or2Wti6Yc5gsL24jMzs2Hk5XUt7LfbOCoqSjtIbI/+mvjMzGyUeHntlrK4QbeHE5SZmdGyrZOVG7eWTRdzcIIyMzNgxboWoHx68IETlJmZkTEGnxOUmZmVk+Vrt1BZIfaZWh5dzMEJyszMSBLUPlPGUlNVPmmhfCIxM7OSeXld+QwS28MJysxslOvs6ubVppayuv4ETlBmZqPea+tb6eiKsupiDk5QZmaj3tJVyYh2c/ccX+JIduQEZWY2yj23chM1VRUcuLsTlJmZlZFnGzcxd4/xVFeWV0oor2jMzKyouruD51Zt4rAZE0sdyk6coMzMRrHX1reyua2Tw52gzMysnDy7chMAh890gjIzszJSrh0kwAnKzGxUK9cOEuAEZWY2akWUbwcJcIIyMxu1Xmsq3w4S4ARlZjZq9XSQcA3KzMzKSjl3kAAnKDOzUeuZtINEOT0DKlN5RmVmZgVV7h0kwAnKzGxUKvcOEuAEZWY2KpV7BwlwgjIzG5WefmNjWXeQACcoM7NR6bFX1vOOvSeVbQcJcIIyMxt1Nm3tYOmqTRy379RSh9InJygzs1Fm8Svr6Q443gnKzMzKySMrmqitqmD+3pNKHUqfnKDMzEaZR1c0cdQ+k6mtqix1KH1ygjIzG0U2trbz/Ormsr/+BE5QZmajymOvrCcCjt/PCcrMzMrIoyuaqKuu4IgyfMR7NicoM7NR5JGXm2jYZ0rZX38CJygzs1FjQ0s7L7y5meP2nVLqUPLiBGVmNko89koTMDyuP0GBE5SkMyUtk7Rc0udzLK+VtDBd/pik2en82ZK2Snoqfd1YyDjNzEaDR1esZ0x1JYfPKO/7n3pUFWrDkiqBbwNnAI3AYkmLIuL5jGKXABsiYn9J5wFfBc5Nl70cEfMLFZ+Z2Wjzx5ffomH25LIefy9TIaM8BlgeESsioh24Azg7q8zZwK3p9F3A6ZJUwJjMzEalV99q4cU1WzjtoN1KHUreCpmgZgBvZLxvTOflLBMRncAmoKdxdI6kJyX9RtLJuXYg6VJJSyQtWbdu3dBGb2Y2gty39E0A3nvo7iWOJH+FTFC5akKRZ5nVwN4RcSTw98CPJU3YqWDETRHREBEN06dP3+WAzcxGqvuWvslhMyYwc/LYUoeSt0ImqEZgVsb7mcCq3spIqgImAusjYltENAFExOPAy8CBBYzVzGzEWtPcxhOvb+TMQ/codSgDUsgEtRg4QNIcSTXAecCirDKLgAvT6XOAX0dESJqedrJA0r7AAcCKAsZqZjZi3b+9eW94JaiC9eKLiE5JVwD3AZXALRGxVNK1wJKIWATcDPxQ0nJgPUkSAzgFuFZSJ9AFXBYR6wsVq5nZSHbf0jXsO30c++9WX+pQBqRgCQogIu4F7s2a96WM6TbgIznW+y/gvwoZm5nZaLCxtZ1HVjRx6Sn7Mtw6SQ+PzvBmZjYoD/55LV3dMeyuP4ETlJnZiParpW+y58S6YTF6eTYnKDOzEaq1vZPfvriO9xyy+7Br3gMnKDOzEeuXz77Jts5u3nf4nqUOZVCcoMzMRqjbHnuNfaeN49g5w+PxGtmcoMzMRqAX3mzmidc38tFj9h6WzXvgBGVmNiL9+LHXqamq4C+PmlnqUAbNCcrMbIRpbe/knidW8v7D9mDKuJpShzNoTlBmZiPMz59ezeZtnXzs2H1KHcoucYIyMxthbnvsNfbfrZ6jZ08udSi7xAnKzGwEeW7lJp5u3MTHjx2+nSN6OEGZmY0gt/zhFeqqK/iLI4dv54geTlBmZiPE8rVb+O8nV3L+sfswcWx1qcPZZU5QZmYjxL8/+BJ11ZVcdtp+pQ5lSDhBmZmNAMve3MzPn1nFhSfMZlp9banDGRJOUGZmI8C/PvAi9TVV/M9T9i11KEPGCcrMbJh7buUmfrX0TS4+aQ6Txg7fG3OzOUGZmQ1jEcE37l/GxDHVXHLynFKHM6ScoMzMhrF7n32Th5at4+/euR8T6oZ/z71MTlBmZsPUhpZ2rl70HIfPmMjFJ46s2hNAVakDMDOzwbn258+zsbWDH1x8LFWVI6++4QRlZjYMPfTCWu55ciVXvmt/DtlrQuF21NkO2zbDtub07+aM980waR844IyC7NoJysxsmNm0tYMv3PMsB+xWz9+9a//chXZILFnJpW1TVrLJSjptGeW7tvUdzNyznKDMzEaFzm071lgyk8W2Zrramvnt4mX8Xet63j+zntqf3Ph2+YEkFgBVQt0EqB0PtROSV/0eMHX/ZDp7We14qK3f8X1d4WpvTlBmZkOhJ7HkrJ3kqMXkrM00Q1d7n7upBM6MSrrr6qltmpQkiJrxMH5PmHZgkjRq6tPkMjEjoYxPE8rEt6er6qCMRzx3gjKz0Sti5xrLDkklR81k+ysrEfWTWACoqNqx5lE7ASbslZFQ0sRRm5FEMmoxdz23kat++Tp/feKBfPFDhxb+/JSYE5SZDT/bE0vzzsmlLce83moybc3Q3dH//iqqsxLIBJgwc8cmr56azA7lMpvH6nepxvLbF9fxufuWccpBM/jHDxwyqG0MN05QZlY8EdDZlqOWkplY+rqAn1FuIIkls8lrwoysJq8JO77PNV1VW9KmsPuXvskVtz/JAbvVc8NHj6Syonyb5YaSE5SZ9S8COrbmTiy9NXntVJvpSSyd/e+vsmbn6yYTZ+VoCpuQI9mMf7smUzX8R/W+58lGPvOTZzhsxkQWXHQ040fYaBF9cYIyG8n6TSzNO9dMeks6eSWW2p2bvCbNykgm9TvXUHao4WTUWEa5iODWP77KNT97nuP3ncr3LmygvnZ0fWWPrqM1Gy4ioKO198SSq2aS8wJ/nomlqi6r99cEmLR3VkLpSTwT2bkpbLwTyxBqbuvgC3c/y8+fWc275+7Otz52JHXVlaUOq+icoMyGUl+JZYcaSi/XWdoyEk509b+/ytqse1XGJ3f273Txvj5NLLnuZal3YikjT76+gSvveJJVG9v4X+89iMtO3W/UXHPK5gRlBm8nlqybIvts8tqpSSxdFt39769qTFaiSBPL9msomU1eOZrG6iYmZapGzrN/RruNre382/99iR8++hp7TKjjzv95PEftM7nUYZWUE5QNbzslllzDuvRxk2RmIsqnxlJVt/NF+XFzsi7e9ySUiTvXZHrWrRw9F7qtb+2d3fzo0V35DDEAAA7BSURBVNf49wdfYnNbB+cevTeff9/BTBzjz4gTlJVGBLS3ZCWOvu5l6eM6y0BqLJk1lClzclxfybqXJfvivROLDZENLe38+E+v88NHXuPN5jZOPmAaV31gLgfvUcCBX4cZJygbmAho39L3/Sl9XrxPy7XnmViqx+58T8q46Rk1kqwkslNNZrwTi5WNru7g0RVNLHpqFT99eiVtHd2ctP80vvKXh3PqgdNRGQ87VApOUKNFdzd0tORZO+mj2/GAEktW7aQnsewwfEsvA1H21GQq/RG14a25rYPHVqznNy+u5VfPvclbW9oZW1PJWfP24uKT5rjG1Af/7y93vSaWHMmj10Eq02mi//1Vj9v5psf63XYcYDLXfSyZNRknFhuluruDV5paeG7lJp5t3MSS1zbwTONGugPqqis4/eDd+cARe/LOg3ZjTM3o6zY+UAX9FpF0JvDvJAPw/mdEfCVreS3wA+AooAk4NyJeTZf9I3AJ0AVcGRH3FTLWIdfdndEU1sd1lB0u4PfSJJZPYqmpfztp9CSK8XvsnFAym7+y78p3YjHrU0TQ0t7F2uY2Vm1sY9XGrTRuaGXFWy2sWNfCK2+1sLUj6WxTW1XBYTMmcsU79+f4/abxjn0mUVvlpDQQBfs2klQJfBs4A2gEFktaFBHPZxS7BNgQEftLOg/4KnCupEOA84BDgb2A/yvpwIh8ulntou2JJfuCfV83Q+ZoEmvfnN/+auqzLsTXJ8Pm52oK234vS46aTIU/+Db6RATdkVzb6Y7k1dUddHdDVwSd3d10dQedXUFHVzcd6d9tnd20d3azrbOLto7k79b2Llrbu2jZ1smW9k5atnWyaWsnm7Z2sGlrB01btvHWlm20dezYxC3BrMlj2Xf6OI7bdyoH7zmew2dMZP/d6qkegY9hL6ZC/lw+BlgeESsAJN0BnA1kJqizgWvS6buAbym5Sng2cEdEbANekbQ83d4jhQr20W9/gsPW/Zx6tuZVfgtjaElfWxhLC2NoZRKb2Wv7+xaNZQtj2cIYWtNyWzLWaaWO7s5K6ARa8400gOb0tXJQx2qWrzzq7juvE5nTO24hennTM9lTPtLtBJH+TWZ2RxCkfwcTXJ5qqiqor61i4phqJoypZuKYauZMHcu0+lqmja9lt/G17DVpDDMmjWH3CXXUVDkRFUIhE9QM4I2M943Asb2ViYhOSZuAqen8R7PWnZG9A0mXApcC7L333rsUbNWsBp6hgm2V45JXxVjatk+Pe3u6chztFWMI5V9jqUtfU3YpQrPSGEy/sr56o2UuUsbWe+Yr472UlhBUpNMV0g7LKitERfq+skJUSlRUiKqK5H3P35qqCqorK6hKp2urKqmpqqCuuoIx1ZWMqalkTHUl42qrXPMpE4VMULk+odm/eXork8+6RMRNwE0ADQ0Nu/R7quGsy3ZldTMzG2KF/JnQCMzKeD8TWNVbGUlVwERgfZ7rmpnZCFbIBLUYOEDSHEk1JJ0eFmWVWQRcmE6fA/w6kkboRcB5kmolzQEOAP5UwFjNzKzMFKyJL72mdAVwH0k381siYqmka4ElEbEIuBn4YdoJYj1JEiMtdydJh4pO4O+K0oPPzMzKhrJ72QxXDQ0NsWTJklKHYWZmAyTp8YhoyJ7vripmZlaWnKDMzKwsOUGZmVlZcoIyM7OyNGI6SUhaB7y2i5uZBrw1BOGMBD4Xb/O5SPg8vM3n4m1DcS72iYjp2TNHTIIaCpKW5OpJMhr5XLzN5yLh8/A2n4u3FfJcuInPzMzKkhOUmZmVJSeoHd1U6gDKiM/F23wuEj4Pb/O5eFvBzoWvQZmZWVlyDcrMzMqSE5SZmZWlUZmgJJ0paZmk5ZI+n2N5raSF6fLHJM0ufpTFkce5+HtJz0t6RtKDkvYpRZyF1t95yCh3jqSQNGK7GOdzLiT9Vfq5WCrpx8WOsVjy+P+xt6SHJD2Z/h95fyniLDRJt0haK+m5XpZL0g3peXpG0juGZMcRMapeJI/+eBnYF6gBngYOySrzt8CN6fR5wMJSx13Cc/FOYGw6fflIPBf5nIe03Hjgt8CjQEOp4y7hZ+IA4Elgcvp+t1LHXcJzcRNweTp9CPBqqeMu0Lk4BXgH8Fwvy98P/JLkaejHAY8NxX5HYw3qGGB5RKyIiHbgDuDsrDJnA7em03cBp0vK9Rj64a7fcxERD0VEa/r2UZKnG480+XwmAP4Z+BrQVszgiiyfc/E/gG9HxAaAiFhb5BiLJZ9zEcCEdHoiI/TJ3xHxW5Jn9vXmbOAHkXgUmCRpz13d72hMUDOANzLeN6bzcpaJiE5gEzC1KNEVVz7nItMlJL+SRpp+z4OkI4FZEfHzYgZWAvl8Jg4EDpT0B0mPSjqzaNEVVz7n4hrgfEmNwL3AJ4sTWtkZ6HdJXgr2RN0ylqsmlN3XPp8yI0HexynpfKABOLWgEZVGn+dBUgXwr8BFxQqohPL5TFSRNPOdRlKj/p2kwyJiY4FjK7Z8zsVHgQUR8Q1Jx5M8IfywiOgufHhlpSDfmaOxBtUIzMp4P5Odq+Xby0iqIqm691W9Ha7yORdIejdwFXBWRGwrUmzF1N95GA8cBjws6VWSNvZFI7SjRL7/P34aER0R8QqwjCRhjTT5nItLgDsBIuIRoI5k8NTRJq/vkoEajQlqMXCApDmSakg6QSzKKrMIuDCdPgf4daRXAkeYfs9F2rT1XZLkNFKvNfR5HiJiU0RMi4jZETGb5FrcWRGxpDThFlQ+/z/+m6TzDJKmkTT5rShqlMWRz7l4HTgdQNJckgS1rqhRlodFwAVpb77jgE0RsXpXNzrqmvgiolPSFcB9JL10bomIpZKuBZZExCLgZpKq+nKSmtN5pYu4cPI8F18H6oGfpP1EXo+Is0oWdAHkeR5GhTzPxX3AeyQ9D3QB/ysimkoXdWHkeS7+AfiepE+TNGldNBJ/zEq6naRJd1p6ve1qoBogIm4kuf72fmA50Ar8zZDsdwSeSzMzGwFGYxOfmZkNA05QZmZWlpygzMysLDlBmZlZWXKCMjOzsuQEZSUjqUvSU5Kek/QTSWMHuP6WAZZfIOmcHPMbJN2QTl8k6Vvp9GWSLsiYv9dA9tdHHCeno4A/JWnMLmxntqSPZbzffhxDEOOHJR0yFNsaKpL+s6+YJJ0m6YRixmSF5QRlpbQ1IuZHxGFAO3BZ5sL0pr+Cf0YjYklEXJlj/o0R8YP07UXAkCQo4OPA9emxb92F7cwGtieo3o5jkD5MMjp32YiIT0TE830UOQ1wghpBnKCsXPwO2D+tFfxZ0neAJ4BZkj4q6dm0pvXVzJUkfUPSE0qeVTU9nfc/JC2W9LSk/8qqmb1b0u8kvSjpg2n50yTtNAispGskfSatdTUAt6W1ng9Iuiej3BmS7s6x/ulKnhP0rJLn6dRK+gTwV8CXJN2WVf6rkv42a///kCbqr6fH/6ykc9MiXwFOTmP6dOZxpOveIulhSSskXZmx3X+S9IKkByTdLukzWXGcAJwFfD3d9n6S5isZGPYZSfdImpzjeHdPlz2dvk5I5/99Gvtzkj6Vzuv5d/5eWpu8X9IYSXMl/Sljm7MlPZNOP6x0eCklz2l6It3Pg0qe2XYZ8Ok05pOz47NhqNTPGfFr9L6ALenfKuCnJM+bmg10A8ely/YiGU5melru18CH02UBfDyd/hLwrXR6asY+/gX4ZDq9APgVyQ+zA0jGD6sj+eX987TMRRnbuQb4TDr9MOkzoEgGxnwBmJ6+/zHwoaxjqyMZ3fnA9P0PgE9lxHFOjvNxJPCbjPfPA3sDfwk8QDKawe7p+dgzM+60fOZxXAP8EaglGRuuieTO/wbgKWAMyRiDL/UcY1YsO8QIPAOcmk5fC/xbjnUWZhxjJckYlkcBzwLjSEYkWZoe52ygE5iflr8TOD+dfgrYN53+HPDFzH+D9LPwBjAnnT8l+9/Lr5Hxcg3KSmmMpKeAJSRfujen81+L5JkyAEcDD0fEukgefXIbycPTIElkC9PpHwEnpdOHpbWkZ0ma0w7N2OedEdEdES+RjB938ECDjuTb8Ickj1mYBBzPzo8hOQh4JSJeTN/fmhF3b9t9EthN0l6S5gEbIuL19Lhuj4iuiFgD/IbkvPTnFxGxLSLeAtaSJLeTSAZ63RoRm4Gf9bcRSROBSRHxm36O5V3A/0mPpSsiNqX7uyciWiJiC3A30FO7eSUinkqnHydJWpAkq79Kp8/l7X/jHscBv41koFoiYiQO5GyMwrH4rKxsjYj5mTOUjPfXkjlrANvrGbdrAUkt62lJF5HULLLL9PY+X98n+XJvA36SJs9Mg33A5V0kAxTvQfKAvF3ZVubI810k/9+L/eDNvvaXHV9Ph5GFJGM/3k3ye+ClHNv0GG2jgGtQVu4eA06VNE1SJcnzd3p+yVeQfJlD0lng9+n0eGC1pGqSGlSmj0iqkLQfyaO8l+UZx+Z0uwBExCqSxwl8kSQhZnsBmC1p//T9X2fE3Zc7SAYnPockWUHymPlzJVWm19lOAf6UHVOefg98SFKdpHrgA72U277ttCa0IeO6Tm/H8iBJMy1prBPS2D8saaykccD/Q3K9sVcR8TJJwvondq49ATxC8pmYk+5rSnbMNjK4BmVlLSJWS/pH4CGSX873RsRP08UtwKGSHid56nFP54F/Iklsr5Fc/8j80lpG8uW6O3BZRLSltbb+LABulLQVOD6S3ne3kVyH2qlnWbrdvyGpCVSRPLrhxjyOd6mk8cDKePtxBfeQNCM+TVJz+GxEvCmpCeiU9HQa35N5bH+xpEXptl4jaV7dlKPoHSSjdF9JkiwvTI9/LEnTaK7Rqv9f4CZJl5AkmMsj4hFJC0gSKsB/RsSTaaeGviwkGUl/To5jWCfpUuBuJb081wJnkNRo75J0Nsl1xz4ToZU/j2ZuNkhK7pd6MiJu7rdwGZFUHxFb0mTzW+DSiHii1HGZZXMNymwQ0lpbC8nzgIabm5Tc8FoH3OrkZOXKNSgzMytL7iRhZmZlyQnKzMzKkhOUmZmVJScoMzMrS05QZmZWlv5/tAvKGbUfXpUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data2 = 11, 1, 'guilty'\n",
    "posterior2 = update(posterior1, data2)\n",
    "plot_marginals(posterior2)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And the third."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "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": [
    "data3 = 11, 1, 'guilty'\n",
    "posterior3 = update(posterior2, data3)\n",
    "plot_marginals(posterior3)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Since the first three verdicts were guilty, we infer that all 36 jurors voted to convict, so the estimated probabilities for both groups are high.\n",
    "\n",
    "The fourth trials ended in a mistrial due to a hung jury, which implies that at least one juror refused to vote to convict.  That decreases the estimated probabilities for both juror pools, but it has a bigger effect on the estimate for black jurors because the total prior data pertaining to black jurors is less, so the same amount of new data moves the needle more."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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pvC+myYmIeHdE7BcRC9LhvHT+HyLi+IiYn37emcs4c23t2rU9r8f40Y9+xDvf+c6eZVu3bmXChAlMmTKFt956i4ceStqJHH300axbt46lS5cCsG3btp53RR1yyCE88MADXHrppX7Vhpnl3dY89MMH7kkiL4455hjuvvtu5s2bx6ZNm7j66qt7ls2fP58TTjiBuXPn8rGPfaynKrCiooLFixdz7bXXMn/+fM455xxaW1t7tjvqqKO45557uOCCC1i9evi35szMhipfJSi/bmMUG+vnb2a58Yvl67jmh8/yyCfO4Mj9Ju3x/vy6DTMzGxE9Jagct+JzgjIzsyHJvO7d96D20GipwhyqsXreZpZ7jS0dlJeKqvLcppBRnaCqqqpoaGgYc3+sI4KGhgaqqqoKHYqZjUJbW5NeJHb1KMxIye1TVgU2c+ZM6urqGIv99FVVVTFz5qjre9fMikA+XrUBozxBlZeXM2fOnEKHYWY2qmxt6ch5AwkY5VV8ZmY28vLxqg1wgjIzsyHa2pr7172DE5SZmQ1R8qqN3N8hcoIyM7NBiwjfgzIzs+LT3N5FZ3f4HpSZmRWXra356SgWnKDMzGwIGvP0qg1wgjIzsyFobM5PR7HgBGVmZkOwtTU/HcWCE5SZmQ1B78sK3czczMyKSL5e9w5OUGZmNgSZEtQk34MyM7NisrW1g0mVZZSW5PZVG+AEZWZmQ5CvV22AE5SZmQ3B1pb8dBQLTlBmZjYEST98+XmVoBOUmZkNWuZ17/ngBGVmZoPme1BmZlaU8vU2XXCCMjOzQero6qapvSsv/fBBjhOUpHMlrZS0StLn+ln+SUkvSlou6VeSDsladpmkv6TDZbmM08zMBratpx++vbyRhKRS4JvAXwHHAhdLOrbPas8CNRExD7gfuCXddhpwA/AO4CTgBklTcxWrmZkNrOdVG+P3/hLUScCqiFgTEe3AvcD52StExGMR0ZxOPgXMTMffCzwaEZsiYjPwKHBuDmM1M7MBbG5uB/LTDx/kNkEdBLyeNV2XztuVK4CHhrKtpCsl1Uqqra+v38Nwzcxsdxq2JwlqxsTKvBwvlwmqv46aot8VpUuAGuBrQ9k2Iu6IiJqIqKmurh52oGZmNrBNTW0ATB8FCaoOmJU1PRNY13clSe8GrgfOi4i2oWxrZmb5szEtQU2fUJGX4+UyQS0FjpA0R1IFcBGwJHsFSScA3yZJThuyFj0MvEfS1LRxxHvSeWZmViAN29uZUFFKVXlpXo6Xs7aCEdEp6RqSxFIK3BURKyTdBNRGxBKSKr2JwI8lAayNiPMiYpOkL5MkOYCbImJTrmI1M7OBNTS15a16D3KYoAAi4kHgwT7zvpg1/u7dbHsXcFfuojMzs6Fo2N7O9In5qd4D9yRhZmaDtHF7G9Mn5K8E5QRlZmaDsqmpnRkuQZmZWTHp7g42NbmKz8zMiszW1g46u8NVfGZmVlx6noFyCcrMzIpJw/a0FwmXoMzMrJg0NLkEZWZmRcgJyszMilKmim/aeCcoMzMrIg3b25k6vpyy0vylDScoMzMbUENTG9Py1It5hhOUmZkNaOP29rx2FAtOUGZmNggN29vy2s0ROEGZmdkgNDS15/UZKHCCMjOzAXR2dbOluSOvTczBCcrMzAawqTnzDJRLUGZmVkQa0n74ZrgVn5mZFZNMgnIzczMzKyoNTWlHsa7iMzOzYpJ51YabmZuZWVHZ1NRGWYmYXFWe1+M6QZmZ2W41bG9n2oQKSkqU1+M6QZmZ2W4VopsjcIIyM7MBNDS1MT3PLfjACcrMzAbQsL09771IgBOUmZkNoGF7W9774QMnKDMz243Wji6a2rtcgjIzs+LS0FSYZ6AgxwlK0rmSVkpaJelz/Sw/Q9IzkjolLeyzrEvSc+mwJJdxmplZ/xq2p71IFKCKryxXO5ZUCnwTOAeoA5ZKWhIRL2attha4HPh0P7toiYgFuYrPzMwGlumHrxBVfDlLUMBJwKqIWAMg6V7gfKAnQUXEq+my7hzGYWZmw7SxgCWoXFbxHQS8njVdl84brCpJtZKekvSh/laQdGW6Tm19ff2exGpmZv3I3IMabY0k+usTI4aw/cERUQN8BPh3SYfttLOIOyKiJiJqqqurhxunmZntwoatbYwrL2V8RWnej53LBFUHzMqangmsG+zGEbEu/VwDPA6cMJLBmZnZwNY3tnDAPlVI+e2HD3KboJYCR0iaI6kCuAgYVGs8SVMlVabjM4DTyLp3ZWZm+bGusZWD9hlXkGPvNkFJeiRr/B+HsuOI6ASuAR4G/gzcFxErJN0k6bx0nydKqgMuAL4taUW6+TFAraRlwGPAV/q0/jMzszxYv6WFA6ZUFeTYA7Xiy76xcwHwL0PZeUQ8CDzYZ94Xs8aXklT99d3uD8DxQzmWmZmNrPbObuq3t3HAlCIsQTG0Rg1mZjaKvLW1lQg4cJ/iLEEdmvbioKzxHhFxXs4iMzOzglrf2ApQsBLUQAnq/KzxW3MZiJmZFZf1jS1AkZagIuKJzLik6nSen4g1MxsD1m0pbAlqoFZ8knSDpI3AS8DLkuolfXF325mZ2d5v3ZYWpowrZ0JlLnvF27WBGkl8HHgncGJETI+IqcA7gNMkfSLn0ZmZWcGsbyxcE3MYOEFdClwcEa9kZqQ9O1ySLjMzs1Fq3ZZWDizQQ7owcIIqj4iNfWem96HKcxOSmZkVg2IvQbUPc5mZme3FWtq72NzcUdAS1EB3vuZL2kpvz+SZB3cFFC6tmplZTmWamBeyBDVQM/P8969uZmYFV+iHdGGABCWpCrgKOBxYDtyVdgJrZmaj2LotSQmqUD2Zw8D3oO4GaoDngfcBX895RGZmVnCZh3T3m5L/V71nDHQP6tiIOB5A0p3An3IfkpmZFdr6xhZmTKyksqxwd3oGKkF1ZEZctWdmNnasa2wtWB98GYNtxQdJy71xWa36IiIm5zQ6MzMriPVbWji0ekJBY3ArPjMz28n6xlZOO3xGQWMYqIrPzMzGmK2tHWxv6yx4FZ8TlJmZ7WB9gV+zkeEEZWZmO1jX86JCJygzMysimYd0XcVnZmZFZf2WVkpLxL6TnKDMzKyIrGtsYb9JlZSWaOCVc8gJyszMdrB+SysHFPj+EzhBmZlZH+saWwreQAKcoMzMLEtbZxevb2pmzvTxhQ7FCcrMzHqtbWimO+CwfScWOpTcJihJ50paKWmVpM/1s/wMSc9I6pS0sM+yyyT9JR0uy2WcZmaWWF3fBMChM0ZxgpJUCnwT+CvgWOBiScf2WW0tcDnwwz7bTgNuAN4BnATcIGlqrmI1M7PE6vrtAMwpcEexkNsS1EnAqohYExHtwL3A+dkrRMSrEbEc6O6z7XuBRyNiU0RsBh4Fzs1hrGZmBqypb2K/yZVMrBzoZRe5l8sEdRDwetZ0XTpvxLaVdKWkWkm19fX1ww7UzMwSazZuL4rqPchtgurvCa8YyW0j4o6IqImImurq6iEFZ2ZmO4oI1tQ3cdi+ha/eg9wmqDpgVtb0TGBdHrY1M7NhaGhqp7GlY0yUoJYCR0iaI6kCuAhYMshtHwbeI2lq2jjiPek8MzPLkTWZFnxF0EACcpigIqITuIYksfwZuC8iVki6SdJ5AJJOlFQHXAB8W9KKdNtNwJdJktxS4KZ0npmZ5ciatAXfYdXFUYLKaTONiHgQeLDPvC9mjS8lqb7rb9u7gLtyGZ+ZmfVas7GJyrKSoujmCNyThJmZpVZv2M6cGRMK3ot5hhOUmZkBSQmqWO4/gROUmZkB7Z3drN3UXDQt+MAJyszMgLWbmunqDpegzMysuKwushZ84ARlZmYU3zNQ4ARlZmYkz0BVT6pkUlV5oUPp4QRlZmZJC74ZxVN6AicoMzMjuQdVDG/RzeYEZWY2xm1qamdLc4dLUGZmVlxWvrkNgMNdgjIzs2KyvG4LAPNm7lPgSHbkBGVmNsYtr2tk5tRxTJtQUehQduAEZWY2xi2r28L8Iis9gROUmdmY1rC9jbrNLcybOaXQoezECcrMbAxb/kYjUHz3n8AJysxsTFv2+hYkON4lKDMzKybL6xo5rHoiEytz+oL1YXGCMjMboyKC5XVbivL+EzhBmZmNWesaW9m4vZ0Fs4rv/hM4QZmZjVnLXy/OB3QznKDMzMaoZXWNlJeKYw6YVOhQ+uUEZWY2Ri17fQtH7z+ZyrLSQofSLycoM7MxqLs7eOGNxqJtIAFOUGZmY9KajU1sa+ssyi6OMpygzMzGoJ4ezGe5BGVmZkWk9rXNTKgo5fDq4noHVDYnKDOzMSYieGJlPacePoOy0uJNAzmNTNK5klZKWiXpc/0sr5S0OF3+R0mz0/mzJbVIei4dbs9lnGZmY8nq+u28saWFM4+sLnQou5WzzpcklQLfBM4B6oClkpZExItZq10BbI6IwyVdBHwVuDBdtjoiFuQqPjOzserxlfUAnHVUcSeoXJagTgJWRcSaiGgH7gXO77PO+cDd6fj9wNmSlMOYzMzGvCderufwfScyc+r4QoeyW7lMUAcBr2dN16Xz+l0nIjqBRmB6umyOpGclPSHp9P4OIOlKSbWSauvr60c2ejOzUai5vZM/rtnEWUVevQe5TVD9lYRikOusBw6OiBOATwI/lDR5pxUj7oiImoioqa4u/ottZlZoT65uoL2rmzOLvHoPcpug6oBZWdMzgXW7WkdSGTAF2BQRbRHRABARTwOrgSNzGKuZ2ZjwxMv1jCsv5aQ50wodyoBymaCWAkdImiOpArgIWNJnnSXAZen4QuDXERGSqtNGFkg6FDgCWJPDWM3MRr2I4PGV9Zx62PSi7X8vW84SVHpP6RrgYeDPwH0RsULSTZLOS1e7E5guaRVJVV6mKfoZwHJJy0gaT1wVEZtyFauZ2VjwakMzazc17xXVe5DDZuYAEfEg8GCfeV/MGm8FLuhnu58AP8llbGZmY83jKzcAcNaR+xY4ksEp3keIzcxsRD2+sp5DZ0zg4OnF3bw8wwnKzGwM2Li9jT+s3sjZx+wdpSdwgjIzGxN++swbdHQFH66ZNfDKRcIJysxslIsI7l26lrcdvA9H7Fecr3fvjxOUmdko98zazayub+KiEw8udChD4gRlZjbK3fun15lQUcr75x1Q6FCGxAnKzGwU29bawS+Wr+e8BQcyoTKnTxaNOCcoM7NR7OfL1tPS0cWFe1n1HjhBmZmNaouXruXo/Scxf+aUQocyZE5QZmaj1LLXt7CsrpEP18xib3zVnhOUmdkoFBF89b9fYtqECi6omVnocIbFCcrMbBT6zV828ofVDVz7rsOZVFVe6HCGxQnKzGyU6e4OvvLQS8yaNo6PvGPvaxyR4QRlZjbKLFm2jj+v38qn33PUXvHep11xgjIzG0XaOru49ZGVzD1wMh+cd2Chw9kje9dTW2ZmuxMB7U3Qti0Z2renQ1Pv0NGcDi3J0NmaDm3JZ1cHdLUnn92d0N2VfEYXRDcEpP8AAglUAiVlUFIKJeVQVgGl6VA+LhnKxkHFBKicCBUToXIyVE2BcftA1T4wfhqMmwqle3a/6K7fvUrd5hb+5a+Pp6Rk72u5l80JysyKS3c3tG6Bls39D62N0LIl+cwe2hqTpBTdgzyQoHw8lFdBWRWUVUJpZW9yKSlPkk5ZVZp4ypJtVJIkpQgg0qTV3ZvIujuTODrbkkSXSYQdLdDRNHB8VVNgwr4wMR0mHQCTD0yGKbNgn4OT5SU7V4A9s3YzX39kJefO3Z/Tj9g73pq7O05QZpZb7U3QtDEZmjdCc0M63pAOm7LGG5LktLs/4hWT0lLHlGTYZxZUHZeWSCZD5aR0mJyUVCompENmfHySmEorkkSTTxFJomrfniSx1jTRNm9Kkm/zpuQaNdXD9g2wfjm8/HBS4stWVpUkq2mHwvTDYfqhbJ94KF/4ry0cMGUKX104L7/nlSNOUGY2NF2daZKph6YNafJJ/6BmxpvqexNS3z+uGSXlMGEGjJ+eVG3tNzcZHz8Nxk3r/Rw3tXeomgKle/GfLSlJkBXjk9LRYEQkSWzrOmh8HbashS2vweZXoWENvPIb6GxhIvBLoLNyKmX3zoX9j4f9j0s+9z12j6sOC2Ev/kmb2Yjp6shKMunn9rey5m2A7R3McYwAABGaSURBVGniaW6g9x5MlpJymFANE6YnVVAzjkwS0IQZMD77c3ryWTkp/yWYvZGUlBjH7QP7Hbvz8u5uvv/okzz8xG+57rgOTppYD2+tgGfu7v1yUFaVJKqD3g4zT4SDT4EpB+X3PIbBCcpstOpsTxNM30SzYcdE1LQhqV7qT/mE3nsh0w+Dg09OxidU9w4T902ST9U+TjgFsOjJ17jxsS287/hzOPHit/X+DLq7YNMrsP45WPcsvPEMPPM9+OPtyfIps5JENeeMZJh6SOFOYhcU0c83ob1QTU1N1NbWFjoMs9zqaMmqStvQp3ST/bkhub/Rn4pJMLF6xxvxE/bdcV4m8VRMyO/52aBFBN96fDVfe3gl7527H7ddfMLAzzx1dcJbL8Dap2Dtk/Da75MvKgBTZ8Nh74LDz0kSVuXEnJ9DhqSnI6Jmp/lOUGYF1N2d3hzf1X2c+qxkVA/t2/rfT+WUpBSTnVx2SkDpsorx+T1HG3Hd3cEtD6/k9idW8z9POIivLZxHWekwHmuNgPqXkvtYax6HNU8kLQ1LK2D2O+HoD8BR74PJuX3RoROUWT5kmkhnGgj0fDb0TvcknfR+TnT1syMlDQYy1WcT0tJNTxLKKvFMqE6aStuYULe5mc/+ZDm/X9XAR99xMF8+/7iRe96psz0pWf3lEVj5IGxak8yfeRIc99dw7IdykqycoMyGKgLatqZNfzdBy6Z+mkZvTMYzzaZbNu26iXTllLQBQXVvo4EJM3oTT09C2jdpwVay93ZRYyMvIvjRn17n5l++CMD17z+Wi0/K4Ws0IqB+Jbz0c3jxZ/Dm84CSktW8C2Huh5KGLiPACcrGrojeZ056HvjMjGeeP9ncO51JRi2bk4cu+6PSpNlzJrGMn7ZjS7Xx03tbq2XWKavM73nbqNDdHTzy4pt86/HVLK9r5NTDpnPLwnnMnJrnqtr6l2HFA/D8j6FhVfIs2THnwdv+Jklae2BXCcqt+Gzv0NkGrVt7ewzYVW8CrVvS+X0++61GS5WNS5JNpquZ6qN2fBZn/PR0PJOIpiWloX6e5DcbKZub2nnohTe583drWF3fxCHTx3PLwnksfNvMwnRhVH0knPU5OPOzUFcLz90DLzyQ/N/awwS1K05QljsRyXMYbdt7n5zPfLZtT6rPMn2m9Qxbe+e3puOtW6GrbffHUmlW7wLpMyP7HJI+PzK1d964aTv3fVY+Lj/Xw2w3IoJXG5p5ak0DDz6/nidXN9DZHRy9/yRuu/gE3nfc/sNrCDHSJJh1YjKc+y/J/88cyWmCknQu8P8CpcB/RsRX+iyvBL4HvB1oAC6MiFfTZf8IXAF0AddFxMO5jHVMikge0Oxs2bG/sB2mm6G9OWnZ0552spnpcLNnfrqsb6ec7dvp94HOvlSS1GVXTEq7qpmcVI1NOzSr+5rJvV3bZI9nhooJfgbH9hqtHV281tDMqg3bWbVhOyvWNfLM2s1s3N4OwCHTx/P3ZxzK+48/gLkHTi7e17VnOsLNkZwlKEmlwDeBc4A6YKmkJRHxYtZqVwCbI+JwSRcBXwUulHQscBEwFzgQ+P8kHRmxu3qaIhCRPBwX3Umxt7ur97NnvHPHHpK7O9Nek7uguyMdTz93GG/vndfVnpQoOvt+pp1TdrZl9czcnnx2ZPfY3NI7PZxLWlqZ9mc2IaufswlJp5aZnpozfZ9VZsYnJeOVk9L5k3rHnVysSEUE3QFd3UF3BJ3dQVdX0NHdTUdXNx2dQXtXN60dXbR1dtHW0U1TexdNbZ1sa+tkW2sHW5o72NzUzubmdt7c2sr6La00NLX3HEOCQ6aN54wjq6k5ZBonzp7K4ftOLN6klEe5LEGdBKyKiDUAku4FzgeyE9T5wI3p+P3AN5T8VM4H7o2INuAVSavS/T2Zq2D/+M0rOKr+v3umRaD0k6zx3vndCCihGxGUMdgelEdWB6V0UEY75bsc2qigjfF0MIVWKtLpCtoop1WVPdOtVNJCZTq+43QLVbRQSSuVdEUptJEMQ9aaDhtH9DrY6DXYZlzZ7b36Nv7KfkNGZK0T6XZBpJ+9Sak7gpFoQ1ZZVsLU8RVMnVDB/pMrmTdzH/afXMUh08dz+L4TOXTGRMZVuMVmf3KZoA4CXs+argPesat1IqJTUiMwPZ3/VJ9td+o4StKVwJUABx+8Z681Lp11Ii/1/W1UJh3tmKKQ6KaEUCZVlRAqScZVQpAM3SqhW6V0U0r0jJcQKqVLZcl0urxbZXQp81lGl8rTz2S8Z35JOZ090+XpcUfOuHQwKyaDLUvsrtQhgdI9ZVZTZr7SJYJSiRIJCUokSktEiaC0pISykmS6rFSUl5akg6gqL6WyrISq8lLGV5QysbKMiZVlTKoqd/LZA7lMUP39pvT9PrKrdQazLRFxB3AHJM3MhxpgtprzrgKu2pNdmJnZCMplk5A6YFbW9Exg3a7WkVQGTAE2DXJbMzMbxXKZoJYCR0iaI6mCpNHDkj7rLAEuS8cXAr+OpPJ4CXCRpEpJc4AjgD/lMFYzMysyOaviS+8pXQM8TNLM/K6IWCHpJqA2IpYAdwLfTxtBbCJJYqTr3UfSoKIT+L+KvgWfmZmNKHd1ZGZmBbWrro6K4LFkMzOznTlBmZlZUXKCMjOzouQEZWZmRWnUNJKQVA+8toe7mYH74Mnwtejla5Hwdejla9FrJK7FIRFR3XfmqElQI0FSbX8tScYiX4tevhYJX4devha9cnktXMVnZmZFyQnKzMyKkhPUju4odABFxNeil69Fwtehl69Fr5xdC9+DMjOzouQSlJmZFSUnKDMzK0pjMkFJOlfSSkmrJH2un+WVkhany/8oaXb+o8yPQVyLT0p6UdJySb+SdEgh4sy1ga5D1noLJYWkUdvEeDDXQtKH09+LFZJ+mO8Y82UQ/z8OlvSYpGfT/yPvK0ScuSbpLkkbJL2wi+WSdFt6nZZLetuIHDgixtRA8uqP1cChQAWwDDi2zzr/ANyejl8ELC503AW8Fv8DGJ+OXz0ar8VgrkO63iTgN8BTQE2h4y7g78QRwLPA1HR630LHXcBrcQdwdTp+LPBqoePO0bU4A3gb8MIulr8PeIjkbegnA38cieOOxRLUScCqiFgTEe3AvcD5fdY5H7g7Hb8fOFtSf6+h39sNeC0i4rGIaE4nnyJ5u/FoM5jfCYAvA7cArfkMLs8Gcy3+HvhmRGwGiIgNeY4xXwZzLQKYnI5PYZS++TsifkPyzr5dOR/4XiSeAvaRdMCeHncsJqiDgNezpuvSef2uExGdQCMwPS/R5ddgrkW2K0i+JY02A14HSScAsyLiF/kMrAAG8ztxJHCkpN9LekrSuXmLLr8Gcy1uBC6RVAc8CFybn9CKzlD/lgxKzt6oW8T6Kwn1bWs/mHVGg0Gfp6RLgBrgzJxGVBi7vQ6SSoB/Ay7PV0AFNJjfiTKSar6zSErUv5V0XERsyXFs+TaYa3ExsCgivi7pFJI3hB8XEd25D6+o5ORv5lgsQdUBs7KmZ7JzsbxnHUllJEX33RVv91aDuRZIejdwPXBeRLTlKbZ8Gug6TAKOAx6X9CpJHfuSUdpQYrD/P34WER0R8QqwkiRhjTaDuRZXAPcBRMSTQBVJ56ljzaD+lgzVWExQS4EjJM2RVEHSCGJJn3WWAJel4wuBX0d6J3CUGfBapFVb3yZJTqP1XsNur0NENEbEjIiYHRGzSe7FnRcRtYUJN6cG8//jv0gazyBpBkmV35q8Rpkfg7kWa4GzASQdQ5Kg6vMaZXFYAlyatuY7GWiMiPV7utMxV8UXEZ2SrgEeJmmlc1dErJB0E1AbEUuAO0mK6qtISk4XFS7i3BnktfgaMBH4cdpOZG1EnFewoHNgkNdhTBjktXgYeI+kF4Eu4H9HREPhos6NQV6LTwHfkfQJkiqty0fjl1lJPyKp0p2R3m+7ASgHiIjbSe6/vQ9YBTQDfzsixx2F19LMzEaBsVjFZ2ZmewEnKDMzK0pOUGZmVpScoMzMrCg5QZmZWVFygrKCkdQl6TlJL0j6saTxQ9x++xDXXyRpYT/zayTdlo5fLukb6fhVki7Nmn/gUI63mzhOT3sBf07SuD3Yz2xJH8ma7jmPEYjxQ5KOHYl9jRRJ/7m7mCSdJenUfMZkueUEZYXUEhELIuI4oB24Knth+tBfzn9HI6I2Iq7rZ/7tEfG9dPJyYEQSFPBR4Nb03Fv2YD+zgZ4EtavzGKYPkfTOXTQi4u8i4sXdrHIW4AQ1ijhBWbH4LXB4Wir4s6RvAc8AsyRdLOn5tKT11eyNJH1d0jNK3lVVnc77e0lLJS2T9JM+JbN3S/qtpJclfSBd/yxJO3UCK+lGSZ9OS101wD1pqef9kn6atd45kh7oZ/uzlbwn6Hkl79OplPR3wIeBL0q6p8/6X5X0D32O/6k0UX8tPf/nJV2YrvIV4PQ0pk9kn0e67V2SHpe0RtJ1Wfv9gqSXJD0q6UeSPt0njlOB84Cvpfs+TNICJR3DLpf0U0lT+znf/dJly9Lh1HT+J9PYX5D08XRe5uf8nbQ0+YikcZKOkfSnrH3OlrQ8HX9cafdSSt7T9Ex6nF8peWfbVcAn0phP7xuf7YUK/Z4RD2N3ALann2XAz0jeNzUb6AZOTpcdSNKdTHW63q+BD6XLAvhoOv5F4Bvp+PSsY/wzcG06vgj4b5IvZkeQ9B9WRfLN+xfpOpdn7edG4NPp+OOk74Ai6RjzJaA6nf4h8ME+51ZF0rvzken094CPZ8WxsJ/rcQLwRNb0i8DBwP8CHiXpzWC/9HockB13un72edwI/AGoJOkbroHkyf8a4DlgHEkfg3/JnGOfWHaIEVgOnJmO3wT8ez/bLM46x1KSPizfDjwPTCDpkWRFep6zgU5gQbr+fcAl6fhzwKHp+GeBz2f/DNLfhdeBOen8aX1/Xh5Gx+ASlBXSOEnPAbUkf3TvTOe/Fsk7ZQBOBB6PiPpIXn1yD8nL0yBJZIvT8R8A70zHj0tLSc+TVKfNzTrmfRHRHRF/Iek/7uihBh3JX8Pvk7xmYR/gFHZ+DclRwCsR8XI6fXdW3Lva77PAvpIOlDQf2BwRa9Pz+lFEdEXEW8ATJNdlIL+MiLaI2AhsIElu7yTp6LUlIrYBPx9oJ5KmAPtExBMDnMu7gP+TnktXRDSmx/tpRDRFxHbgASBTunklIp5Lx58mSVqQJKsPp+MX0vszzjgZ+E0kHdUSEaOxI2djDPbFZ0WlJSIWZM9Q0t9fU/asIewv02/XIpJS1jJJl5OULPqus6vpwfouyR/3VuDHafLMNtwXXN5P0kHx/iQvyNuTfWX3PN9F8v893y/e3N3x+saXaTCymKTvxwdIvg/8pZ99uo+2McAlKCt2fwTOlDRDUinJ+3cy3+RLSP6YQ9JY4Hfp+CRgvaRykhJUtgsklUg6jORV3isHGce2dL8ARMQ6ktcJfJ4kIfb1EjBb0uHp9N9kxb0795J0TryQJFlB8pr5CyWVpvfZzgD+1DemQfod8EFJVZImAu/fxXo9+05LQpuz7uvs6lx+RVJNSxrr5DT2D0kaL2kC8D9J7jfuUkSsJklYX2Dn0hPAkyS/E3PSY03rG7ONDi5BWVGLiPWS/hF4jOSb84MR8bN0cRMwV9LTJG89zjQe+AJJYnuN5P5H9h+tlSR/XPcDroqI1rTUNpBFwO2SWoBTIml9dw/JfaidWpal+/1bkpJAGcmrG24fxPmukDQJeCN6X1fwU5JqxGUkJYfPRMSbkhqATknL0vieHcT+l0paku7rNZLq1cZ+Vr2XpJfu60iS5WXp+Y8nqRrtr7fq/xu4Q9IVJAnm6oh4UtIikoQK8J8R8WzaqGF3FpP0pD+nn3Ool3Ql8ICSVp4bgHNISrT3Szqf5L7jbhOhFT/3Zm42TEqel3o2Iu4ccOUiImliRGxPk81vgCsj4plCx2XWl0tQZsOQltqaSN4HtLe5Q8kDr1XA3U5OVqxcgjIzs6LkRhJmZlaUnKDMzKwoOUGZmVlRcoIyM7Oi5ARlZmZF6f8HQ6Cbh9BCd14AAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "data4 = 7, 5, 'hung'\n",
    "posterior4 = update(posterior3, data4)\n",
    "plot_marginals(posterior4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The effect of the fifth trial is similar; it decreases the estimates for both pools, but the effect on the estimate for black jurors is greater."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "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": [
    "data5 = 9, 3, 'hung'\n",
    "posterior5 = update(posterior4, data5)\n",
    "plot_marginals(posterior5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, here are the posterior distributions after all six trials."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "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": [
    "data6 = 11, 1, 'guilty'\n",
    "posterior6 = update(posterior5, data6)\n",
    "plot_marginals(posterior6)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distributions for the two pools are substantially different.  Here are the posterior means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9795476889311339, 0.6802593488434)"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marginal_p1 = pmf_marginal(posterior6, 0)\n",
    "marginal_p2 = pmf_marginal(posterior6, 1)\n",
    "\n",
    "marginal_p1.mean(), marginal_p2.mean(), "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Based on the outcomes of all six trials, we estimate that the probability is 98% that a white juror would vote to convict, and the probability is 68% that a black juror would vote to convict.\n",
    "\n",
    "Again, those results are based on the modeling simplifications that\n",
    "\n",
    "* All six juries saw essentially the same evidence,\n",
    "\n",
    "* The probabilities we're estimating did not change over the period of the trials, and\n",
    "\n",
    "* Interactions between jurors did not have substantial effects on their votes."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Prediction\n",
    "\n",
    "Now we can use the joint posterior distribution to estimate the probability of conviction as a function of the composition of the jury.\n",
    "\n",
    "I'll draw a sample from the joint posterior distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "sample = posterior6.sample(1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the probability that white jurors were more likely to convict."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.889"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.mean([p1 > p2 for p1, p2 in sample])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following function takes this sample and a hypothetical composition and returns the posterior predictive distribution for the probability of conviction."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "def prob_guilty(sample, n1, n2):\n",
    "    ps = [p1**n1 * p2**n2 for p1, p2 in sample]\n",
    "    return Pmf.from_seq(ps)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to [Wikipedia](https://en.wikipedia.org/wiki/Montgomery_County,_Mississippi):\n",
    "\n",
    "> As of the 2010 United States Census, there were 10,925 people living in the county. 53.0% were White, 45.5% Black or African American, 0.4% Asian, 0.1% Native American, 0.5% of some other race and 0.5% of two or more races. 0.9% were Hispanic or Latino (of any race).\n",
    "\n",
    "A jury drawn at random from the population of Montgomery County would be expected to have 5 or 6 black jurors.\n",
    "\n",
    "Here's the probability of conviction with a panel of 7 white and 5 black jurors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.1536247710661592, array([2.47609900e-04, 5.72165499e-01]))"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf = prob_guilty(sample, 7, 5)\n",
    "pmf.mean(), pmf.credible_interval(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And with 6 white and 6 black jurors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.14068070740861993, array([5.00964985e-05, 5.70871197e-01]))"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf = prob_guilty(sample, 6, 6)\n",
    "pmf.mean(), pmf.credible_interval(0.9)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "With a jury that represents the population of Montgomery County, the probability Flowers would be convicted is 14-15%.\n",
    "\n",
    "However, notice that the credible intervals for these estimates are quite wide.  Based on the data, the actual probabilities could be in the range from near 0 to 50%."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The following figure shows the probability of conviction as a function of the number of black jurors.\n",
    "\n",
    "The probability of conviction is highest with an all-white jury, and drops quickly if there are a few black jurors.  After that, the addition of more black jurors has a relatively small effect.\n",
    "\n",
    "These results suggest that all-white juries have a substantially higher probability of convicting a defendant, compared to a jury with even a few non-white jurors."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "pmf_seq = []\n",
    "n2s = range(0, 13)\n",
    "\n",
    "for n2 in n2s:\n",
    "    n1 = 12 - n2\n",
    "    pmf = prob_guilty(sample, n1, n2)\n",
    "    pmf_seq.append(pmf)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[0.5538327053225913,\n",
       " 0.3418368780199899,\n",
       " 0.25039614520645626,\n",
       " 0.20187886989068096,\n",
       " 0.1726469824064479,\n",
       " 0.1536247710661592,\n",
       " 0.14068070740861993,\n",
       " 0.13168895287399013,\n",
       " 0.12545481771765174,\n",
       " 0.12126313084374142,\n",
       " 0.1186668473680227,\n",
       " 0.11737944315539342,\n",
       " 0.11721642419343986]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "means = [pmf.mean() for pmf in pmf_seq]\n",
    "lows = [pmf.quantile(0.05) for pmf in pmf_seq]\n",
    "highs = [pmf.quantile(0.95) for pmf in pmf_seq]\n",
    "\n",
    "means"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "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": [
    "plt.plot(n2s, means)\n",
    "plt.fill_between(n2s, lows, highs, color='C0', alpha=0.1)\n",
    "\n",
    "decorate(xlabel='Number of black jurors',\n",
    "         ylabel='Probability of a guilty verdict',\n",
    "         title='Probability of a guilty verdict vs jury composition',\n",
    "         ylim=[0, 1])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Double Check\n",
    "\n",
    "Let's compute the results a different way to double check.\n",
    "\n",
    "For the four guilty verdicts, we don't need to make or update the joint distribution; we can update the distributions for the two pools separately."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.stats import binom\n",
    "\n",
    "k1 = 12 + 11 + 11 + 11\n",
    "like1 = binom(k1, ps).pmf(k1)\n",
    "prior_p1 = Pmf(like1, ps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "k2 = 0 + 1 + 1 + 1\n",
    "like2 = binom(k2, ps).pmf(k2)\n",
    "prior_p2 = Pmf(like2, ps)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "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": [
    "prior_p1.plot()\n",
    "prior_p2.plot()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use the posteriors from those updates as priors and update them based on the two trials that resulted in a hung jury."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "prior = Pmf(make_joint(prior_p2, prior_p1).stack())\n",
    "posterior = update(prior, data4)\n",
    "posterior = update(posterior, data5)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior marginals look the same."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "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": [
    "plot_marginals(posterior)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And yield the same posterior means."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(0.9795476889311339, 0.6802593488434)"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "marginal_p1 = pmf_marginal(posterior, 0)\n",
    "marginal_p2 = pmf_marginal(posterior, 1)\n",
    "\n",
    "marginal_p1.mean(), marginal_p2.mean(), "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the probability that a fair jury would convict four times out of six."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.0054864843750000005"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "binom.pmf(4, 6, 0.15)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.7"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}