markdregan/pymc_post_pred_hierarchal.ipnb

## pymc_post_pred_hierarchal.ipnb
{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "###Plot posterior predictive distribution from hierarchal model"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 74,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Import libraries needed\n",
    "import json\n",
    "import matplotlib.pyplot as plt\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pymc3 as pm\n",
    "import scipy\n",
    "import scipy.stats as stats\n",
    "import statsmodels.api as sm\n",
    "import theano.tensor as tt\n",
    "\n",
    "from datetime import datetime\n",
    "from sklearn import preprocessing\n",
    "\n",
    "%matplotlib inline\n",
    "plt.style.use('bmh')\n",
    "colors = ['#348ABD', '#A60628', '#7A68A6', '#467821', '#D55E00', \n",
    "          '#CC79A7', '#56B4E9', '#009E73', '#F0E442', '#0072B2']\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 75,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data = pd.DataFrame(np.random.poisson(10, 100))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 76,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 20000 of 20000 complete in 5.3 sec"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    alpha = pm.Gamma('alpha', alpha=.1, beta=.1)\n",
    "    mu = pm.Gamma('mu', alpha=.1, beta=.1)\n",
    "    y_pred = pm.NegativeBinomial('y_pred', mu=mu, alpha=alpha)\n",
    "    y_est = pm.NegativeBinomial('y_est', mu=mu, alpha=alpha, observed=data)\n",
    "    \n",
    "    start = pm.find_MAP()\n",
    "    step = pm.Metropolis(start=start)\n",
    "    trace = pm.sample(20000, step, start=start, progressbar=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 77,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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6C/4UZ6fp85zIdbUdeAh4xEP7SGnbSbRP2hitTpv8rYj0A54Ffq+qz4UqqGqb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\nA8AAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x151e68b50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "_ = pm.traceplot(trace, vars=['alpha', 'mu'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 78,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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pn5uZtwH3RsQB9URyR/PkWeclSZIkSRpIE7vcbg/gSx3LHgSe2u2JIuJcqkni\nnhERNwMfBE4DzouINwOLgdcAZObCiDgPWEg1Qd3x+fgt/+OBL9bnviAznTROo8a76CrFK/sqwbxT\nKeaeSjDvNCi6LdJ/B+wLXN62bD/gt92eKDOPXM2ql6xm+1OBU4dZ/itgarfnlSRJkiRpUHTb3f0D\nwPci4sPARhHxPmAW8P96FplUwHh+TrrKak04IjXJvFMp5p5KMO80KLoq0jPze8ChwDOB/wWmAK/M\nzB/1MDZJkiRJksaVtXZ3j4iJwG+APTLzuN6HJJXjmHSV4jg5lWDeqRRzTyWYdxoUa72TnpmPAitZ\nh0niJEmSJEnSuut2TPongf+JiEMiYueIeFbr1cvgpKY5Jl2lOE5OJZh3KsXcUwnmnQbFGru7R8TW\n9bPJP1MvemnHJgls0IvAJA2YKB2AJEmSNPjWNib9OmDzzJwAEBHfysxX9j4sqQzHpI/c0h/8nA2e\nuvGI9p242SY88yXPZ8NJm49yVIPDcXIqwbxTKeaeSjDvNCjWVqR33hs7pEdxSBpwv/nQf4543423\n35otD95/FKORJEmSBlO3Y9KlccEx6SrFcXIqwbxTKeaeSjDvNCjWdid9g4h4cf0+gIltbQAy8yc9\niUySJEmSpHFmbUX6MuCMtvadHW2AnUY1Iqkgx6SrFMfJqQTzTqWYeyrBvNOgWGORnpk7NhSHJEmS\nJEnjnmPSpTaOSVcpjpNTCeadSjH3VIJ5p0FhkS5JkiRJUp+wSJfaOCZdpThOTiWYdyrF3FMJ5p0G\nxdomjlPDMpNcuXLE+094ykajGI0kSZIkqUkW6X1m+e+XseCEj7DykRUj2j9XjGw/VRaufMC76Spi\nzpw5XuFX48w7lWLuqQTzToPCIr0P3f3LBaxc/kjpMCRJkiRJDXNMutTGu+gqxSv7KsG8Uynmnkow\n7zQoLNIlSZIkSeoTFulSG5+TrlJ8dqtKMO9UirmnEsw7DQqLdEmSJEmS+oRFutTGMekqxXFyKsG8\nUynmnkow7zQo+qJIj4jFEXFVRFwREXPrZU+PiIsi4rqIuDAitmjb/qSI+G1EXBsRLysXuSRJkiRJ\no6cvinQggUMyc+/M3L9ediJwUWbuBsyu20TEHsBrgT2AQ4HPRUS/fA4NOMekqxTHyakE806lmHsq\nwbzToOin4jY62ocBZ9fvzwaOqN8fDpybmSsyczFwPbA/kiRJkiQNuH4p0hP4cUT8MiLeUi/bKjOX\n1u+XAltanYnyAAAgAElEQVTV77cFbmnb9xZgu2bC1FjnmHSV4jg5lWDeqRRzTyWYdxoUE0sHUDsw\nM2+NiGcCF0XEte0rMzMjItew/5rWSZIkSZI0EPqiSM/MW+s/b4+Ib1F1X18aEVtn5m0RsQ2wrN58\nCbBD2+7b18tWmTVrFjNnzmTKlCkATJo0ialTp666etYaj9Kv7asfvZ9cuWLVXd3WOGnbvW+3j0nv\nh3jGS3ujh+7i+VRK//0r1W4t65d4bI+P9owZMwbq30fbY6fd+d++0vHYHh/tBQsWcNxxx/VNPLbH\nbnvGjBksWLBgVT06efJkhoaG6FZklr0JHRGbABtk5n0RsSlwIfAvwEuAOzPzYxFxIrBFZp5YTxz3\nVapCfjvgx8Au2fZBZs+endOnT2/8s4yGh5Ys5eIDX8vK5Y+UDmVcWrjyAbu8F7Dx9ltz4Oyz2XDS\n00qHUsycOXNW/Yddaop5p1LMPZVg3qmUefPmMTQ01DkH22pN7GUwXdoK+FZEQBXPVzLzwoj4JXBe\nRLwZWAy8BiAzF0bEecBC4FHg+Cx9pUFjhgV6GY/c8QeueucpjPQ5DU/bY1d2fe9b1r5hH/N/GlSC\neadSzD2VYN5pUBQv0jPzRmDaMMv/QHU3fbh9TgVO7XFokhqycvkj3H7hnLVvuBqP3v/QKEYjSZIk\nldMvs7tLfcHnpKuU9vGZUlPMO5Vi7qkE806DwiJdkiRJkqQ+YZEutXFMukpxnJxKMO9UirmnEsw7\nDQqLdEmSJEmS+oRFutTGMekqxXFyKsG8Uynmnkow7zQoLNIlSZIkSeoTFulSG8ekqxTHyakE806l\nmHsqwbzToLBIlyRJkiSpT0wsHYDUTxaufMC76QPowRtu5obPfmXE+2+x73N5+gF7jWJE627OnDle\n4VfjzDuVYu6pBPNOg8IifZQ99vAj3LfwevLRx0a0f2w4EXKUg5LGuOW/X8Z1p3x2xPs/64Q3FC/S\nJUmSJLBIH3UrH1nBr999Kvdfe0PpUDQC3kVXKV7ZVwnmnUox91SCeadB4Zh0SZIkSZL6hEW61Mbn\npKsUn92qEsw7lWLuqQTzToPCIl2SJEmSpD5hkS61cUy6SnGcnEow71SKuacSzDsNCieOkzTu3fqd\n2Ty87M4R77/9UX/JH+03dRQjkiRJ0nhlkS618Tnp49NDi29hyeJbRrz/lgfus95Fus9uVQnmnUox\n91SCeadBYXd3SZIkSZL6hEW61Ma76CrFK/sqwbxTKeaeSjDvNCgs0iVJkiRJ6hOOSZfaOCZdI/HA\n75Zw1+ULRrz/U7baknk33eAVfjXO8ZkqxdxTCeadBoVF+jDu+uWvWXHnXSPaNyZuwKP3PTDKEUnq\nZ4s+PpNFH5854v33+fK/w8ajGJAkSZIGlkX6MG46cxa3fvPC0mGoAO+iq4TYcCLP3/d5PLZ8+cj2\n32AiEzb0P+dad95RUinmnkow7zQo/L86SSrs6vd+nA23eNqI93/u6Scx8WmbjHj/DbfYnA0njfz8\nkiRJGj0DWaRHxKHAfwAbADMz82OFQ9IY4Zh0lfDQ75bwqxtHnnuXvuQN63X+F1zyNYv0ccrxmSrF\n3FMJ5p0GxcDN7h4RGwCfAQ4F9gCOjIjdy0alsWLxypF1N5bWl7mnEhYsGPmEh9L6MPdUgnmnUubP\nn79O2w/infT9geszczFARHwNOBy4pn2jh5YsHdHBJ2w4kXxs5XqGqEH1IP72KqNk7sXEiTx8+x9G\nvP+Gk57GhI02HMWI1JR77rmndAgap8w9lWDeqZQrr7xynbYfxCJ9O+DmtvYtwAGdG815wZEjPsHK\nh1eMeF9JGjSXHf42iBjRvhtuvhl7/vuJ5IpHR7T/hI02ZPNpz2HCxEH850iSJGn0DeL/FWU3G+19\nxkd7HYfGoK//5+ns+873lA5D49Ag595j9z844n0nPGUjYsIEcuXIehLEhIEbtdVXbrrpptIhaJwy\n91SCeadBMYhF+hJgh7b2DlR301eZP38+Z7d1Kdhrr72YNm1aM9FpoB34ikO5aZLddtW88Zt7D8M6\njtPS6Nl3332ZN29e6TA0Dpl7KsG8U1Pmz5//hC7um266bpMDR2ZXN6b7RkRMBH4DDAG/B+YCR2bm\nNWvcUZIkSZKkPjdwd9Iz89GIeAfwI6pHsJ1hgS5JkiRJGgsG7k66JEmSJEljlTPuaNyKiDMjYmlE\nLGhb9vSIuCgirouICyNii5IxauyJiB0i4qcRcXVE/Doi3lUvN/fUUxGxcURcFhHzI2JhRHy0Xm7u\nqeciYoOIuCIizq/b5p16LiIWR8RVde7NrZeZe+qpiNgiImZFxDX1v7cHrGveWaRrPDsLOLRj2YnA\nRZm5GzC7bkujaQXw7szcE/gT4O0RsTvmnnosM5cDL8rMacDzgBdFxEGYe2rGCcBCHn9Kj3mnJiRw\nSGbunZn718vMPfXap4ALMnN3qn9vr2Ud884iXeNWZl4M3NWx+DDg7Pr92cARjQalMS8zb8vM+fX7\n+4FrgO0w99SAzGw9L28jqnld7sLcU49FxPbAXwAzgagXm3dqSnS0zT31TERMAl6QmWdCNZ9aZt7D\nOuadRbr0RFtl5tL6/VJgq5LBaGyLiB2BvYHLMPfUgIiYEBHzqXLsp5l5Neaeeu+TwD8BK9uWmXdq\nQgI/johfRsRb6mXmnnppJ+D2iDgrIuZFxBciYlPWMe8s0qXVyGpWRWdWVE9ExGbAN4ATMvO+9nXm\nnnolM1fW3d23B14YES/qWG/uaVRFxCuAZZl5BU++owmYd+qpAzNzb+DPqYaXvaB9pbmnHpgITAc+\nl5nTgQfo6NreTd5ZpEtPtDQitgaIiG2AZYXj0RgUERtSFehfysxv14vNPTWm7nr3fWAfzD311p8C\nh0XEjcC5wIsj4kuYd2pAZt5a/3k78C1gf8w99dYtwC2ZeXndnkVVtN+2LnlnkS490XeBN9Tv3wB8\new3bSussIgI4A1iYmf/RtsrcU09FxDNas8lGxFOBlwJXYO6phzLzfZm5Q2buBPwN8JPMPBrzTj0W\nEZtExNPq95sCLwMWYO6phzLzNuDmiNitXvQS4GrgfNYh73xOusatiDgXOBh4BtXYkA8C3wHOA6YA\ni4HXZObdpWLU2FPPpv1z4Coe7+p0EjAXc089FBFTqSarmVC/vpSZH4+Ip2PuqQERcTDwnsw8zLxT\nr0XETlR3z6HqgvyVzPyouadei4i9qCbK3AhYBLyJarLWrvPOIl2SJEmSpD5hd3dJkiRJkvqERbok\nSZIkSX3CIl2SJEmSpD5hkS5JkiRJUp+wSJckSZIkqU9YpEuSJEmS1Ccs0iVJkiRJ6hMW6ZIkSZIk\n9QmLdEmSJEmS+oRFuiRJkiRJfcIiXZI0ECLiixFxUY+O/caIWLG6dg/O96GI+G2vjr+uImJqRMyN\niIci4ob1OM7PIuILoxlbPxjp54qIlRFxVC9ikiSNXRbpkqRi6sJ7Zf16JCJuj4iLI+KfImKTjs3f\nCbx6HY79aEQc0+XmXwO27fbY6xDDQfVnm9Kx6uPAAaN9vvXwb8DdwLOB/dbjOFm/xppGPldEvD4i\nVvb6PJKk/maRLkkq7efA1sAU4BDgK8A7gHkRMbm1UWbel5n3rMNxE4g1bRCViZm5PDNvX+fIu/eE\nODLzgcz8Qw/Pt652AX6emTdl5p2lg1lXETGxdAySJI0Wi3RJUmkrMnNZZt6WmVdn5ueB5wPPBE5r\nbdTZ3T0i9oyIH0XEXRFxf0QsjIjX1+sWAxsAZ9V3sh+rl78xIlZExCERcQWwHHjJ6rq3R8RQRFxd\ndwP/RUTs1bbuSftExPb1+V4YETtSXYAAuLFe/pN6uyd1d4+IN9Sf4eGIuDkiTomIDdrW/ywivhAR\n/y8ibo2IOyPi7IjYdE1fbkRsExFfq7+nByPipxGxT71ux/rO7c7Ah+sYP7iGY60xxtoGEXFa3Svi\nnoj4r4h4StsxDoqISyLi3vo1PyJe1rZ+q/q3XlavnxMRL2hbf0gd51/U6x4Cjo+IByLiyI54t617\nVLy4bm9Yf/c31L/pryPi7zr2+eOI+GH9Xd0UEe9c0/fbtt+LIuKq+rhXRsSLhtnmX+vv74H62DMi\nYvPW5wLOqd+3epecWbdfWv/+d0bE3fX79enxIEnqYxbpkqS+k5m/p7qj/ledq9renwvcTlXQPxf4\nB+Cuet2+wGPACVR36bdp228CVfH/91Tdu3+5mjAmAB8D3gbsX5/r+xGxcZcf4ybg8Pr9fnUcnZ8H\ngIh4OXAGcDawJ/Ae4O3AyR2bvhrYAjgY+BvgFcA/ry6AiAjg28BuwMvrz7EUuCgitqxj3Aa4heo7\n2Ro4fT1ijDrGPwIOAl4HHAF8tD7GROC7wP8Be9evk4EH6/VPBX4KbAocCkwDLqjjfU5HSKfXx30O\n8I36cx7dsc3rgSWZ+ZO6/YU6nr+r9/sw8LGIOLbt+/pWHf/BwF/Wr+nDfSdt3822wPeAy+vP9B7g\nU8Ns+iDwFmB34I1UPUc+Xa+7hKoHCVS/w9ZU+Uv9fXwG+BOqfP8t8MOIePqa4pIkDSa7h0mS+tVC\nYPOIeEZm3lEva+82PgU4PTOvrduLWysy846q3uKezFzWcdwA3pOZl6xaEMP2ig/gnzLz4nqbo4Gb\ngaOAM9cWfGaujIjWRYPbh4mj3YnArMz8WN2+PiK2Bk6LiA9n5qOtz5iZ76nfXxcR/wO8BFjd3e8X\nU10g2KP1PUU1Tn8xcHxmngIsjaqnwf2jFOOdwNsyM4HfRMQHgE9HxPuBjakuMpyfmYvq7Re1neO1\nwNOAv8nMx+plp0bES4C3Au9u2/Yjmfn9ViMizgG+FxFbZebSevHRwJfr9TvV7d0z87p6/e/q4v+d\nVL/pENWFgd0y8/p6v6OoLmasyfHAMuAtmbkSuDYiTgLOb98oM/+1rXlTRLyP6mLTGzNzRUTcW2+3\nrGO/b7e3I+KtwKuoLmR8dS2xSZIGjHfSJUn9qlU5r27Crn8HZtbdt0+OiL3X4diXd7nd/7XeZObd\nwDXAHutwnm7tweNd41t+TlXU7ty27MqObW4FtlrDcfcE7my7kEFmPgJcVq/rRYxz6wK95VLgKcDO\nmXkXMBP4UURcEBH/HBG7tW3b6nFwd0Tc13pR3ZXfpePcczvaP6YqlI8CiIjp9Wc8p16/L1VO/arj\n2Ce1HXsP4I5WgQ7VBR/gN6v9Vh7fb25doLdc0rlRRPxVRPw8IpbU5/4ysGF9sWO1ImKniPhSRPw2\nIu4B7gEmUV2okiSNMRbpkqR+tSdw9+omMsvMj1B14z6Pqrv7LyLilC6O+1hdqI5E+y334Wbh3nCE\nx+1GAp1xJyP7tzzo3Wzla5ysLzP/DtgHuIiqS3n7uPAJVBdC9up4PYeqm3i7BzqO+xjVEInWjP7H\nUBXOrQK79T09v+PYewLPW5/PRHeTFB5Alas/o+pyvzfVUIoANlrL8b8HbE91x/4Aqrv9y7rYT5I0\ngCzSJUmlPalYjIjtqMYzf3NN22bmjZk5IzP/mmps83Ftqx+hmjxufTy/LaYtqIrFhfWiZVSTpE1u\n275z7HKrqF5bHFdTFaztDqYaw7zoyZt37Wpgy4jYvbWgnsTtAODXIzhWNzHuFxHt/3/xp8DD7dvU\nEwR+MjP/gmqce6tI/yXwLOC+zLyh43VbFzGeA+wVEdOAI3n8LjrAr+o//3iYY99Yr1sIPCMiVt21\nj4hnUF0MWpOFwP4dn/vAjm0OorpL/8HMvLy+W79DxzaP1OdcVfDXcwfsDpyWmRfVvSIeBiYjSRqT\nLNIlSaU9pZ7Re9uImBoRx1F1M7+NqityuwCIiM0i4rP1jNo71V3dD6UqJFtuBF4c1ezmzxhBXEk1\nqdgLImIqVcF3L4+PAb4MuI9qTPauEXEoTx4b/juqO+4vj4jJETFpNef6KPCqVvfviHgN1UWH09vG\negdrv6P7xA+QOZuqW/hXI+JPI+K59efYCJjRtmk3x+0mRoAtgc9GxHPqyeY+DHw+Mx+KiF0i4mMR\ncWBUs6g/H3gBj/9uX6b63b5fz2i+Y0QcEBEnRcThrEVm/hq4AjgL2JxqvHdr3fVU486/ENXzyHeJ\niL0i4tiIeG+9zY+phhR8OSL2q4v9rwBPmvm/wwyqpxH8d0TsHhFDwL92bHMt8Mz6fM+q5wY4rmOb\n1sWCwyPimVHN3H8X1aSFf1fn2fPrz/XQ2r4PSdJgskiXJJWUVEXarVQF7U+p7oB+Gpje8ezy5PE7\n6SuoJiA7g+ou5g/rYxzVtv17qLpVL6aa0bz9OKuLpd1jwPuA/6Iawz4ZeHlmLgeox1cfSTXj9pXA\n+4F/aj9OPYHZSVSTrv2eaubwzs9CZv4AOBZ4A7AA+ATwWeBfVvP517Ss0xFUBeL3qQr2ycBLO57T\nvtau7+sQ49epLl7MoSomz6f6/AD3U43//hrVOO9ZtM1qnpkPU92d/yVVof0bqpnb96VtYsC1xHs2\nVTf2C+rfqN3fAZ+k+q2uphrHfjRP7AlwBNWY759TzUT/PWDeGs7XehrBX1LNnn9FfY53d2zzfarC\n/VTgKuA1PDlfLqeaFf6/qHL2P+tx7n9NNe7/KqoLDZ+kyndJ0hgUT5zbpX9E9WzQlwPLMnNq2/J3\nUo3Jegz4fmau9tEzkiRJkiQNkn6+k34WVdfFVSLiRcBhwPMy87lUM/tKkiRJkjQm9G2RXj+XtrOb\n2nHARzNzRb3N7U/aUZIkSZKkAdW3Rfpq7Aq8MCJ+ERE/i4h9SwckSZIkSdJomVg6gHU0EfijzPyT\niNiP6nmjzyockyRJkiRJo2LQivRbqJ+Zm5mXR8TKiNgyM+9s3+iwww7L5cuXs/XWWwOw6aabsssu\nuzBt2jQA5s+fD2Db9qi0Z82aZX7ZNt9sj8m2+Wa7ybb5ZrvJtvlmu5ftWbNmsWjRoifUozNmzOj6\nMap9O7s7QETsCJzfmt09It4KbJuZJ0fEbsCPM3NK537HHHNMfupTn2o0Vo1fr//7D7Dsua8a0b7v\nOnAHXrH7SB7frPHqtNNO48QTT1z7htIoMN/UJPNNTTLf1KQTTjiBc845p+sivW/HpEfEucClwG4R\ncXNEvInq2aDPiogFVM9ePWa4fW+77bbmAtW4d+dtS0qHoHHkpptuKh2CxhHzTU0y39Qk8039rG+7\nu2fmkatZdXSjgUiSJEmS1JC+vZO+Pv7sz/6sdAgaR/7k0FeWDkHjyFFHHVU6BI0j5puaZL6pSeab\nmrTXXnut0/ZjskhvDdiXmrDbtP1Lh6Bx5KCDDiodgsYR801NMt/UJPNNTVrX+nRMFumt2fWkJlw3\nf27pEDSOzJkzp3QIGkfMNzXJfFOTzDf1szFZpEuSJEmSNIjGZJFud3c1ye7uapLd89Qk801NMt/U\nJPNN/WxMFumSJEmSJA2iMVmkOyZdTXJMuprkGDo1yXxTk8w3Ncl8Uz8bk0W6JEmSJEmDaEwW6Y5J\nV5Mck64mOYZOTTLf1CTzTU0y39TPxmSRLkmSJEnSIBqTRbpj0tUkx6SrSY6hU5PMNzXJfFOTzDf1\nszFZpEuSJEmSNIj6tkiPiDMjYmlELBhm3XsiYmVEPH24fR2TriY5Jl1NcgydmmS+qUnmm5pkvqmf\n9W2RDpwFHNq5MCJ2AF4K/K7xiCRJkiRJ6qG+LdIz82LgrmFWfQJ475r2dUy6muSYdDXJMXRqkvmm\nJplvapL5pn7Wt0X6cCLicOCWzLyqdCySJEmSJI22iaUD6FZEbAK8j6qr+6rFw217/fXXc/zxxzNl\nyhQAJk2axNSpU1eNPWldObNtezTaAPcums/mO09b9R7oul06ftuD1W4t65d4bI/tdmtZv8Rje2y3\nW8v6JR7bY7vdWtYv8dgeW+0ZM2awYMGCVfXo5MmTGRoaoluRmV1v3LSI2BE4PzOnRsRU4MfAg/Xq\n7YElwP6Zuax9v9mzZ+f06dObDFXj2Lnzb+OsX946on3fdeAOvGL3Z4xyRJIkSZL6xbx58xgaGhr2\nBvNwBqa7e2YuyMytMnOnzNwJuAWY3lmgg2PS1SzHpKtJrSu1UhPMNzXJfFOTzDf1s74t0iPiXOBS\nYLeIuDki3tSxSf92AZAkSZIkaQQmlg5gdTLzyLWsf9bq1vmcdDVpt2n7c8kIu7tL66p9LJ3Ua+ab\nmmS+qUnmm/pZ395JlyRJkiRpvBmTRbpj0tUkx6SrSY6hU5PMNzXJfFOTzDf1szFZpEuSJEmSNIjG\nZJHumHQ1abdp+5cOQeOIY+jUJPNNTTLf1CTzTf1sTBbpkiRJkiQNojFZpDsmXU1anzHpdy9/lBv/\n8NCIX3c/tGIUP4kGgWPo1CTzTU0y39Qk8039rG8fwSaNB+f86lbO+dXIH98245XPZounbjiKEUmS\nJEkqaUzeSXdMuprkmHQ1yTF0apL5piaZb2qS+aZ+NiaLdEmSJEmSBtGYLNIdk64m+Zx0NckxdGqS\n+aYmmW9qkvmmfjYmi3RJkiRJkgZRXxfpEXFmRCyNiAVtyz4eEddExJUR8c2ImNS5n2PS1STHpKtJ\njqFTk8w3Ncl8U5PMN/Wzvi7SgbOAQzuWXQjsmZl7AdcBJzUelSRJkiRJPdDXRXpmXgzc1bHsosxc\nWTcvA7bv3M8x6WqSY9LVJMfQqUnmm5pkvqlJ5pv6WV8X6V04FrigdBCSJEmSJI2GgS3SI+L9wCOZ\n+dXOdY5JV5Mck64mOYZOTTLf1CTzTU0y39TPJpYOYCQi4o3AXwBDw62fNWsWM2fOZMqUKQBMmjSJ\nqVOnrvrL2OreYtv2aLSvmz+XexfdyeY7VxeH7l1UDbdoql3689u2bdu2bdu2bdu2bfvx9owZM1iw\nYMGqenTy5MkMDQ1bug4rMrPrjUuIiB2B8zNzat0+FDgdODgz7xhun9NPPz2PPfbYxmLU+PYvX/wu\nlzy6Q5Fzz3jls9l5y02KnFtlzJkzZ9U/AFKvmW9qkvmmJplvatK8efMYGhqKbrfv6+7uEXEucCnw\n7Ii4OSKOBf4T2Ay4KCKuiIjPFQ1SkiRJkqRRMrF0AGuSmUcOs/jMte3nmHQ1abdp+3PJL28tHYbG\nCa/6q0nmm5pkvqlJ5pv6WV/fSZckSZIkaTwZk0W6z0lXk3xOuprUmphEaoL5piaZb2qS+aZ+NiaL\ndEmSJEmSBtGYLNIdk64m+Zx0NckxdGqS+aYmmW9qkvmmfjYmi3RJkiRJkgbRmCzSHZOuJjkmXU1y\nDJ2aZL6pSeabmmS+qZ+NySJdkiRJkqRBNCaLdMekq0mOSVeTHEOnJplvapL5piaZb+pnPSvSI+Lw\niJjYq+NLkiRJkjTW9PJO+inAbRHxmYg4oIfneRLHpKtJjklXkxxDpyaZb2qS+aYmmW/qZz0r0jPz\necAQsBz4RkRcFxEfiIgde3VOSZIkSZIGWU/HpGfmlZn5j8AOwNuBvwZuiIifR8TrI2K154+IMyNi\naUQsaFv29Ii4qC74L4yILYbb1zHpapJj0tUkx9CpSeabmmS+qUnmm/pZzyeOi4idgZOBzwFPBT4I\nfAF4B/CNNex6FnBox7ITgYsyczdgdt2WJEmSJGlM6OXEce+IiF8AlwNbA8dk5m6Z+ZHM/BLwYuCl\nq9s/My8G7upYfBhwdv3+bOCI4fZ1TLqa5Jh0NckxdGqS+aYmmW9qkvmmftbL2df/HDgdOD8zl3eu\nzMwHI+JV63jMrTJzaf1+KbDVesYoSZIkSVLf6GV391cB32kv0CNio4jYuNXOzB+N9OCZmUAOt84x\n6WqSY9LVJMfQqUnmm5pkvqlJ5pv6WS/vpF8IvBf4RduyfYCPAoeM8JhLI2LrzLwtIrYBlg230axZ\ns5g5cyZTpkwBYNKkSUydOnXVX8ZW9xbbtkejfd38udy76E4237m6OHTvomq4RVPt0p/ftm3btm3b\ntm3btm3bj7dnzJjBggULVtWjkydPZmhoiG5FdUN69EXE3cDTM3Nl27INgDszc9hZ2Yc5xo5U3eWn\n1u1/q/f/WEScCGyRmU+aPO7000/PY489dhQ+hbR2//LF73LJozsUOfeMVz6bnbfcpMi5VcacOXNW\n/QMg9Zr5piaZb2qS+aYmzZs3j6Ghoeh2+152d7+bJ48Znwzc383OEXEucCnw7Ii4OSLeBJwGvDQi\nrqOaeO60UYxXkiRJkqSiJvbw2N8AvhIRJwCLgF2ATwBf72bnzDxyNatesrZ9HZOuJu02bX8u+eWt\npcPQOOFVfzXJfFOTzDc1yXxTP+vlnfQPANcAl1HdPf8FcC1wUg/PKUmSJEnSwOpZkZ6ZD2Xm24HN\nqJ6Tvtn/b+/Ow+yo63yPv79JDCRRGlmCbGEJi6KRRUDAwa1HREW4Oo7CqDMadUavC24jwrgwOiN3\nnCcDeVziVdBRriOj0UFxG3DciCiLIRgIiwlCCCFhJyEsCcn3/lHV4dBJSCfd9TtLv1/P0w/9qzqn\n6ndOf+jO91R9qzLzPRu7HdtI8z7pKsn7pKukgQuTSCWYN5Vk3lSSeVMna/J0dyKiDziQqlAnouqV\nz8yfN7lfSZIkSZK6UWNFekS8BfgC1anuDw1avU9T+wV70lWWPekqyR46lWTeVJJ5U0nmTZ2sySPp\nnwFel5k/aXAfkiRJkiT1jCYvHDcWuLjB7W+SPekqyZ50lWQPnUoybyrJvKkk86ZO1uSR9H8BPh4R\nn8rMdQ3uR6Pc2nXJvKUrWfHo2uL7DuDmex6GvuK7HrbH1q5j3tIHWbl66963/XeawB59247wrCRJ\nkqTRrcki/YPALsBHIuKeluWZmVMa3K896aPQ+VcvY8HyVe3Zed8B7dnvMCXwjbl3cMNdgy8ZMTT/\n/PKpFultYA+dSjJvKsm8qSTzpk7WZJH+pga3LUmSJElSz2nyPum/3NRXU/scYE+6SlqxyLypHHvo\nVJJ5U0nmTSWZN3Wyxor0iNg2Ij4TETdHxIp62XER8Z6m9ilJkiRJUjdr8uruZwPPAd4IDFw47jrg\nf3PdCEUAABoISURBVDe4T8CedJW13VTzpnLsoVNJ5k0lmTeVZN7UyZrsSX8NsF9mPhgRCZCZt0fE\n7sPdcEScTtXzvg6YD7w1Mx8d7nYlSZIkSWqnJo+kP8qgDwEiYmfg7uFsNCL2Bt4BHJaZ06jux35y\n62PsSVdJ9qSrJHvoVJJ5U0nmTSWZN3WyJov07wD/HhH7AkTErsDngQuGud0VwBpgYkSMAyYCtw9z\nm5IkSZIktV2TRfo/AH8C/gD0AQuBO4BPDWejmXkvMANYDCwF7s/Mn7U+xp50lWRPukqyh04lmTeV\nZN5UknlTJ2usJ73uEf9ARHwQ2Bm4OzPXbeZpmxURU4H3A3sDDwDfiYg3ZuY3Bx4ze/Zszj33XKZM\nmQJAX18f06ZNW/8/48DpLY47Z3z3qjXs9ZzDAZh35W8BOOSIo4c0vvb3v+OW+XfCLgcBj59+PlA8\n9/J42crV/PrSOVv0fg2MjzjqGFatWbvV+4epQGfkx7Fjx44dO3bs2LHjThnPmjWL+fPnr69HJ0+e\nTH9/P0MVmTnkB2+JgdPcNyYzbx7Gdt8AvCwz316P3wwclZnvHnjMjBkzcvr06Vu7C7XBZbfez5mX\n/Knd09gqKxbNG5VH0//55VM5Ys/t2j2NUWfOnDnr/wBITTNvKsm8qSTzppLmzp1Lf39/DPXx4xqc\ny8JNLE+qi71trRuAj0fEBOAR4M+BK4axPUmSJEmSOkJjRXpmPqHfPSKeAZwJXDrM7V4TEd8ArqK6\nBdtc4Mutj7EnXSWNxqPoah8/9VdJ5k0lmTeVZN7UyZo8kv4EmbksIt4P3Ah8c3OP38y2Pgt8dkQm\nJkmSJElSh2jy6u4bcyDVLdMa5X3SVZL3SVdJAxcmkUowbyrJvKkk86ZO1tiR9IgYfFr7RODZDPMW\nbJIkSZIk9aomT3c/b9B4FXBNZt7U4D4Be9JVlj3pKskeOpVk3lSSeVNJ5k2drMkLx/17U9uWJEmS\nJKkXNXm6+6epbre2waqW7zMzPzHS+543bx6HHXbYSG9W2qjRep90tYf3dVVJ5k0lmTeVZN7UyZo8\n3X1/4LXAlcCtwF7AEcD3gIepivWNFfHqQqtWr2X5ytVb/fwHH107grORJEmSpO7U9C3YTsnM7w4M\nIuK1wOsz861N7tSe9PJWrV7L+35wI6vXjr7PXTyKrpL81F8lmTeVZN5UknlTJ2vyFmyvBC4ctOyi\nerkkSZIkSRqkySJ9IfCeQcveVS9vlPdJV0neJ10leV9XlWTeVJJ5U0nmTZ2sydPd3wZcGBEfAW4H\ndgceo+pTlyRJkiRJgzR5C7arI2J/4ChgN+AO4LLMXNPUPgfYk66S7ElXSfbQqSTzppLMm0oyb+pk\nTZ7uDo9fvT0z81fANhHx1OFuNCK2j4jZEXF9RCyIiKOGu01JkiRJktqtsSI9IqYBNwFfBs6rF7+o\n5fvhmAn8ODOfBTwXuL51pT3pKsmedJVkD51KMm8qybypJPOmTtbkkfQvAZ/MzGcCA6e4/xI4djgb\njYg+4NjM/CpAZj6WmQ8MZ5uSJEmSJHWCJov0g4DzBy17CJgwzO3uA9wVEV+LiLkR8ZWImNj6AHvS\nVZI96SrJHjqVZN5UknlTSeZNnazJq7vfChwOXNmy7Ajgj8Pc7jjgMOA9mXllRJwDfBT4xDC3K2kL\njAm468HVW/38vm3HMX5c05fFkCRJkrpLk0X6x4AfRsT/BcZHxBnAO4F3DHO7S4AlmTlQ/M+mKtLX\nmzlzJpMmTWLKlCkA9PX1MW3atPWfmA30oDgeufF9D68Bng483qM9cIS518fLLp3NxN3265j5lBqf\neUkwdkxw/8JqvP1+1fqhjCeNH8s3PvR6dhw3viPy203jWbNm+fvMsXlz3JNj8+a45Ni8OW5yPGvW\nLObPn7++Hp08eTL9/f0MVWTm5h+1lSLiUOBvgb2AxcBXMvP3I7DdXwNvz8ybIuJMYEJmnjawfsaM\nGTl9+vTh7kZb4M4HVzP9OwtYvba5PHWqFYvmecr7Ftp+23HMeu2B7DhxfLun0nXmzJmz/g+A1DTz\nppLMm0oybypp7ty59Pf3x1AfP66JSUTEOOBG4KDMfFcDu3gv8M2IGA8sAt7autKedJVkga6S/AeF\nSjJvKsm8qSTzpk7WSJGemY9FxDqqi8Q92sD2r6Hqb5ckSZIkqWc0edWms4H/jIgXR8TUiNh34KvB\nfQLeJ11leZ90lTTQ8ySVYN5UknlTSeZNnWzEj6RHxDMycxnw+XrRywY9JIGxI71fSZIkSZK6XRNH\n0m8CyMwxmTkG+P7A9/VX4wW6PekqyZ50lWQPnUoybyrJvKkk86ZO1kSRPviqdS9uYB+SJEmSJPWc\nJnvS28aedJVkT7pKsodOJZk3lWTeVJJ5Uydr4ur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8CPinet2bgB9n5k8BMvNnwFXAq6iK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\n6hD/H4HCzmkyXHsAAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x15657bcd0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "x_lim = 60\n",
    "y_pred = trace.get_values('y_pred')\n",
    "\n",
    "fig = plt.figure(figsize=(14,6))\n",
    "fig.add_subplot(211)\n",
    "\n",
    "_ = plt.hist(y_pred, range=[0, x_lim], bins=x_lim, histtype='stepfilled', color=colors[1])   \n",
    "_ = plt.xlim(1, x_lim)\n",
    "_ = plt.ylabel('Frequency')\n",
    "_ = plt.title('Posterior predictive distribution')\n",
    "\n",
    "fig.add_subplot(212)\n",
    "\n",
    "_ = plt.hist(data.values, range=[0, x_lim], bins=x_lim, histtype='stepfilled')\n",
    "_ = plt.xlabel('Response time in seconds')\n",
    "_ = plt.ylabel('Frequency')\n",
    "_ = plt.title('Distribution of observed data')\n",
    "\n",
    "plt.tight_layout()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 79,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "people = np.array(['Amy','Peter','Paul','Tom']*25)\n",
    "\n",
    "# Convert categorical variables to integer\n",
    "le = preprocessing.LabelEncoder()\n",
    "#people_map = le.fit(people)\n",
    "people_idx = le.fit_transform(people)\n",
    "n_participants = len(np.unique(people))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 80,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      " [-----------------100%-----------------] 2000 of 2000 complete in 5.6 sec"
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    alpha = pm.Gamma('alpha', alpha=.1, beta=.1, shape=n_participants)\n",
    "    mu = pm.Gamma('mu', alpha=.1, beta=.1, shape=n_participants)\n",
    "    \n",
    "    y_est = pm.NegativeBinomial('y_est', \n",
    "                                mu=mu[people_idx], \n",
    "                                alpha=alpha[people_idx], \n",
    "                                observed=data.values)\n",
    "    \n",
    "    start = pm.find_MAP()\n",
    "    step = pm.Metropolis(start=start)\n",
    "    trace = pm.sample(2000, step, start=start, progressbar=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 81,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "For compute_test_value, one input test value does not have the requested type.\n\nThe error when converting the test value to that variable type:\nWrong number of dimensions: expected 0, got 1 with shape (100,).",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-81-d049367a98c4>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[1;32m     10\u001b[0m     y_pred = pm.NegativeBinomial('y_pred', \n\u001b[1;32m     11\u001b[0m                                  \u001b[0mmu\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmu\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mpeople_idx\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 12\u001b[0;31m                                  alpha=alpha[people_idx])\n\u001b[0m\u001b[1;32m     13\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     14\u001b[0m     \u001b[0mstart\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mpm\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfind_MAP\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/pymc3/distributions/distribution.pyc\u001b[0m in \u001b[0;36m__new__\u001b[0;34m(cls, name, *args, **kwargs)\u001b[0m\n\u001b[1;32m     17\u001b[0m             \u001b[0mdata\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mkwargs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mpop\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m'observed'\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     18\u001b[0m             \u001b[0mdist\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mcls\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0margs\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m**\u001b[0m\u001b[0mkwargs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m---> 19\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mVar\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     20\u001b[0m         \u001b[0;32melif\u001b[0m \u001b[0mname\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     21\u001b[0m             \u001b[0;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__new__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mcls\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;31m#for pickle\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/pymc3/model.pyc\u001b[0m in \u001b[0;36mVar\u001b[0;34m(self, name, dist, data)\u001b[0m\n\u001b[1;32m    148\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mdata\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    149\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mgetattr\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m\"transform\"\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;32mis\u001b[0m \u001b[0mNone\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 150\u001b[0;31m                 \u001b[0mvar\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mFreeRV\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mdistribution\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mdist\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    151\u001b[0m                 \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfree_RVs\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mappend\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mvar\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    152\u001b[0m             \u001b[0;32melse\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/pymc3/model.pyc\u001b[0m in \u001b[0;36m__init__\u001b[0;34m(self, type, owner, index, name, distribution, model)\u001b[0m\n\u001b[1;32m    360\u001b[0m             self.tag.test_value = np.ones(\n\u001b[1;32m    361\u001b[0m                 distribution.shape, distribution.dtype) * distribution.default()\n\u001b[0;32m--> 362\u001b[0;31m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlogp_elemwiset\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mdistribution\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mlogp\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    363\u001b[0m             \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mmodel\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mmodel\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    364\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/pymc3/distributions/discrete.pyc\u001b[0m in \u001b[0;36mlogp\u001b[0;34m(self, value)\u001b[0m\n\u001b[1;32m    194\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    195\u001b[0m         \u001b[0;31m# Return Poisson when alpha gets very large\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 196\u001b[0;31m         pois = bound(logpow(mu, value) - factln(value) - mu,\n\u001b[0m\u001b[1;32m    197\u001b[0m                      \u001b[0mmu\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    198\u001b[0m                      value >= 0)\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/pymc3/distributions/dist_math.pyc\u001b[0m in \u001b[0;36mlogpow\u001b[0;34m(x, m)\u001b[0m\n\u001b[1;32m     54\u001b[0m     \u001b[0mCalculates\u001b[0m \u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m**\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0msince\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0mwill\u001b[0m \u001b[0mfail\u001b[0m \u001b[0mwhen\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mx\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;36m0.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     55\u001b[0m     \"\"\"\n\u001b[0;32m---> 56\u001b[0;31m     \u001b[0;32mreturn\u001b[0m \u001b[0mswitch\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0meq\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m \u001b[0;34m&\u001b[0m \u001b[0meq\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;36m0\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m \u001b[0;34m*\u001b[0m \u001b[0mlog\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m     57\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m     58\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/theano/gof/op.pyc\u001b[0m in \u001b[0;36m__call__\u001b[0;34m(self, *inputs, **kwargs)\u001b[0m\n\u001b[1;32m    515\u001b[0m             \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mins\u001b[0m \u001b[0;32min\u001b[0m \u001b[0menumerate\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mnode\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0minputs\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    516\u001b[0m                 \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 517\u001b[0;31m                     \u001b[0mstorage_map\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mins\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_get_test_value\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mins\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    518\u001b[0m                     \u001b[0mcompute_map\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mins\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mTrue\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    519\u001b[0m                 \u001b[0;32mexcept\u001b[0m \u001b[0mAttributeError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/theano/gof/op.pyc\u001b[0m in \u001b[0;36m_get_test_value\u001b[0;34m(cls, v)\u001b[0m\n\u001b[1;32m    452\u001b[0m             \u001b[0;31m# ensure that the test value is correct\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    453\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m--> 454\u001b[0;31m                 \u001b[0mret\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtype\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mfilter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mv\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtag\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mtest_value\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m    455\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mException\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0me\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    456\u001b[0m                 \u001b[0;31m# Better error message.\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/Library/Python/2.7/site-packages/theano/tensor/type.pyc\u001b[0m in \u001b[0;36mfilter\u001b[0;34m(self, data, strict, allow_downcast)\u001b[0m\n\u001b[1;32m    167\u001b[0m             raise TypeError(\"Wrong number of dimensions: expected %s,\"\n\u001b[1;32m    168\u001b[0m                             \" got %s with shape %s.\" % (self.ndim, data.ndim,\n\u001b[0;32m--> 169\u001b[0;31m                                                         data.shape))\n\u001b[0m\u001b[1;32m    170\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0;32mnot\u001b[0m \u001b[0mdata\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mflags\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0maligned\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m    171\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mTypeError\u001b[0m: For compute_test_value, one input test value does not have the requested type.\n\nThe error when converting the test value to that variable type:\nWrong number of dimensions: expected 0, got 1 with shape (100,)."
     ]
    }
   ],
   "source": [
    "with pm.Model() as model:\n",
    "    alpha = pm.Gamma('alpha', alpha=.1, beta=.1, shape=n_participants)\n",
    "    mu = pm.Gamma('mu', alpha=.1, beta=.1, shape=n_participants)\n",
    "    \n",
    "    y_est = pm.NegativeBinomial('y_est', \n",
    "                                mu=mu[people_idx], \n",
    "                                alpha=alpha[people_idx], \n",
    "                                observed=data.values)\n",
    "    \n",
    "    y_pred = pm.NegativeBinomial('y_pred', \n",
    "                                 mu=mu[people_idx], \n",
    "                                 alpha=alpha[people_idx])\n",
    "    \n",
    "    start = pm.find_MAP()\n",
    "    step = pm.Metropolis(start=start)\n",
    "    trace = pm.sample(2000, step, start=start, progressbar=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": false
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   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
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