{
 "metadata": {
  "name": ""
 },
 "nbformat": 3,
 "nbformat_minor": 0,
 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import numpy as np\n",
      "import matplotlib.pyplot as plt"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def data_to_counts(data):\n",
      "    ''' Convert the data to an array of counts of the numbers\n",
      "        of occurrences of each outcome in each row.\n",
      "    '''\n",
      "    counts = [np.bincount(row, minlength=10) for row in data]\n",
      "    return np.asarray(counts)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def draw_assignments(counts, ps, qs):\n",
      "    ''' Compute the conditional distributions of the assignemnts\n",
      "        of each row and then draw from these distributions.\n",
      "    '''\n",
      "    p_likelihoods = np.product(np.power(ps, counts), axis=1)\n",
      "    q_likelihoods = np.product(np.power(qs, counts), axis=1)\n",
      "    assignments_probs = p_likelihoods / (p_likelihoods + q_likelihoods)\n",
      "    assignments = np.random.uniform(size=len(assignments_probs)) < assignments_probs\n",
      "    return np.asarray(assignments)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def draw_probabilities(counts, assignments):\n",
      "    ''' Compute the total counts in all rows assigned to each\n",
      "        type and draw new sets of rates for each type given\n",
      "        these counts.\n",
      "    '''\n",
      "    ps_rows = counts[np.where(assignments == True)]\n",
      "    ps_counts = ps_rows.sum(axis=0)\n",
      "    ps = np.random.dirichlet(ps_counts)\n",
      "    \n",
      "    qs_rows = counts[np.where(assignments == False)]\n",
      "    qs_counts = qs_rows.sum(axis=0)\n",
      "    qs = np.random.dirichlet(qs_counts)\n",
      "    \n",
      "    return ps, qs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "num_cycles = 10000\n",
      "\n",
      "data = np.loadtxt('data/gibbs_data.txt', dtype=int)\n",
      "num_rows, num_outcomes = data.shape\n",
      "counts = data_to_counts(data)\n",
      "\n",
      "ps_history = np.empty((num_cycles, num_outcomes))\n",
      "qs_history = np.empty((num_cycles, num_outcomes))\n",
      "assignments_history = np.empty((num_cycles, num_rows), dtype=bool)\n",
      "\n",
      "# Draw sensible starting values.\n",
      "ps = np.random.dirichlet(np.ones(num_outcomes) * counts.sum() / 2)\n",
      "qs = np.random.dirichlet(np.ones(num_outcomes) * counts.sum() / 2)\n",
      "\n",
      "for i in xrange(num_cycles):\n",
      "    assignments = draw_assignments(counts, ps, qs)\n",
      "    ps, qs = draw_probabilities(counts, assignments)\n",
      "    \n",
      "    assignments_history[i] = assignments\n",
      "    ps_history[i] = ps\n",
      "    qs_history[i] = qs"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 23
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The posterior distributions of $p$ and $q$ are distinct."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "fig, (ps_ax, qs_ax) = plt.subplots(1, 2, figsize=(16, 8))\n",
      "\n",
      "components_to_plot = 2\n",
      "for label, ax, values in [('p', ps_ax, ps_history), ('q', qs_ax, qs_history)]:\n",
      "    for j in range(components_to_plot):\n",
      "        ax.hist(values[:, j], bins=100, histtype='step', label='{0}[{1}]'.format(label, j))\n",
      "    ax.set_title('Posterior distribution of {0}'.format(label))\n",
      "    ax.legend()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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sOfW5oM9669atJZYfTqagUyaPHTvWbNSokVmpUiWzUqVKZsuWLR1O233hUhd/v7Vs2dJh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\n",
       "text": [
        "<matplotlib.figure.Figure at 0xd3f854c>"
       ]
      }
     ],
     "prompt_number": 46
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(ps_history, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 34,
       "text": [
        "array([ 0.08127113,  0.11901405,  0.07965701,  0.12636537,  0.1126423 ,\n",
        "        0.08212299,  0.07992786,  0.12643449,  0.07814592,  0.1144189 ])"
       ]
      }
     ],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(qs_history, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 35,
       "text": [
        "array([ 0.12044314,  0.08564833,  0.11900612,  0.07219582,  0.08464854,\n",
        "        0.11952155,  0.11796448,  0.07773247,  0.11755809,  0.08528147])"
       ]
      }
     ],
     "prompt_number": 35
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The confidence with which each rat is assigned to a specific cluster is typically not very extreme."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "np.mean(assignments_history, axis=0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 41,
       "text": [
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        "        0.8602,  0.3345,  0.5007,  0.283 ,  0.1966,  0.167 ,  0.1791,\n",
        "        0.7433,  0.5654,  0.3227,  0.7931,  0.9389,  0.4958,  0.6565,\n",
        "        0.6585,  0.2895,  0.2827,  0.9296,  0.4638,  0.41  ,  0.6715,\n",
        "        0.3177,  0.5033,  0.0402,  0.4392,  0.8509,  0.5411,  0.1124,\n",
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        "        0.3437,  0.5589,  0.6028,  0.0462,  0.5423,  0.8259,  0.6507,\n",
        "        0.1538,  0.7066,  0.2495,  0.617 ,  0.3198,  0.1717,  0.8592,\n",
        "        0.4991,  0.8835,  0.7819,  0.6746,  0.7109,  0.5632,  0.6281,\n",
        "        0.3282,  0.7163,  0.8605,  0.0469,  0.7916,  0.5095,  0.3727,\n",
        "        0.0994,  0.9164,  0.4737,  0.7869,  0.7799,  0.4915,  0.4027,\n",
        "        0.7658,  0.0391,  0.9571,  0.6947,  0.5264,  0.489 ,  0.5533,\n",
        "        0.0719,  0.7236,  0.8007,  0.5672,  0.6749,  0.9218,  0.3441,\n",
        "        0.0723,  0.6667,  0.6787,  0.6108,  0.0444,  0.8671,  0.5397,\n",
        "        0.5507,  0.1774,  0.3137,  0.3985,  0.5462,  0.5455,  0.1374,\n",
        "        0.9745,  0.3961,  0.8781,  0.9047,  0.435 ,  0.3795,  0.7464,\n",
        "        0.1889,  0.5587,  0.1067,  0.0695,  0.7714,  0.3965,  0.1943,\n",
        "        0.8852,  0.0926,  0.2663,  0.7182,  0.1763,  0.2659,  0.3488,\n",
        "        0.2324,  0.5601,  0.2141,  0.1314,  0.3958,  0.5102,  0.7597,\n",
        "        0.9137,  0.9224,  0.91  ,  0.1347,  0.2957,  0.749 ,  0.6593,\n",
        "        0.8726,  0.1966,  0.215 ,  0.1866,  0.8574,  0.6652,  0.79  ,\n",
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        "        0.7119,  0.2437,  0.5061,  0.1439,  0.6309,  0.3515,  0.1609,\n",
        "        0.3173,  0.1779,  0.1584,  0.0376,  0.2042,  0.315 ,  0.3191,\n",
        "        0.7348,  0.1668,  0.4395,  0.7161,  0.8222,  0.1696,  0.5626,\n",
        "        0.4996,  0.092 ,  0.6066,  0.6795,  0.75  ,  0.3241,  0.2449,\n",
        "        0.9626,  0.1348,  0.9296,  0.8409,  0.3473,  0.5121,  0.7136,\n",
        "        0.9215,  0.3363,  0.0758,  0.0895,  0.768 ,  0.6656,  0.4672,\n",
        "        0.293 ,  0.6695,  0.1702,  0.8081,  0.4708,  0.1632])"
       ]
      }
     ],
     "prompt_number": 41
    }
   ],
   "metadata": {}
  }
 ]
}