survival.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Bayesian Survival Analysis\n",
    "\n",
    "Copyright 2017 Allen Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "from __future__ import print_function, division\n",
    "\n",
    "%matplotlib inline\n",
    "\n",
    "import warnings\n",
    "warnings.filterwarnings('ignore')\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "import thinkbayes2\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Survival analysis\n",
    "\n",
    "Suppose that you are an auto insurance company interested in the time between collisions for a particular driver.  If the probability of a collision is roughly constant over time, the time between collisions will follow an exponential distribution.\n",
    "\n",
    "Here's an example with parameter $\\lambda = 0.5$ collisions / year."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 99,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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yGX735AaO3fFwt+8zKQ2sXpXt5pExxUWTOsfvVm7iH+/5WdcHG+LcvlNL0oHR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\nZmZlcWCYmVlZHBhmZlYWB4aZmZXl/wMOmV+qwQonfAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16b754950>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkbayes2 import MakeExponentialPmf\n",
    "\n",
    "#pmf = MakeExponentialPmf(lam=0.5, high=30)\n",
    "pmf = MakeWeibullPmf(lam=2.0, k=0.9, high=60)\n",
    "\n",
    "thinkplot.Pdf(pmf)\n",
    "thinkplot.Config(xlabel='Lifetime', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "For the exponential distribution, the mean and standard deviation are $1/\\lambda$.\n",
    "\n",
    "In this case they are only approximate because we truncated the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 100,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(2.3204760330957992, 2.3608256709052506)"
      ]
     },
     "execution_count": 100,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pmf.Mean(), pmf.Std()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the PMF, we can compute the CDF."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 101,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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/aNO20DGPzXGMJOkU8eKzJKklVdXdyZPLgOmq2tLs3wJUVb176JjbgXuqalezfxj44ao6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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16b648310>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "cdf = pmf.MakeCdf()\n",
    "thinkplot.Cdf(cdf)\n",
    "thinkplot.Config(xlabel='Lifetime', ylabel='CDF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And from the CDF, we can compute the survival function, which is the complement of the CDF.\n",
    "\n",
    "$SF(x) = Prob\\{X > x\\} = 1 - Prob\\{X \\le x\\} = 1 - CDF(x)$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 102,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Zs2b2z+GxYmjjNGCXmd0RdgUuNrPh9KNtcQiGoSrWTwWYWTXwK+A6dz/AW9sT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\nJ1FtFgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bca8f50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from survival import MakeSurvivalFromCdf\n",
    "\n",
    "sf = MakeSurvivalFromCdf(cdf)\n",
    "thinkplot.Plot(sf)\n",
    "thinkplot.Config(xlabel='Lifetime', ylabel='Survival function')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "From the survival function we can get the hazard function, which is the probability of a collision at $x$, given no collision prior to $x$."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 103,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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EHBfZnxumNZutpTWizOxoYNs4tycxM8sRBIUfuvudYXLT9K/E3XcDy4HFNEf/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\n/wFoTVYBwmYIBwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16ba3d550>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "hf = sf.MakeHazardFunction()\n",
    "thinkplot.Plot(hf)\n",
    "thinkplot.Config(xlabel='Lifetime', ylabel='Hazard function')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "If the distribution is truly exponential, the hazard function is constant for all $x$.\n",
    "\n",
    "In this case it goes to 1 at the end, again because we truncated the distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** Go back and increase the value of `high`, and confirm that the hazard function is a constant until we approach the point where we cut off the distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Remaining lifetime\n",
    "\n",
    "Given the survival function, we can compute the distribution of remaining lifetime, conditioned on current age.  The following function computes the mean remaining lifetime for a range of ages."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 104,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def RemainingLifetime(sf):\n",
    "    \"\"\"Computes remaining lifetime as a function of age.\n",
    "    \n",
    "    sf: survival function\n",
    "    returns: Series that maps from age to remaining lifetime\n",
    "    \"\"\"\n",
    "    pmf = sf.MakePmf()\n",
    "    d = {}\n",
    "    for t in sorted(pmf.Values()):\n",
    "        pmf[t] = 0\n",
    "        if pmf.Total():\n",
    "            pmf.Normalize()\n",
    "            d[t] = pmf.Mean() - t\n",
    "\n",
    "    return pd.Series(d)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "And here's what it looks like for the exponential survival function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 105,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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3d0coHhGRMe/8iik8/0bgu/nmnYf49HXLRvT60Yxj+Gcz22pm/xCcK0lERGJo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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16be49150>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "mean_rem_life = RemainingLifetime(sf)\n",
    "thinkplot.Plot(mean_rem_life)\n",
    "thinkplot.Config(xlabel='Lifetime', ylabel='Survival function')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The mean time until a collision is pretty much constant, until we approach the point where we truncate the distribution."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Weibull distribution\n",
    "\n",
    "The Weibull distribution is a generalization of the exponential distribution that takes an additional \"shape\" parameter, `k`.\n",
    "\n",
    "When `k=1`, the Weibull is an exponential distribution.  Other values of `k` yield survival curves with different shapes, and hazard functions that increase, decrease, or both.  So the Weibull family can capture a wide range of survival patterns."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 106,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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Yd390lPu/Adju7rsBzOxxYAWwNVBmBfBY4nhrzWySmTW6e6e7dyfK1CTqOmQXWVVId0gl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\nUWCIiEhW/j+9nm9e+kHU7wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16b89f650>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkbayes2 import MakeWeibullPmf\n",
    "\n",
    "pmf = MakeWeibullPmf(lam=2.0, k=1.5, high=30)\n",
    "thinkplot.Pdf(pmf)\n",
    "thinkplot.Config(xlabel='Lifetime', ylabel='PMF')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise**: In the previous section, replace the exponential distribution with a Weibull distribituion and run the analysis again.  What can you infer about the values of the parameters and the behavior of the hazard function and remaining lifetime?"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Bayesian survival analysis"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Suppose you are the manager of a large building with many light fixtures.  To figure out how often you will need to replace lightbulbs, you install 10 bulbs and measure the time until they fail.\n",
    "\n",
    "To generate some fake data, I'll choose a Weibull distribution and generate a random sample (let's suppose it's in years):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 116,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 2.16720062,  1.98553625,  1.44028217,  2.05068265,  2.21505013,\n",
       "        0.70501647,  0.43401449,  0.67833024,  2.12264353,  0.51604502,\n",
       "        1.08257349,  1.87281144,  1.22394111,  4.52782486,  2.93711172,\n",
       "        0.51554485,  2.76548229,  1.03850744,  1.00277524,  2.44457056,\n",
       "        1.51869861,  1.21627947,  1.56841035,  2.12999513,  4.22848361,\n",
       "        1.56491417,  0.60311224,  1.19766456,  1.03450134,  2.92243332,\n",
       "        1.86484473,  2.86674193,  1.23235744,  3.36051109,  1.31944338,\n",
       "        1.24500887,  0.20110738,  0.95085513,  2.69555937,  1.60815994,\n",
       "        1.06081976,  1.55233189,  0.4636843 ,  0.37523309,  3.598693  ,\n",
       "        0.71178144,  3.45432266,  3.69130864,  4.76980241,  0.13617007,\n",
       "        1.64063513,  3.11275242,  3.59233625,  2.10508289,  1.4372327 ,\n",
       "        2.65000013,  0.56371412,  1.91599508,  1.2965953 ,  1.43196784,\n",
       "        3.26251423,  1.44327647,  3.62314075,  0.09964646,  2.98105599,\n",
       "        0.73913421,  5.15253587,  0.66215796,  1.39730136,  2.35781234,\n",
       "        0.95249742,  1.21073558,  1.02168233,  1.83382324,  0.53234007,\n",
       "        1.67364922,  4.61134329,  1.01973895,  1.49467343,  0.46700978,\n",
       "        2.06980669,  1.74940422,  1.7647287 ,  0.27159589,  6.58625972,\n",
       "        1.13996364,  2.55543219,  1.52966509,  6.65205771,  1.62939492,\n",
       "        0.87740876,  2.6108278 ,  2.48292772,  4.39386985,  1.18237998,\n",
       "        0.73134881,  0.99215943,  2.2648305 ,  0.56976736,  2.12071552])"
      ]
     },
     "execution_count": 116,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def SampleWeibull(lam, k, n=1):\n",
    "    return np.random.weibull(k, size=n) * lam\n",
    "\n",
    "data = SampleWeibull(lam=2, k=1.5, n=100)\n",
    "data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Write a class called `LightBulb` that inherits from `Suite` 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 the data above.\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": 117,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hint\n",
    "\n",
    "from thinkbayes2 import Suite, Joint, EvalWeibullPdf\n",
    "\n",
    "class LightBulb(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        x = data\n",
    "        like = EvalWeibullPdf(x, lam, k)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 118,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 119,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "lams = np.linspace(0.001, 6, 101)\n",
    "ks = np.linspace(0.001, 8, 101)\n",
    "\n",
    "suite = LightBulb(product(lams, ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 120,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.3824871049762166e-69"
      ]
     },
     "execution_count": 120,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.UpdateSet(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 121,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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hDGpJKlxXQR0Rb4uIRyLiZxHxkUEXJUl6TjcXt60Afw+8FbgYeFdEvHLQhZWkXq8Pu4SB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\nklQ4g1qSCmdQS1LhDGpJKtz/AxR3FRMcTGh+AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16f756f90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Contour(suite)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 122,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.1274693791709263"
      ]
     },
     "execution_count": 122,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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bEcGO1/cVz2dj2WbcJ2+8tnj8F/9vJ4PnLjSxN2ZzgwO9sXffu5w6OwTA4u6F\nrL16WZN7NLVbb7qW7q75ALx3apBvPPX3Te6R2eznQG8lJZCfvmF1cRbqbNSzaAH/8d/+XPH8Oy/v\n5buv+cGs2XRm799oa4g33jrE/3n+9eL5zTfOrmGVk/nkumv4uU/8RPF82598xw9mzaaRKtBL2iBp\nt6Q9ku6fos3XJe2VtFPSukruteY4cPQkv/mNvyquVrnyyqWsW7uiyb1K59//61uLE7oGhi7wW4/+\nVcmCbGY2YcZAL6kNeAi4HbgBuFPS9WVtPgNcGxHXAZuBh9Pe+0FQzWa+9Xbq7BC//j+eKT7MXNLT\nxQO/+hna2yvfJ6YZ32/Rwvnc/fmfLw633LvvXb70X/+Ep7a/yvDwaKafNRt/flny92t9aTL69cDe\niNgXEcPAk8DGsjYbgccBIuJFoFfSspT3trzZ8gctIvjRj4/wh3/xD/yn3/7fHDuZXwWys6Od//wr\nG7h8aU9V79us7/fR65bz7z57SzHYD4+M8sf/9yXu+vVv8vtP/C3PfW83B46e5PyF4Zo+Z7b8/OrF\n36/1pdlKcDmwP3F+gHwAn6nN8pT3Fv3GI3+Zojtzz9+9vLch3y2I/H8jGB0NxmKMsbFg8NxFBobO\nc2bgPMMjpdmugPt++dOsWT07Vqqs1C/eto6PrrmKh//kO/z4wHEgPxon99KPyL30o2K7zo52ersX\nsmB+Ox0d7XS0z6N9XhsStKmNtjYxPnVAEmJiHkGjfn7N4u/X+lLtGVuFqmbbvPLmvpkbzUGHjp2e\nld+ta0En/+Fzn+ITH/1ws7tSkzWrL+e3fu1f8Zd/9wZPPrODofMX39fm4vBI8V8wlZqtP7+s+Pu1\nPkXE9A2kW4D+iNhQOP8KEBHxm4k2DwN/GxHfKpzvBn4OuHqmexPvMX1HzMzsfSJixsQ6TUa/A1gj\naTVwGNgE3FnW5mngLuBbhV8MpyLiqKTjKe5N3VkzM6vcjIE+IkYlbQG2k394+2hE7JK0Of9ybIuI\nZyTdIektYBD44nT31u3bmJnZ+8xYujEzs7mt6TNjW3lClaRHJR2V9INm96UeJK2Q9JykNyS9Lume\nZvcpS5LmS3pR0muF7/dgs/uUNUltkl6V9HSz+5I1Sf8k6fuFn99Lze5P1iT1SvpTSbsKfwdvnrJt\nMzP6woSqPcBtwCHyzwM2RcTupnUqQ5I+BQwAj0fEx5vdn6xJugK4IiJ2SuoGXgE2tsrPD0BSV0QM\nSZoHfBcMFBRWAAACRklEQVS4JyJaJmhI+hLwU8DiiPhss/uTJUlvAz8VESeb3Zd6kPS/gOcj4jFJ\n7UBXRJyZrG2zM/qWnlAVEX8PtOQfMoCIOBIROwvHA8Au8nMnWkZEDBUO55N/ptUytU5JK4A7gG80\nuy91Ipof4+pC0mLgZyPiMYCIGJkqyEPz/0+YaqKVzTGSPgysA15sbk+yVShtvAYcAf46InY0u08Z\n+l3gy7TQL68yAfy1pB2SfqXZncnY1cBxSY8VSm/bJC2cqnGzA721gELZ5ing3kJm3zIiYiwi/hmw\nArhZ0kea3acsSPoF4GjhX2SiykmOs9ytEXET+X+13FUopbaKduAm4L8XvuMQ8JWpGjc70B8EViXO\nVxSu2RxRqA0+BfxRRHy72f2pl8I/i/8W2NDsvmTkVuCzhTr2HwM/L+nxJvcpUxFxuPDfY8CfM83y\nK3PQAWB/RLxcOH+KfOCfVLMDfXEylqRO8hOqWu3pf6tmS+P+AHgzIr7W7I5kTdJlknoLxwuBfw60\nxIPmiHggIlZFxDXk/949FxFfaHa/siKpq/AvTSQtAv4F8MPm9io7EXEU2C9pfGOG24A3p2pfr7Vu\nUmn1CVWSvgn0AZdKegd4cPzhSSuQdCvweeD1Qh07gAci4tnm9iwzVwJ/WBgd1gZ8KyKeaXKfLJ1l\nwJ8XllZpB56IiO1N7lPW7gGekNQBvE1houpkPGHKzKzFNbt0Y2ZmdeZAb2bW4hzozcxanAO9mVmL\nc6A3M2txDvRmZi3Ogd7MrMU50JuZtbj/D/e8C3lcWa7zAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16ba63b10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_lam = suite.Marginal(0)\n",
    "thinkplot.Pdf(pmf_lam)\n",
    "pmf_lam.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 123,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.5122348979402183"
      ]
     },
     "execution_count": 123,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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Fm0r16Icz1ujTa93MukdvZh1y0BcsPepm/VDGHv069+jNLD8O+oKla/QjGWv03jPWzPLk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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16b7c4cd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_k = suite.Marginal(1)\n",
    "thinkplot.Pdf(pmf_k)\n",
    "pmf_k.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:**  Go back and run this analysis again with `n=20` and see if the posterior distributions seem to be converging on the actual parameters. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Censored data"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "**Exercise:** Now suppose that instead of observing a complete lifespan, 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": 124,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hint\n",
    "\n",
    "from thinkbayes2 import EvalWeibullCdf\n",
    "\n",
    "class LightBulb2(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        x = data\n",
    "        like = 1 - EvalWeibullCdf(x, lam, k)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 125,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 126,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "lams = np.linspace(0.001, 10, 101)\n",
    "ks = np.linspace(0.001, 10, 101)\n",
    "\n",
    "suite = LightBulb2(product(lams, ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 127,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83584776184046183"
      ]
     },
     "execution_count": 127,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.Update(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 128,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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W5qFTbLmEvSaRRHrKn7NmQQ11VT6e2D31QUaFfOxdm1nbNo8P/u33pW66IAiz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\nbyF/+Po1nLno2KmRc5mR0Tg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SS+e2jcRSaHRO4MN+i3DAQ1V23e8hVPRqEfJ7CPksQn53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\nHLrD4XC0Cf8HjhDZi8/j5msAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16b766190>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Contour(suite)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 129,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.6163331229520157"
      ]
     },
     "execution_count": 129,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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8s5uOzu5B61w0r44PXLacD1y2nBm1U4f3LUwSDQ0N1NfXR11GQdB30UffRR99\nF33MDHcf1r+I87kwbTWwx933uXsP8ACwIavNBuB+AHffBtSa2dwcfTcA9wXL9wGfGKyAX/3+pbeF\nQTwe48LlC7jxk1dw599dz3dv/jSf/NAlRRsGkP6PXdL0XfTRd9FH38Xo5HPIaAFwILR+kPSOPleb\nBTn6znX3IwDuftjMct5QaN6saay+8BwuWrGQ88+dR2VFWR7li4hIPsZrUnkkB+4HPXa15qJzuObK\nVVyoyWERkfHj7kM+gDXAI6H1rwM3ZbX5PvDp0PouYO5QfYGdpEcJAPOAnYO8v+uhhx566DH8R679\ne/YjnxHCM8AyM1sCvAVcB1yf1WYL8CXgn81sDdDs7kfM7NgQfbcAnwVuA/4c+OVAbz7cSRERERmZ\nnIHg7ikz2wRspe/U0Z1mtjH9tN/t7g+b2Xoz20v6tNMbh+obvPRtwE/N7HPAPuBTY/7pREQkbzlP\nOxURkdJQsL+HYGZrzWyXme0OrlMoSWa20MweN7OXzWyHmf1V1DVFzcxiZva8mW2JupYomVmtmf3M\nzHYG/31cHnVNUTGzr5rZS2a23cx+bGblUdc0kczsHjM7YmbbQ9vqzGyrmb1qZo+aWc4ffynIQAgu\naLsTuAZYBVxvZiujrSoySeBv3H0V8B7gSyX8XZzxFeCVqIsoALcDD7v7+cA7SZ+oUXLMbD7wZeBd\n7n4R6UPh10Vb1YS7l/T+MuzrwGPuvgJ4HLg514sUZCCQ38VwJcHdD5+5DYi7nyL9f/oF0VYVHTNb\nCKwHfhB1LVEys2nA+9z9XgB3T7p7a8RlRSkOTDWzBFBF+s4IJcPdnwCy7+eT98W/ZxRqIAx2oVtJ\nM7OzgYuBbdFWEqnvAF8jfVpdKTsHOGZm9waHz+42sylRFxUFdz8EfBvYDzSSPsvxsWirKghzwhf/\nAjkv/i3UQJAsZlYNPAh8JRgplBwz+yhwJBgxGSO7ALJYJIB3Af/T3d8FnCZ9iKDkmNl00v8aXgLM\nB6rN7DPRVlWQcv4jqlADoRFYHFpfGGwrScEw+EHgR+4+4PUaJeK9wMfN7HXg/wIfNLP7I64pKgeB\nA+7+bLD+IOmAKEUfAl539xPungJ+AVwRcU2F4EhwTznMbB7QlKtDoQZC5mK44GyB60hfyFaqfgi8\n4u63R11IlNz9G+6+2N3PJf3fxOPufkPUdUUhOBRwwMyWB5uupnQn2vcDa8ys0tL3trma0pxgzx41\nn7n4F4aKn1XVAAAAi0lEQVS4+DesIH8gJ8cFbSXFzN4L/Cdgh5m9QHrY9w13fyTayqQA/BXwYzMr\nA14nuCC01Lj702b2IPAC0BP8vTvaqiaWmf0EqAdmmtl+4Bbgm8DPhnPxry5MExERoHAPGYmIyART\nIIiICKBAEBGRgAJBREQABYKIiAQUCCIiAigQREQkoEAQEREA/j9mNNPkWzwpvAAAAABJRU5ErkJg\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bf23850>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_lam = suite.Marginal(0)\n",
    "thinkplot.Pdf(pmf_lam)\n",
    "pmf_lam.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 130,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.2480876231355253"
      ]
     },
     "execution_count": 130,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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traW2tnZQ6wgSCA3A3Iz52all2W3m9NCmtLe+7n4yY/k/AD/orYAHH3yQfQ88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\nQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bd09350>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_k = suite.Marginal(1)\n",
    "thinkplot.Pdf(pmf_k)\n",
    "pmf_k.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Note: based on this data alone, we can rule out some small values of `lam` and `k`, but we can't rule out large values.  Without more data or a more informative prior, the results are not useful.\n",
    "\n",
    "To see why, try increasing the upper bounds in the prior distribition."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Left censored data\n",
    "\n",
    "**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": 131,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Hint\n",
    "\n",
    "class LightBulb3(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        x = data\n",
    "        like = EvalWeibullCdf(x, lam, k)\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 132,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 133,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "lams = np.linspace(0.001, 20, 101)\n",
    "ks = np.linspace(0.001, 20, 101)\n",
    "\n",
    "suite = LightBulb3(product(lams, ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 134,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.08013753974381374"
      ]
     },
     "execution_count": 134,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.Update(1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 135,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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RZ48GpH0jn/HjL498+uyE/NR2xt+r/7SWDP/k7Wbrkn+TuLB+m7rnb9KW013f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\nIrJIKNBFRBYJBbqIyCLx/wFsRhEhpiTYMgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bf59390>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Contour(suite)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 136,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "2.8365008331664181"
      ]
     },
     "execution_count": 136,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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p6twqaZekbZIua9iWk/QDSZtno9HT8cPRzcxaaxv6knLAbcA1wKXA9ZIubqhzLXBBRFwE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\nzcwWEIe+mdkC4tA3M1tAHPpmZgvI/wd+rviDPkna0wAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bca1bd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_lam = suite.Marginal(0)\n",
    "thinkplot.Pdf(pmf_lam)\n",
    "pmf_lam.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 137,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "7.3098570578312811"
      ]
     },
     "execution_count": 137,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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LtBz6ZmZTNWnoS8oA9wAfA64EbpJ0RUmfDcDqiFgDbALuBYiIfuBDEXE1sBbYIOna6Ra7\nbImHd8zMZqKcI/1rgZ6I2BsRg8ADwMaSPhuB+wEi4kmgU9LSZP5M0qcFaASmfYvMJYs6aGjIl3zs\n5Bn6zg5Md1NmZnNSOaG/DNhXNL8/aZuoz4HhPpIykp4BXgd+GBE7pltsQ0OGCy8oPoPHV+aamU1F\nY7V3EBE54GpJC4DvSHpnRLw0Vt8tW7YUpru6uujq6npLn4uWdLI/uffOwcPHWb1ycRWqNjNLn+7u\nbrq7u2e0jXJC/wCwsmh+edJW2mfFRH0i4qSkx4D1wKShP57icf39/jDXzOaQ0oPhO++8c8rbKGd4\nZwdwqaRVkpqBG4HtJX22AzcDSFoHHI+IQ5IukNSZtLcCvwvsmnKVRXwGj5nZ9E16pB8RWUmbgUfJ\nv0lsi4idkjblF8fWiHhY0g2S9gC9wC3J6hcCX03OAMoAD0bEwzMp2PfVNzObvrLG9CPiEeDykrb7\nSuY3j7HeC8A1MymwVPFVuQcPHycikFTJXZiZzVp1dUUuQEf7POa3tQAwMDjEm8d7a1yRmVn9qLvQ\nB1i29LzC9AGP65uZla0uQ7/4bpt+dKKZWfnqMvRXvG1RYfo3+9+oYSVmZvWlLkP/slVLCtM9rx6u\nYSVmZvWlLkN/9crFZDL50vcfOkZvX3+NKzIzqw91GfrNTY1csuz8wnzPXh/tm5mVoy5DH+Cyi5cW\npne/eqiGlZiZ1Y86Dv2RcX2HvplZeeo29NesKj7SP0zEtG/Tb2Y2Z9Rt6L/tggV0tM8DoLevn4NH\nfB8eM7PJ1G3oS+Ky4qP9VzzEY2Y2mboNfYDLLikK/b0OfTOzydR36K8q/jDXp22amU2mrkP/0pVL\nGL6p8t4Db3C2f7Cm9ZiZpV1dh35bazPLL8zfhyeAX+87UtuCzMxSrq5DH0YP8bzsD3PNzCZU96F/\n+SW+MtfMrFx1H/qXXfy2wvSLew4yNJStYTVmZulWVuhLWi9pl6Tdkm4bp8/dknokPStpbdK2XNKP\nJb0o6QVJt1ayeIDlSxey+LwOAM6cHeCFnoOV3oWZ2awxaehLygD3AB8DrgRuknRFSZ8NwOqIWANs\nAu5NFg0Bn4uIK4H3AZ8pXXemJHHdVZcU5p98/jeV3LyZ2axSzpH+tUBPROyNiEHgAWBjSZ+NwP0A\nEfEk0ClpaUS8HhHPJu2ngZ3AsopVn7ju3SOhv+OFvb4Pj5nZOMoJ/WXAvqL5/bw1uEv7HCjtI+li\nYC3w5FSLnMwVlyxlwfxWAI6fOuOzeMzMxtF4LnYiaT7wLeCzyRH/mLZs2VKY7urqoqurq6ztZzIZ\n3vuuVfztz3cB8OTzr3DF2982yVpmZvWlu7ub7u7uGW1Dkw2FSFoHbImI9cn87UBExOeL+twLPBYR\nDybzu4APRsQhSY3A94EfRMRdE+wnZjIs88sX9/Jftv4AyN+B857/fBOSJlnLzKx+SSIiphR05Qzv\n7AAulbRKUjNwI7C9pM924OakiHXA8YgYHmP5MvDSRIFfCVddtpx5LU0AvP7GSf7+taPV3J2ZWV2a\nNPQjIgtsBh4FXgQeiIidkjZJ+nTS52HgFUl7gPuAPwSQdD3wL4DfkfSMpKclra/GD9LU1MA171xZ\nmP/5c69UYzdmZnVt0uGdc2WmwzsATzzza77wVz8EYNVF5/OF2/5pJUozM0ulag3v1I1r3rGCxsYG\nAPYefJN9rx+rcUVmZukyq0K/dV4z17xjRWH+e489V8NqzMzSZ1aFPsDvdV1VmO7esZtjJ8/UsBoz\ns3SZdaH/ztUXcunK/O2Ws9kcP/jpr2pckZlZesy60JfExg+/uzD/yOMv+olaZmaJWRf6AOuuuoS3\nXbAAgN6+/sKVumZmc92sDP1MJsM/6ho52v/eY8+TzeZqWJGZWTrMytAH+NB1lzG/rQWAI8dO8bNf\n9tS4IjOz2pu1od/S3MSGD7yrMP9X3/k7Tp7uq2FFZma1N2tDH+ATXe/m/IXtAJzqPcu2h56ocUVm\nZrU1q0O/rbWZTZ/6QGH+8V/u4Rcv7q1hRWZmtTWrQx/gPVeu4gP/cE1h/r4Hf0pvX38NKzIzq51Z\nH/oA/+aT1xeerHX0RC9f+tbjfqSimc1JcyL0O9rn8W9//7cK8z/9RQ/f+JsdNazIzKw25kToA7x/\n7dv50HWXF+b/zw+f5m9+8kINKzIzO/fmTOhL4t996gO8552rCm1ffugJfvYLn79vZnPHnAl9gMbG\nBv7DLR/h8ktGHpp+11//Ld/98XMe4zezOWFWPTmrXKd6z/Jnd3931ENWrr/mUv79jR8sPGfXzCzt\npvPkrDkZ+gDHTp7hv3/5UV5+5fVC28oLF3Hrv/wdLll+wTmrw8xsuqoW+snDzL9IfjhoW0R8fow+\ndwMbgF7gloh4JmnfBvwecCgiripdr2j9cxr6AENDWbY99ASPPvHSSB3AR6+/kps+/l462ued03rM\nzKaiKqEvKQPsBj4MHAR2ADdGxK6iPhuAzRHxcUnXAXdFxLpk2W8Bp4H70xb6w370dzvZ+s2fjboT\n5/y2Fj75u9fwkfddQXtrS03qMjObSLVCfx1wR0RsSOZvB6L4aF/SvcBjEfFgMr8T6IqIQ8n8KuB7\naQ19gAOHj7PtW4/z3Mv7R7XPa2niI+vewYYPvKtwj34zszSYTug3ltFnGbCvaH4/cO0kfQ4kbYem\nUkwtLVuykD/7w4/z1Auv8pWH/h9Hjp0C4Gz/IN//yfN8/yfPs2bVEn77PWt4/9WrOW9BW40rNjOb\nunJC/5zZsmVLYbqrq4uurq5zun9JXHfVJVz9jhX87Jc9bP/x8+w/NHKGT8/ew/TsPcyXH3qCi5dd\nwNVXLOfdV6zgsouX0NLss37MrLq6u7vp7u6e0TbKHd7ZEhHrk/lyhnd2AR+sp+GdsUQEz+zcxyM/\ne5Fndu0jlxv76VsZiVXLzueyVUtZs2oJKy9cxIoLz6O5KVXvqWY2y1RrTL8BeJn8B7mvAU8BN0XE\nzqI+NwCfST7IXQd8cfiD3GT5xeRD/x9MsJ/UhX6xk6f7+Plzr/D403vY+evXyE32ugEXLu7koiUL\nuWjJQi5c3MnSCxawZFEHFyycT1NTw7kp3MxmrWqfsnkXI6ds/rmkTeSP+Lcmfe4B1jNyyubTSfvX\ngS7gfPJj/HdExFfG2EeqQ7/Ymb4BfrXnIM/u3MeLew6OGgIqh4DOjjYWLWzn/M52FnW209nRynkL\n2ujsaKVzfisd8+exoH0e89takKb0b2pmc4QvzqqR3r5+evYeZverh9h74E32vnaU14+coBI/jYC2\n1hbmt+W/2lqbaZ/XTFtrC23zmmltbaK1pZnWliba5jXT0tLIvOYm5rU00tLcxLyWJlqaGmlpbqS5\nqYFMZk7decNsVnPop8jZ/kFeO3KCA4ePc/DwcV47coIjR09z+OhJjh7vrcgbwnQ0NGRoaWqkuSn/\nJtDc1EjT8PfGTL69sYGGxgaaGhtoaszQ1NhAY0N+vrExU5genm/I5PtkGkRjQwMNGdHY2EBjQ35Z\nY0OGhuKvpC2T0ciyTPLVICT5rxuzMjj068TQUJZjJ89w9EQvbxzv5fjJM5w41cex5PvJ3j5O9Z7l\nxOmz9J0dqHW5NZGRyBTeDEQmIzLF08q/QWQkGhoySCXLM5n8Ngr9R9Ybbht+c8lkRENmZFqMrCc0\n8kbE8Hr5+obX1xhtmeRNa3g/+WUkyxm1vZF+IDS6T1EbJW1Afr/JX2/D2xKM1JasU/y6Dq833D5c\n97DiZaP3ld/e8HRpX3jr/t7Sn9HLi7c7ar0x+42/brL3cfdbuk5xn6mt+9btTLSNSfc7wcFNOQc+\n1TpP3yqssbGBxYs6WLyog8sn6ZvN5ujt6+f0mfzXmbMD9PYN0Humn77+Qc6cHeDs2UH6+gfo6x+k\nv3+Ivv4B+geG6B8Y4uzAYGF6cHCoZn9hTFUugtxQliGytS7FLHVm8newQz/lGhoyLJjfWnjc40xE\nBINDWQYGs/QPDDIwmJ8eHBxiYCjLYPI1MDjE0PD8YI7BoSxD2fz80FCObC7H0FCu0D+byzGUzZEd\nyua/5/LLstlgKJslmwuGhrLkclFYN5tLvrI5srlIvufIZXN188ZkVisz+T/i0J9DJCVj+Y3Mb0vv\n/YQi8m8CuYjCG8XwfDabS9qCXC5X+J7L5fvmonh65Pvw+jHclrRH0ToRjJ5Olg1PB5EsG+47PD2y\nrQhG5mNkO8CobQFjbm/45x/ZBkVt+e9EECVtw/1ykUv6j+xneF/Dw6eF/cdwO6P2W1g2PM3ofbyl\nb7JC8XaKvxdvY2T90T/XcI1vWa9km6PaGF1TaV2j28fYDmO0jbG9saYn2sZY+2WM12Ss7ZwLHtM3\nM0ux8d9QgoaGBo/pm5nNJuN9oDvdM9x80raZ2Rzi0Dczm0Mc+mZmc4hD38xsDnHom5nNIQ59M7M5\nxKFvZjaHOPTNzOYQh76Z2Rzi0Dczm0Mc+mZmc0hZoS9pvaRdknZLum2cPndL6pH0rKS1U1nXzMzO\njUlDX1IGuAf4GHAlcJOkK0r6bABWR8QaYBNwb7nrWuV1d3fXuoRZxa9nZfn1rK1yjvSvBXoiYm9E\nDAIPABtL+mwE7geIiCeBTklLy1zXKsz/qSrLr2dl+fWsrXJCfxmwr2h+f9JWTp9y1jUzs3OkWh/k\nzuQRjmZmViWTPjlL0jpgS0SsT+ZvByIiPl/U517gsYh4MJnfBXwQuGSydYu24cdmmZlNUTWenLUD\nuFTSKuA14EbgppI+24HPAA8mbxLHI+KQpDfKWHdahZuZ2dRNGvoRkZW0GXiU/HDQtojYKWlTfnFs\njYiHJd0gaQ/QC9wy0bpV+2nMzGxCqXkwupmZVV/Nr8j1xVuVJelVSc9JekbSU7Wup95I2ibpkKTn\ni9rOk/SopJcl/V9JnbWssV6M81reIWm/pKeTr/W1rLGeSFou6ceSXpT0gqRbk/Yp/X7WNPR98VZV\n5ICuiLg6Iq6tdTF16Cvkfx+L3Q78KCIuB34M/KdzXlV9Guu1BPhCRFyTfD1yrouqY0PA5yLiSuB9\nwGeSvJzS72etj/R98Vblidr/u9atiHgcOFbSvBH4ajL9VeAfn9Oi6tQ4ryX4lO5piYjXI+LZZPo0\nsBNYzhR/P2sdDr54q/IC+KGkHZL+oNbFzBJLIuIQ5P/jAUtqXE+925zco+tLHiqbHkkXA2uBnwNL\np/L7WevQt8q7PiKuAW4g/+ffb9W6oFnIZz9M3/8C3h4Ra4HXgS/UuJ66I2k+8C3gs8kRf+nv44S/\nn7UO/QPAyqL55UmbTVNEvJZ8PwJ8m/wQms3MoeReUkh6G3C4xvXUrYg4EiOnDP4l8N5a1lNvJDWS\nD/y/jojvJs1T+v2sdegXLvyS1Ez+4q3tNa6pbklqS44CkNQOfBT4VW2rqkti9LjzduBfJ9P/Cvhu\n6Qo2rlGvZRJKwz6Jfz+n6svASxFxV1HblH4/a36efnLK1l2MXLz15zUtqI5JuoT80X2Qv/Dua349\np0bS14Eu4HzgEHAH8B3gm8AKYC/wqYg4Xqsa68U4r+WHyI9F54BXgU3D49E2MUnXAz8FXiD/fzyA\nPwWeAv43Zf5+1jz0zczs3Kn18I6ZmZ1DDn0zsznEoW9mNoc49M3M5hCHvpnZHOLQNzObQxz6ZmZz\niEPfzGwO+f+WmJ4AzLrYpAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bc7c890>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_k = suite.Marginal(1)\n",
    "thinkplot.Pdf(pmf_k)\n",
    "pmf_k.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "This example has some of the same problems as the previous one.  Based on this data alone, we can't pin down the parameters much."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Pulling it together"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Exercise:** 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",
    "3. If `flag` is `lt`, it means that `x` is the elapsed time between installation and the first time the bulb is seen broken, so it is an upper bound on the lifespan."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "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": 138,
   "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>2.774019</td>\n",
       "      <td>2.825285</td>\n",
       "      <td>5.599304</td>\n",
       "      <td>7.174715</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.033192</td>\n",
       "      <td>2.500699</td>\n",
       "      <td>2.533891</td>\n",
       "      <td>7.499301</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1.925105</td>\n",
       "      <td>2.532305</td>\n",
       "      <td>4.457409</td>\n",
       "      <td>7.467695</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1.624698</td>\n",
       "      <td>2.734737</td>\n",
       "      <td>4.359435</td>\n",
       "      <td>7.265263</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>3.059679</td>\n",
       "      <td>9.948350</td>\n",
       "      <td>13.008029</td>\n",
       "      <td>0.051650</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   lifespan     start        end     age_t\n",
       "0  2.774019  2.825285   5.599304  7.174715\n",
       "1  0.033192  2.500699   2.533891  7.499301\n",
       "2  1.925105  2.532305   4.457409  7.467695\n",
       "3  1.624698  2.734737   4.359435  7.265263\n",
       "4  3.059679  9.948350  13.008029  0.051650"
      ]
     },
     "execution_count": 138,
     "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": 139,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "('eq', 2.7740187876376514)\n",
      "('eq', 0.033191835029170835)\n",
      "('eq', 1.9251045164134486)\n",
      "('eq', 1.6246975808450324)\n",
      "('gt', 0.051650080517378072)\n",
      "('eq', 0.54033658915724336)\n",
      "('eq', 3.4794664666831596)\n",
      "('eq', 1.1735920449857651)\n",
      "('eq', 1.5235002423078943)\n",
      "('gt', 2.8280320250229369)\n",
      "('eq', 0.30605110358253595)\n",
      "('eq', 1.1068715160667255)\n",
      "('eq', 0.59315846063572297)\n",
      "('eq', 0.67589677779779023)\n",
      "('eq', 1.7580469646846322)\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": 140,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Hint\n",
    "\n",
    "class LightBulb4(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        lam, k = hypo\n",
    "        flag, x = data\n",
    "        like = 1\n",
    "        return like"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 141,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 142,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "from itertools import product\n",
    "\n",
    "lams = np.linspace(0.001, 10, 101)\n",
    "ks = np.linspace(0.001, 10, 101)\n",
    "\n",
    "suite = LightBulb4(product(lams, ks))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 143,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9999999999998264"
      ]
     },
     "execution_count": 143,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "suite.UpdateSet(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXQAAAEACAYAAACj0I2EAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bbaa710>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Contour(suite)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0005000000008701"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uRplRnALsqKqdVbUb2ARMDtRMAtcCVNWtwLIky4f0PaaqbumWbwLO3rOzJJPAg8A9szus\nxcV/BE/xXDzFc/EUz8XcjBIUhwMP960/0rWNUtPqe3eSs7rlc4AVAN0lqLXA5UBGGJ8kaR7N183s\nUX7Bvx24MMltwEHAL7r2y4APVtXPZ7AvSdJ8qarmC1gF3NC3fglw8UDN1cCb+tbvA5aP0rdrXwl8\nvVv+Kr3LTg8CjwE/Ai7YS5/y5cuXL18zfw37vT/4WspwtwEvTnIU8H3gXGD1QM1m4ELgs0lWAY9X\n1XSSH+2rb5LnV9UPuxve76O7AV5Vr9qz0ySXAT+tqo8ODqqqnGlI0jNgaFBU1RNJLgK20rtUtb6q\ntiVZ09tc11TVliRnJHkA+Blwfqtvt+vVSS6kl3BfqKpPPu1HJ0mas3SXcSRJ2qv98snsUR4AXAyS\nrEhyc5J7knw7yTvHPaZxSrIkyTeTbB73WMYtybIkn0+yrfv78Ypxj2lckvx1kruT3JXk00kOHPeY\nnilJ1ieZTnJXX9shSbYm2Z7kxiTLhu1nvwuKUR4AXER+Cby7qo4H/pjep8gW67kAeBdw77gHsUB8\nGNhSVS8BTgS2Dan/rZTkBcBfASdX1Qn0LrefO95RPaM20Ptd2e8S4KaqOha4Gbh02E72u6BgtAcA\nF4WqerSq7uiW/5veL4PBZ1wWhSQrgDPoPfG/qCX5PeBPq2oDQFX9sqp+MuZhjdMBwEFJlgLPAb43\n5vE8Y7qHmh8baJ4ENnbLG4E3DtvP/hgUozwAuOgkeSFwEnDreEcyNh8E3kPvwxGL3R8AP0qyobsU\nd02S3xn3oMahqr5H7+uAHgJ20ftE5k3jHdXYHVpV09B7swkcOqzD/hgUGtA9zX4d8K5uZrGoJDkT\nmO5mV8GHNJcCJwMfqaqTgZ/Tu9yw6CR5Lr130EcBLwAOTvLm8Y5qwRn65mp/DIpdwJF96yu6tkWp\nm05fB3yqqq4f93jG5JXAWUkeBP4VeE2Sa8c8pnF6BHi4qm7v1q+jFxyL0euAB6vqx1X1BPAF4E/G\nPKZxm+6+i48khwE/GNZhfwyKJx8A7D69cC69B/4Wq38B7q2qD497IONSVe+tqiOr6kX0/j7cXFXn\njXtc49JdVng4yTFd02tZvDf5HwJWJXl2ktA7F4vtxv7gLHsz8NZu+S3A0DeYozyZvaAMeYhvUUny\nSuAvgW8n+Ra9KeR7q+qG8Y5MC8A7gU8neRa9r8M5f8zjGYuq+kaS64BvAbu7P68Z76ieOUk+A0wA\nz0vyEL3v0ns/8PkkbwN20vtS1vZ+fOBOktSyP156kiQ9gwwKSVKTQSFJajIoJElNBoUkqcmgkCQ1\nGRSSpCaDQpLU9P9+FQO0RdI8uwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bd40f10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_lam = suite.Marginal(0)\n",
    "thinkplot.Pdf(pmf_lam)\n",
    "pmf_lam.Mean()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "5.0005000000008701"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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uRplRnALsqKqdVbUb2ARMDtRMAtcCVNWtwLIky4f0PaaqbumWbwLO3rOzJJPAg8A9szus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\nGRSSpCaDQpLU9P9+FQO0RdI8uwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16be16c10>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pmf_k = suite.Marginal(1)\n",
    "thinkplot.Pdf(pmf_k)\n",
    "pmf_k.Mean()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "## Prediction\n",
    "\n",
    "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": "markdown",
   "metadata": {},
   "source": [
    "The probability that any given bulb has burned out comes from the CDF of the distribution."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.29781149867344037"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "lam = 2\n",
    "k = 1.5\n",
    "p = EvalWeibullCdf(1, lam, k)\n",
    "p"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The number of bulbs that have burned out is distributed Binom(n, p).\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "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 0x7fc16b9b1510>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from thinkbayes2 import MakeBinomialPmf\n",
    "\n",
    "n = 100\n",
    "pmf_c = MakeBinomialPmf(n, p)\n",
    "thinkplot.Pdf(pmf_c)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Or we can approximate the distribution with a random sample."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "(29.881, 4.560135853239462)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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h+eevuhyRiXaW9KNQYJ2dUYMzSGmX5GI0JpRatkhgzNCeTnvDTts/1zSOJf0o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\nCi48IzzusgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7fc16bf4a050>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "n = 100\n",
    "sample = np.random.binomial(n, p, 1000)\n",
    "pdf_c = thinkbayes2.EstimatedPdf(sample)\n",
    "thinkplot.Pdf(pdf_c)\n",
    "np.mean(sample), np.std(sample)"
   ]
  },
  {
   "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": 44,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# Solution goes here"
   ]
  },
  {
   "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": "2.7.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}