Hypergeometric sampling of Tigers.

Tigers.ipynb

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  {
   "cells": [
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Hypergeometric sampling can be used to estimate population sizes. For example, to assess the population of tigers in a certain area, the following method could be used:\n",
      "Capture 20 tigers without replacement. Tag all of these tigers and return them to the wild. The next month capture 30 tigers without replacement. The number of tagged tigers in the second group (eg 7), together with the sample size (30) and the total tagged population (20) can be modelled together with the (unknown) population as a hypergeometric distribution, allowing the following formula to be used to estimate parameter likelihood."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "$$ L(x|\\theta) = \\frac{\\binom{D}{s}\\binom{M-D}{n-s}}{\\binom{M}{n}}$$\n",
      "\n",
      "$where$\n",
      "$D = $ the number of individuals in the subpopulation of interest,\n",
      "$M = $ the total population size,\n",
      "$n = $ the sample size, and\n",
      "$s = $ the number of individuals from the subpopulation of interest present in the sample."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "import pymc as pm\n",
      "import numpy as np\n",
      "np.random.seed(12345)\n",
      "import matplotlib.pyplot as plt\n",
      "import seaborn as sns\n",
      "from IPython.display import display, Math, Latex\n",
      "from IPython.core.pylabtools import figsize\n",
      "%matplotlib inline\n",
      "from scipy import stats\n",
      "from scipy.optimize import curve_fit"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 1
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Little is known about the population size, except that there must be between 43 (ie the number of tigers that have been captured), and some upper bound. A uniform prior is therefore used, with an upper bound of 300 set based on a rough guess of how many tigers there could possibly be out there."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "population = pm.Uniform(\"population\",43,300)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 24
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hypergeo = pm.Hypergeometric(\"hypergeo\",30,20,population,value=7,observed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 25
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model([population,hypergeo])"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 26
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "map_ = pm.MAP( model )\n",
      "map_.fit()\n",
      "mcmc = pm.MCMC(model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 27
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc.sample(100000,50000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            15%                  ] 15170 of 100000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      31%                  ] 31348 of 100000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------47%                  ] 47734 of 100000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------59%--                ] 59730 of 100000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------71%-------           ] 71588 of 100000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------82%-----------       ] 82979 of 100000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------94%---------------   ] 94128 of 100000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 100000 of 100000 complete in 3.8 sec"
       ]
      }
     ],
     "prompt_number": 28
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "from pymc.Matplot import plot as mcplot"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 29
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcplot(mcmc.trace(\"population\", 1), common_scale=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting population\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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JpI6mPQXF3PXqrFhXw7V25IY3kW0sV8t5MMS8PRGRxix2wVYIvTnROInk7i1m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\nAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10ea28810>"
       ]
      }
     ],
     "prompt_number": 30
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posterior_population = mcmc.trace(\"population\")[:]\n",
      "posterior_mean = np.mean(posterior_population)\n",
      "posterior_sd = np.std(posterior_population)\n",
      "posterior_mean,posterior_sd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 31,
       "text": [
        "(108.97833877723366, 38.190521118025721)"
       ]
      }
     ],
     "prompt_number": 31
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So there are probably somewhere between 37 and 109 tigers out there.\n",
      "\n",
      "If I was the one running this experiment, I would not be happy with the level of accuracy achieved so far. What would happen if we did the experiment again, using the population distribution from the last experiment as the prior? Let's say we marked the unmarked tigers from the second group, and released them to give a total of 20-7+30 = 43 marked tigers in the wild. If the next month 30 tigers are caught and 16 have tags, what does that do to the population estimate?"
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "#The population posterior from the last experiment looks lognormal.\n",
      "shape,loc,scale = stats.lognorm.fit(posterior_population)\n",
      "x= range(40,300)\n",
      "pdf = stats.lognorm.pdf(x, shape, loc=loc, scale=scale)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 32
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "plt.hist(posterior_population,bins=70,normed=True)\n",
      "plt.plot(x,pdf,color=\"red\")"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 33,
       "text": [
        "[<matplotlib.lines.Line2D at 0x10b94ce50>]"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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/y3UJQnRAAiFKmOpqsdbWUJosU16fqBarjeKbbsbU2EjSHxYaXY4QEUcCIUqY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\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10d331610>"
       ]
      }
     ],
     "prompt_number": 33
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pop2=pm.stochastic_from_data(\"pop2\",posterior_population)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 34
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "hypergeo2 = pm.Hypergeometric(\"hypergeo2\",30,43,pop2,value=16,observed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 35
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model([pop2,hypergeo2])\n",
      "map_ = pm.MAP( model )\n",
      "map_.fit()\n",
      "mcmc = pm.MCMC(model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 36
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc.sample(20000,10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [                  2%                  ] 432 of 20000 complete in 0.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-                 4%                  ] 898 of 20000 complete in 1.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--                6%                  ] 1386 of 20000 complete in 1.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---               9%                  ] 1898 of 20000 complete in 2.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----             12%                  ] 2418 of 20000 complete in 2.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----            14%                  ] 2945 of 20000 complete in 3.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------           16%                  ] 3310 of 20000 complete in 3.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          18%                  ] 3711 of 20000 complete in 4.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------          20%                  ] 4107 of 20000 complete in 4.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------         22%                  ] 4543 of 20000 complete in 5.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------        25%                  ] 5041 of 20000 complete in 5.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [----------       27%                  ] 5560 of 20000 complete in 6.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------      30%                  ] 6084 of 20000 complete in 6.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [------------     33%                  ] 6612 of 20000 complete in 7.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-------------    35%                  ] 7142 of 20000 complete in 7.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [--------------   38%                  ] 7674 of 20000 complete in 8.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------  41%                  ] 8206 of 20000 complete in 8.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [---------------- 43%                  ] 8732 of 20000 complete in 9.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------46%                  ] 9261 of 20000 complete in 9.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------48%                  ] 9786 of 20000 complete in 10.0 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------51%                  ] 10306 of 20000 complete in 10.5 sec"
       ]
      },
      {
       "output_type": "stream",
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        "\r",
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      {
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        "\r",
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      },
      {
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        "\r",
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      },
      {
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       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 20000 of 20000 complete in 20.1 sec"
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      }
     ],
     "prompt_number": 37
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcplot(mcmc.trace(\"pop2\", 1), common_scale=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting pop2\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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4XeWyLV+9nZmvuJpJpJl5n69n+l8Ws3J9dMvSxKK+3ktldS2X3TePe/+yOPIL\nXI5hf/G/rTw/52t+82SEBRhcBOnTHgu+4LZfTlZm2OeD2e3LUatv8DJvyXouuPfdqI8hItIRdMhA\nK1h3QODlJvDa0yqIavHSj75sHei09L/15a6KFctiz/475drKzl11zfKrtgckk9fW1bNpmzM1wzcb\nmte5ZTOGur676Zz789tfc/GMudTsDp1Q7gE2ba9uta31+VqfcPmaHSz9ZhsvRDk7fyw8GbB6kzOU\nHWo4NZC/tB6P87m65dEPgv4IqNjpbGsMSOPo9AzXzv6yNHvs4piBPyr+7/XlSe/hlOgpxyg+aj9x\nKy1ztJIh8Hobbmjy/SUb+OXxwxofv/juipD7RiuVS/8EunjGXC767v6MGNyj1XOX/HFu44SoAFt2\nNAVa5//hPX56zL5Bj5mMXOyFyzZxxIH9qa2r54nXltGra16z51u+j/5Hn9jSVtuCKYuxZzAaby9a\nx9uLokgQ9zYNHd7zwmfU7K6nf888Tps4JNhuTY9DHS6KsobS8lMb7pj+HMdwifuSHpRjFB+1n7iV\norsOwwccO0PM7QNOrkvERZUjxDORfsEHSmTCeaLDLDdF++t/VvDfVduabauuqeOpN5eHfE3g0GR1\nizsKQw2j1jU4PRaR6hhN/t37Xzh3Pb7x4RoWLtvM6x8GzG/laT2sGfyEoZ/aUhY8Xy2ZVq4va/V+\nBPLXyYOHel/PYkOQziBvi4oFrjjQtFPwnLD5X0S5jmgUPxD85fLfTCEi0tml5dDh0/+yIZ+77L55\nXHbfvLCvjzSEtNLFUF99QwO1dQ0Jndy05fUq6MUxwd5cuIZ7X2idG+S2WvUtohn/0kYt7fAlVG/c\nttOZWDMB7eY/wivvt55Gw0ProC/Ye+W6FG3U2Xj7058EfT9aiZgM3/zx7oB5u8L9kPnif1tbzQEG\nTvD92gerYimKiIiEkZKhw0R9ca9cX+Z6iCLay/7VDy6grGo3XQsTc2u61+ttNQt3y5678p272V1b\n32qILBla9oiE8m1p8/ZdV9q0DuDcgDUL6wICsHCJ7InsIWx5rGCznKdyFYBYNJY3QrED77aEMNOS\nuKz+y3P/x9shJmpds8n9uoYePO2uzTsrrdUXH7WfuJWSQGt2gvKebn/6k6Dbg96OHuV3f1mVM3zm\n5prxxGvLOHBoLwrzskLuE2wCz5aHvuL+9wESsqZgSzt3NR9u3VZew38+jX5yyQVLNzb+/eQbTcOP\ngTOhJ2qg7A+jAAAgAElEQVRC0LBH8bS+oBfnZ1FeFVveVbr12qz4NvQdkfc8/1lUifVuhBtGnR/w\nnrvx2KtfRrW/pIYChPio/cSttBw6jNcz//6q1baYf2W7fN2KdZGmCnB/Ka+tq+eFOV836z2K153P\nfdpq27Mt2ukf81Ym5FweT5i7DhNyBseSlVubPQ42fUY6d644a0E25ybvLFiQ1RDQss1aweXHLlH3\naazZVMGH/209G7+ISGfVIQOtYHZFkQAfyO112os3QjDX+rlQOTGvfbCaf3+8lpufWOjy7JGtK408\nxPpYDHNShRJyaDKKyCf83W2tA441m1oHpm7Ptrsu9PQDi5Zv5lcPvN+4XNOWHdUh943G2s1B3pMY\nI8N3Pg2yBJCXNp8ZP9iNKoErL4iIdDbtJtCqDXMhdKPZHWtRqKp2twj0K/O+4ey73gl6oSmr2s1j\nr7ZOQA71y790R9vfDZdIZVW7E9KjFS5wdX0cl4FLqPwkgKfeXE5Z1W7m+9Z+vPv5xNxRl5PV+p9f\nqNLGuki1W4maeiTYTRA5XdrN10ynonmg4qP2E7ci5mgZYw4F7rTWHmmMGQo8CTQAS4GLrbVeY8y5\nwHlAHXCbtfa1RBf02ocXMOOSCTG/PtyUEeG4vXtu7WanN2XFujJG7dOr2XOvf7C6VfJyOL27Jz8Z\nPpl+838f8/PvmOBPRhFpxTPs9+r7/6N3cY7r/cNN+bGzMbnfCUYSMS3EP97/JmjwH6rK0fzQ+DDI\nQtptJeh7lm4JcAIoxyheaj9xK+xPTWPMtcBjgP+KNR2YZq2diPP1eYoxpi9wKTAOOA64wxgT9a16\nkdZTi3tyyTb6ss/wteiXq7bxxGtfUl1Tx/Yop3HIauc9ADW19SEjhmhip7CfiQhR2CMvf8HvnlqU\nkBytaBZ6dhuYv/L+N0GHK/3Dk4mSDilqibo5QkSkPYp0RV8BnEbTNWa0tXau7+83gCnAwcB8a22t\ntbbc95qR0RbkyzCTOAYT9TxNAbvv3b84utdGwT8E84cXFjP/i43OEjouyvq7pz5u/Lsj3B6/IsQ6\ngtHULRHN0HIesGitDLj7b7Fvwexw3vssSK5UFPxL6wSq2V3PrCBzXyXSp1+VRt7JhWCtvTqK6SFE\nRDqasEOH1trZxphBAZsCf5pWAF2BYqAsyHbX6hsa+DiKoTWAB2d/EdX+gSJd7N0saBzKhi1VzS7O\nX/xvK31cDAV+s6FjXYyCJmdHKdz7dP0j4RdC9nMTHIUTuB7i2s2VET87y9fsiOt8wcyJYRoOv6/X\nJb480jFoHqj4qP3ErWjn0Qoc6ygGdgDlQFHA9iIg8iQ/AZauLmPeksjLghQU5Tb+/dnX0V1As3Oa\nqpqZGb4jb3aQmcjdeuE/recIa7n4cSQFBe5yi/JysygpaWr6VRvKufQP4RfATqWK3Q1RvW9rNlfy\n26cWJbFEke1qkYReWhl6+aeSkqJmn7O2snZb8M/X5h3VbE7QHZKBCgtzm33uAmUGmWJD0pMChPio\n/cStaK8KnxljJllr3wOmAnOAhcDtxpgcIBcYhpMo79rnX7nrzVq+MvbeiZqAXqrdEe7g+trFZJDJ\nVOkyp6u6upZH/vY5WV0yOGncIF58K/TSRengnmc+jrxTC6s2RF4uKZla5old/+D7IfctLa1o9jlr\nK7c8+kGbnq+iYhelpRVB5wELNjGviEhn5jbQ8l9trgIe8yW7fwm85Lvr8H5gHk7O1zRrbVSZ64ma\nLNGtSLk/qc6Q2h3kAhbKqwtWAXDSuEFtsnZiPNzM5ZVuNmxNbHJ6R7J6Y5AJdVP9j0dEJM1EDLSs\ntatw7ijEWvs1MDnIPo8Dj8daiAyXdyXFkyQe+Fr/VAzp6tUFsc35lRVhSFSSa/XGiqim8Wiv/D+M\nggX2yRiqlORQjlF81H7iVkrWOmypLXq0Ig0XtkfvfxE5r03azm+ejH5otL2qratnZgJXEpC2pwAh\nPmo/cSstukDiucvPrf+ucp93Fe+UAKmwZOUWPknQLfoikVzxQOhcNRERaZIWgVZVjLO2J8v6Le0v\nl+iPLy5JdRGkk/B6obqm4/UQi4gkQ1oEWhU745z1XUREoqK1+uKj9hO30iJHa+V6d7fwVwRZsFlE\nRKKnHKP4qP3ErbTo0XLrYSXfiqRcW0/HIiLSnrWrQCvdcrlEOqMOsBSniEibaVeBloiIJIZyjOKj\n9hO30iJHS0RE2pZyjOKj9hO31KMlIiIikiQKtEQkKiu+LUt1EURE2g0FWiISlY++3JTqIkgCKMco\nPmo/cUs5WiIinZByjOKj9hO3og60jDEZwOPAvkADcC5QDzzpe7wUuNhaq5vARUREpFOLZejwWKDA\nWjsB+C3we+BeYJq1diLgAU5JXBFFRERE2qdYAq1qoKsxxgN0BXYDY6y1c33PvwFMSVD5REQkCZRj\nFB+1n7gVS47WfCAXWA70BE4CJgY8X4kTgImIJJ0xJguYBQwEcoDbgGUESWcwxpwLnAfUAbdZa18z\nxuQBzwIlQAVwprV2S5tXpI0pxyg+aj9xK5YerWuB+dZaA4wCngayAp4vAnYkoGwiIm78FCj1pS58\nB3iQIOkMxpi+wKXAOOA44A5jTDZwIfC5b9+ngV+noA4i0kHFEmgVAOW+v7fj9Ip9ZoyZ5Ns2FZgb\n7IXpItSiuBkZWi1XpB16EbjZ93cGUAuMDpLOcDDOj8Raa205sAIYCYwH3vTt+yZKfRCRBIol0LoH\nOMwYMw+YA9wAXAL8xhizACfweinSQQ4c0jOGUyfGw1dNCrr9+5OGtHFJRCRe1toqa22lMaYIJ+j6\nNc2/2ypw0hmKgbIQ28tbbOvwlGMUH7WfuBV1jpa1dgdwapCnJkdznB7FudGeOmGyumQG3d6nR14b\nl0QiKczLorK6NuTze/UpZM2myjYskaQjY8wAYDbwoLX2eWPM3QFPF+OkM5TjpDb4FQXZ3mlSH5Rj\nFB+1n7iVsglLQw3fpdKoob1SXQQAThw3kFcXrE51MdJCpM+JBw89inMozs9m1caKtilUgnUtyKas\naneqi9FuGWP6AP8GLrLWvuPb/JkxZpK19j2cdIY5wELgdmNMDs4NPcNwEuXnA8cDHxNF6kNJSVHk\nndpQssuTlVVPRht+cffoXpDQOqXb+wXpVyaVJzlSFmilKh+qMC8r5HMej4fMDA/1Damda/W0iUOo\nq/Py5sI1KS1HJB4g2S118vjBPPfWV6HL4IF7LhxHg9fLuXe/m+TStL3igmy6FWSzZnPzXruJB/Zj\n7ucbUlSq6P3652OTefhpOMN9Nxtj/LlalwP3+5LdvwRe8t11eD8wD2docZq1tsYY8xDwlC8dogb4\niZuTlpamT2BfUlKU9PKUlVXQ4G2778Zt26sSVqe2aJ9opVuZVJ7w4gn6UhZomQHdeXvRujY9Z7+e\n+Vz/09Fh99lnz64sX5O6kYOLT93f+SMJceioob1YvCJxd63H+pXbtTCbssrIPTh3X3A4vbrlMeGA\nflw4/b2g+2RkePB4PB120c6nbjmO2574sFWglWpD+hezcn15q+0H7dOLz75u/Rnbu39x0spirb0c\nJ7BqaXKQfR/HWdkicFs18MOkFC6N+fOLNAQWG7WfuJWy61Nmpofhg7q73r9fz/y4z1mQm0VRfnbY\nfTIDetqOPGgPjhy9R0znKszL4ryThkf9ujGmNxA+zsrOiu1t69U1dXlxgbIyI5d/YJ8ienVzcuZy\nspvn1N1x/mGNf/tHMjwRhjRuPevgiOfs4qJcba1LZgY/mBzsJo3k9ghf+cMDwz7ftTAn6PbTdENJ\nu3HRRVcqSIiD2k/cSumV5bLvjXS1X6+uuVz2vZEcvF/vuM7nZrRyyB7ODUf7792Dnx6zb8yXs/sv\nP4Jhg3rE+GrCXkdv/FnwYZjDhvcJe8jhg+MoDyQsPyM/J3JH6lFjQge4fbo3Bd09g9xU0b2odRCQ\nnxv8nOMP6Nv498ghPSnObz60PGXMnhHLmkiZQT6kJd0Sd5NGIvIQv3vEYBpCDK93Kwz/Q0ZEpLNJ\nWaDlAbKzMnn82iMZ1Df82OfdF46jT498Lvzu/o3bBvQujP6cLgKFqYcO5OfHGS48ZX8yMjxx5SC5\n6bkJxRMQaR09uuli369nftC6n3fScLqF6GXwGzW0F8cePKDx8c+PM632KczL4oJTRgR9/eEjmgK5\nzAwPEw/sH/Z88ZhwQD9X+33n0L1abfvBka17VTwhItefHrNv499Hj96D3559aLPn9987vuA0mFOP\nGNzsceBnbMrY1oFdsM9trDHvZd9v/eNmrCnhkGG9efSayY3b+vcqaLbPyeMHNf69/+CeeH25Onv0\nKuCuCw5vfK4gN3QOpIhIZ5S6QMt3ocjI8ETMmwomWE9GJG4S8HOyM5l80B7k+XpdAnM/wyXSBxPY\ni3LA3tHNGxZ4Ie0bMGx6zekHAc6w5uEjmnpjDhvRlz1Kml8cgwkcPpx8UOteo/sum8Ahw/o0niew\nB2TIns2nFwoW5IQzbKAzVHx0hF6iey8e7yoohuBTdfQoim2ItGe3PPJyMpsNISYj9/ek8YNDPhfq\nfBcF/MhItJMnDOaCU/anS2YGj193JPdffkSzoL13tzwODegtbfB6G4PDrC4Z5LYY2s3JCj59iqQX\nzQMVH7WfuJXCocOmC2l2wBfz0D27hg2i7rtsAndfcHhjILJnSSHTfjbG3Rlj6QUIuPJ5XVx1Jx+0\nBzMuGd9q+9A9o5sDMbCs/qGwLpkZjRfAnx1nmvXGABy+f18u/d4BYY/bsgaBE8cee+jAxgBnv726\ncfWPR3HOicManz90WB8mjWrqxerbI5/pAXX1B1LgXIADXfa9kVxz+kE8dOUkjojQE5aZGVt3jT93\nrSg/i64BQ1jfnzwk5Hvf7C31esnqktmsTsm6xyrU8Gm2yyAlsDp79Ym+dzfQniVNr8/weFr/oPBA\nv55NQbzX6228+8zjgaL8bE6fsg/TzhjTqnAH7dOrWU+ZpA/lGMVH7SdupbxHq6URg3pQECKfBpwv\n9V7d8hoDAi9ehu4RPog5aB+nVyZY7k4kgako4WZ96N0tj+9PHsKPjxoaMlE4Gv6L36ihvRg1tBcn\njx/ELS0Suru0CEgyPB4O2qckqvNc/oMDmXX9UTxy9WQu/eGoxu0ej4fhg3qQn5vVmIye1SWDqYcN\nJKtLBuf6Ev27FeZw2fdHctcFhze7YeG6nzT1Uv78OMMo33vQMrE9GDdhlj9ALArIqfr9uYdx6WkH\n0K9nQWMAdeRBe3D8YQObvTbUTQH+3jH/8OlPj9m3WaQ1fFB3bvlF5KT6QMeMHcCs649qtf2Wsw5m\nhP9mkIBo7zuHNPUSnjKhqeerKL9l8NPUSlf84MCggbnfSeMGRVXmlloOgTc0eBuL7P93eMzYAUF/\nTBTlZ6XlTQYiIm0lJdM7DB3QrdmvaIAxpoRPbCl9euRx1Jg9efKN5WGP0XhhidDl0KtrLr+Yuh+D\n+q1napChrpPHD6IgLytkon3zXqzQJxs2qHurC3okhwzrzcJlmxsfByZCH7xfb/JzuzB0j65kZHj4\n7hF7t3p9dlYmxx48oNXQzeB+xXyzofWt9+G07IEK9JuzDqamtoEumRn07pbHI1dPbvZ8ywTrwrws\nBvRu6gFxM2T7y+OHMev1ZSGf908b4O+puuCU/dlRVUNxwF2kPYpzG1ccaAoEWh/r7gvHMffz9dg1\nO8jNzuTWsw5m1caKZgHKIcOcobKqXU2z0p99wnC6FWZz8vhB/GP+qpBlzcnKpKa2HoDTp+zT7Dn/\n8G5JtzxKuufDqu3Nng8cbg5stn0HdOPnxxme/pdtdb5uhTn87DjD0286z004oB//XOCU74ofHMgB\ne/dofAxOHlikqVW8AZ/177W4k7DB2/TvItgNEhecPIL7XloS9vgiIp1FSn5qzrhiUqtf3Wccazjr\n+P04eL/ejDGRe2X8F8IjRjpJ0xefuj8jAu6qe/Sayfxkyj5c9r2RFOVnc9K4QUF/WWdmeDhm7ICQ\nieSBoVWDF27+xVhODNJD4CaXp6Rb856Us09oGpYbt3/fZonKHo+H/Qf3JDc7fCz846P3aRWEXfhd\nJ5m9a2F26x6kGMbCencPnoDfkv897dsj33WOFTiJ/BNGhk9+H+67g3O4b3gyJzuz2d2HLU325YHt\nt5ezf8vyTDywP+eeNByPx8NefYpCJvYHJnd3L8rB42ke9I7Zt4Rx+/dt9pojwtTl9KObAq+jx+xJ\nl8wMzpy6X/CdA8rs8Xia5dS1bN3AYDtw2pSRQ3q2qvtPpuwbNOk+FH9v5A8mD6FbYTYD+xSGDWQP\nHNqLQ4Y5P1x6h3mPJLWUYxQftZ+4lbIJS1vqWpDNESOdi11etoec7ExqdtcHvUsKnB4fc9mExh6N\nMaY3Y0xvfnnnfwAnn2nK2AFBXxuVgMBkcN8iBvUtZlDfYsoqa5i3ZAPdi3LYXlHTemgniIu+ewDv\nf7GBOZ84vQmBQ5HnnBj9nFuh9Oqax7SfjaFncS7//WYbs15f1jhtQb9ezoXPDOiWsPP5+e9oHH9A\nv6iGiw4b0TfiPpMP6k/P4txmeWDhnH3y/hxqShIy/1o4F37XuTt1wdKNAJxw+ECmHroXb38SeTLe\nPXoVxJ6/1CLA2XdP5/08ZuwAV0F/pKk6gh1j6mED+c6he+HxeDB7dWPZ6u0h348fH70Pe/QqaHbH\nrKQX5RfFR+0nbqVNoBUoI8PDQ1dOirhfcZDJR/0BmmsRLjjj9u/L+19sYEj/Yi46tSnR/BdT9+PH\nR+9DfmEuL75lQw4bjt2vN4uWb2ZQ3yIG9i1ij5IC5nyyzrnQJXE1C3/e2mEj+rB5RzXjfb0uIwb1\n4Jofj2JQv8TP1J3VJZMTDh/U+HjE4B7895ttrYaJIwnWG5aZkdHYs+JGZoan1RQFSdGiqFPG7El+\nbhanTBjcakg3yO6NbjpzbKvgNJpbAnoU5/LoNZPpkpnB8tXbWz1/2Ig+DOrTNI1K3x5OABqqpzLU\nPwv/e3PC4QMxA7qFvMmjW2FO2LsrRUQ6i7QMtOLxwOVHJPSW/P0Gdm+8gAXyeDzk5XShly8JPpRz\nTxzO8YftxUDfRa5LZga3n3soRfnOsN53jxgccR6xeHTJzOC0iU1DXR6PJ76JVKNw2fcOYOO26qjn\nPHNzd2e03PQ4xuPEcQP5ctX2xpUHAhPZ3RgcEPj6c7yyw+TNDehdSL+e+Uwe1TSc6P+MBmu9805q\nPjfaEQf2Iyc7k5FDgk87kpmRwelH7xMyWM3MyMDs5X5lBxGRziqmQMsYcwNwEpAF/AmYDzwJNABL\ngYuttSlZmdntkNXpR+/D83O+Zsy+kfPB4rlrKqtLBoP6Nu89CrxV/uQO/Ks/q0tmTBPLJoM/wI1l\nEtkZl4xnZ01d2H1OmziE0ybGWrrmbjhjNP9auJZJo1rPc5bVJYPaugaK87O5/dzDgry6ab63cHfj\nZmZkNJuHLZhjDk7A0LukLa3VFx+1n7gVdaBljJkMHG6tHWeMKQCuBU4Dpllr5xpjHgJOAV5JaEkT\n7JiDB3D0mD1d3REnyRNsuodoEumjERjgRqNrYU7IKTuiLWmBi0lv9+pT1Dh9Rku3nnUwHy/bHHYY\ndUDvQq760ShXE9hK56UAIT5qP3Erlq6aY4EvjDGvAP8E/gGMsdbO9T3/BjAlQeVLKgVZqRc45caQ\n/k7PX7DcpvbujvMO4xdT92OvPvENE/frWcDJEwZHTGYfMbhHxCWZREQk+WIZOiwBBgAnAnvjBFuB\n3/qVQHTToIsAN/xsDLW++braCy/uerX69MinTw9NdSAi0tnEEmhtAZZZa+uAr4wxu4DAZJIiYEek\ng5SUJC8BvK2pLtFrzDUqyk3aOZNZl2vPGMs3G8ro0zvxd2+21JE+X5I+lGMUH7WfuBVLoPU+cDkw\n3RjTH8gH5hhjJllr3wOmAnMiHaS0tCKGU6efkpIi1SUG1/90NK8uWMWhpiQp50x2Xfbbs5j99ixO\nent1tM+XpA8FCPFR+4lbUQda1trXjDETjTELcXK8LgJWAY8ZY7KBL4GXElpK6XAG9yvm0u8Fn4xW\nRESko4hpegdr7XVBNk+OrygiIiIiHUv7yToWEZGE0Vp98VH7iVsdbmZ4ERGJTDlG8VH7iVvq0RIR\nERFJEgVaIiIiIkmiQEtEpBNSjlF81H7ilnK0REQ6IeUYxUftJ26pR0tEREQkSRRoiYiIiCSJAi0R\nkU5IOUbxUfuJW8rREhHphJRjFB+1n7ilHi0RERGRJFGgJSIiIpIkCrRERDoh5RjFR+0nbilHS0Sk\nE1KOUXzUfuJWzIGWMaY38AlwNNAAPOn7/1LgYmutNxEFFBEREWmvYho6NMZkAY8AVYAHmA5Ms9ZO\n9D0+JWElFBEREWmnYs3Rugd4CNjgezzaWjvX9/cbwJR4CyYiIsmjHKP4qP3EraiHDo0xvwBKrbX/\nNsbcgNOD5QnYpRLompjiiYhIMijHKD5qP3ErlhytswCvMWYKMAp4CigJeL4I2BHhGJ6SkqIYTp2e\nVJf01FHq0lHqEQ1jTL61dmeqyyEiEq+oAy1r7ST/38aYd4ALgHuMMZOste8BU4E5iSuiiHRCtxtj\nAF601i5IdWFERGKViOkdvMBVwGPGmGzgS+ClBBxXRDopa+2vjDFDgSeNMWXAn621z6W6XB2JP78o\nHYfAsnIL+dNzb5GdPTfyzgEG9Mzmqot/maRSNZfO7SfpJa5Ay1p7ZMDDyfEVRUTEYYx5CtgInGut\nXWaM+QOgQCuB0jlAyM4tZBcHsCvK1+2sXZOU8gSTzu0n6UUTlopIOnoWWA0MMMb0sNZeneoCiYjE\nQkvwiEg6OhP4H/AOcF6KyyIiEjP1aIlIOqoBDvL9rVUmkkA5RvFR+4lbbRpoGWMygJnASJwv0nOs\ntSvbsgxu+Ga+nwUMBHKA24BlBFlmyBhzLs4v7jrgNmvta8aYPJyhjxKgAjjTWrulzSsSwM2SSe2h\nLr65204CsoA/AfNpZ3Xx/Tt4HNjXV+5zgfp2WI9DgTuttUf6E9fjKb8x5jDgj7595wFjcL6jrm3j\nqnUKChDio/YTt9p66PC7QLa1dhxwPXBvG5/frZ/iTMo6EfgO8CBOWZstM2SM6QtcCowDjgPu8N15\neSHwuW/fp4Ffp6AOjdwsmdQe6mKMmQwc7vv8TAb2pn2+L8cCBdbaCcBvgd/TzuphjLkWeAznhwgk\n5jP1MHC6r11OAk7ACbbuaptaiYgkXlsHWuOBNwGstR8BY9v4/G69CNzs+zsDqCX4MkMHA/OttbXW\n2nJgBU5vXWM9ff9P9ZJEbpZMag91ORb4whjzCvBP4B/AmHZYl2qgqzHGg7OKwm7aXz1WAKfRtCpE\nXJ8pY0wRzo+wb3zbvwXes9aeZa09K/nVERFJjrYOtIqB8oDH9b5hlLRira2y1lb6vvxfxPnFHVjO\nCpwLZDFQFmJ7eYttKRG4ZJJvU8slk9pNXXCGmsYA38eZKPfPtM+6zAdygeU4PY33087qYa2djTPE\n5xdv+Vt+N/QAjjbGnG2MaZuJkToZrdUXH7WfuNXWyfDlOEv0+GVYaxvauAyuGGMGALOBB621zxtj\n7g54uhhnmaGW9SkKst3NkkTJFGnJpPZUly3AMmttHfCVMWYXsEfA8+2lLtfi9PTcaIzZE+fOuqyA\n59tLPQIF/juOpfwt9/0AyMTpBXOlRc7YQTi9nl/7np5prX0xnXPe2ppyjOKj9hO32ro3aT5wPIAv\n8XVJG5/fFWNMH+DfwLXW2id9mz8zxviXH5oKzAUWAkcYY3KMMV2BYTiJwI31DNg3Jay1k6y1k32T\nyy4Gfg682R7rAryPkzOHMaY/kA/MaYd1KaCp92Y7zg+edvn5ChBX+a21FcBuY8zeviHVKTg3C/TD\n6cUMK0jO2BhgurX2SN9/L6ZzzpuIdFxt3aP1MnCMMWa+73G65l5MwxnOuNkY48/Vuhy4P3CZId9d\nVffj3CGVgZMMXGOMeQh4yhgzD+fuyp+0fRVCCrpkUnuoi6/3YaIxZqGvjBcBq2h/dbkH+D9fObKA\nG3DuCG1v9YCmqRcS8Zm6AGf290ygEvjYWvuCMeZPLsrhzxl7xvd4DLCvMeYUnF6tK4BD8OWMAbXG\nmMCcMX/C/ZvATbE0hIhIMB6vV1PUiEh6McbchzMs/DYw0VobMZg0xgwCnrfWHu7LTfzcWvuZMWYa\n0B2nR/cAa+31vv2fwunBuh641Fq73JczutpaOyDC6bylpRUx1i7xSkqKiLY80c4DVVa2gwt+9zx5\nvUzU5fN7dfp3ATjxyldiPkY4g3PXcNMVv2i1PZb2iSTeebSSUaZ4qDzhlZQUeSLvFZwmLBWRdHQ1\ncAxO79YvYnj9y9ZafyL+y8ADOMOZCct5KykpirxTG4q2PLfccktU+2dl1ZPhifla0yZyc7uEbIdE\nv1/Rtl8w7f0zlGzpVp5YKdASkXT0qO//3YDzgROjfP2bxpjLrLUf4+R7LcLJGbvdGJODc9dny5yx\nj4ki5y3Nfm0nvTxlZRU0pPkIyK5ddUHbId16RyD9yqTyhBdP0KdAS0TSTuDcWcaYP0bxUn8kcAHw\noDGmFmf+uPN8U7ake86biHQwCrREJO0YY37n+7MLsJeb11hrV+HcUYi19nNgQpB9HsdZ/ihwWzXw\nwziK2y5prb74qP3ELQVaIpKO/MFQHbA+lQXpqBQgxEftJ24p0BKRdPQnYC1OoLW/MWaxtVZXNhFp\ndxRoiUg6+tJaex2AMeYP1tqrU10gEZFYKNASkXSUbYy5Bmd6B31PJYFyjOKj9hO39AUmIunoGmAf\noLu1dkGqC9MRKUCIj9pP3GrrtQ5FRNy4H2dpogJjzCOpLoyISKwUaIlIOqoD1llr3wJqU10YEZFY\nKdASkXS0CjjKGPM8LpfEkejMnDm9Mc9Ioqf2E7eUoyUi6agcZ+mcDGtteaoL0xEpxyg+aj9xS4GW\niNQ1QQIAABsQSURBVKSjHwH5QJUxxmutnZXqAomIxEKBloikFWPME8BtwGDgmxQXR0QkLsrREpF0\nk22tfQ+YZK19z/e3JJhyjOKj9hO3UtKjVVdX792+fWcqTp1w3bvno7qkn45Sl45SD4CSkiKPy137\nGmOOBvoZY44CPNbaOUksWqekHKP4qP3ErZQEWl26ZKbitEmhuqSnjlKXjlKPKD0H7Ak8DwxIcVlE\nROKiHC0RSSvW2idTXQYRkURRjpaISCekHKP4qP3ELfVoiYh0Qsoxio/aT9xSj5aIiIhIkijQEhER\nEUkSBVoiIp2Qcozio/YTt6LK0TLGHArcaa09ssX2k4CbgDpglrX28cQVUUREEk05RvFR+4lbrgMt\nY8y1wBlAZYvtWcB0YCywE5hvjPmHtXZzIgsayZo1q5k161F69uzFjh3buO66m8jOzm7LIoiIiIg0\nE02P1grgNOCZFtuHASustWUAxpj3gYnAS7EU6PXX/8mHHy5g+PARbNiwnssuu4p33/0PH3zwPllZ\n2QwZMoQJEyZx003Xc9RRx7B69Tecc86F7NixnQsuuIS+ffsxY8bdrFmzmqFD9wFg6dIlvPrq38nN\nzaOqqpIbb7yVOXP+zWeffUp5eRlTp55Abm4ef//7bIqKiikqKuK88y7iBz84mdGjxzJs2HBef/1V\n9t3XcMUV19Cli27WFBERkchcRwzW2tnGmEFBnioGygIeVwBdYy2Qx+PhqKOmMHny0fzlL8/x6aeL\nePnlF/nTnx4F4KqrLmP06IMZNmw4p59+Bl99tZzZs//KeeddBMB7770D0BhkAXTv3oOpU09iy5ZS\nHn74AQBeffXvzJjxILW1taxevYqZM+/jrrtmkJWVxV133c6qVd9QUFDIDTfczGeffcKIEQdw+eVX\nxVotEZG04s8v0hBYbNR+4lYiumbKgKKAx0XA9nAvGDRoEKtWrQr6XFFRLjk52ZSUFJGZ6aVnzyK6\ndMmgpMQ5RXZ2Jt265ZGdnUlJSRGrV3vo2rWAHj3yuffee9lrr734/e9/1+yYjzzyN/bee2/Gjh1L\n9+7dKCkpwuPxUlJSRF1dHUuXbiErK5NevQrJzs4mLy+L7t3z6dHD2bdr1zz69u3VWIaWQm1vj1SX\n9NNR6iHpRQFCfNR+4lYiAq3lwD7GmO5AFc6w4T2RXlRaWhF0e3l5NW+//Xc+/PBj6uvrOe20/Tjx\nxFO58spryM8v4JBDxrN7t4eFCz/m5pt/y9atW7j88qu4554ZzJ07l6FDh7JgwYecccZZDB68NwBd\nu/bko48WsXLlarxeWLFiLVOmTOXqq69n165qpk49kR/96GdcffV1dO/eg6Ki7nTt2ofa2npKSyso\nK6tm587dQctcUlIUsi7tjeqSfjpKPUABo4h0TrEEWl4AY8zpQKG19jFjzJXAv3Cmi3jCWrsh1gJ5\nPB5OOeVUJk06qnHblCnHMWXKcY2PN27cwOjRY7n00l81bjv77PM5++zzgx7zxz8+o9W2448/ieOP\nP6nZttGjxzZ7/MADjwBw0EFjOOigMdFXRkQkDW3cuJEtW7dE9ZqKigq83iQVSKQDiyrQstauAsb5\n/n4+YPurwKuJKNDUqSdG3Kdv335cccU1iTidiEin8/SLr1OYuQOAuWv7uX5dTvfBySpSu6McLXFL\nt8+JiHQyWdk5LNo+CoD8mG9d6twUYIlbmhleREREJEkUaImIiIgkiQItEZFOaGzxYsYWL051Mdot\nrXUobilHS0SkE1pUPirVRWjXlKMlbqlHS0RERCRJFGiJiIiIJIkCLRGRTkg5WvFRjpa4pRwtEZFO\nSDla8VGOlrilHi0RERGRJFGgJSIiIpIkCrRERDoh5WjFRzla4pZytEREOiHlaMVHOVrilnq0RERE\nRJJEgZaIiIhIkijQEhHphJSjFR/laIlbytESEemElKMVH+VoiVuuAi1jTAYwExgJ1ADnWGtXBjx/\nKjAN8AKzrLUPJ6GsIiIiIu2K26HD7wLZ1tpxwPXAvS2enw4cA4wHrjLGdE1cEUVERETaJ7eB1njg\nTQBr7UfA2BbP1wLdgDzAg9OzJSIiaUo5WvFRjpa45TZHqxgoD3hcb4zJsNY2+B7fC3wCVAF/s9aW\ntzyAiEgyGWMOBe601h5pjBkKPAk0AEuBi621XmPMucB5QB1wm7X2NWNMHvAsUAJUAGdaa7ekpBJt\nSDla8VGOlrjltkerHCgKfJ0/yDLG7AVcAgwEBgF9jDHfT2QhRUTCMcZcCzwG5Pg2TQemWWsn4vSy\nn2KM6QtcCowDjgPuMMZkAxcCn/v2fRr4dVuXX0Q6Lrc9WvOBk4AXjTGHAUsCnssF6oEaa22DMWYz\nzjBiWCUlRZF2aTdUl/TUUerSUeqRZCuA04BnfI9HW2vn+v5+AzgW53tqvrW2Fqg1xqzAucFnPHCX\nb983gZvarNQi0uG5DbReBo4xxsz3PT7LGHM6UGitfcwY8xSwwBizC+cL78lIBywtrYilvGmnpKRI\ndUlDHaUuHaUekNyA0Vo72xgzKGCTJ+DvCqArTgpEWYjt5S22dXj+/CwNIcbGn5+lIUSJxFWgZa31\n4nSvB/oq4PkZwIwElktEJB4NAX8XAztonQJRFGS7f1tE6dbTGE158vKyWbi+4wVYubldQrZDot+v\nW265Je5jtOfPUFtIt/LEShOWikhH9JkxZpK19j1gKjAHWAjcbozJwUl5GIaTKD8fOB742Lfv3OCH\nbC6dehqj7fmsrt6dxNKkzq5ddUHbIR17htOtTCpPePEEfVqCR0Q6Ev/UMlcBvzHGLMD5QfmStXYT\ncD8wDyfwmmatrQEeAkYYY+YB5wC/aftii0hHldIerTFj9gfgk0+WprIYItIBWGtX4dxRiLX2a2By\nkH0eBx5vsa0a+GHyS5helKMVH+VoiVsaOhQR6YQUYMVHAZa4paFDERERkSRRoCUiIiKSJBo6FBHp\nhDpijtaGDRt5+oXZrbYXFuZQWVkT9DUNDXX86NSTyMvLi+pcytEStxRoiYh0Qh0pwPLb1f0Q3l0V\n6tnggVT11pVMPbo86kBLAZa4paFDERERkSRRoCUiIiKSJAq0REQ6obHFixvztCR6M2dOb8zTEglH\nOVoiIp1QR8zRakvK0RK31KMlIiIikiQKtERERESSRIGWiEgnpByt+ChHS9xSjpaISCekHK34KEdL\n3FKPloiIiEiSKNASERERSRJXQ4fGmAxgJjASqAHOsdauDHj+YOBe+P/27j5Krro84Ph3l2w2JNkk\nKosWoSqgD9gc3zZFDEXgKFq1OVK1p2KtbRSsgB417fGF+tJarK0cbYWqRVARW+05UPGoVMQqCNlz\nBKQvwEGfCBYpvtQlQhIQAslu/7gzZLLZ7N7Z2Zm5M/v9/JO59869+/zu/c3uk9995v4YAH4CvC4z\nH174cCVJC6Ef5zrsJOc6VFlla7ROAZZm5vqIeC5FUnUKQEQMAJ8CXpmZP4qI04GnANmOgCVJrTPB\nao0Jlsoqe+vwOOBKgMy8HljXsO1pwFZgU0RcA6zJTJMsSZK06JVNtFYB2xuWd9duJwIcBKwHzgde\nCLwgIk5auBAlSZJ6U9lbh9uBkYblwcycrL3eCtxeH8WKiCspRryunu2Ao6MjDA4OPPq6l/V6/I1s\nS/X0SztULdZotcYaLZVVNtEaBzYAl0bEscDNDdt+BKyMiCNqBfLHAxfNdcCJiR1MTk49+rpXjY6O\n9HT8jWxL9fRLO8CEsWpMsFpjgqWyyiZalwMnR8R4bXljRJwKrMzMCyPiDcAXaoXx45n59XYEK0mS\n1EtKJVqZOQWcMW31lobtVwPPXcC4JEmSep4PLJWkRci5DlvjXIcqqxJzHY6NrQXgpptu7XIkkrQ4\nWKPVGmu0VJYjWpIkSW1ioiVJktQmJlqStAhZo9Uaa7RUViVqtCRJnWWNVmus0VJZjmhJkiS1iYmW\nJElSm5hoSdIiZI1Wa6zRUlnWaEnSImSNVmus0VJZjmhJkiS1iYmWJElSm5hoSdIiZI1Wa6zRUlnW\naEnSImSNVmus0VJZjmhJkiS1iYmWJElSm5hoSdIiZI1Wa6zRUlmlarQiYhD4BPAMYCdwWmbeMcP7\nPgVszcx3L2iUkqQFZY1Wa6zRUlllR7ROAZZm5nrgXcBHpr8hIv4EWAtMLVx4kiRJvatsonUccCVA\nZl4PrGvcGBHrgWOAC4CBVgIaG1vL2NjaVg4hSZJUCWUTrVXA9obl3bXbiUTErwHvA95Mi0mWJKkz\nrNFqjTVaKqvsc7S2AyMNy4OZOVl7/SrgIODfgCcAyyPi+5l5yWwHHB0dYXBwYL/rRkdHZtqtknop\n1rnYlurpl3aoWqzRao01WiqrbKI1DmwALo2IY4Gb6xsy83zgfICI+CPgqLmSLICJiR1MTk7td93E\nxI6SoXXX6OhIz8Q6F9tSPf3SDjBhlLQ4lU20LgdOjojx2vLGiDgVWJmZF057r8XwkiRJlEy0MnMK\nOGPa6i0zvO9zCxGUJKm96vVZ3kKcn3p9lrcQNRfnOpTUtyLiP4BttcUfAR8CLgYmgVuBszJzKiJO\nB94I7ALOycwruhBuR5lgtcYES2WZaEnqSxGxDCAzT2pY9xXg7My8NiI+Cbw8Ir4LvAUYAw4ENkfE\nNzPz4W7ELam/mGhJ6lfPpPgW9Dcoftf9OfCczLy2tv3rwIuA3cB4Zj4CPBIRt1PMgvG9LsQsqc84\n16GkfvUAcG5mvhh4E/DP07bvAFZTPCdw2wzr+5rP0WqNz9FSWY5oSepXW4DbATLzhxGxFXh2w/ZV\nwH3s+5zAEeDeuQ5etcdVNBPPgQcu5YafWqMFMDAwwEEHrWz6er7//e9v+Wf3ch/qhKrFM18mWpL6\n1UaKW4BnRcQhFAnUVRFxQmZ+B3gJ8C3gBuCDETEMLAOOpiiUn1WVnm/W7PPWHnzQ8rO6qakp7rnn\nfg44oLPXs2rPyDOe2bWS9JloSepXnwY+GxH1mqyNwFbgwohYCtwGXFb71uF5wHUU5RRnWwi/eEwC\n11y3mTVrHtPUfk867DCOiqe2Jyj1lUonWvXJpW+6ac7/XErSXjJzF/CHM2w6cYb3XgRc1O6YqsTn\naBWWP+bJXHHbw8CDTe137EFf5dvf8jEPmlulEy1JUnss9gSrbmDwAJYsPbDp/X41cDB/dsZr2xCR\n+o3fOpQkSWoTEy1JkqQ2MdGSpEXI52i1ZvnUL3yOlkqxRkuSFiFrtFpjjZbKckRLkiSpTUy0JEmS\n2sRES5IWIWu0WmONlsqyRkuSFiFrtFpjjZbKKpVoRcQg8AmKecN2Aqdl5h0N208F3grsAm4BzszM\nqYUK0ifES5KkXlT21uEpwNLMXA+8C/hIfUNEHAj8FXBiZv4WsBr4nYUOVJIkqdeUTbSOA64EyMzr\ngXUN2x4CnpeZD9WWl9DspFGSpI6yRqs11miprLI1WquA7Q3LuyNiMDMna7cIJwAi4i3Aisz89wWO\nU5K0gKzRao01WiqrbKK1HRhpWB7MzMn6Qq2G68PAkcArFy48SZKk3lU20RoHNgCXRsSxwM3Ttl9A\ncQvxd8sWwY+OjjA4OLDfdfvbXkVVjWs+bEv19Es7JGkxKptoXQ6cHBHjteWNtW8argS+B7weuBb4\ndkQAfCwzvzzbAScmdjA5ObXfdfvbXrVvII6OjjAxsaPbYSwI21I9/dIOMGGsmnp9lrcQ56deo3Xm\nmZu6HYoqrlSiVRulOmPa6i0Nrw9YsIgkSW1ngtUaa7RUlk+GlyRJahMTLUmSpDYx0ZKkRcjnaLXG\n52ipLOc6lKRFyBqt1lijpbJ6dkRrbGzto99AlCRJqqKeTbQkSZKqzkRLkhYha7RaY42WyrJGS5IW\nIWu0WmONlsrqi0Srak+LlyT1t+//+D7e/oF/bGqfB+77GR//2/cwNDTUpqhURX2RaEmS1ElTa57O\ntib32TnwcFtiUbX1VY2W30SUpHKs0WqN509lOaIlSYuQNVqt8fyprL4a0Wrk6JYkSeq2vk20JEmS\nuq3vEy1HtiRpX9YYtcbzp7Ks0ZKkRcgao9Z4/lRW349oNXJ0S5IkddKiSrTqTLgkSVInlLp1GBGD\nwCeAZwA7gdMy846G7RuA9wK7gM9k5kVtiLUtpidcPl1e0mJQry/yFtj8eP5UVtkarVOApZm5PiKe\nC3ykto6IGAI+CqwDfgWMR8RXMvMX7Qi4E5zSR1K/M0FojedPZZVNtI4DrgTIzOsjYl3DtqOB2zNz\nG0BEbAaeD1y2kIF2Q2PCZfKlmeyvj8w2Utqr/crRX0lqXtlEaxWwvWF5d0QMZuZkbVvjlE87gNWz\nHezuuzczNraCn/50817rG9fNtb1b64rXPwHgkEOeyOAgTE6umK25PcO2zK7xutdfw779df99aPZ9\nZtKta7In1kLR5v236ZBDnjjnMe+6a+Hik6ReUTbR2g6MNCzXkywokqzGbSPAvbMd7NBDD639e9gM\n2w6b8XWV1k3fPjg4yN133z3t/Ye2bV07j93rcc13nzKa6Zut9LVunZvG87AQ8Zc9r+oOa4xa4/lT\nWWUTrXFgA3BpRBwL3Nyw7QfAUyPiMcADFLcNz53tYHfeCRMTO5qPtoJGR0dqbZk+iLeDsbHj9lpz\n4423Nr1uz+2ZPcebz3HKrBscHGBycmrex2tXXPOJYXBwgBtvvKX2jpmvz551VeuLe2KdrX/V19Vv\n6c33+iz8edjf8Uamv1EL4Pde/3ZGDj6cyd2Tc7+5ZvfAUoYea4LQChMslVU20bocODkixmvLGyPi\nVGBlZl4YEZuAb1A8LuLTmfmzNsTac+pJ0nweJTFT/Uvjurm2z+fYe/6ot/4zummmtvSzmfrFXH2u\nF66jyhle8+uw5jeaelbPonyuj9QlpRKtzJwCzpi2ekvD9q8BX1vAuPpK2T+E7fjj14k/qAv9M+aT\nUJo47G1/58PzJEmd5RQ8XTJXMtGrWhnFU3v0U//SwrHGqDXzPX/337+DoaEhli0rXpcxNLSU4eHh\npmNUNZhoqS3mcxvThEDqHBOs1szn/A2OPImzzvkXAAYGB5iq1cTOZd0Rw2w68w1N/zxVg4mW2s5b\nfZIEQ8tGGFp2VPP7Lf15G6JRp5hoSZJUYdu33csdd/ywqX0GBgY4/PAj2xSRmmGiJWnRm2s+135k\njVZrOnn+brnnsfz3Bd9tap+pbT/k0gs+0KaI1AwTLUmaZT7XfmWC1ZpOnr/lqx/f9D6TU79sQySa\nDxMtSZp9Plep5zyye5JLvvivpd+/YuUwD9y/k3XPXsvTj4o2Rrb4mGhJ0uzzuUo9Z/jgZ3LNj5vd\nazkT91zN8mVLm9pryZIlM07HpYKJliTNPp9rpe287y6Gh5ewe1dz4R7zlN0A3PA/Byx4TAcsGZw1\nnsmtt+x3WzvMFc98tHr+2hFTK+rxbM67ue6m85vad+v/3soxz2r+25Rbf3kvK1aumnHbsuElPLRz\n1z7rjzjiCDa9bVPTP6ubBqamyj3HQ5L6VUS8AtiQmRtr87m+NzNf1u24JPU+R7QkaYb5XLsZjKT+\n4YiWJElSmziJuyRJUpuYaEmSJLWJiZYkSVKbmGhJkiS1SUe/ddjr84lFxBDwGeBJwDBwDvB94GJg\nErgVOCsze+YbBhFxMHAT8AKKNlxMj7UlIt4NbACGgH8AxunNdgwCFwFPo4j9dGA3PdSW2vQ1f5OZ\nJ0XEkcwQe0ScDrwR2AWck5lXdC3gkqr2OalSn69Sv61a/5sWz7OA8yjOzU7gdZn5i27F07DuNcCb\nM3N9bbmjn89p5+hg4EJgDTBAcY7u7OI1O4qib08BWyhylqb7UKdHtB6dTwx4F8V8Yr3kD4CJzHw+\n8NvAxynacHZt3QDw8i7G15Ra4ngB8ABF7B+lx9oSEScCz6v1qROBw+nda/IiYEVm/hbwAeCv6aG2\nRMQ7KH5JDtdW7dOfIuIJwFuA9cCLgQ9FRHOPoe6wqn1OKtjnK9Fvq9b/Zojn7ykSmpOALwHvjIjH\ndzEeIuLZwOsbljv6+Zwhpg8Dn8/ME4D3AWu7fM3+giKROr627mXziafTidZe84kBvTaf2KUUFx+K\nc/cI8JzMvLa27uvAC7sR2DydC3wS+FltuRfb8iLgloj4MvBV4CvAWA+2A+BBYHVEDACrgYfprbbc\nDryC4o8azNyffhMYz8xHMnN7bZ9ndDzS5lTtc1K1Pl+Vflu1/jc9nldn5s2110MU5+2YbsUTEY8D\nPgi8rSHGTsazT0wUycthEfFNioGNb3c4punxPAg8rta3Ryj6dtPxdDrRmnE+sQ7HMG+Z+UBm3h8R\nIxRJ13vY+xzeT/GLpvIi4o8pRueuqq0aYE/ngt5pyygwBrwKeBPwBXqzHVDc/lkG/IBiBOU8eqgt\nmfkliqH0usbYd1DEvgrYNsP6Sqro56Rqfb4S/bZq/W96PJn5c4CIWA+cBfxdt+Kp/d39NLCJ4vrU\ndfTzOcM1ezLwy8w8GbgLeCdFgtOVawacD3wMuA04GPgO8zhHnU5yenY+sbqIOIwiy74kM79Icf+/\nbgS4ryuBNW8jxZOwrwaeBXyO4hd4Xa+05R7gqszclZlbgIfYu9P3SjsA3kHxP6WguCaXUPzPt66X\n2gJ7fzZWUcQ+/XfACHBvJ4NqUhU/J1Xr81Xtt5XrfxHx+xSjoy/NzK1djGcMOLIWyxeBp0fERykS\niG5+PrdSjNBCMVq7ju5es38Cjs/Mo4HPU9wSb/ocdTrRGgdeClCbT+zm2d9eLbX76VcB78jMi2ur\n/zMiTqi9fglw7Uz7Vk1mnpCZJ9bqBf4LeB1wZQ+2ZTNFvRwRcQiwHPhWD7YDYAV7RnzvpfiySk/2\nr5qZYr8BOD4ihiNiNXA0RaFyJVX0c1K1Pl/Vflup/hcRr6UYyToxM++sre5KPJl5Y2aurfXrVwO3\nZeYm4MZuxNNgM1CfY/SE2s/u5u+M5RQjVlCUDqyZTzydnuuw1+cTO5vif47vi4h6rdZbgfNqxXC3\nAZd1K7gWTQF/ClzYS23JzCsi4vkRcQPFfxzOBO6kx9pRcy7w2Yi4jmJE4N0U33TrtbbUv122T3+q\nfWPnPOA6iut1dmY+3KU456Prn5MK9vmq9duq9b+p2q26jwE/Br4UEQDXZOZfdiOeacsD9XWZ+fMu\nfT4br9lFEXEGxQjkazJzWxfP0WnAZRHxEMU3RU/PzP9rNh7nOpQkSWqTnilElyRJ6jUmWpIkSW1i\noiVJktQmJlqSJEltYqIlSZLUJiZakiRJbWKiJUmS1CYmWpIkSW3y/y2JaI+7ZhlaAAAAAElFTkSu\nQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10bdaeb50>"
       ]
      }
     ],
     "prompt_number": 38
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posterior_population = mcmc.trace(\"pop2\")[:]\n",
      "posterior_mean = np.mean(posterior_population)\n",
      "posterior_sd = np.std(posterior_population)\n",
      "posterior_mean,posterior_sd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 39,
       "text": [
        "(86.383601130383909, 11.873161982197798)"
       ]
      }
     ],
     "prompt_number": 39
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc.summary()"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\n",
        "pop2:\n",
        " \n",
        "\tMean             SD               MC Error        95% HPD interval\n",
        "\t------------------------------------------------------------------\n",
        "\t[[ 86.384]]      [[ 11.873]]      [[ 0.277]]   [  67.628  111.84 ]\n",
        "\t\n",
        "\t\n",
        "\tPosterior quantiles:\n",
        "\t\n",
        "\t2.5             25              50              75             97.5\n",
        "\t |---------------|===============|===============|---------------|\n",
        "\t[[ 68.957]]      [[ 78.167]]     [[ 84.027]]    [[ 92.849]]   [[ 114.578]]\n",
        "\t\n"
       ]
      }
     ],
     "prompt_number": 40
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Now, what if instead of simply tagging the untagged members collected in the first experiment, we also added a second tag. This means that there would be thirty tigers with \"Tag Two\" present in the population. If 11 of the currently captured tigers have this second tag, can we use this information to improve the accuracy of the prediction? The current posterior can be used as the prior."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "pop3=pm.stochastic_from_data(\"pop3\",posterior_population)\n",
      "hypergeo3 = pm.Hypergeometric(\"hypergeo3\",30,30,population,value=11,observed=True)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 16
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "model = pm.Model([pop3,hypergeo3])\n",
      "map_ = pm.MAP( model )\n",
      "map_.fit()\n",
      "mcmc = pm.MCMC(model)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [],
     "prompt_number": 17
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcmc.sample(20000,10000)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
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      },
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        "\r",
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       "stream": "stdout",
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        "\r",
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        "\r",
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        "\r",
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      },
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       "stream": "stdout",
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        "\r",
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       ]
      },
      {
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       "stream": "stdout",
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        "\r",
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      },
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       "stream": "stdout",
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        "\r",
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      {
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        "\r",
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      },
      {
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        "\r",
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      },
      {
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       "stream": "stdout",
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        "\r",
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       ]
      },
      {
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        "\r",
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      },
      {
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       "stream": "stdout",
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        "\r",
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       ]
      },
      {
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        "\r",
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      },
      {
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       "stream": "stdout",
       "text": [
        "\r",
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
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       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------99%----------------- ] 19849 of 20000 complete in 21.5 sec"
       ]
      },
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "\r",
        " [-----------------100%-----------------] 20000 of 20000 complete in 21.7 sec"
       ]
      }
     ],
     "prompt_number": 18
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "mcplot(mcmc.trace(\"pop3\", 1), common_scale=False)"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "output_type": "stream",
       "stream": "stdout",
       "text": [
        "Plotting pop3\n"
       ]
      },
      {
       "metadata": {},
       "output_type": "display_data",
       "png": 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R5riofbxQeUKLtzLFW3nqK26Cre35zvNZPTEpgmkI6rhqBF5oCvaE/wtSEmau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\nOzC8nYYHAAAAAElFTkSuQmCC\n",
       "text": [
        "<matplotlib.figure.Figure at 0x10c1dee90>"
       ]
      }
     ],
     "prompt_number": 19
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [
      "posterior_population = mcmc.trace(\"pop3\")[:]\n",
      "posterior_mean = np.mean(posterior_population)\n",
      "posterior_sd = np.std(posterior_population)\n",
      "posterior_mean,posterior_sd"
     ],
     "language": "python",
     "metadata": {},
     "outputs": [
      {
       "metadata": {},
       "output_type": "pyout",
       "prompt_number": 20,
       "text": [
        "(109.01559100253894, 38.44675752241632)"
       ]
      }
     ],
     "prompt_number": 20
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "Interestingly, this attempt to get an extra experiment \"for free\" didn't work at all, and lowered the accuracy of the prediction."
     ]
    },
    {
     "cell_type": "markdown",
     "metadata": {},
     "source": [
      "So, going back to the more accurate estimate from earlier, there are between 67 and 112 tigers in the area, with the most likely number being 86."
     ]
    },
    {
     "cell_type": "code",
     "collapsed": false,
     "input": [],
     "language": "python",
     "metadata": {},
     "outputs": []
    }
   ],
   "metadata": {}
  }
 ]
}