Bayesian Survival Models (Part 1).ipynb

{
 "metadata": {
  "name": "Bayesian Survival Models (Part 1)"
 },
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   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "# Bayesian Survival Models\n",
      "\n",
      "In order to implement survival models (or any other type of model) in a Bayesian framework, it is important to be aware of the Three Easy Steps in Bayesian modeling:\n",
      "    \n",
      "1. Specify a full probability model\n",
      "2. Calculate the posterior distribution of the model\n",
      "3. Check the model\n",
      "\n",
      "If any of these steps are omitted, you are not doing Bayesian modeling!"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Binomial Model "
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Rat tumor data from Tarone (1982). Data come from 71 experiments conducted with rats. $n_j$ is the total number of rats\n",
      "in the $j$th experiment and $y_j$ is the number of rats that develop a tumor during the experiment."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "y = 0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,3,2,2,2,2,2,2,2,2,2,1,5,2, \\\n",
      "5,2,7,7,3,3,2,9,10,4,4,4,4,4,4,4,10,4,4,4,5,11,12,5,5,6,5,6,6,6,6,16,15,15,9,4\n",
      "\n",
      "N = 20,20,20,20,20,20,20,19,19,19,19,18,18,17,20,20,20,20,19,19,18,18,27,25,24,23,20,20,20,20,20,20,10,49,19,46,17, \\\n",
      "49,47,20,20,13,48,50,20,20,20,20,20,20,20,48,19,19,19,22,46,49,20,20,23,19,22,20,20,20,52,46,47,24,14"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Two Extremes: Pooled and Unpooled"
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The simplst model is one in which we pool all the experiments, which implies that all the experiments are measuring the exact same quantity: a single, global probability of tumor development.\n",
      "    \n",
      "The sampling distribution (likelihood) in this case is binomial:\n",
      "    \n",
      "$$y_i \\sim \\text{Bin}(N_i, p)$$\n",
      "\n",
      "The unknown quantity is the probability $p$, to which we can ascribe a flat Beta prior:\n",
      "    \n",
      "$$p \\sim \\text{Beta}(1, 1)$$\n",
      "\n",
      "Note that a beta distribution with both scale and shape parameters equal to one is the equivalent of a uniform distribution on the unit interval.\n",
      "\n",
      "In this example, calculating the posterior distribution is easy. The beta distribution is a *conjugate prior* for the binomial proportion. This means that the posterior distribution is also a beta distribution.\n",
      "\n",
      "$$Pr(p | y, n) \\propto L(y | p, n) Pr(p) \\rightarrow \\text{Beta} = \\text{Binomial}\\times\\text{Beta}$$\n",
      "\n",
      "Specifically, for a beta prior distribution with parameters $\\alpha$ and $\\beta$, the posterior distribution is:\n",
      "    \n",
      "$$\\text{Beta}(y+\\alpha-1, n-y+\\beta-1)$$\n",
      "\n",
      "Hence, the posterior estimates of alpha an beta for this dataset are:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "alpha = sum(y) + 1 - 1\n",
      "beta = sum(N) - sum(y) + 1 - 1\n",
      "\n",
      "alpha, beta"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 2,
       "text": [
        "(267, 1472)"
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "1.*alpha/(alpha+beta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 3,
       "text": [
        "0.1535365152386429"
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import beta_like\n",
      "\n",
      "x = linspace(0, 1, 1000)\n",
      "plot(x, [exp(beta_like(i, alpha, beta)) for i in x])\n",
      "plot(array(y, dtype=float)/array(N), ones(len(y))+abs(random.randn(len(y)))*0.7, 'ro')\n",
      "xlim(0, 0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "(0, 0.5)"
       ]
      },
      {
       "output_type": "display_data",
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NGzYAcMUVVwxZdtOmTTxy8cWc8aUvlSzUMwYfCONZSWT7IDjpdNLT1YW9o4Mo\nUNXQwJdXrszaxnAsQcuBIM+0/IMFZ0zi63NPHdX2C70vdhwM8sCW95g3o5YvNE6mcUolbufw38xG\nakch21is7Uyk99REbI8UTsmD/U9/+hN/+ctfuPnmmwHYunUre/fu5YYbbhiy7KZNm/jV0fRX9cEb\nG7r1VJZ/ZV82NewPWZ7bf705XnH/X4/UvsG/H7rN4R9IjbCebM/tisY5EYrzsWmVfPnsacz/yMS6\nbG53T4INbx1l275ODgQi+D1OaiqcVDhtuB12XA7boBPng36yDfebbA+IlIcrpwRGFewlO3l65VRz\nX+p14uiCo120HR3vdgz1ceDjMzM/9fT+JyKlNupgr6ur49ixY30/Hz9+nLosw9KAUX3iiIjI6Ix6\niMoZZ5zB4cOHOXLkCPF4nD/+8Y/MNXjNFRERKZ5R97FDerjjs88+2zfc8dJLLy1k20REZBTGFOwi\nIjLxlG62kIiIlETBRsUYmYX685//nLa2NioqKvjWt77FaaedVqjNTzi59sfBgwd57LHH2L9/P1dd\ndRVf/GIpr1RfWrn2xbZt23jllVcAmDFjBldeeSUNDUNn1Jpdrv3Q0tLCiy++CKQHJ3zlK19h9uzZ\n49HUojM6a33v3r3cfffdfPe73+W8884rcStLI9e+eOutt7j//vupr0/fTOe8885j8eLFI680VQCJ\nRCL17W9/O9Xe3p6KxWKppUuXpg4cODBgmR07dqTuu+++VCqVSu3evTu1cuXKQmx6QjKyPwKBQGrv\n3r2pX/ziF6lXXnllnFpafEb2xTvvvJPq7u5OpVKp1Ouvv27J94aR/RAOh/v+/dZbb6V+8IMflLqZ\nJWFkX2SWu/fee1OrV69Obd++fRxaWnxG9sWbb76ZWrNmTV7rLUhXzN69e5k+fTrTpk3D6XTymc98\nhtZBN6/YsWMHTU1NAMyZM4fu7m46OzsLsfkJx8j+qK2t5YwzzsDhKOWtR0rPyL5obGyksrISgHPO\nOYfjx4+PR1OLysh+8Hg+vEpnKBTC5XKVupklYWRfAPz2t7/l/PPPp7Y2/3vrmoXRfZGvggT7iRMn\nmDJlSt/PdXV1nDhxYsgykyd/eO3uyZMnD1nGKozsj3KR7774wx/+wLx580rRtJIyuh/eeOMNbrvt\nNh5//PG+Wd1WYzQvWltbWZS585bNmtOPjewLm83GO++8wx133MHq1av54IMPcq63pCdPUxqAIyN4\n88032baH81WUAAAB80lEQVRtG1ddddV4N2XczJ8/n3Xr1vGNb3yDBx54YLybM26effZZrrnmGmw2\nG6lUqqyzY9asWTz++OPcf//9zJ8/n7Vr1+Z8TkFOnhqZhVpXVzfgK/ZIM1XNLp9ZuVZndF+89957\nPPXUU6xcuZKqqqpSNrEk8n1PfPrTn+aZZ54hFAr1dVNZhZF98e677/LII48A0NXVxZ///GecTqfl\nJkEa2Rder7fv3xdddBEvvPACJ0+epLq6etj1FqRiNzIL9dxzz2Xr1q1A+sqQVVVV+P3+Qmx+wtGs\n3A8Z2RfHjh3joYceYsmSJUyfPn2cWlpcRvbD4cOH+yrTtrY23G635UIdjO2L5uZm1q1bx7p16zj/\n/PP55je/acljyMi+6Ozs7Htf7NixA7fbPWKoQwEnKGWbhfraa68B8PnPfx6AF154gba2NjweD7fe\nemvWa7dbRa790dnZyYoVKwiFQtjtdjweDz/5yU8GnECzilz74oknnuCNN97o62t0OBysXr16PJtc\nFLn2w69//Wu2bt2Kw+Fg1qxZXHzxxcwadKtBqzCSFxmPPfYY5557rqWHO460L373u9/x2muvYbfb\nOf3007n00kv56Ec/OuI6NfNURMRiNPNURMRiFOwiIhajYBcRsRgFu4iIxSjYRUQsRsEuImIx/x9U\nh50xP7yORwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10acd4550>"
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "The directed acyclic graph (DAG) of this simple model:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from IPython.display import Image\n",
      "Image(url=\"http://f.cl.ly/items/00093p0d243n0H1r3T0W/pooled.png\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<img src=\"http://f.cl.ly/items/00093p0d243n0H1r3T0W/pooled.png\"/>"
       ],
       "output_type": "pyout",
       "prompt_number": 5,
       "text": [
        "<IPython.core.display.Image at 0x108dfd890>"
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import Binomial, Beta, Normal, MCMC, Matplot, Lambda, observed, binomial_like"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 6
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Here is the prior on $p$:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p = Beta('p', 1, 1, value=0.5)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 7
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p.parents"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 8,
       "text": [
        "{'alpha': 1, 'beta': 1}"
       ]
      }
     ],
     "prompt_number": 8
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p.value"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 9,
       "text": [
        "array(0.5)"
       ]
      }
     ],
     "prompt_number": 9
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "p.logp"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 10,
       "text": [
        "-4.440892098500626e-16"
       ]
      }
     ],
     "prompt_number": 10
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now the sampling distribution:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "ps = [p]*len(y)\n",
      "tumor = Binomial('tumor', n=N, p=ps, value=y, observed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 11
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "In order to do model checking, we will also simulate some data from our model:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "tumor_pred = Binomial('tumor_pred', n=N, p=ps, value=y)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 12
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We now can create an `MCMC` object, and sample from it:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M_pooled = MCMC([p, tumor, tumor_pred])\n",
      "M_pooled.sample(15000, burn=10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  15000 of 15000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 13
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Matplot.plot(p)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting p\n"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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mYhW9vnRoCr4MpFahbsnBRSzH9lDMI5afI02zTVNTEzIzM4X3LpcLTU1Nhjqu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\ndEMMAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ad07d90>"
       ]
      }
     ],
     "prompt_number": 14
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Checking model fit"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Matplot.gof_plot(tumor_pred.trace(), y, bins=10)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting MCMC[0]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[1]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[2]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[3]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[4]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[5]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[6]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[7]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[8]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[9]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[10]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[11]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[12]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[13]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[14]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[15]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[16]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[17]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[18]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[19]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[20]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[21]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[22]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[23]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[24]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[25]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[26]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[27]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[28]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[29]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[30]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[31]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[32]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[33]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[34]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[35]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[36]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[37]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[38]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[39]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[40]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[41]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[42]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[43]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[44]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[45]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[46]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[47]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[48]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[49]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[50]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[51]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[52]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[53]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[54]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[55]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[56]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[57]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[58]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[59]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[60]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[61]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[62]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[63]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[64]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[65]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[66]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[67]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[68]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[69]-gof\n",
        "Plotting"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " MCMC[70]-gof\n"
       ]
      },
      {
       "output_type": "display_data",
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       "text": [
        "<matplotlib.figure.Figure at 0x10ad0b410>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b235a90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b398b50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b4e5a10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b5a41d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b65bb50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b714650>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b7d5b90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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AAFOEBQDAFGEBADBFWAAATP1fmt1y5UdCN0QAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b88eb50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b949550>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10b95b750>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10bac2dd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10bb76790>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10bc37810>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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bgJH1jAoKCjhx4kSCP7XIhWlkITKG2267jXfffZf33nuPBQsW8Ic//IF58+aF\nX7dYLOH9/v73v9Pf3x9e3fPUqVOjFrs0m80Rz/XGG2+En8miW59kMlJYiIzhyxVabTYbJpOJVatW\n0draGn59cHAQgOzsbPbt24fL5Qp/0V9//fWj1i/7ct+xHD9+nDfffJP29nb27t070R9FJGaahhKJ\nYN26dcDI+jmhUIiuri5efPFFhoeH+c53vhPeb9u2bVxxxRUcOHAAgDvuuIP6+nr6+/sZHBzkhz/8\n4aj3/d3vfscnn3zCCy+8wIYNG3jwwQeBkaea3XHHHQn6dCIXT8t9iCTIzp07eeihhy56/3/+85+c\nPHmSO++8M45ViVwcTUOJJMjMmTMv+omOAwMDNDc343A44lyVyMXRyEJERKLSyEJERKJSWIiISFQK\nCxERiUphISIiUSksREQkqv8H/DP40vdWUkQAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bcf6e90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10bdae3d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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mIyMj2Gw2cnNzAfj+97/Pzp07g9c6cOAAZrOZOXPmkJqaysyZMykoKOCjjz6K\n/jcucg6ahhI5j5tvvpk333yTt956i0WLFvHHP/6RBQsWBF9PSEgInvePf/yDwcHB4O6eJ06cGLfZ\npdlsnvBaR44c4bbbbuMb3/gGDQ0NEfhuRMKjsBA5j892aLVarZhMJlatWkV7e3vw9eHhYQCysrLY\nu3cvTqczuIHh1VdfPW7/ss/OPZ+MjAzmzJlDUlKS4XfMlfikaSiRCaxbtw4Y2z8nEAjQ09PDc889\nx+joKF/72teC523bto0ZM2awf/9+AL7+9a/T0NDA4OAgw8PDfOc73xn3ub///e95//33efbZZ9mw\nYQNLly7l1VdfZXBwkNtuuy1636DIBdJ2HyJRsnPnTh588MELPv9f//oXx48fV4Nb4oKmoUSiJDk5\n+YKf6Dg0NERLSwt2uz3CVYlcGI0sREQkJI0sREQkJIWFiIiEpLAQEZGQFBYiIhKSwkJEREL6/xiS\nj9sDlyAqAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ad252d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ddBPBYJC//vWvFBcXh/YwGx4exm63k5ubC8APf/hDdu7cGbrWsmXLWLZsGXv2\n7KGgoICpU6dSWFjIJ598EvtvXOQ8NA0lcgGLFi3irbfe4u2332bBggX84Q9/YN68eaHXLRZL6Ly/\n//3vDAwMhHb3PHHixKjNLs1mc9jrDQwM0N3dzezZsyf4OxGJnMJC5AK+2KHVZrNhMplYuXIlbW1t\nodeHhoYAyMrKYt++fbhcrtAGhrNnzx61f9kX547lzTffZNGiRRP5LYhMGE1DiYxh7dq1wLn9c4LB\nIN3d3bzwwguMjIzwzW9+M3Tetm3bmDJlCgcOHADg29/+NvX19QwMDDA0NMT3vve9UZ/7u9/9jg8/\n/JDnn3+e9evXY7FYeOutt3jggQdi982JXAJt9yESIzt37uTBBx+86PP/+c9/cvz4cTW4JSFoGkok\nRpKTky/6iY6Dg4M0NzfjcDiiXJXIxdHIQkREwtLIQkREwlJYiIhIWAoLEREJS2EhIiJhKSxERCSs\n/w/sAaCbE+hlpgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ad0b690>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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MJnbv3k12djZut5vPPvts4n9wkTNQWIicxfXXX8+7775Lf38/c+fO5Y9//CMb\nNmwIv56SkhLe7+9//zsDAwPhp3seOXJk1MMuzWZzxGPNnz8fj8eDyWTirrvuisNPIxIbdRYiZ/HV\nE1qtVismk4lly5bR1tYWfn1oaAiAnJwcdu7cicvlCj/A8LLLLhv1/LKv9j2bN954g0ceeYSHH36Y\nN954Y7x/FJGYaWUhEsGqVauAU8/PCYVCdHd388ILLzAyMsJ3v/vd8H4bN25kypQp7NmzB4Dvfe97\nNDQ0MDAwwNDQED/+8Y9Hfe7vf/97Pv74Y55//nnWrFnDDTfcwMsvvwycWqmIJBs97kNkgmzdupX7\n7rvvnPf/17/+xeHDh1VwS1LQaSiRCZKWlnbO3+g4ODhIc3Mzdrs9zlOJnButLEREJCqtLEREJCqF\nhYiIRKWwEBGRqBQWIiISlcJCRESi+n+gzIVDKGZIAwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ae1e0d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Dhw5RU1MDnLrvva2tjSuuuIK5c+dy5ZVX8swzz/CVr3yF7373uwn+vyGisBA5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\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10b34bc10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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4dM/Dhw+fctil2Ww+7fu/9dZb4c2Thw8fZs6cOcyZM4fu7u5Y/lgiE6KwEDmL\nkye02mw2TCYTK1eupL29Pfz6yMgIAFlZWezatQu32x0+wPCyyy475fyyk/ee9NZbb+Hz+bjxxhvD\n9/f29hIIBEhPT4/pzyUyEVqGEhnH2rVrgRPn54RCIXp6enjmmWcYGxvjRz/6Ufi+rVu3MmPGDPbs\n2QPAT37yExoaGhgaGmJkZIRf/OIX4Xs//fRTXnzxRXJzc3n++ef51a9+xZIlS3j55ZcJhUIsX748\nvj+kyDnQcR8icfLYY49x9913n/P9//nPfzh06JAa3DIlaBlKJE5SUlLO+RMdh4eHaWlpweFwxLgq\nkXOjmYWIiESkmYWIiESksBARkYgUFiIiEpHCQkREIlJYiIhIRP8LIFZeOUaviCQAAAAASUVORK5C\nYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c000410>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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+/PJLAKZPn05xcXH4a5FE0zSUyDnceOONvP/++xw8eJCFCxfyl7/8hfnz54df\nT0lJCZ/39ttvMzw8HN7d8+uvvz5ts0uz2XzG57/99tuGXzwpU4fCQuQcvtuh1Wq1YjKZWLVqFZ2d\nneHXg8EgALm5uezevRun0xnewPCKK644bf+y7879zttvv43X6+Xmm28OH9P6WElmmoYSGce6deuA\nU/vnhEIh+vr6eO655xgbG+PHP/5x+LytW7cybdo09u7dC8Att9xCc3Mzw8PDBINBfv7zn4fP/eyz\nz3j55ZcpKCjgxRdf5Be/+AWHDh3i73//O9988w02m40bbrghvt+oSATa7kMkTrZv3879999/3uf/\n61//4siRI9x6660xrErk/GgaSiRO0tLSzvuJjiMjI7S3t2O322Nclcj50chCREQi0shCREQiUliI\niEhECgsREYlIYSEiIhEpLEREJKL/B80Gn+lq/8jqAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c0b8cd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ICwCAJcICAGCJsAAAWCIsAACW/gffae5Rvsu9GAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c16d6d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c22add0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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RcWRkRG1tbXK73UmuCjgzzCwAAJaYWQAALBEWAABLhAUAwBJhAQCwRFgAACz9\nH5/R2z4QPDmxAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c2ec390>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c3a6210>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c3b5310>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ePXvIz8/nkksuoaCggM8++yw+X17kP2gaSuQsFi1axNtvv827777LggUL+Mtf\n/sK8efPCryckJITPe+ONNxgYGAjv7nns2LEzNru0Wq1f+/w33njjjMWTAwMDdHV1MWvWLKO+ksiY\nKSxEzuKrHVrtdjsWi4VVq1bR2toafn1oaAiAzMxM6uvrcbvd4Q0MZ82adcb+ZV+d+5U33ngDv9/P\nTTfdFD721ltvsWjRIsO+j8iF0DSUSATr1q0DRvfPCYVCdHV18cwzzzAyMsL3v//98Hnbtm1jypQp\n7N+/H4Af/OAH1NXVMTAwwNDQED/5yU/C53788cc8//zz5OTk8Oyzz/Kzn/0MgLfffpu77747ht9O\n5Nxpuw+RGHnssce45557zvn8f/7znxw9elQNbpkQNA0lEiNJSUnn/ETHwcFBmpubcTqdBlclcm40\nshARkag0shARkagUFiIiEpXCQkREolJYiIhIVAoLERGJ6n8BjHzIovVe+D4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c51e610>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c5d4f50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c68df50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c69b450>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10c805710>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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y32Ix+f1+Dh06xLJly4wuJWEu1tbs6dOnOXz4cPTPzmw2k5aWNuH50/Jv7fmu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\nRCSm/w/M5uc2rBFXMQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c8bdd10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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RiZ8puQwlIiLxpbAQEZGoFBYiIhKVwkJERKJSWIiISFS6g1vkJBoaGqitreXR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\nUliIiEhUCgsREYnq/wEZdPstdHhQ+AAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c978750>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10ca3ea90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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8vDzKy8sjP7ATISUlhU2bNrF161ZuueUWHn30Udxud8Lq+VMDAwM4HA4A7HY7\nAwMDCa7o4xobG5PilxGfz4fL5eLuu+9OdCkR58+f5/Tp0xw6dIjU1FQ2bNjAfffdl9Ca1q9fz7PP\nPssPfvADnE4n3/rWt6K+56acWSS7kZERXnzxRTZs2BD3teU/d/LkSex2O/feey9Gklz4NjExwdmz\nZ3nwwQfZvXs34+Pj/PKXv0xoTYODg7z88su88MILeL1ezpw5g9/vT2hN12KxWBJdwse8/vrrpKam\nsmTJkoTWMTo6yuHDh1m9enXkWDL8Pz8xMUFvby+7du3iy1/+MocOHUp0SdTV1fHII4/wyiuv8MUv\nfpGXXnop6ntuyrCI5Q7veAuHw+zbt48vfOELFBUVJboczpw5Q2trK1u3bqWmpoa3336b2trahNbk\ncrmYN28eHo+HlJQUiouLaW9vT2hNXV1d5ObmkpWVxac+9SmWLFnC6dOnE1rTFXa7nf7+fgBCoRB2\nuz3BFf1/zc3NtLW1sW3btkSXQm9vLx9++CGVlZVs3bqVYDDIM888k/CZmMvl4qGHHiIlJQWPx8MH\nH3zA2NhYQmt65513WL58OVarleXLl9PR0RH1PTdlWCTrHd6GYfDSSy+RnZ3NypUrE10OAGvXrqWu\nrg6v18tTTz3FggULePLJJxNak8PhICsri87OTiYnJ/H7/Xzuc59LaE35+fmcPXuWixcvMj4+Tltb\nGwsXLkxoTVd4PB6am5sBOH78eFL8EgLQ3t7OT37yE3bu3JnQJcQrcnJyOHDgAF6vF6/Xi9Pp5Nvf\n/nbCw7WoqIi2tjYMw6Czs5P58+cn/N9rwYIFkT6vz+e7of/Xb9qb8pLxDu933nmH5557jpycnMhy\nwVe/+lUWLVqU4Mou6+jo4I033kiKS2c/+OADvF4vg4OD5OTkJORy0D/X3NxMU1MTY2NjLFq0iNWr\nVzNnTnx/n6qpqaGjo4OhoSHsdjtr1qzh85//fMIvnb1S1+DgIA6Hg9WrV3PkyBHC4XDkQoC8vDw2\nbdoU95r+9N+qtLQ08vqTTz5JdXV1XC9UuFZNy5Yt4+DBg7z99tvYbDY2b95Mfn5+3Gu68t9uzZo1\nuN1uXn/9dbq7u/nrv/5rVq1axV133TXl59y0YSEiIvFzUy5DiYhIfCksREQkKoWFiIhEpbAQEZGo\nFBYiIhLVTbndh8hsa25upqGhgeeff55wOMw///M/s3HjRk6ePMnIyAhz587l7/7u72hqaiI9PZ3H\nH3+cP/wlu/krAAACKUlEQVThD3zta1/jlVde4dKlS5EdT+fMmcM//uM/smfPHh577DEWL17Myy+/\nDFy+wXTVqlX86Ec/oru7m3nz5vGVr3yFefPmceDAAe677z4eeeSRBP9riCgsRK7rrrvu4syZM/T3\n9/OZz3wGi8VCQUEBS5cuBS7frX9lS/OxsTFOnDjB3/zN32AYBm+++Sbl5eWRPcwmJiZwOp0UFhYC\nsHnzZoDIltFWqxWbzcZtt93GvHnzuOWWWygpKeEPf/hDAr5zkY9TWIhcx4MPPsivf/1rRkdHWbhw\nIT/60Y/YsWNH5PUru4g++OCD/PznP2dsbCyye+f58+ev2uzSarVe9dnd3d388Ic/JDMzE4DHHnsM\ni8XCz372M06ePMnnP//52f72RGKinoXIdVzZksHhcGCxWFi9evVVe+iEw2Hg8p3LjY2NeDyeyMZ1\nd95551X7l10594rs7Gy2b9/OwMAAly5ditzxb7fbuXjx4qx+XyLToZmFyBSuPBfh+PHjGIZBX18f\nr7zyCpOTkzz00EOR83bt2sWcOXM4ceIEAF/84hdpaGhgbGyMcDjMP/zDP0TODYVCHDlyBIA77riD\n9PR0Dh8+TCAQYHJyMmHPYhCZirb7EImT73znOzz99NM3fP5vf/tbzp07pwa3JAUtQ4nESXp6+g0/\n0XF8fJzW1lZcLtcsVyVyYzSzEBGRqDSzEBGRqBQWIiISlcJCRESiUliIiEhUCgsREYnq/wFz+Avh\nKHEklQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10caf2c10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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krMMuzWbzWZ/d3d1NTU0NWVlZABw4cIA77riD733vezQ2Nhr9q4lcMoWFyAWc\nOaHVZrNhMplYvnw5HR0d0dfD4TAAubm57Nq1C4/HEz3A8Oqrrz7r/LIz157hdDopLy8nFApx6tQp\ncnJymDVrFunp6VP+xFyZmLQNJRLD6tWrgdPn50QiEXp7e3nllVcYHR3lO9/5TvS6LVu2MG3aNPbs\n2QPAd7/7XRobGxkaGiIcDvPjH/84em0wGGTnzp0AXHXVVWRkZLB48WLeeusthoaGuOOOOxL4G4pc\nHB33IZIgzz33HA8//PBFX/+vf/2Lw4cPq8EtE4K2oUQSJCMj46K/0XF4eJjW1lYcDofBVYlcHK0s\nREQkLq0sREQkLoWFiIjEpbAQEZG4FBYiIhKXwkJEROL6b0i3aqw1jL0PAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cb9fd90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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CCy88pffntA0LERFJnmm5DSUiIsmlsBARkZgUFiIiEpPCQkREYlJYiIhITHqC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\nCxERiUlhISIiMSksREQkJoWFiIjE9P8A5mTvIUKgWqkAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cbada50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10cd2b610>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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,
       "text": [
        "<matplotlib.figure.Figure at 0x10cdde510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10ce9bbd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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2djYnTpzg3LlzDAwMcOTIEebNmxfrsmLK5XLR0NAAwIEDBy7rl8wJuylPO7zP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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10cf5a0d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d01a650>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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IY2Mj3/3ud+NaU25uLnv27OHw4cP09/ezc+dOJk6cGNeajvF4PNTX1wOwdetW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d0d5b10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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9xKxZs/j3v/8d/qyGhgZuueUWYGQ/o4KCAo4ePZqA71zkXBpZiFzArbfeyscf\nf8ynn37K3Llz+ctf/sLs2bPDr6ekpITP++c//0l/f394d8/jx4+ftdml2WwO///UqVMcPnz4rBXV\n77zzTviZLFr6JGORwkLkAr7fodVqtWIymVi1ahWtra3h1wcHBwHIzs6mvr4el8sV/kU/ffr0s/Yv\n+/5cgAMHDhAMBnnzzTf5/PPPOX78OEeOHOG9996jvb2dDz74IB7fnsioaBpKJIJ169YBI/vnhEIh\nurq6eOWVVxgeHuZnP/tZ+LynnnqKCRMmsGfPHgDuuOMO6urq6O/vZ3BwkF/+8pfhcxcuXMjChQv5\n5ptveP/995k+fToPP/wwMPJUszvuuCOO36HIxdF2HyJx8uyzz/LII49c9Pmff/45x44d484774xh\nVSIXR9NQInEyZcqUi36i48DAAM3Nzdjt9hhXJXJxNLIQEZGoNLIQEZGoFBYiIhKVwkJERKJSWIiI\nSFQKCxERiep/ARNy/K6mtEdoAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d198190>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d256490>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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w2Wxce+21AGzbto3W1lZmz55NOBzmhRde4NChQ0yZMgWbzcazzz5LIBAYd1tp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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d311310>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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n5psX+R9ahhK5jPnz5/PWW2/x9ttvM2fOHP70pz8xa9asyOspKSmR8/7xj3/Q\n19cXebrnyZMnL3rYpdlsjvz9zJkzfPjhh5fsqO7r66Ozs5Np06aN5LclMiwKC5HLuPCEVqvVislk\nYvny5bS0tEReD4VCAOTm5rJv3z5cLlfkAYbTpk276PllF84FOHr0KMFgkJdeeol3332Xjo4O4Pxs\nY/78+SP+fYkMh5ahRKJYvXo1cP75OeFwmM7OTl544QUGBwf5xje+ETlvy5YtTJgwgQMHDgDwzW9+\nk7q6Ovr6+giFQnz3u9+NnLtgwQIWLFjAp59+ymuvvYbD4QDgrbfe4sEHH4zjdydy5fS4D5E4efrp\np3nooYeu+Px3332XEydOqMEto4KWoUTiJD09/Yo/0bG/v5+mpibsdvsIVyVyZTSzEBGRmDSzEBGR\nmBQWIiISk8JCRERiUliIiEhMCgsREYnp/wE70noezJK7tQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c974b10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d47ad10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d532110>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d5ec1d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Dw8M4HA5WrFhBV1cXn376KTabjYKCAn70ox9F1tzl2N5//33uu+8+5s+fH1lu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\nEtX/BcSbE3F5o3w6AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d6a96d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d764410>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10d81c4d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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R1y0WS/S8v//97/T29kZ39zxy5MiQzS7NZvOQz37mmWdYuXIlb731FgDbt2+P\nPpNFtz7JWKSwEDmH0zu02mw2TCYTixcvprm5Ofp6f38/ALm5uezcuRO32x39i/6KK64Ysn/Z6XO/\nymKxRO8i/uyzz/jLX/5Ca2srO3bsGLXvJDJSWoYSiWH58uXAqf1zIpEIHR0dvPLKKwwODvK9730v\net769eu56KKL2L17NwC33nortbW19Pb20t/fzw9/+MPouYcPH+bNN9/EYrFEl6UefPBB4NRTzW69\n9dZEfT2R86btPkQS5Nlnn+Whhx467/P/+c9/cujQIW6//fZRrErk/GgZSiRBpkyZct5PdOzr66Ox\nsRGHwzHKVYmcH80sREQkLs0sREQkLoWFiIjEpbAQEZG4FBYiIhKXwkJEROL6Pyc2bbKFDcYqAAAA\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d8d7d10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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UYQEAMEVYAABM/X9Ox8bPNWgQVgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d995810>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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RkfiZkctQIiISXwoLERGJSmEhIiJRKSxERCQqhYWIiERl/cUvfvGLRBchYpqW\nlhbq6uq4/PLLCYVC3HbbbcybN48XX3yR1tZW9u7dS0pKCs888wwdHR0sWLCATz75hIqKCq655hoG\nBgaora1l7969tLe3k5OTw3333Yfdbue0006jsrKSf//73wQCAc466yyCwSBPPPEEe/fuJS0tDbvd\nzqOPPorP58Ptdif62yGi7T5Ejub000/nvffeo7+/n3POOQeLxUJ+fj6LFi0CJu6KbWlpYXR0lJGR\nEXbt2sV3v/tdwuEwL7/8MuXl5ZE9zMbGxnA6nRQUFACQnJxMOBzmm9/8JgCtra1YrVbmzp1LRkYG\nJ5xwAiUlJXzyySeJ+ceL/C9ahhI5iosuuojXX3+dvXv3ct555/Hss89y7rnnRh632WyR81599VVG\nRkYiG9vt37//kM0urVbrIa+9YcMGVq1axUsvvQTA22+/zWWXXcYVV1xBY2NjrP9pIsdNYSFyFElJ\nScDEFs8WiyVyF/GXQqEQALm5uezYsYPCwsLIFtqnnnrqIfuXfXnuV9lsNubMmfgRzM7OZu7cuaSk\npES2XhExiZahRCZxww03ABN754TDYfr6+nj88ccZHx/n4osvjpy3bt065syZw65duwC4/PLLaWxs\nZGRkhFAoxI9+9KPIuZ9++ikvvPACNpstsiy1aNEitm/fzsjIiLaHFyNpuw+ROHnwwQe58847j/n8\nf/3rX+zbt48rr7wyhlWJHBstQ4nESVpa2jF/ouPo6ChtbW24XK4YVyVybDSzEBGRqDSzEBGRqBQW\nIiISlcJCRESiUliIiEhUCgsREYnq/wLWBtqkKzfmIwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10da4cf10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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bnbB6Pmt4eBiHwwGA3W5neHg4wRV9XnNzc1L8MOLz+XC5XHz1q19NdCkR586d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\nQkREolJYiIhIVAoLERGJ6v8DFuzv1I7s6BgAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10db08fd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10dbd21d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10dc0cc50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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c0DSUSIrk5uae9Tc6Dg8P09bWhtfrtbgqkbOjkYWIiJjSyEJEREwpLERExJTC\nQkRETCksRETElMJCRERM/R+7dvlMXEV4eQAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10dd3cfd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10ddf34d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10deb5f50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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wAK/Xy5IlSygsLOTzzz+P2/sX+W9ahhK5gJtvvpn333+fDz74gLlz5/KnP/2J\n2bNnRx5PSkqKnPf3v/+dYDAY2d3zyJEjZ212aTabI18fPnyYqVOnsmbNGj7++GNOnz4NwBtvvMHL\nL79MXl5eLN6eyKgoLEQu4MsdWq1WKyaTiWXLltHW1hZ5PBQKAZCdnc3OnTtxuVyRDQyvvPLKs/Yv\n+/JcgKuuuiqyl1lKSkokLH7wgx/w85//nLfffnt835jIGGgZSmQEq1atAs7snxMOh+nu7uall15i\neHiY733ve5HzNm3axJQpU9i9ezcA3//+92loaCAYDBIKhbjnnnsi506dOpWrr76aV199lZSUFGbO\nnEljYyOfffYZwWCQ22+/PbZvUuQiaLsPkRh55plneOihhy76/H/+858cPnxYDW6ZELQMJRIjqamp\nF/2JjoODg7S0tGC328e5KpGLo5mFiIhEpZmFiIhEpbAQEZGoFBYiIhKVwkJERKJSWIiISFT/Cwwv\ndwrbsj7/AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10df5fa90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e01aa90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e0d8d90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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gMKiBgQE999xzmpyc1Le+9a3Qedu2bdOCBQu0Z88eSdK1116rpqYmjY6Oanx8\nXN///vdD5y5cuFAXXnihduzYoaSkJJ1zzjlauXKl3nzzTY2OjrI9POYktvsAouTxxx/Xvffee8bn\n/+tf/1JPT4++853vzGJVwJlhGQqIkuTk5DN+ouPY2Jja29tlt9tnuSrgzDCzAACExcwCABAWYQEA\nCIuwAACERVgAAMIiLAAAYf1fdxARtdW71QoAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e195290>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x10e24b710>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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I5s2bmTVrFg8//DBerzdh9XxWf38/LpcLAKfTSX9/f4IrMmtoaJgRb0b8fj8e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\nAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e30c9d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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sAACWCAsAgCXCAgBgibAAAFj6/zIlx/x4MDvwAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e3b96d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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MDPDTn/6UJ598Eq/Xy/Hjx2ltbZ3w/GkZEBez0louTDgcZteuXXzxi1+kuLg4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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e47d150>"
       ]
      }
     ],
     "prompt_number": 15
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "### Unpooled Model"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "def unpooled_model(y=y, N=N):\n",
      "    \n",
      "    # Prior on probability of tumor\n",
      "    p = [Beta('p_{0}'.format(i), 1, 1) for i in range(len(y))]\n",
      "    \n",
      "    # Binomial likelihood\n",
      "    tumor = Binomial('tumor', n=N, p=p, value=y, observed=True)\n",
      "    \n",
      "    return locals()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M_unpooled = MCMC(unpooled_model())\n",
      "M_unpooled.sample(15000, 10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  15000 of 15000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5,8))\n",
      "\n",
      "Matplot.summary_plot(M_unpooled.p, x_range=(0,0.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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5MtauXQsAqK6uxtmzZ+Hj44PY2FipN+1wjDoSUUewWMjtnXh548aN+r9v3rwZ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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10e513a50>"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "## Binomial with Random Effects\n",
      "\n",
      "Obviously, this is a poor model. We have little reason to expect that 71 experiments conducted at different times and places are measuring precisely the same quantity. The \"true\" value in each case is likely to vary somewhat from the others, due perhaps to variables that we have not measured. In this case, we can think of estimating distinct, but related, parameters; perhaps parameters that can be thought of as coming from a \"population\" of similar experiments. The effect of a random effect model is to *partially pool* the data from replicates of similar experiments.\n",
      "\n",
      "**How do we implement this?** \n",
      "\n",
      "Rather than just placing a prior over a global probability $p$, we would like to model a sample of $p$ as coming from some population, as discussed. The easiest way to do this in the context of the model we have already implemented is to use a beta distribution to *model the distribution* of the probabilities. This distribution has unknown parameters ($\\alpha, \\beta$) that we need to estimate. So, we need to specify our uncertainty about these parameters using *hyper* prior distributions. Since the parameters of a beta distribution are positive continuous, a gamma distribution is a convenient choice, but others (e.g. uniform, lognormal) could be used as well."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image(url=\"http://f.cl.ly/items/0g1P0p2v2a1t3k321h3A/Screen%20Shot%202013-03-15%20at%209.26.48%20AM.png\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<img src=\"http://f.cl.ly/items/0g1P0p2v2a1t3k321h3A/Screen%20Shot%202013-03-15%20at%209.26.48%20AM.png\"/>"
       ],
       "output_type": "pyout",
       "prompt_number": 19,
       "text": [
        "<IPython.core.display.Image at 0x10dff84d0>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "Image(url=\"http://f.cl.ly/items/0j323X29440X183b0h1K/random_effect.png\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "html": [
        "<img src=\"http://f.cl.ly/items/0j323X29440X183b0h1K/random_effect.png\"/>"
       ],
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "<IPython.core.display.Image at 0x108e081d0>"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import rgamma\n",
      "hist(rgamma(1, 0.01, size=10000), bins=20)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 21,
       "text": [
        "(array([3335, 2219, 1500,  971,  651,  454,  303,  178,  134,   87,   60,\n",
        "         33,   24,   17,   11,    7,    9,    2,    3,    2]),\n",
        " array([   0.0027,   41.1899,   82.377 ,  123.5642,  164.7513,  205.9384,\n",
        "        247.1256,  288.3127,  329.4998,  370.687 ,  411.8741,  453.0612,\n",
        "        494.2484,  535.4355,  576.6227,  617.8098,  658.9969,  700.1841,\n",
        "        741.3712,  782.5583,  823.7455]),\n",
        " <a list of 20 Patch objects>)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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zPT2Nx+PRCiMRkSSzbCA88cQTVx276667/uX5ZWVllJWVXXXc5XLxzDPPXGd5IiKyXrRT\nWUREAAWCiIhEKRBERARQIIiISJQCQUREAAWCiIhEKRBERARQIIiISJQCQUREAAWCiIhEKRBERARQ\nIIiISJQCQUREAAWCiIhEKRBERARQIIiISJQCQUREAAWCiIhEKRBERARQIIiISJQCQUREAAWCiIhE\nKRBERAQAy3InnD17lp6eHqxWK6dPnwZgamqKpqYmRkZG2Lp1KzU1NaSlpQHQ2tpKe3s7ZrOZ6upq\n8vLyABgaGqK5uZmZmRk8Hg+VlZVr2C0REbley44QiouL+f73v3/FsZaWFnJzczl16hQ5OTm0tLQA\ni3/0Ozo6qK+v5/Dhw/h8PgzDAMDn83HgwAFOnTrFpUuXuHjx4hp0R0REVmrZQMjPzycjI+OKY93d\n3ezZswdYDAy/3w+A3++nqKgIi8VCZmYmWVlZ9Pf3EwqFiEQiuN1uAHbv3h1rIyIiyWFFzxDC4TB2\nux0Am81GOBwGIBQK4XQ6Y+c5nU6CwSChUAiHwxE77nA4CAaDq6lbRETibNUPlU0mUzzqEBGRBFv2\nofLHsdlsjI2NYbfbCYVC2Gw2YPGdfyAQiJ0XCARwOp1XjQgCgcAVI4Z/F2aTid9/MLHi9pkZqXzG\nujGOFYmIXLsVBUJBQQHnz5/nnnvu4cKFCxQWFsaONzY2UlFRQTAYZHh4GLfbjclkIj09nf7+ftxu\nN52dndx9991x7UgyCEfm+I83/rri9g3lbgWCiCTMsoHQ2NhIX18fExMTHDx4kAceeIB7772XpqYm\njhw5Elt2CuByuSgpKaG2thaz2YzX641NKXm9Xpqbm5mensbj8bBjx4617ZmIiFyXZQPhiSee+Njj\nR48e/djjZWVllJWVXXXc5XLxzDPPXGd5IiKyXrRTWUREAAWCiIhEKRBERARQIIiISJQCQUREAAWC\niIhEKRBERARQIIiISJQCQUREAAWCiIhEKRBERARQIIiISJQCQUREAAWCiIhEKRBERARQIIiISNSK\nvkJT1sZqvpNZ38csIqulQEgiq/lOZn0fs4islqaMREQEUCCIiEiUAkFERAAFgoiIRCkQREQEWOUq\no0OHDpGenk5KSgpms5m6ujqmpqZoampiZGSErVu3UlNTQ1paGgCtra20t7djNpuprq4mLy8vLp0Q\nEZHVW/Wy0xMnTnDDDTfEfm5paSE3N5ejR4/y2muv0dLSwkMPPcTQ0BAdHR3U19cTDAY5efIkjY2N\npKRokCIikgxW/dfYMIwrfu7u7mbPnj0AFBcX4/f7AfD7/RQVFWGxWMjMzCQrK4uBgYHVXl5EROJk\nVSMEk8nE008/jclkYu/evXz5y18mHA5jt9sBsNlshMNhAEKhEDk5ObG2TqeTYDC4msuLiEgcrSoQ\nTp48yebNmxkaGqKuro6bbrrpitdNJtOS7Zd7XURE1s+qpow2b94MgMvl4o477mBgYACbzcbY2Biw\nOCqw2WwAOBwOAoFArG0gEMDhcKzm8iIiEkcrHiFMT0+zsLBAeno64+Pj9Pb2Ul1dTUFBAefPn+ee\ne+7hwoULFBYWAlBQUEBjYyMVFRUEg0GGh4dxu91x68innT4YT0RWa8WBEA6HaWhoAODGG2+kvLyc\nL3zhC+Tm5tLU1MSRI0diy05hcRRRUlJCbW0tZrMZr9erKaM40gfjichqrTgQMjMzY4Hw36Wnp3P0\n6NGPbVNWVkZZWdlKLykiImtImwBERARQIIiISJQCQUREAAWCiIhEKRBERARQIIiISNSqP+1UPvm0\nqU1EQIEgaFObiCzSlJGIiAAKBBERiVIgiIgIoEAQEZEoBYKIiAAKBBERidKyU1mV1exhAO1jEEkm\nCgRZldXsYQDtYxBJJpoyEhERQCMESTB9bIZI8lAgSELpYzNEkoemjEREBNAIQT7BNN0kEl8KBPnE\n0nSTSHytayD09fXx0ksvMT8/T2lpKXffffd6Xl4kRvsnRK62boGwsLDA2bNn+cEPfoDD4eB73/se\nt912Gy6Xa71KEInR/gmRq61bIAwMDJCVlUVmZiYARUVFdHd3KxDkE2k1I4yMDWYmZ+dX1FYjE1lL\n6xYIwWCQLVu2xH52OBwMDAz8y/O/9b/+x4qus2XTBsYicytqK3KtVjPCOP7lz6647bMVOYxOzqyo\nLawujBLVFhSE68VkGIaxHhf6zW9+w+9//3u+9a1vAfDmm28yMDDAgQMHrjq3ra1tPUoSEfm3U1pa\nuuK26zZCcDgcXL58OfZzIBDA4XB87Lmr6ZCIiKzMum1Mu+WWWxgeHmZ0dJS5uTneeustCgoK1uvy\nIiKyjHWbMoLFZac//elPY8tOy8rK1uvSIiKyjHUNBBERSV76LCMREQGS8KMrErWb+ezZs/T09GC1\nWjl9+jQAU1NTNDU1MTIywtatW6mpqSEtLQ2A1tZW2tvbMZvNVFdXk5eXF/eaLl++jM/nIxwOY7Va\nKS4upri4OKF1zczMcOLECWZnZ0lNTWXXrl1UVFQk/F7B4ubHY8eO4XQ6qa2tTXhNhw4dIj09nZSU\nFMxmM3V1dQmvCSASifDiiy/yt7/9jdnZWbxeLy6XK2F1vf/++5w5cyb288jICF//+tcpKSlJ6L16\n4403OH/+PLOzs+Tn57N///6E//7OnTvHr371K1JTUykvL6e0tDS+NRlJZH5+3nj88ceNkZERY3Z2\n1jhy5IgxODi4Ltfu6+sz/vKXvxhPPvlk7Ngrr7xivPbaa4ZhGMYvf/lL42c/+5lhGIYxODhoHDly\nxJidnTVGRkaMxx9/3Jifn497TaFQyPjrX/9qGIZhhMNh49FHHzUGBwcTXlckEjEMwzBmZmaMJ598\n0nj//fcTXpNhGMbrr79uNDY2GvX19YZhJP735/V6jYmJiSuOJbomwzCMpqYmo62tzTAMw5ibmzMm\nJyeToi7DWPwb8Nhjjxn/+Mc/ElrTxMSE4fV6jampKWN+ft545plnjN7e3oTWNDk5aXz72982JiYm\njKmpKePYsWPGBx98ENeakmrK6L/vZrZYLLHdzOshPz+fjIyMK451d3ezZ88eAIqLi/H7/QD4/X6K\nioqwWCxkZmaSlZW15Ca7lbLb7Wzbtg0Aq9WK2+0mGAwmvK6NGxc3CEUiERYWFtiwYUPCawoEAvT2\n9nLXXXfFjiW6JgDj/3tEl+iaPvzwQ/70pz/F7pPZbGbTpk0Jr+sjf/jDH8jKymLLli0JrSk1NRVY\nvF8zMzNMT0+TkZGR0Jreffddbr75Zm644QbS0tK49dZb+e1vfxvXmpIqED5uN3MwGExYPeFwGLvd\nDoDNZiMcDgMQCoVwOp2x85xO55rXOTw8zODgILm5uQmva2FhgaNHj/LYY4+xb98+tmzZkvCaXnrp\nJb7xjW+QkvL//ksnuiaTycTTTz/NU089xRtvvJEUNY2OjmK1WvH5fBw+fJgf/ehHTE9PJ7yuj7z1\n1lsUFRUBib1XqampPProoxw6dIhvfvObbN++nZycnITWlJ+fz8DAAKOjo4RCIXp6eggGg3GtKeme\nISQrk8m0qtdXIxKJcObMGaqqqmJzg4msKyUlhYaGBkZHR6mrq2P79u0Jrentt9/GZrPx2c9+lj/+\n8Y8ruuZa3KeTJ0+yefNmhoaGqKur46abbkp4TfPz87z33nt87Wtf47HHHuPHP/4xv/71rxNeF8Dc\n3Bzd3d089NBD133NeNc0Pj7OT37yE/7zP/+TjIwMnn32Wd5+++2E1pSWlkZVVRUvvvgiH374IZ/7\n3OeueAMUj5qSKhCuZzfzerDZbIyNjWG32wmFQthsNmCxzkAgEDtvLeucm5vj9OnT3HnnnRQWFiZN\nXQCZmZns3LmTvr6+hNb05z//me7ubnp6epidnWVqaornn38+4fdp8+bNALhcLu644w4GBgYSXpPT\n6eSGG26IbQotKirizTffxG63J/z/VG9vLzfffDNWqxVI7P/zgYEBcnJyyMrKAmDXrl288847Cf/9\nFRQUxH53v/jFL3A6nXGtKammjJJtN3NBQQHnz58H4MKFC7E/yAUFBXR1dTE3N8fo6CjDw8O43e64\nX98wDF544QVcLhfl5eVJUdf4+DiTk5MATExM0NvbS3Z2dkJrqqys5OzZs/h8Pr7zne9w6623UlNT\nk9CapqenmZqaAhbvWTLcJ1h8LpWVlUV/fz8LCwv09PRw66234vF4EloXQFdXV2y66KNrJ6qmvLw8\n3nvvPf75z38yOztLb28vn//85xP++/toOujy5cv87ne/40tf+lJca0q6jWmJ2s3c2NhIX18fExMT\n2Gw2HnjgAb74xS8uuZyrra0ttpwrPz8/7jW98847HD9+nOzs7NhQ78EHH2T79u0Jq+vvf/87Pp+P\nhYUF7HY7u3bt4q677lp26dta36uP9PX18frrr1/TstO1rGl0dJSGhgYAbrzxRnbt2sVXvvKVpLhP\n77//Pj6fj/HxcbKzs6mpqcEwjITWFYlEOHToEE1NTaSnpwPLL/te65rOnz9PR0cHMzMz7Nixg/vv\nv5/p6emE1nT8+HEmJydJS0tj//79uN3uuN6npAsEERFJjKSaMhIRkcRRIIiICKBAEBGRKAWCiIgA\nCgQREYlSIIiICAD/FwfAlv6oq+ZeAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x108e08150>"
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import Gamma\n",
      "\n",
      "def random_effect_model(y=y, N=N):\n",
      "    \n",
      "    # Hyperpriors\n",
      "    alpha = Gamma('alpha', 1, 0.01, value=1)\n",
      "    beta = Gamma('beta', 1, 0.01, value=1)\n",
      "    \n",
      "    # Population distribution of tumor probabilities\n",
      "    p = Beta('p', alpha, beta, value=[0.5]*len(y))\n",
      "    \n",
      "    # Binomial likelihood\n",
      "    tumor = Binomial('tumor', n=N, p=p, value=y, observed=True)\n",
      "    \n",
      "    return locals()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 22
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "M_random = MCMC(random_effect_model())\n",
      "M_random.sample(15000, 10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        " \r",
        "[****************100%******************]  15000 of 15000 complete"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n"
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5,8))\n",
      "a = M_random.alpha.stats()['mean']\n",
      "b = M_random.beta.stats()['mean']\n",
      "\n",
      "Matplot.summary_plot([M_random.p], vline_pos=a/(a+b), x_range=(0,0.5))"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "display_data",
       "png": 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uHRJpm/XZbDYyMjKorq5G0zQWLFjAjBkzmDp1KlVVVYwePRpoyfpef/11Ll++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\nRBrBAZuISCP+C70/gUQdTOb5AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ad07350>"
       ]
      }
     ],
     "prompt_number": 24
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "We can see that, relative to the unpooled model, estimates are *shrunk* towards the overall mean.\n",
      "\n",
      "Clearly, this is a more appropriate fit for the data:"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "figure(figsize=(5,8))\n",
      "scatter(array(y, dtype=float)/array(N), range(len(y))[::-1], N)\n",
      "xlim(0, 0.5)\n",
      "ylim(0, 71)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 25,
       "text": [
        "(0, 71)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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