Bayesian Survival Models.ipynb

{
 "metadata": {
  "name": "Bayesian Survival Models"
 },
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 "worksheets": [
  {
   "cells": [
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "%load_ext save_on_exec"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 1
    },
    {
     "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": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 2
    },
    {
     "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": 3,
       "text": [
        "(267, 1472)"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 3
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "1.*alpha/(alpha+beta)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "pyout",
       "prompt_number": 4,
       "text": [
        "0.1535365152386429"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 4
    },
    {
     "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": 5,
       "text": [
        "(0, 0.5)"
       ]
      },
      {
       "output_type": "display_data",
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EYgx2IrVhsAuqkBkxScmqnYjUhcEuqEAkDjuDnUiTGOyCCkRisOY51TGpzMyZMURqxGAX\nlD8SQ5m5wIrdxIqdSI0Y7ILyhWOwF7DzFADKLAx2IjVisAvKH46jzFx4K4bBTqQ+DHZB+cKxwoPd\nZMAZBjuR6jDYBeWPxGAvuGLn0adEasRgF1SiYldiuiNPBEakNgx2QSmy89RsgJ+n7iVSHQa7oPwR\n7jwl0ioGu6CUqtgZ7ETqw2AXlF+BWTF2BjuRKjHYBeWLxGAvcOdpOYOdSJUY7ILyKXSAEuexE6kP\ng11Q/nAMZUrMiuHFNohUh8EuoHA0DgmAyZDf1ZOSjHodjHodQryoNZGqMNgFlDizowE6XWHBDvAg\nJSI1YrALKDHVUZm3llMeidSHwS4gnwIHJyWVWwwYDEcVeS4iKg0Gu4D84cJPAJZUYTFiMMSKnUhN\nGOwC8ikwIybJYTHAG2TFTqQmDHYBKXFmxySHlRU7kdow2AWkxLnYkyosRnhDrNiJ1ITBLiAljjpN\nqrAYWLETqQyDXUB+Bc7smOSwGtljJ1IZBruAzoRjKFeoYndYDGzFEKkMg11A3lAUFValgt0Ib5Ct\nGCI1YbALyBuMwWExKvJciXnsrNiJ1ITBLqDBUBQOqzLB7rAa4OXOUyJVyfrp37x5M7q7u+FwOLBh\nwwYAQCAQQEtLC3p7e1FVVYWmpiZYrdaiD5bk8YaiqLAo04qxGvWIxyWEo3GYjawDiNQg6ye1oaEB\na9euHXZfa2sramtr8cwzz2DOnDlobW0t2gApN5IkYVDBVoxOp0MFd6ASqUrWYL/44otRVlY27L6u\nri7U19cDSAR/Z2dncUZHOQtF49DrAIuC1XUFjz4lUpW8Pv0ejwculwsA4HQ64fF4FB0U5c8biqFC\noWo9ycGjT4lUpeCyTomLOZByvMEoHApNdUxyWA2c8kikInkFu9PphNvtBgAMDAzA6XQqOijKX2LH\nqbIVO88XQ6QueQV7XV0d2tvbAQAdHR1YsGCBkmOiAgyGYopNdUxy8HwxRKqSNdifffZZPProozh+\n/Djuu+8+vPfee2hsbMTBgwexcuVKHDx4EI2NjaUYK8ngDSo31THJYTXCE2DFTqQWWUu7Bx54IO39\nq1atUnwwVDhvSLmpjkmVNhM+6wso+pxEVDw84kQwiaNOla3YK+1G9Pkjij4nERUPg10wg8Wo2O0m\nDLAVQ6QaDHbBJHrsyrdi+lmxE6kGg10wiYpd2VZMhcWAUDSOUDSu6PMSUXEw2AWTOBe7shW7TqfD\nJLsRAwFW7URqwGAXjCcYVbxiBxLtGO5AJVIHBrtAIrE4ApG44gcoAYkdqP1+7kAlUgMGu0DcZ88T\noy/C+Xsm201sxRCpBINdIAP+KCptpqI8d6JiZ7ATqQGDXSADgQgmFSnYJ9l4kBKRWjDYBTIQiKLS\nrnx/HWCPnUhNGOwC6fdH4CpmK4Y9diJVYLALJNGKKU7FPsVuwmkfg51IDRjsAjnli2BKWfF67IFI\nDEEefUo04THYBXLKF8bUMnNRnlun02FquRknB8NFeX4iUg6DXSCnfRGcV6RgB4CqcjNOnGGwE010\nDHZBhGNxDIZicBWpxw4AVRVm9A6Givb8RKQMBrsg+nwRVNqNMOiVP+o06XxW7ESqwGAXxClfuKht\nGACY5rTgKy8rdqKJjsEuiOODYXytorjBPsNpxRduBjvRRMdgF8Rxbwhfc1iK+hrTHBYcHwwhFpeK\n+jpEVBgGuyC+9IYwrcjBbjXq4bIZccrHPjvRRMZgF8Rxb7jowQ4A1S4rjgwEi/46RJS/kgX7U42N\n2N3WVqqX0xRJkvBVCSp2AJhZacNnfYGiv45W7G5rw1ONjdhwww38jJBiijfpeYR1772HNUeOAAAu\nX7KkVC+ruN1tbejYsgWmcBgRsxn1y5eP++/T54/AqNfBWYQrJ410YaUNHxz1FP11tGB3Wxt2rVmD\ndYcPp+4T4TNC469kwQ4AzYcPY/WLL6r2j7YYH0QlNhRHBoKoqbQq/rzpXFhpw2t7TxT8PAR0bNky\n7G8JUP9nhCaGkgX7IwCWADCG1DtdbqwP4l1PPplXiCq1oTgyEEDNJJviz5tOtcuKfn8Eg6EoKiyj\n/3wK3aCU6huRnNcZaxmlxmgKp98JrebPCE0MJQv2XwF4GMDBL78s1UumVciHMt0HcScA84EDWBc8\nt0NxrBAd+druvj5sUaBi++++AL75tYrU7WJWgga9DnOm2PHpST8W/p1j2M/kblAyBWYpWhO729rQ\n9sAD2Njbm7rvxz09wLPPpl5nrLF82t2N06+/rsgYI+b0xx1ELcXfV6K0idii1LKStmKeAHD9ifH7\nGi/nA51Jug9iG4AXgsNniaQL0fuvvx6W99/Hb4Ys98/W4e2TpFwrtr+d9OOfvlGVul3sSvDrVWXo\n6T0zKtjlbFB2t7XhpeXLYfJ4YAMQAHCwuxvYsgUdW7bgusOH8QgSf5hRAN89fBhvK9yaeOPJJ7Fl\nyN8AAGzs7cW9zc2pDcy2++7DHwYGRv0ut2zdmvb+fDaa9cuXY82RI2gess5W19Tgyh/+MMffaHxx\nX8HEU7JgvwHAJQDs0dJeXm1oJfFfH3+MN86cGfbzoR/obNJ9ED+3WoHg6Ol/Q0P0X++5B77338dr\nZ2/vRGKDEE7zOCBRscmtgDzBKAYCEVRPOreRSLcB2glgz0cf4d6ZM2HR6WCrrsaNa9fm9cH7n9Mq\n8HLnV7izbvj9cjYoWx96CEGPB0PPGh/wePDSQw+h0m7H/0OiAEh6GMDp48fTPm+uVWJy+YF9+9L+\n3H/0aCqkLhkR3km2WCzr7yh3bJcvWYJPu7txy0svwRaNImA0YtEttwBIzCJTS/XLfQUTT8mC/S0A\n9wA4WsJg393Whv91112Y7ffDCGCsL7j+o0dlPV/yj3T1iy/CGAoharHAdvo08Ne/jlp26Nfpg3/8\nI6af/fdOIBVeO5EIrqFBtrqmBufV1cmugPb1nsFFU8ug1507+dfIDdBOAC16Pab5fPgaEm/6F243\nXli2DO/MnQtbVVVO4fH1qjIccwfhCUaHzcSR01o4efQoLgXwwpCf3wug++hRRIxGvDTisU8AuGVE\ndQ3kXiUOXf7WMX6vEM6F1CNjLBMwGNLeP/R3zKUltW/bNtT296e+ofxlyxYcs1qHfauc6NUv9xVM\nPCVtxWwF8N0Svt7mpiZ8w+/HrwA8D2DPGMvl8ud3+ZIlw9oKrz/xBO61Woe1Y0Z+nR6Mx3Hq7L/b\ncC7Irzz7/0cB7DcaoSsvh72iAgPvvCO79955zIu6GRXD7hu5ATrQ0wPHwACqkNjXkdy4vBSLAT09\nQE9PTuFhMugxf7oDu496cM3cyan75bQWnBge6gBwOxLvgWuMjf75558/6j65bZ9k1XygpyfVQinH\n6A3qWgBl1dWpkFqSZpnVNTVYdMstWPP66xl/R7kV7OtPPIFpJ0/iV0OW+yePBxs9njEfm+6bQPI1\nx6vCF2lfgShKGuxA4kNVMqdO4QkkQv2vAKow9gc6V8mq7N8OH8ZOJML5qNUK+9y5+Mc1a4Z9sMoA\nPHj2tUdeuO7Ks/89Ho3icbcbcLtl997jkoQPj3nx5NdnjVp26AZoww034NBf/pKqhoduXJJy/er8\n97Mm4Y2eU8OCPd03mit/+MNR62KkNgD/BmDFGK8VNo2+3F+2KnFk1fz4kGX+GcArSLxnBgAxACfO\nOw83r12Lji1bAAzf6BoA9FRW4s6nnkqE67x5GX9HuRWs//PPR70PF6d9ZOKx6b4J/LinB15Jwm9O\nnkzdV+oKX5R9BSIpebCfyb6IYpL1QgeA3yNRqY71gc7V0KosGc4IBrF68uRRH6hynAuKTWM839DO\nbXWG3vtQ/3XiDMrNBlS70m8IkiJm87A21Fhvei5fnRdWO9Dy/jEc7g9gZuW5qZZDNyjppHv/k+MJ\nIf2GNyyNPulYtipxZNU89LtA8r14F8BnLhemzZuHm4eEczKkku/r6pqaVKjL+R3lVrAW3ehz54/V\nqIxaLGm/CWzs7cWjI5YtdX9bzgadSqukwX4PAHcJX8+n1wPxOJKxM/QDDQB/NRiw/Lnnij4H2X92\nHMnXTxde1wy5vQTI2t4BgLd6TuMf5k6GLk1ADFW/fDle/I//ACIRAJnDQy6zQY+b/sdUvLr3BB5d\nPFP24wYBLAewZch9H5/9/wwAV2H4hvcaAG0Vw1tNQPYqceT7M7K1ciWAt2tqcOuQwAaUCSm5Fayt\nuhpwD/9ELAFwj9mMrUPGn3zs+889l/b10nX9S93fzraxo9IqKNh7enrwyiuvIBaLYfHixfjud8fu\noCdnxbgKecEczV26FD9obcXQM5ukqmsAtzidef8x5tJXnLN0Ke5pbcXWIa+9FEDZlCkIx+O4v78/\ndX9yjNtqa7F6ypQxw+XAaT8+OXEGK6/M3ka6fMkSfPrgg7h740a8FA6P2T/O9avzTV8/D/f8n0/x\nwVEPLrvAKesxFWVlOOXz4VYAVgBBAD4A/6LTYbokDXt/kt5Os06zBfDI9yf1nldWovbiizMGdqEh\nJXfjcOPatfjxiOm3/7eqChfdcQdWd3WNemyyTTRSunk67G9rW97BHo/HsXnzZjz66KOorKzEmjVr\ncOmll2LGjBlpl38LwN0AKq+4It+XzNljW7fiXwH8rbUV9yCx8zZpudGIRXffnfdz59JXTI7jhjfe\nQJkkwafTYdaNN+KxrVuxu60Nf1qzBleOeJ6bM0xF9ASjWPfeEdyzaDqspvSzNEa6a/XqYb3h44OD\nuFenw5Ty8ry/OluNeqz5+xo89u5neMRcM+wgqbFcvWIF/vOZZzAnHk9V5X/T6+FcuhRfHTyIew8c\nyPpNJSlTAKd7f94e0VIpJjkbh8uXLAGefXbYBmBJhvch3e/046oqeCUJGNJjZ3+bdJKUpoEpw4ED\nB/D666/j4YcfBgBs374dAHDTTTeNWnbHjh3YcPXVmHTFFWj5938vYLj5+81TT+E/h84Xvvtu3LV6\ndUHPubutDTsV6CvKfZ5AJIbOY1683PkVGmZNwr/UTSto/ErZ86UX6zuOYsEMB/6hdjJqp9hhNo59\n4tBM74VS61Tp55oo0v1OAIT7PSmhu7sbixcvzvlxeQf7Bx98gI8//hjLz0632rlzJw4dOoS77rpr\n1LI7duzAH08lvqqPfLHRry6l+Vf6ZaUxb6R57NDnzfIbD/1xpvGN/Pno1xz7DinD86R77GAoin5/\nFBdNtePmS6di4d/Ja32Uii8cw/Z9p7DrsBvHPEG4rEZUWIywGHUwG/QwGXQYvidgxC3dWD9JdweR\nNiyd4skr2Eu283TpeTzVqzIGgVOD6D6VfclSuxjAxTXJW+Gz/xFRqeUd7JWVlTh9+nTqdl9fHyor\nK9Mum88Wh4iI8pP3FZRmzZqFEydO4OTJk4hGo3j//fdRV1eX/YFERFRUeffYgcR0x23btqWmO157\n7bVKjo2IiPJQULATEdHEU7KLWRMRUWkoNitGzlGov/3tb9Hd3Q2LxYIf/ehHmD59eppnEkO29fHl\nl1/i+eefx5EjR3DrrbfihhtuGKeRFl+2dbFr1y68+eabAIAZM2Zg6dKlqM7jxGwTXbb10NnZiT/8\n4Q8AEpMTvve972H27NnjMdSik3vU+qFDh/DII4/gwQcfxKJFi0o8ytLIti727duHp59+GlVViYvp\nLFq0CI2NjZmfVFJALBaT7r//fqm3t1eKRCLSypUrpWPHjg1bZs+ePdKTTz4pSZIkHThwQFq7dq0S\nLz0hyVkfHo9HOnTokPS73/1OevPNN8dppMUnZ13s379f8vl8kiRJ0nvvvSfk34ac9RAIBFL/3rdv\nn/Tzn/+81MMsCTnrIrnc448/LjU3N0u7d+8eh5EWn5x18cknn0hPPfVUTs+rSCvm0KFDOP/88zF1\n6lQYjUZ861vfQldX17Bl9uzZg/r6egDAnDlz4PP54HaX8pRgpSNnfTgcDsyaNQuGMS7cIAo566K2\nthZ2ux0AMG/ePPT19Y3HUItKznqwDjlds9/vhynN6YpFIGddAMCf/vQnXHbZZXA4HGmeRQxy10Wu\nFAn2/v5+TJkyJXW7srIS/f39o5aZPPncubsnT548ahlRyFkfWpHruvjzn/+MBQsWlGJoJSV3PXz4\n4YdYsWILeXjhAAACL0lEQVQFNm/enDqqWzRy86KrqwtLzp4aIdsZTNVKzrrQ6XTYv38/fvKTn6C5\nuRlffPFF1uct6c5TiRNwKINPPvkEu3btwq23jnXxOvEtXLgQmzZtwg9+8AOsX79+vIczbrZt24bb\nb78dOp0OkiRpOjtmzpyJzZs34+mnn8bChQuxbt26rI9RZOepnKNQKysrh33FznSkqtrlclSu6OSu\ni6NHj+LFF1/E2rVrUVaW7jpL6pbr38QVV1yBl19+GX6/P9WmEoWcdfHZZ59h48aNAIDBwUF89NFH\nMBqNwh0EKWdd2GznLmRz1VVX4bXXXsOZM2dQXj729egUqdjlHIU6f/587Ny5E0DizJBlZWVwuUp5\ndvbS4VG558hZF6dPn8aGDRvQ1NSU9vqmIpCzHk6cOJGqTLu7u2E2m4ULdUDeumhpacGmTZuwadMm\nXHbZZbj77ruF/AzJWRdutzv1d7Fnzx6YzeaMoQ4oeIBSuqNQ3303ca2i73znOwCA1157Dd3d3bBa\nrbjvvvvGPHe7CLKtD7fbjTVr1sDv90Ov18NqteLXv/71sB1oosi2Ll544QV8+OGHqV6jwWBAc3Pz\neA65KLKthzfeeAM7d+6EwWDAzJkzcc0112DmTPlXp1ITOXmR9Pzzz2P+/PlCT3fMtC7eeecdvPvu\nu9Dr9bjgggtw7bXX4sILL8z4nDzylIhIMDzylIhIMAx2IiLBMNiJiATDYCciEgyDnYhIMAx2IiLB\n/H8OkIrL30zzzAAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113632bd0>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 5
    },
    {
     "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": 6,
       "text": [
        "<IPython.core.display.Image at 0x111759b90>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 6
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc import Binomial, Beta, Normal, MCMC, Matplot, Lambda, observed, binomial_like"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 7
    },
    {
     "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": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
           ""
       ]
      }
     ],
     "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)"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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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H8Gn95WA9wqKk4WJdvVowMEuFtfVgPV46EA1AKkre+jIT8tMVgh+9AUCECBdD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       "text": [
        "<matplotlib.figure.Figure at 0x1136821d0>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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 0x113678410>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x113ce4b10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x113d290d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x113e74550>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x113f350d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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RFgAAU4QFAMAUYQEAMPX/AAJWYfB2gKubAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113fecf10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1140a8d10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114169790>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114222c50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1142d8090>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1142cf4d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11444ee90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11450f250>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1145c8750>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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bNw+A73//++zcuTN8rWAwSGNjI7fddhswsp9RcXExJ06cSPBPLXJhGlmIXMQd\nd9zBW2+9xdtvv82cOXP4wx/+wKxZs8Kvp6Wlhc/7+9//zsDAQHh3z1OnTo3a7NJsNke81quvvhp+\nJouWPkkqUliIXMTnO7RarVZMJhPLli2jra0t/HowGAQgLy+P/fv343Q6w7/ob7zxxlH7l31+7sV8\n9NFHvPbaa3R0dLBv377x/lFEYqZpKJEIVq1aBYzsnxMKheju7uYXv/gFw8PDfOMb3wift2XLFq66\n6ioOHjwIwF133UVDQwMDAwMEg0G++93vjvrc3/3ud3z44Yc8//zzrFmzhoceeggYearZXXfdlaCf\nTuTSabsPkQTZuXMnDz/88CWf/89//pOTJ09y9913x7EqkUujaSiRBJk6deolP9FxcHCQlpYW7HZ7\nnKsSuTQaWYiISFQaWYiISFQKCxERiUphISIiUSksREQkKoWFiIhE9f8AzwivxyueeYQAAAAASUVO\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114689690>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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F9zAbGRnBbrdTUFAAwA9/+EN27NgRvpbZbMZisXDFFVeQlpbG9OnTKS4u5pNP\nPon/Ny5yDpqGEjmPm266iTfffJO3336bBQsW8MILLzBv3rzw6xaLJXze3//+d4aGhsK7ex47duys\nzS7NZvO417rzzjupqKggIyODgwcPxuC7EYmOwkLkPD7fodVms2EymVixYgUdHR3h14PBIAC5ubns\n2bMHl8sV3sDw6quvPmv/ss/PPZ/PV99brVZOnz49qd+HyGTQNJTIONasWQOM7Z8TCoXo7e3l2Wef\nZXR0lG9+85vh87Zs2cK0adPYv38/AN/+9rdpampiaGiIYDDI9773vbM+9/e//z0ffvghzzzzDOvW\nrePll1/G6/UyOjoavqZIMtF2HyJxsmPHDh544IELPv+f//wnR48eVYNbkoKmoUTiJDU19YKf6Dg8\nPExraysOhyPGVYlcGI0sREQkIo0sREQkIoWFiIhEpLAQEZGIFBYiIhKRwkJERCL6X/nMlM/zlEf4\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11473f310>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11369c490>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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lpptu4p577uHZZ59l7ty5/PjHP07w/w0RhYXIZd14440cP36cM2fO8M1vfhOT\nyUReXh5LliwBzj9lf2Gb7qGhIQ4dOsRtt91GKBTi73//O6WlpeE9zEZGRrDZbOTn5wPwi1/8gt27\nd4fHWrZsGcuWLWPfvn0UFRUxbdo0iouL+eyzz+J/4SKXoGUokctYtGgR77zzDu+++y4LFizgL3/5\nC/PmzQu/npycHD7vn//8J0NDQ+HdPU+dOnXRZpdmsznieENDQ/T29jJnzpwYX4nI1VNYiFzGhW0Q\nrFYrJpOJVatW0d7eHn49GAwC559+bWxsxOl0hjdGnDNnzkX7l104dyxvv/02ixYtiuUliMSMlqFE\nxrB27Vrg/P5AoVCI3t5eXnjhBUZHR/ne974XPm/btm0kJSVx6NAhAH74wx/S0NDA0NAQwWCQn/70\npxd97p/+9Cc+/vhjnn/+edatW0dycjLvvPMODz/8cPwuTiQK2u5DJE52797NI488csXn//vf/+bk\nyZNqcMukoGUokThJTU294m90HB4eprW1FbvdPsFViVwZzSxERCQizSxERCQihYWIiESksBARkYgU\nFiIiEpHCQkREIvq/PARcIweYGaMAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x113678e50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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xj39kw4YNkcctFkvkef/4xz8YGhqK3N3zyJEjY252aTabo55r/vz5eDweTCYT\nd999dwJ+GpH4qLMQOYvTd2i12WyYTCaWLl1Ke3t75PFQKARAbm4uO3fuxO12R25geMUVV4y5f9np\n557N66+/ziOPPMLDDz/M66+/PtE/ikjctLIQiWLlypXAqfvnhMNhenp6eP755xkdHeWb3/xm5Hmb\nNm3ioosuYs+ePQB8+9vfpqmpiaGhIUKhED/84Q/HvO/vf/97PvzwQ5577jlWr17NTTfdxEsvvQSc\nWqmITDa63YdIkmzdupX777//nJ//73//m8OHD6vglklB21AiSZKenn7O3+g4PDxMa2srDocjwVOJ\nnButLEREJCatLEREJCaFhYiIxKSwEBGRmBQWIiISk8JCRERi+n+OgGev/DN1owAAAABJRU5ErkJg\ngg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11376ee50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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zxH0tX76choYGLBYLR48ejcNPIxIbdRYi5/D5HVptNhsmk4lVq1bR0dERfnxk\nZASAnJwc9uzZg9vtDt/A8Iorrhh3/7LPn3suWVlZrF27lvz8fHJzcyf7RxGJmVYWIhGsW7cOOH3/\nnFAoRG9vL88++yxjY2N885vfDD9v69atzJgxg3379gHwrW99i8bGRoaGhhgZGeF73/veuPf93e9+\nxwcffMAzzzzDhg0b+Oc//8nf//53AoEAmzdvTtwPKHKedLsPkQTZsWMH99xzz3k//1//+hdHjhxR\nwS1Tgg5DiSRIWlraeX+i4/DwMK2trTgcjjhPJXJ+tLIQEZGotLIQEZGoFBYiIhKVwkJERKJSWIiI\nSFQKCxERier/AQusWJgdBmdmAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114913350>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1149cfe50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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x4MABFi1axF/+8hcWLFgQeT0tLS1y3ttvv83w8HBkd8+vvvrqlM0uzWbzaZ//\n9ttvG37xpEwfCguRs/h2h1ar1YrJZGLVqlV0dnZGXh8dHQUgLy+PXbt24XK5IhsYXnbZZafsX/bt\nud96++238fv93HjjjZFjWh8rqUzTUCITWLduHXBy/5xwOExfXx/PPvss4+Pj/PjHP46ct3XrVmbM\nmMGePXsAuOmmm2hubmZ4eJjR0VF+9rOfRc799NNPeemllygsLOSFF17g5z//OQcPHuSNN97g66+/\nxmazce211yb2GxWJQtt9iCTIY489xr333nvO5//rX//i8OHD3HzzzXGsSuTcaBpKJEEyMjLO+YmO\nIyMjtLe3Y7fb41yVyLnRyEJERKLSyEJERKJSWIiISFQKCxERiUphISIiUSksREQkqv8HRgue8fXl\nmxAAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114a8e2d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114b415d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Pf/xDBw8epMENI7AMBaRIbm7uWX+j49DQkFpbW+V2u5NcFXB2mFkAACwxswAA\nWCIsAACWCAsAgCXCAgBgibAAAFj6/7I12F+77mMtAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114bff5d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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QWQAALNFZAAAsERYAAEuEBQDAEmEBALBEWAAALP1/+u3YL1ah5RIAAAAASUVO\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114cbb590>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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3t8vlcsW5KuD00FkAACzRWQAALBEWAABLhAUAwBJhAQCwRFgAACz9P89ZxeGU\nw434AAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114d789d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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lra2NYDDIjBkzCAaDPP/88xw4cID09HRsNhtPP/00fr//ottKQyamCbk3lEgi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\npbAQEZGo/j80sYQM7N8ypgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x114e31350>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114ef38d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x114fa6650>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115062750>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115120150>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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F7373uxw5coRTp05x3XXXYTKZKCgoYMmSJcC5lfNfbXs9NDTEvn37+MEPfkAo\nFOJvf/sbpaWl4T3MRkdHsdlsLFq0CIB77rkHILxl9MKFC5k+fTqff/45AJdddhkulyv8tUi8aRpK\n5AJuuukm3n//fQ4fPsz8+fP585//zNy5c8Ovp6SkhM/7xz/+wdDQUHh3z+PHj5+32aXZbD7vs7u7\nu6mpqSEzMzMG34nIt6ewELmAr3ZotVqtmEwmVq9eTUdHR/j1kZERAPLy8mhqasLpdIY3MJw9e/Z5\n+5d9de5XsrOzqaioIBgMcvbsWYApv/mhJDZNQ4lEsH79euDc/jmhUIje3l5eeuklxsbG+NGPfhQ+\nb9u2bUybNo19+/YBcOutt9LY2MjQ0BAjIyPccccd4XMDgQB79uwB4OqrryYtLY0jR47w1ltv8eWX\nX2Kz2bjxxhtj+F2KRKftPkRi5Omnn+bBBx+86PP/9a9/cezYMW677TYDqxK5OJqGEomR9PT0i36i\n4/DwMG1tbdjtdoOrErk4GlmIiEhUGlmIiEhUCgsREYlKYSEiIlEpLEREJCqFhYiIRPX/ADe55T0j\nAwfyAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1151d6810>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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/PskVzW9qair68MMPRz/66KNkl3KZsbGxaEVFRfTixYvRqamp6JNPPhnt6emZ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\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x115292390>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11534f8d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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NLs1m80Wf3dXVRU1NDZmZmQDs3bs38kwW3fokk5HCQuQyLuzQarVaMZlMrF69\nmvb29sjroVAIgNzcXPbv34/L5Yr8oJ89e/ZF+5ddOPcCh8NBRUUFwWCQzz77jI8//pi//OUvdHZ2\nsm/fPqO/NZEx0zKUSBTr168HRvfPCYfD9PT08MorrzAyMsK3v/3tyHnbtm1j2rRpHDx4EIA777yT\nxsZGBgcHCYVC/OAHP4icGwgE2LNnDwA33HAD6enpPPLII8DoU83uvPPOeH17IldM232IxMmzzz7L\no48+esXn//Of/+TkyZPcfffdBlYlcmW0DCUSJ+np6Vf8RMehoSFaW1ux2+0GVyVyZTSzEBGRmDSz\nEBGRmBQWIiISk8JCRERiUliIiEhMCgsREYnpfwBs5Y4E4WHbigAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x115411a50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1154c5fd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11557c510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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7HpKSkti8eTPbtm3jtttu45FHHsHtdsetnt83NDSEw+EAwG63MzQ0FOeKrtbU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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11563fe50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ZGfsHOxnS0tLYsGEDmzdv5qabbuLhhx/G7XYnrZ4/FA6HcTgcANjtdsLhcJIr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\nTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1156f0510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1157baa90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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/H9AD5gtlt9sOAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1158792d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1159364d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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FarWyfPlyvv71r+vS2Qn6/OfZ39+PzWZj2bJltLe3c/DgQSwWC9nZ2XzrW98K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\nGVGKMMubygAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1159f2790>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115aa64d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115b63690>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115c21690>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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7bDYb1113HQDPP/88bW1tzJ07l1AoxEsvvcShQ4dITU3FZrPx3HPP4ff7J9xW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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x115cd8310>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115b61c10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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ud4KrAs4PMwsAgCFmFgAAQ4QFAMAQYQEAMERYAAAMERYAAEP/H6rbLVHc5kVk\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x115e44910>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115f03a50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x115fbcc90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x116077610>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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u55prrqG8vJx///vfhMNhvv/977NlyxZ27drFBx98wJQpUwB48cUXCQaDY24r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\nREQSUliIiEhC/w8sZGVmKh476QAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116137790>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1161efad0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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59OjRMza7NJvNZ3z2M888w+rVq3nrrbcA2LFjR/SZLLr1ScYihYXIeXy5Q6vN\nZsNkMrF06VJaWlqirw8MDACQm5vLrl27cLvd0V/0V1111Rn7l3157ldZLJboXcSffvopf/nLX2hr\na2Pnzp2j9jOJjJSWoURiWLlyJXB6/5xIJEJnZyevvPIKQ0NDfO9734uet3HjRi655BL27NkDwK23\n3kpdXR19fX0MDAzwwx/+MHrukSNHePPNN7FYLNFlqQceeAA4/VSzW2+9NVE/nsgF03YfIgny7LPP\n8uCDD17w+f/61784fPgwt99++yhWJXJhtAwlkiBTpky54Cc69vf309TUhMPhGOWqRC6MZhYiIhKX\nZhYiIhKXwkJEROJSWIiISFwKCxERiUthISIicf0v5yxuYUmazjcAAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1162ad9d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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3O8lVAWeGmQUAwBQzCwCAKcICAGCKsAAAmCIsAACmCAsAgKn/D76N0HECVdjZ\nAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116367b10>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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9999PZmZmZLnp5ptv5rLLLjul9+eUDQsREYmfKbkMJSIi8aWwEBGRqBQWIiIS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\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x11641c150>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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yl7+c6FIizp07x8mTJzl48CBpaWls3ryZe+65J6E1bdq0iaeffpof//jHOBwO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\nrkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x1164dd1d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11659afd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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HR0fV3t4ut9ud4qqAM0NnAQAwRGcBADBEWAAADBEWAABDhAUAwBBhAQAw9P8A\nQzG7EUWAnU4AAAAASUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116653a50>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x116711650>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x1167cea90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x11680dcd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x116934bd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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mFgAAQ8wsAACGCAsAgCHCAgBgiLAAABgiLAAAhv4PR7vIcNOkZOcAAAAASUVO\nRK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116944090>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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       "text": [
        "<matplotlib.figure.Figure at 0x116aabe90>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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WIiISlsJCRETCUliIiEhYCgsREQnL/Mtf/vKXsS5CZKJpaGigqqqKG2+8kaGh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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116b62fd0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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/uOF0dU6dOpU1a9bw0UcfkZCQwL333ktWVtaA7xO3YSEiIrFj/lcdERGxPIWF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\nD7vj2iXIBscgAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116c21550>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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gscceY8aMGaHlpjvvvJMrrrjitK7PSRsWIiISPZNyGUpERKJLYSEiImEpLERE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\n/wtb79nKdhU3UgAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116cd55d0>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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Ac0NnAQCwRGcBALBEWAAALBEWAABLhAUAwBJhAQCw9P8ButXBn37gkr8AAAAA\nSUVORK5CYII=\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116d9b510>"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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sWBDvUiLq7+/nscce45FHHsHr9XL8+HFaWlomPH9aBsTFrLSWCzMyMsKePXv4\nyle+QmFhYbzL+UTp6enMnz+ftra2eJdynuPHj9Pc3MyWLVuorq7mjTfeoKamJt5lRTRr1iwAMjMz\nufnmm6fcSNztdjNz5kwKCgpISEigqKiIY8eOxbusCbW2tnL99deTmpoa71Ii6ujoIDs7m4yMDK64\n4goWLFgw6R8F0zIgtNI6ugzD4Je//CWZmZksW7Ys3uVMqL+/nzNnzgAwMDBAa2srWVlZca7qfKtX\nr6a2thav18s999zDnDlzuPPOO+Nd1nmGhobCU2D9/f1T8vvpdDrJyMigvb2dsbExWlpa+MIXvhDv\nsiZ05MgRioqK4l3GhHJzczlx4gQffPABw8PDtLa2Mnfu3AnPn5Y9CLvdzubNm6mqqgrf5jpVtwKv\nrq6mra2NgYEBNm/ezKpVqygpKYl3WeO89dZbHD58mKysLO677z4A7rjjDubNmxfnysbr7e3F6/Uy\nNjaG0+lk+fLlU/qXxVTX19fH7t27AbjiiitYtmwZN910U5yrOt+WLVvwer309/eTlZXFmjVr4l1S\nRIODg/zjH/8IbzI6FSUnJ7NixQp2795NKBRi3rx53HjjjROer5XUIiIS0bScYhIREfMpIEREJCIF\nhIiIRKSAEBGRiBQQIiIS0bS8zVXEbE1NTdTX1/PQQw8xMjLCXXfdxYYNGzh69CiDg4MkJSXx5S9/\nmcbGRlJSUli/fj3//ve/+e53v8vjjz/OmTNn2L9/PzNnzmTGjBl861vfYvfu3XzjG9/A4/Hwhz/8\nATi3sOrhhx+mt7eX5557DoDly5fjdrvZt28f119/PV/72tfi+a2QTzEFhMgErrnmGo4fP05vby+f\n//znsdls5OXlsXDhQuDc6vOPtk0OhUIcPnyYL37xixiGwQsvvEBZWVl4r6jR0VFcLhf5+fkAbNq0\nif7+foaHh0lMTOSll15ixYoVwLntmFeuXElxcTH//ve/4/PFi6ApJpEJ3XLLLbz66qu8/vrrzJ07\nlz/+8Y/ccMMN4ec/2kn2lltu4eWXXyYUCoV37j116tS4jQTtdvt579/Y2MiiRYvC58+aNYtZs2bR\n1dVl5pclcsEUECIT+GjHUKfTic1mY+XKleP2fhoZGQEgJyeHgwcPUlBQEN6c7+qrrx63X9hH537E\nMAza2trCq1ivvvpqent7CQaDZGRkmPp1iVwoTTGJTGLt2rUAHDp0CMMw6Onp4fHHH2dsbIwvfelL\n4fN27twH3hkGAAAAlElEQVTJjBkzOHz4MABf/epXqa+vJxQKMTIywu233z7ufdva2sjLyws/Xrhw\nIU8//TSGYUzpT8mTTxdttSESIw8//DD33nvvBZ//z3/+k5MnT6pJLXGjKSaRGElJSbngTz4cHh6m\nubkZt9ttclUiE9MIQkREItIIQkREIlJAiIhIRAoIERGJSAEhIiIRKSBERCSi/wfL1GUDjJyLIwAA\nAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116e52090>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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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QU1ODU6dOwcvLC9HR0VJv2mEYbySijmSxkNs78fLGjRv1f9+8eTOioqLcqojr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\nmYweHj9+HDk5OWhoaMDKlSul2RMn5XwFjpwF3xu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       "text": [
        "<matplotlib.figure.Figure at 0x116f0ccd0>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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 0x116cce750>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "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 0x116cceb50>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "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', 0.1, 0.1, value=1)\n",
      "    beta = Gamma('beta', 0.1, 0.1, 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": [
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 21
    },
    {
     "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"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 22
    },
    {
     "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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hXG26JNK4W9+lsb7Zs2frsb6SkhIGDx4M0CTWt2fPHt5//32WL19OcXEx2dnZ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\nREQuggM2EZGL4IBNROQiOGATEbmI/wJauppbQfWvlwAAAABJRU5ErkJggg==\n",
       "text": [
        "<matplotlib.figure.Figure at 0x116cdcb10>"
       ]
      },
      {
       "javascript": [
        "IPython.notebook.save_notebook()"
       ],
       "output_type": "display_data",
       "text": [
        ""
       ]
      }
     ],
     "prompt_number": 23
    },
    {
     "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": 24,
       "text": [
        "(0, 71)"
       ]
      },
      {
       "output_type": "display_data",
       "png": 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hi4882rFDh4cfjgQA7Nqlw9tvNyEri/f5SB3Y4iOPTp36/kvDPZGZSC0YfOTR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\n6dIYrFvXghtu4AS+UMauLtE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