{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# The Lincoln Index Problem"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "tags": [
     "remove-cell"
    ]
   },
   "source": [
    "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": {
    "tags": [
     "remove-cell"
    ]
   },
   "outputs": [],
   "source": [
    "# If we're running on Colab, install libraries\n",
    "\n",
    "import sys\n",
    "IN_COLAB = 'google.colab' in sys.modules\n",
    "\n",
    "if IN_COLAB:\n",
    "    !pip install pymc3\n",
    "    !pip install arviz\n",
    "    !pip install graphviz"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "In [an excellent blog post](http://www.johndcook.com/blog/2010/07/13/lincoln-index/), John D. Cook wrote about the Lincoln index, which is a way to estimate the\n",
    "number of errors in a document (or program) by comparing results from\n",
    "two independent testers. \n",
    "\n",
    "Here's his presentation of the problem:\n",
    "\n",
    ">\"Suppose you have a tester who finds 20 bugs in your program. You\n",
    "want to estimate how many bugs are really in the program. You know\n",
    "there are at least 20 bugs, and if you have supreme confidence in your\n",
    "tester, you may suppose there are around 20 bugs. But maybe your\n",
    "tester isn't very good. Maybe there are hundreds of bugs. How can you\n",
    "have any idea how many bugs there are? There's no way to know with one\n",
    "tester. But if you have two testers, you can get a good idea, even if\n",
    "you don't know how skilled the testers are.\"\n",
    "\n",
    "Suppose the first tester finds 20 bugs, the second finds 15, and they\n",
    "find 3 in common; how can we estimate the number of bugs?\n",
    "\n",
    "I'll use the following notation for the data:\n",
    "\n",
    "For this model, I'll express the data in different notation:\n",
    "\n",
    "* k11 is the number of bugs found by both testers,\n",
    "\n",
    "* k10 is the number of bugs found by the first tester but not the second,\n",
    "\n",
    "* k01 is the number of bugs found by the second tester but not the first, and\n",
    "\n",
    "* k00 is the unknown number of undiscovered bugs.\n",
    "\n",
    "Here are the values for all but `k00`:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "k10 = 20 - 3\n",
    "k01 = 15 - 3\n",
    "k11 = 3"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "32"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "num_seen = k01 + k10 + k11\n",
    "num_seen"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here's the model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pymc3 as pm\n",
    "\n",
    "with pm.Model() as model5:\n",
    "    p0 = pm.Beta('p0', alpha=1, beta=1)\n",
    "    p1 = pm.Beta('p1', alpha=1, beta=1)\n",
    "    N = pm.DiscreteUniform('N', num_seen, 350)\n",
    "    \n",
    "    q0 = 1-p0\n",
    "    q1 = 1-p1\n",
    "    ps = [q0*q1, q0*p1, p0*q1, p0*p1]\n",
    "    \n",
    "    k00 = N - num_seen\n",
    "    data = pm.math.stack((k00, k01, k10, k11))\n",
    "    y = pm.Multinomial('y', n=N, p=ps, observed=data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "CompoundStep\n",
      ">NUTS: [p1, p0]\n",
      ">Metropolis: [N]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 2000/2000 [00:01<00:00, 1577.49draws/s]\n",
      "The rhat statistic is larger than 1.05 for some parameters. This indicates slight problems during sampling.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with model5:\n",
    "    trace5 = pm.sample(500)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 1490.4x331.2 with 3 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model5:\n",
    "    pm.plot_posterior(trace5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'int' object has no attribute 'astype'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-6-5ba0275a3a86>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[1;32m      1\u001b[0m \u001b[0;32mwith\u001b[0m \u001b[0mmodel5\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 2\u001b[0;31m     \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtraceplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mtrace5\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/envs/ThinkBayes2/lib/python3.8/site-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36mwrapped\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     21\u001b[0m                 \u001b[0mwarnings\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarn\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mformat\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mnew\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     22\u001b[0m                 \u001b[0mkwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mnew\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 23\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mfunc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     24\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mwrapped\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     25\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/ThinkBayes2/lib/python3.8/site-packages/pymc3/plots/__init__.py\u001b[0m in \u001b[0;36mtraceplot\u001b[0;34m(*args, **kwargs)\u001b[0m\n\u001b[1;32m     39\u001b[0m     \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     40\u001b[0m         \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetdefault\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'compact'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 41\u001b[0;31m         \u001b[0;32mreturn\u001b[0m \u001b[0maz\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot_trace\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     42\u001b[0m     \u001b[0;32mexcept\u001b[0m \u001b[0mTypeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     43\u001b[0m         \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'compact'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/ThinkBayes2/lib/python3.8/site-packages/arviz/plots/traceplot.py\u001b[0m in \u001b[0;36mplot_trace\u001b[0;34m(data, var_names, coords, divergences, figsize, rug, lines, compact, combined, legend, plot_kwargs, fill_kwargs, rug_kwargs, hist_kwargs, trace_kwargs, backend, backend_kwargs, show)\u001b[0m\n\u001b[1;32m    216\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    217\u001b[0m     \u001b[0mplot\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mget_plotting_function\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"plot_trace\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"traceplot\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbackend\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 218\u001b[0;31m     \u001b[0maxes\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mtrace_plot_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    219\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    220\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0maxes\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/ThinkBayes2/lib/python3.8/site-packages/arviz/plots/backends/matplotlib/traceplot.py\u001b[0m in \u001b[0;36mplot_trace\u001b[0;34m(data, var_names, divergences, figsize, rug, lines, combined, legend, plot_kwargs, fill_kwargs, rug_kwargs, hist_kwargs, trace_kwargs, plotters, divergence_data, colors, backend_kwargs, show)\u001b[0m\n\u001b[1;32m    129\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    130\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvalue\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mshape\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;36m2\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 131\u001b[0;31m             _plot_chains_mpl(\n\u001b[0m\u001b[1;32m    132\u001b[0m                 \u001b[0maxes\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m                 \u001b[0midx\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/ThinkBayes2/lib/python3.8/site-packages/arviz/plots/backends/matplotlib/traceplot.py\u001b[0m in \u001b[0;36m_plot_chains_mpl\u001b[0;34m(axes, idx, value, data, colors, combined, xt_labelsize, rug, trace_kwargs, hist_kwargs, plot_kwargs, fill_kwargs, rug_kwargs)\u001b[0m\n\u001b[1;32m    262\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mcombined\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    263\u001b[0m             \u001b[0mplot_kwargs\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m\"color\"\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcolors\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mchain_idx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 264\u001b[0;31m             plot_dist(\n\u001b[0m\u001b[1;32m    265\u001b[0m                 \u001b[0mvalues\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mrow\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    266\u001b[0m                 \u001b[0mtextsize\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mxt_labelsize\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/ThinkBayes2/lib/python3.8/site-packages/arviz/plots/distplot.py\u001b[0m in \u001b[0;36mplot_dist\u001b[0;34m(values, values2, color, kind, cumulative, label, rotated, rug, bw, quantiles, contour, fill_last, textsize, plot_kwargs, fill_kwargs, rug_kwargs, contour_kwargs, contourf_kwargs, pcolormesh_kwargs, hist_kwargs, ax, backend, backend_kwargs, show, **kwargs)\u001b[0m\n\u001b[1;32m    151\u001b[0m             \u001b[0mhist_kwargs\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m{\u001b[0m\u001b[0;34m}\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    152\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 153\u001b[0;31m         \u001b[0mhist_kwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetdefault\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"bins\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mget_bins\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvalues\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    154\u001b[0m         \u001b[0mhist_kwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetdefault\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"cumulative\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcumulative\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    155\u001b[0m         \u001b[0mhist_kwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msetdefault\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"color\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mcolor\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/envs/ThinkBayes2/lib/python3.8/site-packages/arviz/plots/plot_utils.py\u001b[0m in \u001b[0;36mget_bins\u001b[0;34m(values)\u001b[0m\n\u001b[1;32m    129\u001b[0m     \u001b[0mbins_fd\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m2\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0miqr\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mvalues\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m**\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0;36m1\u001b[0m \u001b[0;34m/\u001b[0m \u001b[0;36m3\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    130\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 131\u001b[0;31m     \u001b[0mwidth\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mround\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmax\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbins_sturges\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mbins_fd\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mastype\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mint\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    132\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    133\u001b[0m     \u001b[0;32mreturn\u001b[0m \u001b[0mnp\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0marange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx_min\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx_max\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0mwidth\u001b[0m \u001b[0;34m+\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwidth\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'int' object has no attribute 'astype'"
     ]
    },
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 864x432 with 6 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "with model5:\n",
    "    pm.traceplot(trace5)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "celltoolbar": "Tags",
  "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": "3.8.5"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}