solutions/shuttle_soln.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Think Bayes\n",
    "\n",
    "Copyright 2018 Allen B. Downey\n",
    "\n",
    "MIT License: https://opensource.org/licenses/MIT"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Configure Jupyter so figures appear in the notebook\n",
    "%matplotlib inline\n",
    "\n",
    "# Configure Jupyter to display the assigned value after an assignment\n",
    "%config InteractiveShell.ast_node_interactivity='last_expr_or_assign'\n",
    "\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "\n",
    "# import classes from thinkbayes2\n",
    "from thinkbayes2 import Pmf, Cdf, Suite, Joint\n",
    "\n",
    "import thinkplot"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## The Space Shuttle problem\n",
    "\n",
    "Here's a problem from [Bayesian Methods for Hackers](http://nbviewer.jupyter.org/github/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/blob/master/Chapter2_MorePyMC/Ch2_MorePyMC_PyMC2.ipynb)\n",
    "\n",
    ">On January 28, 1986, the twenty-fifth flight of the U.S. space shuttle program ended in disaster when one of the rocket boosters of the Shuttle Challenger exploded shortly after lift-off, killing all seven crew members. The presidential commission on the accident concluded that it was caused by the failure of an O-ring in a field joint on the rocket booster, and that this failure was due to a faulty design that made the O-ring unacceptably sensitive to a number of factors including outside temperature. Of the previous 24 flights, data were available on failures of O-rings on 23, (one was lost at sea), and these data were discussed on the evening preceding the Challenger launch, but unfortunately only the data corresponding to the 7 flights on which there was a damage incident were considered important and these were thought to show no obvious trend. The data are shown below (see [1](https://amstat.tandfonline.com/doi/abs/10.1080/01621459.1989.10478858)):\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !wget https://raw.githubusercontent.com/CamDavidsonPilon/Probabilistic-Programming-and-Bayesian-Methods-for-Hackers/master/Chapter2_MorePyMC/data/challenger_data.csv"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>Temperature</th>\n",
       "      <th>Damage Incident</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1981-04-12</td>\n",
       "      <td>66</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1981-11-12</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1982-03-22</td>\n",
       "      <td>69</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1982-01-11</td>\n",
       "      <td>68</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1983-04-04</td>\n",
       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1983-06-18</td>\n",
       "      <td>72</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1983-08-30</td>\n",
       "      <td>73</td>\n",
       "      <td>0</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1983-11-28</td>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1984-02-03</td>\n",
       "      <td>57</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1984-04-06</td>\n",
       "      <td>63</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1984-08-30</td>\n",
       "      <td>70</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>1984-10-05</td>\n",
       "      <td>78</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>1984-11-08</td>\n",
       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1985-01-24</td>\n",
       "      <td>53</td>\n",
       "      <td>1</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>1985-04-12</td>\n",
       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>1985-04-29</td>\n",
       "      <td>75</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>1985-06-17</td>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>1985-07-29</td>\n",
       "      <td>81</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>1985-08-27</td>\n",
       "      <td>76</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>1985-10-03</td>\n",
       "      <td>79</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>1985-10-30</td>\n",
       "      <td>75</td>\n",
       "      <td>1</td>\n",
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       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1985-11-26</td>\n",
       "      <td>76</td>\n",
       "      <td>0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1986-01-12</td>\n",
       "      <td>58</td>\n",
       "      <td>1</td>\n",
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      "text/plain": [
       "         Date  Temperature Damage Incident\n",
       "0  1981-04-12           66               0\n",
       "1  1981-11-12           70               1\n",
       "2  1982-03-22           69               0\n",
       "4  1982-01-11           68               0\n",
       "5  1983-04-04           67               0\n",
       "6  1983-06-18           72               0\n",
       "7  1983-08-30           73               0\n",
       "8  1983-11-28           70               0\n",
       "9  1984-02-03           57               1\n",
       "10 1984-04-06           63               1\n",
       "11 1984-08-30           70               1\n",
       "12 1984-10-05           78               0\n",
       "13 1984-11-08           67               0\n",
       "14 1985-01-24           53               1\n",
       "15 1985-04-12           67               0\n",
       "16 1985-04-29           75               0\n",
       "17 1985-06-17           70               0\n",
       "18 1985-07-29           81               0\n",
       "19 1985-08-27           76               0\n",
       "20 1985-10-03           79               0\n",
       "21 1985-10-30           75               1\n",
       "22 1985-11-26           76               0\n",
       "23 1986-01-12           58               1"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "columns = ['Date', 'Temperature', 'Incident']\n",
    "df = pd.read_csv('challenger_data.csv', parse_dates=[0])\n",
    "df.drop(labels=[3, 24], inplace=True)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
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       "      <td>67</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>1985-01-24</td>\n",
       "      <td>53</td>\n",
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       "      <td>1.0</td>\n",
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       "      <td>67</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>75</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>17</th>\n",
       "      <td>1985-06-17</td>\n",
       "      <td>70</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>18</th>\n",
       "      <td>1985-07-29</td>\n",
       "      <td>81</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>1985-08-27</td>\n",
       "      <td>76</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <th>20</th>\n",
       "      <td>1985-10-03</td>\n",
       "      <td>79</td>\n",
       "      <td>0</td>\n",
       "      <td>0.0</td>\n",
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       "      <td>1985-10-30</td>\n",
       "      <td>75</td>\n",
       "      <td>1</td>\n",
       "      <td>1.0</td>\n",
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       "      <td>1985-11-26</td>\n",
       "      <td>76</td>\n",
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       "      <td>0.0</td>\n",
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       "      <td>1986-01-12</td>\n",
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      "text/plain": [
       "         Date  Temperature Damage Incident  Incident\n",
       "0  1981-04-12           66               0       0.0\n",
       "1  1981-11-12           70               1       1.0\n",
       "2  1982-03-22           69               0       0.0\n",
       "4  1982-01-11           68               0       0.0\n",
       "5  1983-04-04           67               0       0.0\n",
       "6  1983-06-18           72               0       0.0\n",
       "7  1983-08-30           73               0       0.0\n",
       "8  1983-11-28           70               0       0.0\n",
       "9  1984-02-03           57               1       1.0\n",
       "10 1984-04-06           63               1       1.0\n",
       "11 1984-08-30           70               1       1.0\n",
       "12 1984-10-05           78               0       0.0\n",
       "13 1984-11-08           67               0       0.0\n",
       "14 1985-01-24           53               1       1.0\n",
       "15 1985-04-12           67               0       0.0\n",
       "16 1985-04-29           75               0       0.0\n",
       "17 1985-06-17           70               0       0.0\n",
       "18 1985-07-29           81               0       0.0\n",
       "19 1985-08-27           76               0       0.0\n",
       "20 1985-10-03           79               0       0.0\n",
       "21 1985-10-30           75               1       1.0\n",
       "22 1985-11-26           76               0       0.0\n",
       "23 1986-01-12           58               1       1.0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df['Incident'] = df['Damage Incident'].astype(float)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "\n",
    "plt.scatter(df.Temperature, df.Incident, s=75, color=\"k\",\n",
    "            alpha=0.5)\n",
    "plt.yticks([0, 1])\n",
    "plt.ylabel(\"Damage Incident?\")\n",
    "plt.xlabel(\"Outside temperature (Fahrenheit)\")\n",
    "plt.title(\"Defects of the Space Shuttle O-Rings vs temperature\");"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Grid algorithm\n",
    "\n",
    "We can solve the problem first using a grid algorithm, with parameters `b0` and `b1`, and\n",
    "\n",
    "$\\mathrm{logit}(p) = b0 + b1 * T$\n",
    "\n",
    "and each datum being a temperature `T` and a boolean outcome `fail`, which is true is there was damage and false otherwise.\n",
    "\n",
    "Hint: the `expit` function from `scipy.special` computes the inverse of the `logit` function."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy.special import expit\n",
    "\n",
    "class Logistic(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"\n",
    "        \n",
    "        data: T, fail\n",
    "        hypo: b0, b1\n",
    "        \"\"\"\n",
    "        return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Solution\n",
    "\n",
    "from scipy.special import expit\n",
    "\n",
    "class Logistic(Suite, Joint):\n",
    "    \n",
    "    def Likelihood(self, data, hypo):\n",
    "        \"\"\"\n",
    "        \n",
    "        data: T, fail\n",
    "        hypo: b0, b1\n",
    "        \"\"\"\n",
    "        temp, fail = data\n",
    "        b0, b1 = hypo\n",
    "        \n",
    "        log_odds = b0 + b1 * temp\n",
    "        p_fail = expit(log_odds)\n",
    "        if fail == 1:\n",
    "            return p_fail\n",
    "        elif fail == 0:\n",
    "            return 1-p_fail\n",
    "        else:\n",
    "            # NaN\n",
    "            return 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "b0 = np.linspace(0, 50, 101);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "b1 = np.linspace(-1, 1, 101);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<itertools.product at 0x7f25c84d75e8>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from itertools import product\n",
    "hypos = product(b0, b1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "suite = Logistic(hypos);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(66, 0.0)\n",
      "(70, 1.0)\n",
      "(69, 0.0)\n",
      "(68, 0.0)\n",
      "(67, 0.0)\n",
      "(72, 0.0)\n",
      "(73, 0.0)\n",
      "(70, 0.0)\n",
      "(57, 1.0)\n",
      "(63, 1.0)\n",
      "(70, 1.0)\n",
      "(78, 0.0)\n",
      "(67, 0.0)\n",
      "(53, 1.0)\n",
      "(67, 0.0)\n",
      "(75, 0.0)\n",
      "(70, 0.0)\n",
      "(81, 0.0)\n",
      "(76, 0.0)\n",
      "(79, 0.0)\n",
      "(75, 1.0)\n",
      "(76, 0.0)\n",
      "(58, 1.0)\n"
     ]
    }
   ],
   "source": [
    "for data in zip(df.Temperature, df.Incident):\n",
    "    print(data)\n",
    "    suite.Update(data)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(suite.Marginal(0))\n",
    "thinkplot.decorate(xlabel='Intercept',\n",
    "                   ylabel='PMF',\n",
    "                   title='Posterior marginal distribution')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "thinkplot.Pdf(suite.Marginal(1))\n",
    "thinkplot.decorate(xlabel='Log odds ratio',\n",
    "                   ylabel='PMF',\n",
    "                   title='Posterior marginal distribution')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "According to the posterior distribution, what was the probability of damage when the shuttle launched at 31 degF?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9909003512180481"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "T = 31\n",
    "total = 0\n",
    "\n",
    "for hypo, p in suite.Items():\n",
    "    b0, b1 = hypo\n",
    "    log_odds = b0 + b1 * T\n",
    "    p_fail = expit(log_odds)\n",
    "    total += p * p_fail\n",
    "    \n",
    "total"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9909003512180481"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "pred = suite.Copy()\n",
    "pred.Update((31, True))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### MCMC\n",
    "\n",
    "Implement this model using MCMC.  As a starting place, you can use this example from [the PyMC3 docs](https://docs.pymc.io/notebooks/GLM-logistic.html#The-model).\n",
    "\n",
    "As a challege, try writing the model more explicitly, rather than using the GLM module."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "from warnings import simplefilter\n",
    "simplefilter('ignore', FutureWarning)\n",
    "\n",
    "import pymc3 as pm"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "logp = -18, ||grad|| = 11.915: 100%|██████████| 27/27 [00:00<00:00, 1502.12it/s]      \n",
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [Temperature, Intercept]\n",
      "Sampling 2 chains: 100%|██████████| 4000/4000 [00:06<00:00, 594.28draws/s]\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "with pm.Model() as model:\n",
    "    pm.glm.GLM.from_formula('Incident ~ Temperature', df, \n",
    "                            family=pm.glm.families.Binomial())\n",
    "    \n",
    "    start = pm.find_MAP()\n",
    "    trace = pm.sample(1000, start=start, tune=1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 864x288 with 4 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(trace);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [Temperature, Intercept]\n",
      "Sampling 2 chains:   0%|          | 0/4000 [00:00<?, ?draws/s]\n"
     ]
    },
    {
     "ename": "RuntimeError",
     "evalue": "Chain 0 failed.",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mRemoteTraceback\u001b[0m                           Traceback (most recent call last)",
      "\u001b[0;31mRemoteTraceback\u001b[0m: \n\"\"\"\nTraceback (most recent call last):\n  File \"/home/downey/anaconda3/lib/python3.6/site-packages/pymc3/parallel_sampling.py\", line 73, in run\n    self._start_loop()\n  File \"/home/downey/anaconda3/lib/python3.6/site-packages/pymc3/parallel_sampling.py\", line 113, in _start_loop\n    point, stats = self._compute_point()\n  File \"/home/downey/anaconda3/lib/python3.6/site-packages/pymc3/parallel_sampling.py\", line 139, in _compute_point\n    point, stats = self._step_method.step(self._point)\n  File \"/home/downey/anaconda3/lib/python3.6/site-packages/pymc3/step_methods/arraystep.py\", line 247, in step\n    apoint, stats = self.astep(array)\n  File \"/home/downey/anaconda3/lib/python3.6/site-packages/pymc3/step_methods/hmc/base_hmc.py\", line 117, in astep\n    'might be misspecified.' % start.energy)\nValueError: Bad initial energy: inf. The model might be misspecified.\n\"\"\"",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[0;31mValueError\u001b[0m                                Traceback (most recent call last)",
      "\u001b[0;31mValueError\u001b[0m: Bad initial energy: inf. The model might be misspecified.",
      "\nThe above exception was the direct cause of the following exception:\n",
      "\u001b[0;31mRuntimeError\u001b[0m                              Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-20-18c7e811f775>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m      5\u001b[0m                             family=pm.glm.families.Binomial())\n\u001b[1;32m      6\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m----> 7\u001b[0;31m     \u001b[0mtrace\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtune\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;36m1000\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/pymc3/sampling.py\u001b[0m in \u001b[0;36msample\u001b[0;34m(draws, step, init, n_init, start, trace, chain_idx, chains, cores, tune, nuts_kwargs, step_kwargs, progressbar, model, random_seed, live_plot, discard_tuned_samples, live_plot_kwargs, compute_convergence_checks, use_mmap, **kwargs)\u001b[0m\n\u001b[1;32m    447\u001b[0m             \u001b[0m_print_step_hierarchy\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mstep\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    448\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 449\u001b[0;31m                 \u001b[0mtrace\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0m_mp_sample\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0msample_args\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    450\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mpickle\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mPickleError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    451\u001b[0m                 \u001b[0m_log\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mwarning\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m\"Could not pickle model, sampling singlethreaded.\"\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/pymc3/sampling.py\u001b[0m in \u001b[0;36m_mp_sample\u001b[0;34m(draws, tune, step, chains, cores, chain, random_seed, start, progressbar, trace, model, use_mmap, **kwargs)\u001b[0m\n\u001b[1;32m    997\u001b[0m         \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    998\u001b[0m             \u001b[0;32mwith\u001b[0m \u001b[0msampler\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 999\u001b[0;31m                 \u001b[0;32mfor\u001b[0m \u001b[0mdraw\u001b[0m \u001b[0;32min\u001b[0m \u001b[0msampler\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   1000\u001b[0m                     \u001b[0mtrace\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mtraces\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mdraw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchain\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mchain\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   1001\u001b[0m                     \u001b[0;32mif\u001b[0m \u001b[0mtrace\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msupports_sampler_stats\u001b[0m \u001b[0;32mand\u001b[0m \u001b[0mdraw\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mstats\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/pymc3/parallel_sampling.py\u001b[0m in \u001b[0;36m__iter__\u001b[0;34m(self)\u001b[0m\n\u001b[1;32m    303\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    304\u001b[0m         \u001b[0;32mwhile\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_active\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 305\u001b[0;31m             \u001b[0mdraw\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mProcessAdapter\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mrecv_draw\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_active\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    306\u001b[0m             \u001b[0mproc\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mis_last\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdraw\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtuning\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mstats\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mwarns\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdraw\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    307\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_progress\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0;32mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/pymc3/parallel_sampling.py\u001b[0m in \u001b[0;36mrecv_draw\u001b[0;34m(processes, timeout)\u001b[0m\n\u001b[1;32m    221\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'error'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    222\u001b[0m             \u001b[0mold\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m1\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 223\u001b[0;31m             \u001b[0msix\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mraise_from\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mRuntimeError\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'Chain %s failed.'\u001b[0m \u001b[0;34m%\u001b[0m \u001b[0mproc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mchain\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mold\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    224\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mmsg\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;36m0\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m==\u001b[0m \u001b[0;34m'writing_done'\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    225\u001b[0m             \u001b[0mproc\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_readable\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;32mTrue\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m~/anaconda3/lib/python3.6/site-packages/six.py\u001b[0m in \u001b[0;36mraise_from\u001b[0;34m(value, from_value)\u001b[0m\n",
      "\u001b[0;31mRuntimeError\u001b[0m: Chain 0 failed."
     ]
    }
   ],
   "source": [
    "# Solution\n",
    "\n",
    "with pm.Model() as model:\n",
    "    pm.glm.GLM.from_formula('Incident ~ Temperature', df, \n",
    "                            family=pm.glm.families.Binomial())\n",
    "    \n",
    "    trace = pm.sample(1000, tune=1000)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The posterior distributions for these parameters should be similar to what we got with the grid algorithm."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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