CAR all cause (single year).ipynb

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  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pandas\n",
      "import pymc as mc\n",
      "import numpy as np\n",
      "import theano\n",
      "import pysal"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# which selection to model\n",
      "age = 75\n",
      "sex = 2\n",
      "year = 2009"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# load data\n",
      "data = pandas.read_csv('deaths.csv')\n",
      "pop = pandas.read_csv('pop.csv')\n",
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>sex</th>\n",
        "      <th>cause</th>\n",
        "      <th>age</th>\n",
        "      <th>year</th>\n",
        "      <th>state_fips</th>\n",
        "      <th>deaths</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 1</td>\n",
        "      <td> A_1</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 1</td>\n",
        "      <td>   0.280154</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 1</td>\n",
        "      <td> A_2</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 1</td>\n",
        "      <td>  23.155050</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 1</td>\n",
        "      <td> A_3</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 1</td>\n",
        "      <td>   0.000000</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 1</td>\n",
        "      <td> A_4</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 1</td>\n",
        "      <td> 307.781800</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 1</td>\n",
        "      <td> A_5</td>\n",
        "      <td> 0</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 1</td>\n",
        "      <td>  26.419190</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "   sex cause  age  year  state_fips      deaths\n",
        "0    1   A_1    0  1979           1    0.280154\n",
        "1    1   A_2    0  1979           1   23.155050\n",
        "2    1   A_3    0  1979           1    0.000000\n",
        "3    1   A_4    0  1979           1  307.781800\n",
        "4    1   A_5    0  1979           1   26.419190"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# aggregate into all-cause mortality\n",
      "g = data.groupby(['age', 'sex', 'year', 'state_fips'], as_index=False)\n",
      "data = g.aggregate(np.sum)\n",
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>age</th>\n",
        "      <th>sex</th>\n",
        "      <th>year</th>\n",
        "      <th>state_fips</th>\n",
        "      <th>deaths</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 1</td>\n",
        "      <td>  611.000019</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 2</td>\n",
        "      <td>   95.999997</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 4</td>\n",
        "      <td>  447.999997</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 5</td>\n",
        "      <td>  335.999996</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 6</td>\n",
        "      <td> 2927.000216</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "   age  sex  year  state_fips       deaths\n",
        "0    0    1  1979           1   611.000019\n",
        "1    0    1  1979           2    95.999997\n",
        "2    0    1  1979           4   447.999997\n",
        "3    0    1  1979           5   335.999996\n",
        "4    0    1  1979           6  2927.000216"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# add on population\n",
      "data = data.merge(pop, how='left', on=['age', 'sex', 'year', 'state_fips'])\n",
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>age</th>\n",
        "      <th>sex</th>\n",
        "      <th>year</th>\n",
        "      <th>state_fips</th>\n",
        "      <th>deaths</th>\n",
        "      <th>pop</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>0</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 1</td>\n",
        "      <td>  611.000019</td>\n",
        "      <td> 148573</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>1</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 2</td>\n",
        "      <td>   95.999997</td>\n",
        "      <td>  19876</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>2</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 4</td>\n",
        "      <td>  447.999997</td>\n",
        "      <td> 105594</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>3</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 5</td>\n",
        "      <td>  335.999996</td>\n",
        "      <td>  88702</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>4</th>\n",
        "      <td> 0</td>\n",
        "      <td> 1</td>\n",
        "      <td> 1979</td>\n",
        "      <td> 6</td>\n",
        "      <td> 2927.000216</td>\n",
        "      <td> 844222</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "   age  sex  year  state_fips       deaths     pop\n",
        "0    0    1  1979           1   611.000019  148573\n",
        "1    0    1  1979           2    95.999997   19876\n",
        "2    0    1  1979           4   447.999997  105594\n",
        "3    0    1  1979           5   335.999996   88702\n",
        "4    0    1  1979           6  2927.000216  844222"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# aggregate age groups\n",
      "for a in range(5, 76, 10):\n",
      "    data.age[data.age.isin([a,a+5])] = a\n",
      "data.age.value_counts()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 6,
       "text": [
        "75    6324\n",
        "65    6324\n",
        "55    6324\n",
        "45    6324\n",
        "35    6324\n",
        "25    6324\n",
        "15    6323\n",
        "5     6304\n",
        "85    3162\n",
        "0     3162\n",
        "dtype: int64"
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# sum up deaths and population by new age groups\n",
      "g = data.groupby(['age', 'sex', 'year', 'state_fips'], as_index=False)\n",
      "data = g.aggregate(np.sum)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# fix rounding errors\n",
      "data.deaths = data.deaths.astype(int)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# keep just the current selection\n",
      "data = data[(data.age == age) & (data.sex == sex) & (data.year == year)]\n",
      "data.head()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
        "<table border=\"1\" class=\"dataframe\">\n",
        "  <thead>\n",
        "    <tr style=\"text-align: right;\">\n",
        "      <th></th>\n",
        "      <th>age</th>\n",
        "      <th>sex</th>\n",
        "      <th>year</th>\n",
        "      <th>state_fips</th>\n",
        "      <th>deaths</th>\n",
        "      <th>pop</th>\n",
        "    </tr>\n",
        "  </thead>\n",
        "  <tbody>\n",
        "    <tr>\n",
        "      <th>28407</th>\n",
        "      <td> 75</td>\n",
        "      <td> 2</td>\n",
        "      <td> 2009</td>\n",
        "      <td> 1</td>\n",
        "      <td>  6218</td>\n",
        "      <td> 129573</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>28408</th>\n",
        "      <td> 75</td>\n",
        "      <td> 2</td>\n",
        "      <td> 2009</td>\n",
        "      <td> 2</td>\n",
        "      <td>   371</td>\n",
        "      <td>   7988</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>28409</th>\n",
        "      <td> 75</td>\n",
        "      <td> 2</td>\n",
        "      <td> 2009</td>\n",
        "      <td> 4</td>\n",
        "      <td>  5656</td>\n",
        "      <td> 160754</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>28410</th>\n",
        "      <td> 75</td>\n",
        "      <td> 2</td>\n",
        "      <td> 2009</td>\n",
        "      <td> 5</td>\n",
        "      <td>  3622</td>\n",
        "      <td>  79262</td>\n",
        "    </tr>\n",
        "    <tr>\n",
        "      <th>28411</th>\n",
        "      <td> 75</td>\n",
        "      <td> 2</td>\n",
        "      <td> 2009</td>\n",
        "      <td> 6</td>\n",
        "      <td> 28903</td>\n",
        "      <td> 793861</td>\n",
        "    </tr>\n",
        "  </tbody>\n",
        "</table>\n",
        "</div>"
       ],
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "       age  sex  year  state_fips  deaths     pop\n",
        "28407   75    2  2009           1    6218  129573\n",
        "28408   75    2  2009           2     371    7988\n",
        "28409   75    2  2009           4    5656  160754\n",
        "28410   75    2  2009           5    3622   79262\n",
        "28411   75    2  2009           6   28903  793861"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# create US state adjacency map\n",
      "mat,fips = pysal.queen_from_shapefile('states/gz_2010_us_040_00_20m.shp', 'STATE').full()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "WARNING: there are 3 disconnected observations\n",
        "Island ids:  ['02', '72', '15']\n"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# get list of states\n",
      "state_list = pandas.read_csv('states/state_names.csv')\n",
      "states = state_list.state_fips.unique().tolist()\n",
      "states.sort()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# keep only states/DC and sort by fips\n",
      "adj_mat = np.zeros((len(states), len(states)))\n",
      "for i1,s1 in enumerate(states):\n",
      "    for i2,s2 in enumerate(states):\n",
      "        adj_mat[i1, i2] =  mat[fips.index('%02d' % s1), fips.index('%02d' % s2)]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# set the following neighbors manually:\n",
      "# AK: HI, WA\n",
      "# HI: AK, CA\n",
      "# ME: VT\n",
      "pairs = [('AK', 'HI'), ('AK', 'WA'), ('HI', 'CA'), ('ME', 'VT')]\n",
      "for p in pairs:\n",
      "    p0 = state_list.ix[state_list.abbrev == p[0], 'state_fips'].values[0]\n",
      "    p1 = state_list.ix[state_list.abbrev == p[1], 'state_fips'].values[0]\n",
      "    adj_mat[states.index(p0), states.index(p1)] = 1\n",
      "    adj_mat[states.index(p1), states.index(p0)] = 1"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# extract data\n",
      "A = adj_mat\n",
      "D = np.diag(adj_mat.sum(0))\n",
      "deaths = np.array(data.deaths)\n",
      "pop = np.array(data['pop'])\n",
      "N = data.shape[0]"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 14
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# model parameters\n",
      "with mc.Model() as model:\n",
      "    # intercept\n",
      "    alpha = mc.Flat('alpha')\n",
      "    # random effect precision parameter\n",
      "    tau = mc.Gamma('tau', alpha=10.0, beta=1.0)\n",
      "    # strength of spatial correlation\n",
      "    p = mc.Uniform('p', lower=0.0, upper=1.0)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 15
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# precision matrix for CAR\n",
      "def find_Tau(tau, D, p, A):\n",
      "    return tau * (D - p * A)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# CAR random effects\n",
      "with model:\n",
      "    beta = mc.MvNormal('beta', mu=0., Tau=find_Tau(tau, D, p, A), shape=N)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# apply sum-to-zero constraint to beta\n",
      "def stz(x):\n",
      "    return x - theano.tensor.mean(x)\n",
      "with model:\n",
      "    beta_stz = stz(beta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# make predictions\n",
      "def pred(beta, pop, alpha):\n",
      "    return theano.tensor.exp(np.log(pop) + alpha + beta)\n",
      "with model:\n",
      "    mu = pred(beta_stz, pop, alpha)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# add in data likelihood\n",
      "with model:\n",
      "    obs = mc.Poisson('obs', mu, observed=deaths)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "# run HMC\n",
      "with model:\n",
      "    #start = mc.find_MAP()  ### breaks...\n",
      "    nuts = mc.NUTS()\n",
      "    trace = mc.sample(1e4, nuts)\n",
      "# interestingly the one time this gave good values it took over 100 times longer..."
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
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       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      31%                  ] 3107 of 10000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     34%                  ] 3404 of 10000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   36%                  ] 3694 of 10000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  39%                  ] 3988 of 10000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 42%                  ] 4282 of 10000 complete in 7.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------45%                  ] 4579 of 10000 complete in 8.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 4867 of 10000 complete in 8.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------51%                  ] 5164 of 10000 complete in 9.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------54%                  ] 5453 of 10000 complete in 9.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------57%-                 ] 5754 of 10000 complete in 10.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------60%--                ] 6051 of 10000 complete in 10.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------63%----              ] 6350 of 10000 complete in 11.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------66%-----             ] 6639 of 10000 complete in 11.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------69%------            ] 6938 of 10000 complete in 12.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------72%-------           ] 7228 of 10000 complete in 12.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------75%--------          ] 7520 of 10000 complete in 13.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------78%---------         ] 7809 of 10000 complete in 13.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------80%----------        ] 8079 of 10000 complete in 14.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------83%-----------       ] 8372 of 10000 complete in 14.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------86%------------      ] 8668 of 10000 complete in 15.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------89%--------------    ] 8954 of 10000 complete in 15.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------92%---------------   ] 9243 of 10000 complete in 16.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------95%----------------  ] 9537 of 10000 complete in 16.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------98%----------------- ] 9832 of 10000 complete in 17.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 10000 of 10000 complete in 17.3 sec"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "for v in trace.varnames:\n",
      "    print '{}: {}'.format(v, np.mean(trace.samples[v].vals))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "alpha: -0.7476808905\n",
        "tau: 1.51141960347\n",
        "p: 0.988399237271\n",
        "beta: 0.613987564203"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mc.traceplot(trace)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "png": 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QEBAgXmaIiYlRydelXTumXBhCGqtYVI2IXNt4RZEgghs3RkMU+5KZIjNUQVuBKzUSVMbL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       "prompt_number": 23,
       "text": [
        "<matplotlib.figure.Figure at 0x1095fd4d0>"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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SrnFxcfD09ERQUBDmz5+P3377DW3btsXp06cxf/58AEBubi7effddAMJ4e+Hh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       "text": [
        "<matplotlib.figure.Figure at 0x1095fd4d0>"
       ]
      }
     ],
     "prompt_number": 23
    }
   ],
   "metadata": {}
  }
 ]
}