{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Survival Analysis\n",
    "\n",
    "This notebook presents code and exercises from Think Bayes, second edition.\n",
    "\n",
    "Copyright 2016 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "% matplotlib inline\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import math\n",
    "import numpy as np\n",
    "\n",
    "from thinkbayes2 import Pmf, Cdf, Suite, Joint\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Weibull distribution\n",
    "\n",
    "The Weibull distribution is often used in survival analysis because it models the distribution of lifetimes for manufactured products, at least over some parts of the range.\n",
    "\n",
    "The following functions evaluate its PDF and CDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def EvalWeibullPdf(x, lam, k):\n",
    "    \"\"\"Computes the Weibull PDF.\n",
    "\n",
    "    x: value\n",
    "    lam: parameter lambda in events per unit time\n",
    "    k: parameter\n",
    "\n",
    "    returns: float probability density\n",
    "    \"\"\"\n",
    "    arg = (x / lam)\n",
    "    return k / lam * arg**(k-1) * np.exp(-arg**k)\n",
    "\n",
    "def EvalWeibullCdf(x, lam, k):\n",
    "    \"\"\"Evaluates CDF of the Weibull distribution.\"\"\"\n",
    "    arg = (x / lam)\n",
    "    return 1 - np.exp(-arg**k)\n",
    "\n",
    "def MakeWeibullPmf(lam, k, high, n=200):\n",
    "    \"\"\"Makes a PMF discrete approx to a Weibull distribution.\n",
    "\n",
    "    lam: parameter lambda in events per unit time\n",
    "    k: parameter\n",
    "    high: upper bound\n",
    "    n: number of values in the Pmf\n",
    "\n",
    "    returns: normalized Pmf\n",
    "    \"\"\"\n",
    "    xs = np.linspace(0, high, n)\n",
    "    ps = EvalWeibullPdf(xs, lam, k)\n",
    "    return Pmf(dict(zip(xs, ps)))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "SciPy also provides functions to evaluate the Weibull distribution, which I'll use to check my implementation."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33093633846922332"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from scipy.stats import weibull_min\n",
    "\n",
    "lam = 2\n",
    "k = 1.5\n",
    "x = 0.5\n",
    "\n",
    "weibull_min.pdf(x, k, scale=lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.33093633846922332"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EvalWeibullPdf(x, lam, k)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1175030974154046"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "weibull_min.cdf(x, k, scale=lam)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.11750309741540454"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "EvalWeibullCdf(x, lam, k)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what the PDF looks like, for these parameters."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AwAEL3t3kb0AiEhcCmUwOHyvyjvv0yIq7BR6bc/2M2trJmyu2Una2wsdoRCQeBDKZHDle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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb922231d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf = MakeWeibullPmf(lam, k, high=10)\n",
    "thinkplot.Pdf(pmf)\n",
    "thinkplot.Config(xlabel='Lifetime',\n",
    "                 ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use np.random.weibull to generate random values from a Weibull distribution with given parameters.\n",
    "\n",
    "To check that it is correct, I generate a large sample and compare its CDF to the analytic CDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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ZuU8E6p1zDc65VuBZ4KZu+9wE/AHAObcMCJtZ5fkO9qOH57HdV8FBXyF+n49x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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8fdb2d50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def SampleWeibull(lam, k, n=1):\n",
    "    return np.random.weibull(k, size=n) * lam\n",
    "\n",
    "data = SampleWeibull(lam, k, 10000)\n",
    "cdf = Cdf(data)\n",
    "model = pmf.MakeCdf()\n",
    "thinkplot.Cdfs([cdf, model])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Write a class called `LightBulb` that inherits from `Suite` and `Joint` and provides a `Likelihood` function that takes an observed lifespan as data and a tuple, `(lam, k)`, as a hypothesis.  It should return a likelihood proportional to the probability of the observed lifespan in a Weibull distribution with the given parameters.\n",
    "\n",
    "Test your method by creating a `LightBulb` object with an appropriate prior and update it with a random sample from a Weibull distribution.\n",
    "\n",
    "Plot the posterior distributions of `lam` and `k`.  As the sample size increases, does the posterior distribution converge on the values of `lam` and `k` used to generate the sample?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "class LightBulb(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        if lam == 0:\n",
    "            return 0\n",
    "        x = data\n",
    "        like = EvalWeibullPdf(x, lam, k)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from itertools import product\n",
    "\n",
    "lams = np.linspace(0, 5, 101)\n",
    "ks = np.linspace(0, 5, 101)\n",
    "\n",
    "suite = LightBulb(product(lams, ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.5677896093212706e-09"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "datum = SampleWeibull(lam, k, 10)\n",
    "lam = 2\n",
    "k = 1.5\n",
    "suite.UpdateSet(datum)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3583976257450225"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Os9g2kUyp4VRYWEhhYeENX+dNEjgNTLSV093nPOtk9FZHRMJwJYBfGWPeuF7BGHPBVv9n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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8fd39fd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf_lam = suite.Marginal(0)\n",
    "thinkplot.Pdf(pmf_lam)\n",
    "pmf_lam.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2969100506973927"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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VM6eyYc2SxLLFP371Xb787+4PuSqRaKqvr6e+vn7E56UT9G1AMMmq4sdS2ywY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\nEclzCnoRkTynoBcRyXP/H8Yjw91rIwTXAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8fd3f550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf_k = suite.Marginal(1)\n",
    "thinkplot.Pdf(pmf_k)\n",
    "pmf_k.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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z8c9+l/ffdl1N22ut+fRdT3LbzvWLbvv08RQhU7FqjlvGTzaRL5/wkNzFREMm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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8f73f310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "thinkplot.Contour(suite)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Now suppose that instead of observing a lifespan, `k`, you observe a lightbulb that has operated for 1 year and is still working.  Write another version of `LightBulb` that takes data in this form and performs an update. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "class LightBulb2(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        if lam == 0:\n",
    "            return 0\n",
    "        x = data\n",
    "        like = 1 - EvalWeibullCdf(x, lam, k)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from itertools import product\n",
    "\n",
    "lams = np.linspace(0, 10, 101)\n",
    "ks = np.linspace(0, 10, 101)\n",
    "\n",
    "suite = LightBulb2(product(lams, ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83566549505291599"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "suite.Update(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.6166427208116056"
      ]
     },
     "execution_count": 18,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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wHbjF3XdntFkPbHL3j5jZVcAD7r52qL5mdh9w0t3vN7O7gGp3v3uAv+9v7G3g\n24/9mlNn2gatc8k5s6i9chXXvm9FwR4aqquro7a2NugyJgV9F330XfTRd9HHzHD3Yf2LOJ8L064E\n9rr7AXePAU8AG7LabAAeA3D3l4AZZjY/R98NwKOp5UeBjw9WwD3f2XpWGITDIS5ZWcMdn7iav/sv\nn+Jbd9/Mhg+9t2DDAJL/sUuSvos++i766LsYnXwOGS0C6jPWD5Hc0edqsyhH3/nu3gjg7kfNbNAb\nCvWOYSrKS/nwH13IJatquODc+ZSWRPMoX0RE8jFek8ojOXA/5LGrC887hy9/5npmz6wYYUkiIjIk\ndx/yAawFnslYvxu4K6vNd4F/m7G+G5g/VF9gF8lRAsACYNcgf9/10EMPPfQY/iPX/j37kc8IYTuw\nwsyWAkeAW4Bbs9psBb4I/NjM1gJN7t5oZieG6LsV+CxwH/AZ4KmB/vhwJ0VERGRkcgaCuyfMbBOw\njb5TR3eZ2cbky/6Iuz9tZjeZ2T6Sp53ePlTf1FvfB/zEzO4ADgA3j/mnExGRvOU87VRERIrDpP09\nBDNbZ2a7zWxP6jqFomRmNWb2vJm9aWY7zeyvgq4paGYWMrNXzWxr0LUEycxmmNk/mNmu1H8fVwVd\nU1DM7Mtm9oaZvW5mPzKzkqBrmkhmtsXMGs3s9Yxt1Wa2zczeNrNnzWxGrveZlIGQuqDtIeBGYDVw\nq5ldEGxVgYkD/9HdVwN/BHyxiL+LXl8C3gq6iEngAeBpd78QeC/JEzWKjpktBO4ELnP3S0geCr8l\n2Kom3A9I7i8z3Q085+6rgOeBr+Z6k0kZCOR3MVxRcPejvbcBcfdWkv/TLwq2quCYWQ1wE/C9oGsJ\nkplVAde6+w8A3D3u7s0BlxWkMDDdzCJAOck7IxQNd38ByL6fT94X//aarIEw2IVuRc3MlgFrgJeC\nrSRQ3wK+QvK0umJ2LnDCzH6QOnz2iJlNC7qoILj7YeCbwEGggeRZjs8FW9WkMC/z4l9g0It/e03W\nQJAsZlYBPAl8KTVSKDpm9hGgMTViMkZ2AWShiACXAX/n7pcB7SQPERQdM5tJ8l/DS4GFQIWZfSrY\nqialnP+ImqyB0AAsyVivSW0rSqlh8JPAD919wOs1isTVwMfMbD/wf4DrzOyxgGsKyiGg3t3/JbX+\nJMmAKEYfBva7+yl3TwA/A94fcE2TQWPqnnKY2QLgWK4OkzUQ0hfDpc4WuIXkhWzF6vvAW+7+QNCF\nBMndv+b2SCI8AAAAv0lEQVTuS9z9PJL/TTzv7rcFXVcQUocC6s1sZWrT9RTvRPtBYK2ZlVnyfvfX\nU5wT7Nmj5t6Lf2GIi38zTcofyMlxQVtRMbOrgU8DO83sNZLDvq+5+zPBViaTwF8BPzKzKLCf1AWh\nxcbdXzazJ4HXgFjq+ZFgq5pYZvY4UAvMNrODwD3AN4B/GM7Fv7owTUREgMl7yEhERCaYAkFERAAF\ngoiIpCgQREQEUCCIiEiKAkFERAAFgoiIpCgQREQEgP8PVS3YLX++YKkAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8f839b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf_lam = suite.Marginal(0)\n",
    "thinkplot.Pdf(pmf_lam)\n",
    "pmf_lam.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.2481865102083747"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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jWkc6gdAMzE2Yrw6WJbeZM0Cb0sH6uvuxhOX/Avx4sAI2btzIZ/7n95h4/Cyg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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8fd0b750>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf_k = suite.Marginal(1)\n",
    "thinkplot.Pdf(pmf_k)\n",
    "pmf_k.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Now let's put it all together.  Suppose you have 15 lightbulbs installed at different times over a 10 year period.  When you observe them, some have died and some are still working.  Write a version of `LightBulb` that takes data in the form of a `(flag, x)` tuple, where:\n",
    "\n",
    "1. If `flag` is `eq`, it means that `x` is the actual lifespan of a bulb that has died.\n",
    "2. If `flag` is `gt`, it means that `x` is the current age of a bulb that is still working, so it is a lower bound on the lifespan.\n",
    "\n",
    "To help you test, I will generate some fake data.\n",
    "\n",
    "First, I'll generate a Pandas DataFrame with random start times and lifespans.  The columns are:\n",
    "\n",
    "`start`: time when the bulb was installed\n",
    "\n",
    "`lifespan`: lifespan of the bulb in years\n",
    "\n",
    "`end`: time when bulb died or will die\n",
    "\n",
    "`age_t`: age of the bulb at t=10"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>lifespan</th>\n",
       "      <th>start</th>\n",
       "      <th>end</th>\n",
       "      <th>age_t</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>2.669393</td>\n",
       "      <td>3.884926</td>\n",
       "      <td>6.554320</td>\n",
       "      <td>6.115074</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>4.439592</td>\n",
       "      <td>1.024761</td>\n",
       "      <td>5.464353</td>\n",
       "      <td>8.975239</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.013455</td>\n",
       "      <td>2.801937</td>\n",
       "      <td>3.815392</td>\n",
       "      <td>7.198063</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.632849</td>\n",
       "      <td>8.844007</td>\n",
       "      <td>10.476856</td>\n",
       "      <td>1.155993</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.774843</td>\n",
       "      <td>8.325410</td>\n",
       "      <td>9.100254</td>\n",
       "      <td>1.674590</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   lifespan     start        end     age_t\n",
       "0  2.669393  3.884926   6.554320  6.115074\n",
       "1  4.439592  1.024761   5.464353  8.975239\n",
       "2  1.013455  2.801937   3.815392  7.198063\n",
       "3  1.632849  8.844007  10.476856  1.155993\n",
       "4  0.774843  8.325410   9.100254  1.674590"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "import pandas as pd\n",
    "\n",
    "lam = 2\n",
    "k = 1.5\n",
    "n = 15\n",
    "t_end = 10\n",
    "starts = np.random.uniform(0, t_end, n)\n",
    "lifespans = SampleWeibull(lam, k, n)\n",
    "\n",
    "df = pd.DataFrame({'start': starts, 'lifespan': lifespans})\n",
    "df['end'] = df.start + df.lifespan\n",
    "df['age_t'] = t_end - df.start\n",
    "\n",
    "df.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now I'll process the DataFrame to generate data in the form we want for the update."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('eq', 2.6693934023350288)\n",
      "('eq', 4.4395922794570097)\n",
      "('eq', 1.0134550944499816)\n",
      "('gt', 1.1559931554468044)\n",
      "('eq', 0.7748433201074556)\n",
      "('eq', 0.58523684453682523)\n",
      "('eq', 1.5050346559516292)\n",
      "('eq', 0.0043263460781409529)\n",
      "('eq', 3.1183238430930049)\n",
      "('eq', 2.5497343435244648)\n",
      "('eq', 1.426995199412439)\n",
      "('eq', 2.8969617422395997)\n",
      "('eq', 1.2143990874080592)\n",
      "('gt', 0.28161850035970559)\n",
      "('eq', 1.4219175345313229)\n"
     ]
    }
   ],
   "source": [
    "data = []\n",
    "for i, row in df.iterrows():\n",
    "    if row.end < t_end:\n",
    "        data.append(('eq', row.lifespan))\n",
    "    else:\n",
    "        data.append(('gt', row.age_t))\n",
    "        \n",
    "for pair in data:\n",
    "    print(pair)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "class LightBulb3(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        if lam == 0:\n",
    "            return 0\n",
    "        flag, x = data\n",
    "        if flag == 'eq':\n",
    "            like = EvalWeibullPdf(x, lam, k)\n",
    "        elif flag == 'gt':\n",
    "            like = 1 - EvalWeibullCdf(x, lam, k)\n",
    "        else:\n",
    "            raise ValueError('Invalid data')\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from itertools import product\n",
    "\n",
    "lams = np.linspace(0, 10, 101)\n",
    "ks = np.linspace(0, 10, 101)\n",
    "\n",
    "suite = LightBulb3(product(lams, ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.7937515916258046e-12"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "suite.UpdateSet(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.2717545445867739"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SsjkAdHf38OKvjoUckYgkg5L+GNSenbz1/KBgiafqJZV4RCYDJf0xqAkm/QUz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\nrkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8f900f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf_lam = suite.Marginal(0)\n",
    "thinkplot.Pdf(pmf_lam)\n",
    "pmf_lam.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.2410798895283741"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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SwUIvWMCHEqtWtqqBgQFu23o9/+HBX2Nt3woApiL40tef41//0X/jmedeLf9m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\n+mZmOeLQNzPLkf8PYl9lQ9EHuHgAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8f656a10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pmf_k = suite.Marginal(1)\n",
    "thinkplot.Pdf(pmf_k)\n",
    "pmf_k.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Suppose you install a light bulb and then you don't check on it for a year, but when you come back, you find that it has burned out.  Extend `LightBulb` to handle this kind of data, too."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "class LightBulb4(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        if lam == 0:\n",
    "            return 0\n",
    "        flag, x = data\n",
    "        if flag == 'eq':\n",
    "            like = EvalWeibullPdf(x, lam, k)\n",
    "        elif flag == 'gt':\n",
    "            like = 1 - EvalWeibullCdf(x, lam, k)\n",
    "        elif flag == 'lt':\n",
    "            like = EvalWeibullCdf(x, lam, k)\n",
    "        else:\n",
    "            raise ValueError('Invalid data')\n",
    "        return like"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Prediction\n",
    "\n",
    "**Exercise:** Suppose we know that, for a particular kind of lightbulb in a particular location, the distribution of lifespans is well modeled by a Weibull distribution with `lam=2` and `k=1.5`.  If we install `n=100` lightbulbs and come back one year later, what is the distribution of `c`, the number of lightbulbs that have burned out?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29781149867344037"
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The probability that any given bulb has burned out comes from the CDF of the distribution\n",
    "p = EvalWeibullCdf(1, lam, k)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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5UxjS5wpoXwGRKFESKDJh1ATq68ZRWVEOxNYt6rlyPS/vKyJjpyRQZILbSuYrCZhZypLS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\n9Vv7ZX4P1OAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8f5441d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "# The number of bulbs that have burned out is distributed Binom(n, p)\n",
    "n = 100\n",
    "from thinkbayes2 import MakeBinomialPmf\n",
    "\n",
    "pmf_c = MakeBinomialPmf(n, p)\n",
    "thinkplot.Pdf(pmf_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Now suppose that `lam` and `k` are not known precisely, but we have a `LightBulb` object that represents the joint posterior distribution of the parameters after seeing some data.  Compute the posterior predictive distribution for `c`, the number of bulbs burned out after one year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "n = 100\n",
    "t_return = 1\n",
    "\n",
    "metapmf = Pmf()\n",
    "for (lam, k), prob in suite.Items():\n",
    "    p = EvalWeibullCdf(t_return, lam, k)\n",
    "    pmf = MakeBinomialPmf(n, p)\n",
    "    metapmf[pmf] = prob"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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OcbrV7S07zomTdZ7GY4xXLDl4YI+rSiln4iiSkuyfIVYMGdiXudOznO13tpZ6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fdb8f53c8d0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "from thinkbayes2 import MakeMixture\n",
    "\n",
    "mix = MakeMixture(metapmf)\n",
    "thinkplot.Pdf(mix)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 2",
   "language": "python",
   "name": "python2"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 2
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython2",
   "version": "2.7.11"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}