Statistical Rethinking - Chapter 10.ipynb

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   "source": [
    "#### Chapter 10: Counting and Classification"
   ]
  },
  {
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   "execution_count": 1,
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   "source": [
    "%matplotlib inline\n",
    "import pandas as pd\n",
    "import numpy as np\n",
    "\n",
    "import collections\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "import pymc3 as pm\n",
    "\n",
    "import scipy.stats as stats"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There are two experimental conditions:\n",
    "1. _partner_ condition - chimp standing at other end\n",
    "2. _control_ condition - nobody standing at other end\n",
    "\n",
    "Two counterbalancing treatments alternate which side is social:\n",
    "* Left is prosocial option\n",
    "* Right is prosocial option\n",
    "\n",
    "**The motivating question is whether a focal chimp chooses the prosocial option more often when another animal is present.**\n",
    "\n",
    "In terms of linear model, we want to estimate the interaction between condition (presence or absence of another animal) and option (which side is prosocial). \n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('./rethinking/data/chimpanzees.csv', sep=';')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
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   "outputs": [
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       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>actor</th>\n",
       "      <th>recipient</th>\n",
       "      <th>condition</th>\n",
       "      <th>block</th>\n",
       "      <th>trial</th>\n",
       "      <th>prosoc_left</th>\n",
       "      <th>chose_prosoc</th>\n",
       "      <th>pulled_left</th>\n",
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      "text/plain": [
       "   actor  recipient  condition  block  trial  prosoc_left  chose_prosoc  \\\n",
       "0      1        NaN          0      1      2            0             1   \n",
       "1      1        NaN          0      1      4            0             0   \n",
       "2      1        NaN          0      1      6            1             0   \n",
       "3      1        NaN          0      1      8            0             1   \n",
       "4      1        NaN          0      1     10            1             1   \n",
       "\n",
       "   pulled_left  \n",
       "0            0  \n",
       "1            1  \n",
       "2            0  \n",
       "3            0  \n",
       "4            1  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* `pulled_left` - outcome to predict: 0 or 1 indicator if the focal animal pulled the left-hand lever. \n",
    "* `prosoc_left` - predictor variable: 0 or 1 indicator that the left-hand level was (1) attached or (0) not attached to the prosocial option.\n",
    "* `condition` - predictor variable: 0 or 1 indicator that there (1) was an animal on the other side, and (0) if there wasn't"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "$$L_i \\sim Binomial(1, p_i)$$\n",
    "$$logit(p_i) = \\alpha + (\\beta_P + \\beta_{PC}C_i)P_i$$\n",
    "$$\\alpha \\sim Normal(0, 10)$$\n",
    "$$\\beta_P \\sim Normal(0, 10)$$\n",
    "$$\\beta_{RC} \\sim Normal(0, 10)$$"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* $L_i$ indicates `pulled_left`\n",
    "* $P$ indicates `prosoc_left`\n",
    "* $C$ indicates `condition`"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
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       "<div>\n",
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>pulled_left</th>\n",
       "      <th>prosoc_left</th>\n",
       "      <th>condition</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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      "text/plain": [
       "   pulled_left  prosoc_left  condition\n",
       "0            0            0          0\n",
       "1            1            0          0\n",
       "2            0            1          0\n",
       "3            0            0          0\n",
       "4            1            1          0"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
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   "source": [
    "data[['pulled_left', 'prosoc_left', 'condition']].head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Two other models to compare with:\n",
    "\n",
    "$$L_i \\sim Binomial(1, p_i)$$\n",
    "$$logit(p_i) = \\alpha$$\n",
    "$$\\alpha \\sim Normal(0, 10)$$\n",
    "\n",
    "--- \n",
    "\n",
    "$$L_i \\sim Binomial(1, p_i)$$\n",
    "$$logit(p_i) = \\alpha + \\beta_P P_i$$\n",
    "$$\\alpha \\sim Normal(0, 10)$$\n",
    "$$\\beta_P \\sim Normal(0, 10)$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:00<00:00, 2438.38it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m101:\n",
    "    \n",
    "    alpha = pm.Normal('alpha', mu=0, sd=10)\n",
    "    p_i = pm.Deterministic('p_i', np.exp(alpha) / (1 + np.exp(alpha)))\n",
    "    L_i = pm.Binomial('L_i', 1, p_i, observed=data['pulled_left'])\n",
    "    \n",
    "    m101_map = pm.find_MAP(model=m101)\n",
    "    m101_traces = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "{'alpha': array(0.32014145398132277)}"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m101_map"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Now to interpret the estimate for $\\alpha$, remember that the parameters in the logistic regression are on the scale of log-odds. To get them back onto the probability scale, we have to use the inverse link function. In this case, the inverse link is logistic.\n",
    "\n",
    "In this case:\n",
    "$$p_i = \\frac{e^{\\alpha}}{1 + e^{\\alpha}}$$"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
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   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.57935872518109255"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m101_alpha = m101_map['alpha']\n",
    "\n",
    "np.exp(m101_alpha) / (1 + np.exp(m101_alpha))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So the above summary implies that there is about $\\sim$ 0.58 probability of left lever being pulled. "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:01<00:00, 965.60it/s]\n",
      "100%|██████████| 1000/1000 [00:01<00:00, 569.93it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m102:\n",
    "    \n",
    "    alpha = pm.Normal('alpha', mu=0, sd=10)\n",
    "    beta_p = pm.Normal('beta_p', mu=0, sd=10)\n",
    "    \n",
    "    params = alpha + beta_p * data['prosoc_left']\n",
    "    \n",
    "    p_i = pm.Deterministic('p_i', np.exp(params) / (1 + np.exp(params)))\n",
    "    L_i = pm.Binomial('L_i', 1, p_i, observed=data['pulled_left'])\n",
    "    \n",
    "    m102_map = pm.find_MAP()\n",
    "    m102_traces = pm.sample(1000)\n",
    "\n",
    "    \n",
    "with pm.Model() as m103:\n",
    "    \n",
    "    alpha = pm.Normal('alpha', mu=0, sd=10)\n",
    "    beta_p = pm.Normal('beta_p', mu=0, sd=10)\n",
    "    beta_pc = pm.Normal('beta_pc', mu=0, sd=10)\n",
    "    \n",
    "    params = alpha + (beta_p + beta_pc * data['condition']) * data['prosoc_left']\n",
    "    \n",
    "    p_i = pm.Deterministic('p_i', np.exp(params) / (1 + np.exp(params)))\n",
    "    L_i = pm.Binomial('L_i', 1, p_i, observed=data['pulled_left'])\n",
    "    \n",
    "    m103_map = pm.find_MAP()\n",
    "    m103_traces = pm.sample(1000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "class ComparableModel(object): \n",
    "    \n",
    "    def __init__(self, name, model, traces):\n",
    "        self.name = name\n",
    "        self.model = model\n",
    "        self.traces = traces\n",
    "        \n",
    "        self.waic, self.waic_se, self.n_eff_params = pm.waic(self.traces, self.model, n_eff=True)\n",
    "        \n",
    "    \n",
    "class ModelComparator(object):\n",
    "    \n",
    "    \n",
    "    def __init__(self, models):\n",
    "        self.models = sorted(models, key=lambda x: x.waic, reverse=False)\n",
    "        \n",
    "    def to_df(self):\n",
    "        \n",
    "        self.comparison_df = pd.DataFrame(columns=['Model Name', 'pWAIC', 'WAIC', 'SE'])\n",
    "        \n",
    "        for model in self.models:\n",
    "            self.comparison_df = self.comparison_df.append({\n",
    "                    'Model Name' : model.name, 'pWAIC' : model.n_eff_params,\n",
    "                    'WAIC' : model.waic, 'SE' : model.waic_se  }, ignore_index=True)\n",
    "        \n",
    "        # compute dWAIC\n",
    "        self.comparison_df['dWAIC'] = self.comparison_df['WAIC'] - self.comparison_df['WAIC'].min()\n",
    "        \n",
    "        # helper for weight\n",
    "        self.comparison_df['dWAIC_exp'] = np.exp( -0.5 * self.comparison_df['dWAIC'])\n",
    "        \n",
    "        # compute weight\n",
    "        self.comparison_df['weight'] = self.comparison_df['dWAIC_exp'] / np.sum(self.comparison_df['dWAIC_exp'].sum())\n",
    "                \n",
    "        return self.comparison_df[['Model Name', 'WAIC', 'pWAIC', 'dWAIC', 'weight', 'SE']].round(2)\n",
    "    \n",
    "    \n",
    "    def to_plot(self):\n",
    "        \n",
    "        # they're plotted in reverse order, so sort by WAIC\n",
    "        comparison_df = self.to_df()\n",
    "        \n",
    "        fig, ax = plt.subplots(1, 1, figsize=(10, 1.5))\n",
    "\n",
    "        ax.scatter(comparison_df['WAIC'], comparison_df.index, facecolors='none', edgecolors='k', s=60)\n",
    "        ax.scatter(comparison_df['WAIC'] - comparison_df['pWAIC'] * 2, comparison_df.index, facecolors='k', edgecolors='k', s=20)\n",
    "\n",
    "        ax.hlines(comparison_df.index, comparison_df['WAIC'] - comparison_df['SE'], comparison_df['WAIC'] + comparison_df['SE'] )\n",
    "\n",
    "        ax.set_title('WAIC')\n",
    "        ax.set_xlabel('deviance')\n",
    "\n",
    "        ax.set_yticks([0, 1, 2])\n",
    "        ax.set_yticklabels(comparison_df['Model Name'])\n",
    "\n",
    "        ax.grid();\n",
    "        \n",
    "        return (fig, ax);\n",
    "        "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "model_comparator = ModelComparator([\n",
    "        ComparableModel('m101', m101, m101_traces),\n",
    "        ComparableModel('m102', m102, m102_traces),\n",
    "        ComparableModel('m103', m103, m103_traces)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model Name</th>\n",
       "      <th>WAIC</th>\n",
       "      <th>pWAIC</th>\n",
       "      <th>dWAIC</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>m102</td>\n",
       "      <td>680.85</td>\n",
       "      <td>2.18</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.68</td>\n",
       "      <td>9.26</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>m103</td>\n",
       "      <td>682.49</td>\n",
       "      <td>3.07</td>\n",
       "      <td>1.64</td>\n",
       "      <td>0.30</td>\n",
       "      <td>9.59</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>m101</td>\n",
       "      <td>688.16</td>\n",
       "      <td>1.11</td>\n",
       "      <td>7.31</td>\n",
       "      <td>0.02</td>\n",
       "      <td>7.27</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "  Model Name    WAIC  pWAIC  dWAIC  weight    SE\n",
       "0       m102  680.85   2.18   0.00    0.68  9.26\n",
       "1       m103  682.49   3.07   1.64    0.30  9.59\n",
       "2       m101  688.16   1.11   7.31    0.02  7.27"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_comparator.to_df()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {
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   "outputs": [
    {
     "data": {
      "image/png": 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jU5/6VLfbpkyZwr59+9i1a1eRIqteaYxzO5Rznj7nvPKM7ON+7xastxe023s5x07glIL2\nyUkfAJLmAZ8Ezj/ch8+bN4/6+noAamtrmThx4sHB1nGZttjttWvXsnjx4sOFZUXW1tbG6NGjSx1G\nxZg/f36P20455ZQet5mVWkNDA4sWLRqy32+33U6z3bHe3NxMUUTEYRfyV8S2FLSXA5f1sK0B+GpB\n+wjg1WS/o4DNwIRk2xzyV9+O6+Xzw9K1Zs2aIf+M1tbWyGQyARxcMplMtLa2Dvlnl6P+5Pzpp5+O\ncePGxf79+7tsW7FiRZx33nlFjKx6pTHO7VDOefqc8/QldUuv9VVPS19vZUYP6wAhabSkHcCNwC2S\ntks6OiLeB24g/xeYLwIrIuKl5LjvAEcDP5W0SdJdfYzFqkBdXR2NjY1kMhlqamrIZDI0NjZSV1dX\n6tDK3vTp0znttNO4+uqrefPNNwFob29n1apVzJ8/nyVLlpQ4QjMzGyi/K9NKKpfL0dzcTH19vYuy\nfmhra+Pmm2/m+9//PmPGjCGXy3H88cdz++23M2vWrFKHZ2Y2bA32OWYuzMwq2N69e9m6dSvHHHMM\nY8eORRrwb4GZmRVBuTxg1qqIn3uTvoHmvKamhilTpjBu3DgXZf3kcZ4+5zx9znnlcWFmZmZmViZ8\nK9PMzMysSHwr08zMzKxKuDCzLjwnIX3Oefqc8/Q55+lzziuPCzPrYvPmzaUOYdhxztPnnKfPOU+f\nc155XJhZF2+//XapQxh2nPP0Oefpc87T55xXHhdmZmZmZmXChZl1UbQXsVqfOefpc87T55ynzzmv\nPBXxuIxSx2BmZmbWV1X9SiYzMzOz4cK3Ms3MzMzKhAszMzMzszJR8sJM0ihJKyW9JOlFSR+XtELS\n85I2SXpD0qaC/b8uaVuy/4WljL1S9SfnkrKS3kn6N0m6q9TxV6Iecn6mpP9M8v5zSVMK9vc4H6T+\n5NzjvDh6yPkZkv5D0n9J+qGkowv29zgfpP7k3ON88CSNLfh/5fOS9kj6iqRjJa2W9Iqkn0gaVXBM\n/8Z5RJR0Ae4Hrk3WRwI1nbbfDvxdsj4BeD7Zrx54lWSenJchy3kWeKHUMVf60k3ORwE/AS5M+v4M\nWJOs/7HHeeo59zgfupz/HJie9M0DliTrHufp59zjvLi5HwHsAv4ncBvwtaT/ZuCbyXq/x3lJr5hJ\nqgFmRMRygIg4EBF7O+12JfBgsn4psCLZrxnYBkxNK95q0I+cNxUellZ81aiHnO8B2sn/iALUAjuT\n9UvwOB+UAeQcPM4H5TA5/1hEPJPs9jPg8mTd43yQBpBz8DgvpguA1yJiB/n65HtJ//eATyfr/R7n\npb6VOQbYLWl5clnwXkmZjo2SZgC/jojXk66TgB0Fx+9M+qzv+prz1wqOqU/2XSNpeuoRV76ecn4j\ncLuk7cC3gK8n+3ucD15/cw4e54PVXc4/DLwo6ZJknyuBk5N1j/PB62/OweO8mP6SDy4cnRARvwGI\niF8Do5P+fo/zUhdmI4HJwHcjYjLwDof+UM7l0Cs3Nnj9zfku4JRk368CDxbOEbE+6Zzz35PP+d8A\nfxsRp5AvGP6xdCFWnf7m/E08zgeru9+Wm4HPAddLWg/8IbC/dCFWnf7m3OO8SCQdSf5q2Mqkq/Oz\nxwb8LLJSF2a/AnZExIak/c/AJABJRwCXAQ8V7L+T/L3cDidz6K0I612/ch4R70XEfyfrm4DXgLGp\nRlz5Ouf8EfI/pp+NiH8BiIh/Bs5OtnucD15fcz41Wd/vcT5o3f22TI6IrRFxUUScDawgn1vwOC+G\nfuXc47yo/gzYGBG7k/ZvJJ0AIOlEoDXp7/c4L2lhllz22yGpY2DMAn6ZrM8GXoqIXQWHrAKuknSU\npDHAaeQnOVof9Tfnko6XNCJZP5V8zl/H+qyHnL8I7JL0CQBJs8jPPQCP80HrR863Juse54PU02+L\npDqAJL9/B9yTbPc4H6T+5tzjvKg6311aRf4PLQCuAX5Y0N+vcT6yuHEOyFeAf0ouC74OXJv0/yWd\nbmNGxC8lPUy+kHgP+HIkf/Zg/dLnnAPnAUsk7Sc/cfqLEfF2apFWj+5yvgr4h+RK5T7gC+BxXkR9\nzjke58XSXc6vkXQ9+Vs7j0bE/eBxXkR9zjke50WRzOO7gA9+PyD/V5kPS/oc0EJ+bt+AxrlfyWRm\nZmZWJko9x8zMzMzMEi7MzMzMzMqECzMzMzOzMuHCzMzMzKxMuDAzMzMzKxMuzMzMzMzKhAszM6so\nkhokLRjAcYslnT8UMZmZFUs5PGDWzGzIRURDqWMwM+uNr5iZWdmTdIukVyQ9DYxL+k6V9KSk9ZKe\nkjRWUo2k5oLjPixpu6QjJC2XdFnS/78lPSfpBUn3FOy/RtI3k20vSzo36R8haamkLZI2J09VR9Jk\nSWuTGJ7seFeemdlAuTAzs7ImaTL515ucAVzMBy97vxe4IXlR803A3RGxF3i+432YwKeAH0fE+51O\n+52I+HhEnAF8WNLFBduOiIiPAzcCi5K+LwJZ4IyImEj+FTgjge8AlycxLAduLdoXN7Nhybcyzazc\nzQB+EBHvAu9K+iGQAf4UWClJyX5HJv99mPx7X58CrgK+2805Z0m6CfgwcCzwC+DxZNujyX83ki/G\nIP9y6Ls73nEXEW9LOh34E+CnSQwjgF1F+L5mNoy5MDOzStNRBP13REzuZvsq4O8lHQtMBv7tkIOl\nPyBfrE2OiF2SGoAPFezybvLf9zn8b6SAX0TEuQP7GmZmXflWppmVu6eBT0v6A0nHAH8O/B54Q9IV\nHTtJOgMgIn4PbAD+AXis4ypXgQ8BAbwl6WjgCnrWcTXup8AXJR2RfNaxwCtAnaRzkr6Rkv54cF/V\nzIY7F2ZmVtYi4nngIeAF8rcbf55suhq4LpmM/wvgkoLDHkq2ryg8VXK+PcB9wIvAkwXnO7hPN+37\ngB3AC5KeB+ZGxHvki7rbJG0GngemDeKrmpmhrv+YNDMzM7NS8BUzMzMzszLhwszMzMysTLgwMzMz\nMysTLszMzMzMyoQLMzMzM7My4cLMzMzMrEy4MDMzMzMrEy7MzMzMzMrE/wdc936Qsk2qFQAAAABJ\nRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x120e4f860>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "model_comparator.to_plot();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "### I hate the chimp example"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 10.1.3 Aggregate binomial: Graduate school admission"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data = pd.read_csv('./rethinking/data/UCBadmit.csv', sep=';')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>dept</th>\n",
       "      <th>applicant.gender</th>\n",
       "      <th>admit</th>\n",
       "      <th>reject</th>\n",
       "      <th>applications</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>A</td>\n",
       "      <td>male</td>\n",
       "      <td>512</td>\n",
       "      <td>313</td>\n",
       "      <td>825</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>A</td>\n",
       "      <td>female</td>\n",
       "      <td>89</td>\n",
       "      <td>19</td>\n",
       "      <td>108</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>B</td>\n",
       "      <td>male</td>\n",
       "      <td>353</td>\n",
       "      <td>207</td>\n",
       "      <td>560</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>B</td>\n",
       "      <td>female</td>\n",
       "      <td>17</td>\n",
       "      <td>8</td>\n",
       "      <td>25</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>C</td>\n",
       "      <td>male</td>\n",
       "      <td>120</td>\n",
       "      <td>205</td>\n",
       "      <td>325</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  dept applicant.gender  admit  reject  applications\n",
       "1    A             male    512     313           825\n",
       "2    A           female     89      19           108\n",
       "3    B             male    353     207           560\n",
       "4    B           female     17       8            25\n",
       "5    C             male    120     205           325"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data['is_male'] = (data['applicant.gender'] == 'male').astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "data['dept_id'] = (data.dept.rank(method='dense') - 1).astype(int)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "data['applications'] = data['applications'].astype(np.int32)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Our job is to evaluate whether these data contain evidence of gender bias in admissions. We will model the admission decisions, focusing on applicant gender as a predictor variable. So we want to fit at least two models:\n",
    "\n",
    "1. A binomial regression that models `admit` as a function of each applicant's gender. This will estimate the association between gender and the probability of admission.\n",
    "2. A binomial regression that models `admit` as a constant, ignoring gender. This will allow us to get a sense of any overfitting committed by the first model.\n",
    "---\n",
    "This is what the first model looks like:\n",
    "\n",
    "$$n_{admit, i} \\sim Binomial(n_i, p_i)$$\n",
    "$$logit(p_i) = \\alpha + \\beta m_i$$\n",
    "$$ \\alpha \\sim Normal(0, 10)$$\n",
    "$$ \\beta_m \\sim Normal(0, 10)$$\n",
    "\n",
    "The variable $n_i$ indicates `applications[i]`, the number of applications on row `i` The predictor $m_i$ is a dummy that indicates \"male\"."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {
    "collapsed": false,
    "scrolled": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 10000/10000 [00:05<00:00, 1698.65it/s]\n",
      "100%|██████████| 10000/10000 [00:02<00:00, 3974.00it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m106:\n",
    "    \n",
    "    alpha = pm.Normal('alpha', 0, 10)\n",
    "    beta_m = pm.Normal('beta_m', 0, 10)\n",
    "    \n",
    "    lin = alpha + beta_m * data['is_male']\n",
    "    p = np.exp(lin) / (1 + np.exp(lin))\n",
    "    \n",
    "    admit = pm.Binomial('admit', n=data['applications'].values, p=p, observed=data['admit'])\n",
    "        \n",
    "    m106_map = pm.find_MAP()\n",
    "    m106_traces = pm.sample(10000, start=m106_map)\n",
    "    \n",
    "    \n",
    "with pm.Model() as m107:\n",
    "    \n",
    "    alpha = pm.Normal('alpha', 0, 10)\n",
    "    \n",
    "    lin = alpha\n",
    "    p = np.exp(lin) / (1 + np.exp(lin))\n",
    "    \n",
    "    admit = pm.Binomial('admit', n=data['applications'].values, p=p, observed=data['admit'])\n",
    "        \n",
    "    m107_map = pm.find_MAP()\n",
    "    m107_traces = pm.sample(10000, start=m107_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/Users/horatiu/anaconda/lib/python3.5/site-packages/pymc3/stats.py:178: UserWarning: For one or more samples the posterior variance of the\n",
      "        log predictive densities exceeds 0.4. This could be indication of\n",
      "        WAIC starting to fail see http://arxiv.org/abs/1507.04544 for details\n",
      "        \n",
      "  \"\"\")\n",
      "/Users/horatiu/anaconda/lib/python3.5/site-packages/pymc3/stats.py:178: UserWarning: For one or more samples the posterior variance of the\n",
      "        log predictive densities exceeds 0.4. This could be indication of\n",
      "        WAIC starting to fail see http://arxiv.org/abs/1507.04544 for details\n",
      "        \n",
      "  \"\"\")\n"
     ]
    }
   ],
   "source": [
    "model_comparator = ModelComparator([\n",
    "        ComparableModel('m106', m106, m106_traces),\n",
    "        ComparableModel('m107', m107, m107_traces)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Model Name</th>\n",
       "      <th>WAIC</th>\n",
       "      <th>pWAIC</th>\n",
       "      <th>dWAIC</th>\n",
       "      <th>weight</th>\n",
       "      <th>SE</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>m106</td>\n",
       "      <td>994.67</td>\n",
       "      <td>116.17</td>\n",
       "      <td>0.0</td>\n",
       "      <td>1.0</td>\n",
       "      <td>315.36</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>m107</td>\n",
       "      <td>1034.77</td>\n",
       "      <td>80.11</td>\n",
       "      <td>40.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>309.39</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "  Model Name     WAIC   pWAIC  dWAIC  weight      SE\n",
       "0       m106   994.67  116.17    0.0     1.0  315.36\n",
       "1       m107  1034.77   80.11   40.1     0.0  309.39"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "model_comparator.to_df()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m106_traces_df = pm.trace_to_dataframe(m106_traces)\n",
    "m107_traces_df = pm.trace_to_dataframe(m107_traces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alpha</th>\n",
       "      <th>beta_m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>-0.879437</td>\n",
       "      <td>0.694930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>-0.879437</td>\n",
       "      <td>0.694930</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>-0.787371</td>\n",
       "      <td>0.586264</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>-0.953573</td>\n",
       "      <td>0.762096</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>-0.988030</td>\n",
       "      <td>0.720946</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "      alpha    beta_m\n",
       "0 -0.879437  0.694930\n",
       "1 -0.879437  0.694930\n",
       "2 -0.787371  0.586264\n",
       "3 -0.953573  0.762096\n",
       "4 -0.988030  0.720946"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m106_traces_df.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.025    0.112786\n",
       "0.500    0.141444\n",
       "0.975    0.170436\n",
       "dtype: float64"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "p_admit_male = m106_traces_df.apply(lambda row: row['alpha'] + row['beta_m'], axis=1)\n",
    "p_admit_female = m106_traces_df.apply(lambda row: row['alpha'], axis=1)\n",
    "\n",
    "p_admit_male = p_admit_male.apply(lambda x: np.exp(x) / (1 + np.exp(x)))\n",
    "p_admit_female = p_admit_female.apply(lambda x: np.exp(x) / (1 + np.exp(x)))\n",
    "\n",
    "diff_admit = p_admit_male - p_admit_female\n",
    "\n",
    "#\n",
    "# The difference in the probability of admission is\n",
    "#\n",
    "\n",
    "diff_admit.quantile([0.025, 0.5, 0.975])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
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      "text/plain": [
       "<matplotlib.figure.Figure at 0x11f6f6748>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(4,3))\n",
    "\n",
    "# diff_admit.plot(ax=ax, kind='kde')\n",
    "diff_admit.plot(ax=ax, kind='kde')\n",
    "ax.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "post = m106_traces_df.apply(lambda row: row['alpha'] + row['beta_m'] * data['is_male'], axis=1)\n",
    "post = post.apply(lambda x: np.exp(x) / (1 + np.exp(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "quantiles = post.quantile([0.05, 0.975])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>1</th>\n",
       "      <th>2</th>\n",
       "      <th>3</th>\n",
       "      <th>4</th>\n",
       "      <th>5</th>\n",
       "      <th>6</th>\n",
       "      <th>7</th>\n",
       "      <th>8</th>\n",
       "      <th>9</th>\n",
       "      <th>10</th>\n",
       "      <th>11</th>\n",
       "      <th>12</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.050</th>\n",
       "      <td>0.429676</td>\n",
       "      <td>0.285294</td>\n",
       "      <td>0.429676</td>\n",
       "      <td>0.285294</td>\n",
       "      <td>0.429676</td>\n",
       "      <td>0.285294</td>\n",
       "      <td>0.429676</td>\n",
       "      <td>0.285294</td>\n",
       "      <td>0.429676</td>\n",
       "      <td>0.285294</td>\n",
       "      <td>0.429676</td>\n",
       "      <td>0.285294</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.975</th>\n",
       "      <td>0.464330</td>\n",
       "      <td>0.325570</td>\n",
       "      <td>0.464330</td>\n",
       "      <td>0.325570</td>\n",
       "      <td>0.464330</td>\n",
       "      <td>0.325570</td>\n",
       "      <td>0.464330</td>\n",
       "      <td>0.325570</td>\n",
       "      <td>0.464330</td>\n",
       "      <td>0.325570</td>\n",
       "      <td>0.464330</td>\n",
       "      <td>0.325570</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             1         2         3         4         5         6         7   \\\n",
       "0.050  0.429676  0.285294  0.429676  0.285294  0.429676  0.285294  0.429676   \n",
       "0.975  0.464330  0.325570  0.464330  0.325570  0.464330  0.325570  0.464330   \n",
       "\n",
       "             8         9         10        11        12  \n",
       "0.050  0.285294  0.429676  0.285294  0.429676  0.285294  \n",
       "0.975  0.325570  0.464330  0.325570  0.464330  0.325570  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "quantiles"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAXcAAAEACAYAAABI5zaHAAAABHNCSVQICAgIfAhkiAAAAAlwSFlz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\nxHM6AAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1229d0048>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
    "\n",
    "real_acceptance = data['admit'] / data['applications']\n",
    "\n",
    "ax.scatter(real_acceptance.index, real_acceptance.values)\n",
    "\n",
    "ax.vlines(real_acceptance.index, ymin=quantiles.iloc[0, :], ymax=quantiles.iloc[1, :])\n",
    "\n",
    "ax.grid();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:01<00:00, 796.81it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m108:\n",
    "    \n",
    "    alphas = pm.Normal('alphas', 0, 10, shape=6)\n",
    "    beta_m = pm.Normal('beta_m', 0, 10)\n",
    "    \n",
    "    lin = alphas[data['dept_id']] + beta_m * data['is_male']\n",
    "    p = np.exp(lin) / (1 + np.exp(lin))\n",
    "    \n",
    "    admit = pm.Binomial('admit', n=data['applications'].values, p=p, observed=data['admit'])\n",
    "        \n",
    "    m108_map = pm.find_MAP()\n",
    "    m108_traces = pm.sample(1000, start=m108_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "alphas:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  0.687            0.098            0.004            [0.496, 0.873]\n",
      "  0.649            0.112            0.004            [0.437, 0.881]\n",
      "  -0.580           0.073            0.002            [-0.726, -0.445]\n",
      "  -0.608           0.088            0.003            [-0.777, -0.437]\n",
      "  -1.060           0.103            0.003            [-1.252, -0.845]\n",
      "  -2.624           0.152            0.007            [-2.916, -2.351]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  0.506          0.620          0.685          0.753          0.888\n",
      "  0.433          0.580          0.646          0.721          0.879\n",
      "  -0.721         -0.633         -0.576         -0.530         -0.428\n",
      "  -0.777         -0.667         -0.606         -0.552         -0.437\n",
      "  -1.261         -1.126         -1.062         -0.992         -0.851\n",
      "  -2.925         -2.724         -2.633         -2.510         -2.354\n",
      "\n",
      "\n",
      "beta_m:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  -0.109           0.080            0.004            [-0.257, 0.055]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  -0.270         -0.162         -0.109         -0.058         0.050\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pm.summary(m108_traces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m108_traces_df = pm.trace_to_dataframe(m108_traces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "m108_quantiles = m108_traces_df.quantile([0.025, 0.5, 0.975])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>alphas__0</th>\n",
       "      <th>alphas__1</th>\n",
       "      <th>alphas__2</th>\n",
       "      <th>alphas__3</th>\n",
       "      <th>alphas__4</th>\n",
       "      <th>alphas__5</th>\n",
       "      <th>beta_m</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.025</th>\n",
       "      <td>0.505806</td>\n",
       "      <td>0.433363</td>\n",
       "      <td>-0.721414</td>\n",
       "      <td>-0.777186</td>\n",
       "      <td>-1.261313</td>\n",
       "      <td>-2.925237</td>\n",
       "      <td>-0.269922</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.500</th>\n",
       "      <td>0.685313</td>\n",
       "      <td>0.645970</td>\n",
       "      <td>-0.575914</td>\n",
       "      <td>-0.606222</td>\n",
       "      <td>-1.061942</td>\n",
       "      <td>-2.632821</td>\n",
       "      <td>-0.109100</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>0.975</th>\n",
       "      <td>0.887086</td>\n",
       "      <td>0.878526</td>\n",
       "      <td>-0.435654</td>\n",
       "      <td>-0.437914</td>\n",
       "      <td>-0.851461</td>\n",
       "      <td>-2.354369</td>\n",
       "      <td>0.049703</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       alphas__0  alphas__1  alphas__2  alphas__3  alphas__4  alphas__5  \\\n",
       "0.025   0.505806   0.433363  -0.721414  -0.777186  -1.261313  -2.925237   \n",
       "0.500   0.685313   0.645970  -0.575914  -0.606222  -1.061942  -2.632821   \n",
       "0.975   0.887086   0.878526  -0.435654  -0.437914  -0.851461  -2.354369   \n",
       "\n",
       "         beta_m  \n",
       "0.025 -0.269922  \n",
       "0.500 -0.109100  \n",
       "0.975  0.049703  "
      ]
     },
     "execution_count": 34,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "m108_quantiles.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# model_comparator = ModelComparator([\n",
    "#         ComparableModel('m106', m106, m106_traces),\n",
    "#         ComparableModel('m107', m107, m107_traces), \n",
    "#         ComparableModel('m108', m108, m108_traces)])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "post = data.apply(lambda row: row['is_male'] * m108_quantiles['beta_m'] + m108_quantiles['alphas__%d' % row['dept_id']], axis=1)\n",
    "post = post.applymap(lambda x: np.exp(x) / (1 + np.exp(x)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UXb1e56abbtIz8Byt2omb2SbgCeAa4BngYeBGd5/r2WcncMzdf2hmu4Exd9+5wrHUiYsk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\n0xAXEakwDXERkQrTEBcRqTANcRGRCvt/PIEGdeUgCusAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x1282a5a90>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots(1, 1, figsize=(6, 4))\n",
    "\n",
    "real_acceptance = data['admit'] / data['applications']\n",
    "\n",
    "ax.scatter(real_acceptance.index, real_acceptance.values)\n",
    "ax.vlines(post.index, post.iloc[:,0], post.iloc[:,2])\n",
    "\n",
    "\n",
    "ax.set_xlim([0, 13]);\n",
    "ax.grid();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {
    "collapsed": true
   },
   "source": [
    "### 10.2 Poisson regression"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "d = pd.read_csv('./rethinking/data/Kline.csv', sep=';')\n",
    "\n",
    "d['log_pop'] = np.log(d['population'])\n",
    "d[['contact_high', 'contact_low']] = pd.get_dummies(d['contact'])\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "100%|██████████| 1000/1000 [00:03<00:00, 299.12it/s]\n"
     ]
    }
   ],
   "source": [
    "with pm.Model() as m1010:\n",
    "    \n",
    "    alpha = pm.Normal('alpha', mu=0, sd=100)\n",
    "    beta_p = pm.Normal('beta_p', mu=0, sd=1)\n",
    "    beta_c = pm.Normal('beta_c', mu=0, sd=1)\n",
    "    beta_pc = pm.Normal('beta_pc', mu=0, sd=1)\n",
    "    \n",
    "    lambda_ = np.exp(alpha\n",
    "                     + beta_p * d['log_pop']\n",
    "                     + beta_c * d['contact_high']\n",
    "                     + beta_pc * d['log_pop'] * d['contact_high'])\n",
    "                     \n",
    "    tools = pm.Poisson('tools', mu=lambda_, observed=d['total_tools'])\n",
    "    \n",
    "    m1010_map = pm.find_MAP()\n",
    "    m1010_traces = pm.sample(1000, start=m1010_map)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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AO+ooOT/fysviVKqRpqYmNDU1pd4uM1+ceqNlxmeQfOxjuXlQPpHlrklje7AA\nEWkLFsjjurpcI8bsl8QYY5YCDe66Tj6jySeytm4Vg983U25C+Fpa5DZ8uIy1uTk3EZ9ZDEJ7/SOX\nxx7LH7fdn/Fkueci6vijCl/YxlptLbB6tXjB3nkHuOCC3OPt1y+3TLRdpY0ZeOONIBfFxjYGC/Fk\n1dTkei/DPFk1Nf5zsWaNhG5ecIEIT3ehXSPkfSxdCowYERje9fVSMtzN/TFtuWM34sj1ZM2bJ9fK\nqFHhfdvXhplgCLte4kLqGhrkuG1PmruN7YUppPBFoV6RbdvEA7jzzjKWzZuB2bODinju+OK+11H9\nm7YaGvKP3ffdN69H/R7Y+7z0Um7YrtnX7GOH+tXW5hbxsPsICwm0QyZ9E9JuGHDYZzV3bpDzbXu/\n0iINkdXbFj7MvNl4siJoBmB/hXbLvmZzMYCfZttcRESLAUxAyBootshSlK7EqlWyyPDZZ0slQRVY\nfoYMkYTZI48EdtgB+NznKj0iJQ53wmvmzJmp90FEp0Jyez8KIGHmH6beUYm4BhKzeHSMBwDI9y61\ntMTPnNvGiSvImMUAsQ1N03bfvrlrBGUyIpKMZ8O8boyO7dsDw6W9XbwIBx8cjPsf/wD22UfCunbc\nMdcYrakBNm3KfT5smIgsOy/GiJKoxU7d4zC4nqzevcML5thGV6GerObmoAT57NnAGWcE/bsG2saN\n4SFOr7wCTJgg5zxKVJtxuZgwQFuUFRouaEKxtm/P/XxMG3b/7vM5c6Tctjnujg5Zz80suUEEPPII\nMHmyX2TZx2vumXMLmIQRFdaXZFt7n4YG+Q7V14fnZNkiKyxc0BbU776be2xRbNgg53633eS67d9f\n/t+YA4Fxyy0itDIZ4LDDgtA887uxbJns747bFyZnF76YMkUmPJYtS+7J8olnn8hyJxPMb4fv87An\nRFyBZ3uMTQ6neWzfu5jr3rQVdn28+26+tzJN0tBsLUQ02TwhogMBxK05PxfAHkS0OxE1ALgAwCxn\nm/cgHjIQ0XAA4wG8m8J4FaVqWLNGQgTPPhv40Y9UYMUxYoTMvM6YEb34pdIzIKJrAJwP4DIABODj\nAHav6KBCCCsg4BpqgLy2fbt4b+OIElmZjBiR7oz3rrsCp52WbzCZUsrm+ebNQfsbNgSGy9at4tGx\nK4QBwOuvy/fTPpZJk/Jno2tqgoI+xhC9997AYPcZY08/netZcQ08W6B++KEciw97jR5AhFBSkWX6\nMIUpbK/dzOvrAAAgAElEQVSVr+iDXZzCbXf+/PxQ0DBvSZgnK0pkmcfbt4eHC5rP1gho+xhtwgzP\ntWsDceFeY5mMTCAuX55MZBkvR5IS+UnCUw32BIOvkIOZ5PCFrAG5448S/48+GoT9GvFjXw9r1gSh\novY45s6V9SDNeGpqgs/bzZNilskJQ2urnPennvJvG0UmIwIrTDz6qjqGFb6w+zKhiT5bJsxbaHtj\nXYHnC3W2+w77PIxnPWwsYaQtstLwZP0XgL9nc6cIwM6QP71QmLmDiC6FhBXWALiemd8kokvkbb4W\nwI8B/JmIXs3u9k1mjnBeK0rXYv164MQTZS2oH1bdvHv1sscekvh7wgmyQOjJJ1d6REoFOYyZ9yOi\nV5l5JhH9EsD9aTVORNdDcrxWMPN+IdtcDWAagBYAFzHzPN92Pk+W+7otHFavTjZGuxKdGxYW5sky\nYWa28W4MTpvZswND65FH5N4UOADyC2LYZDLiLRs4UAweWwzU1opnuk+f3BnrKJH1/vu51dpckWUK\nTxiROGCAf409kzdk2l+92h/iBogB3NaWb/D51ieKCjUy59kNXfOVra6tja8uaBvj9rHY9+a8PP98\n4BlxMcexalWQi+Iau0B+QRXD2rUSImkLQzMGE8Jlj8XgXrPmnjloJ6kny13Q2yUuXLCuTj7XMJG1\nYUNwLqJysrZuDTynpqiDOYbnn5ccxP79gdNPz93PFS22yLL7sj29htbW4Ljb2nK/v77rxu7Pvl7D\nPHRJc7J8uVK+70KYyLI9WXGeR7dvc798ObDLLsH7W7fmfg5hx+RSdZ4sZp4LCeP7IoAvANiLmV9M\nsN8DzLxntuzuFdnX/pgVWGDm5cx8EjPvl73dEt2ionQdNm4UcXDkkcDPfqYerELZbz8JT7rwQqAM\nKT9K18FETWwhol0BtAHYJWL7QrkBkh/shYimARjLzOMAXALgmrBtw5LE7QqitjfGZxz6qub5DE77\nPbdyl+nX3LvhgoDkw/hEoOnDjGPbNtknTGTV1gbCzz5OI6TOOit3H3sGPWm4oLtda6uM3y3XbZg1\nSwzS44+XogAmHweQe9vrtnChlKY275vPxF0s2D5eH7bImjQpeM2INvv332fIu54sOxTKPle+cEHf\nc4MRWc89J6GMRnCYfewx+TDeTdt47ugQD4kt1ty+H344eOzmzZj97LA2F/t67t8/fDsXn5fSFln2\n+/a6TGHhgvbnYntOzTGZ796iRf7xvPpqvsiyc/js8RiRZYuXxYslRBPwF9aJE1l2GKx7vSQJF/SJ\nrCgxU4gny2b06PywWrvv9vZcO2DFCplgMeG5cYUv3LGkSVopXgcD2A/AZMiaV59OqV1F6XZs2SKh\nOpMmAb/6lQqsYjnsMOC224CPf1wWVFR6JP8kosEAfg5ZSmQJgJvTajy75ta6iE3OBHBTdtvnAAzK\nhrfnEVZ6/IQTghloX7iXjSkWYBMlsowRGZZHYj+3PVkNDeFGSW1tYIhv2ybbhlVlM7PyQK7oCfP4\nRHmybKKMpi1bxLiK6gOQcMW+feWcmtBFE+Lmhr6ZYzBGW5iojMvBMZXjAPG0uULaGPJbtkjhgPXr\nZTx2u7fcIufdV/o87Prp6IgWWYB4ntzcGNuT5Y6ztlaE87p1MhazJlMmI22ZXJqtW6MNXFcsxolr\n+zgB+R8Iq8bnYrZ5+GEpsc4cXM+2uLXDQM1+vlBOu023XHlNjYStPvts8Lr7X79sWb5oMRMTrshq\na/NfY2Z9qqQiy2CXK/cVvkgist5+W4SiT2SFfReGDs1/zZ4I8o27vj73O79yZRBqm8nk53M98YTk\nTu6wQ3B8cZjfvqpbJ4uI/gLgFwCOgIitgwEcVGq7itId2bZN8q/GjAF+/3sVWKVy7LHArbcC550X\nxLUrPQdm/hEzr2fmOyG5WBOY+fudOAR3OZJm5C9HAiDck9XQkLsQKBAusnwGQBJPVlghBbcAhClD\n7s4a27ierN69g2IZhvb2IEfJ9GWvcxQlgOIKDAC5hRzc9zKZXJHl/sYOGRI8NiFte+4p9yZnJpPJ\nNVpNGxMn5q455PabJFywrk763XNPef7ee4EgMeKluVkMWLPOkuvZWLcuECe+cEGfJ8u+N2zbBhxw\nQHAuWlrE8He39c3uZzJyvbS0yPiOOUYKgpjFdI23b9WqaAFk5/DYOVlJwwX79Iku+W9jzsvq1UF+\nnxGW9vfEVwTEXJd2IQZfYQnTh/mu2tVDN22S/W1vkntcRty4IZBGFNrfqTOt1WUL9WQB0eGC5nh9\n4zMsXSoVM5nlczzqqHyR5ZaPP+yw3N8CIPd3zfc52scMiLAzEyGZTCCKTd9DhsjklRF0vvPQ0SET\nFm54q/GMpkUamu0gAHszJ3XGKUrPpK0NOP98yVG4/vr0S4X2VI47Tn4szzkHuPNO+aFXegbZnN1b\nAdzGzIsAeAK5qoO//GUGnntOHjc2NoK58aM//xEj8teD8RkbYaWKDW6omU9k2du74YLGwIhaV8le\nh2rrVknEHzZMjC1Dc7N4OUzeFyCGlVk7Key3b9EiMYxM/5s3izE83PENhomsffcFXnst17vmGlgD\nBgB77y2PzQy48bKNHy/H8e67ud4MW7CFFdQoRGSdd554qRYskEpxplqhOTa7TXt/89wWWWGeLPe6\nMG24OT3GEDXXif05usdvMO03NASerNpaaWPbtuA6HT48XmSZ8+nmZEXhTixEXa/uuE375rM3nqy+\nfcNDUI248OWmmX3M62vWBCLLFB3JZOT6N0sY2Pu4OU5hhS/M4s52OKF9rdgiy+zrExd2f76QU7N/\nlCdr8uRgSYb6+ty+7GsWkM/XnpQBpKrh3Xfnj8Puwz52U2be953fsEFy3kzf5lji7Kvly4PH8+c3\nYdGiJmzbJr8faZKGyHodUuxiedyGitJT6egALrpIfsxvvz19l3RP5/jjA4/W9dfnJxcr3ZbTIYWW\nbieiDIDbANzOzEujd0uNZgAjree+5UgAANOnz8i5LmfPDh7vv78IHGMsuAZWVH6KmyPiCxeMysmy\n26mtFQOoV6/wwhvG0wIEBrUJtwOA3XcXMXX44bkz0Hb58igDyIRLdXSId3r9+qBMur2Nz+Ayxr39\nfljRCCDfYO7dW4ztednSJQMGiPfBzZlysT0QUbS3B/vX1QULK9uGqa+wgPv524v+GqNy69bckCv7\nvNiGu2HLlsDrB8i5GzNGRK1d7ME+5kmT5NwYA994rOzryXiyAAkhXLky/7odN07Oq10F0oyvUE+W\n7fmJY/HiwGvc3p4rnOwJCvfcmbyzXr2k7L5Zm8seo7mWmpqktL05B6ZEPCATD3Y+n1vpMkpk2cc7\ndKicP/taSerJMvtMmJBfdMTd1yeyamrEC/vhh4EX0+f5svPSXFzPvU9k2dTVhX/GrrgE8kWW/di0\nbU9q7b13Iw49tBFHHinf+Z/+dGZ+R0WSxlz6UADziehBIpplbim0qyjdgkwG+I//kGTMO+7Ir+Cl\npMNxx0kZ6M99Dvjznys9GqUzYOb3mPlKZj4QwCchucGLU+6GsjcfswB8GgCIaCqA9cy8wrdhR4cY\nJmGLbvrEgK+NqNeMwd3WJt5dO7zIJ0pcT1ZNDTB2bHTytwkXHDIkEHEmzBAQA3r79vyS5vX1wCmn\nBG342GknWe/HHIcJ23LPhZ2D4xrEQCDUfH3Z49pnH6nw6h6fYfRoufeFWNnEzZx3dABvvplbHMMX\nImWMfns/87rtyXJF1qZNUgjIzk2xz5nxZNkG6YMPyrk246irk4Ihpl3feTX35royQsLN7TFtGO+Q\n+/kddFDgTbSLE7S1BSIkqcgynqxVq8K3tzG5PLbIcqsLul5AI4ZqaiS8co89gjEyy3/7xo2yPtzI\nkdLOkCFyPgcODNqy18Szx2Afl/19nTMneM/+jh1zjHyXihFZdoESg0/A+ESWWyzDPge2h23p0sDz\nlqSQhHsOzPgNbiVU+7ht0Wp7dKN+W4EgNNjGPsdpkYbImgHgLACXA/ildVOUHg8z8MUvSvjJPffk\nz+Ao6XLwwTKT+IMfAFdemSyEROnaZNdb/CYkbHACgG+m2PbNAP4FYDwRLSWii4noEiL6PAAw830A\nFhPRQgB/BPCfYW11dMg6OqZ4hXtt2oZAW1tu7ofdhl1A4sMPc9eOMuLE7GvnOLlGlbm3xYrvdRdj\n4Jj1eurqxAtnjOaGBnmttTWoLGiIKu8MiOgxAskINZ8BGObJsj0vdjidjS2IGhrEMA7D5F8l8WRF\nGZMrVwYLS5u+e/cOvDj2ZzNsmHhCgPzqg3aYme9cmlL5Pk9WR0cQomXO7eGH54o+t8qbwef5tEWW\n/b5t4NoeiL33DgoR2OO2wwWNZy8OV2QRSfiar2S/D9s7ZcJf7WvKbT8shNF8T4zAMaLcePqM4DL0\n6iWiwO4nSmQZhg7NXWy4piYIoTMkFVm+77UvlzMqXNAcu/u6Gfdia5rLfM4jvJmq4W3Z9OoVPlFk\nT1oxyzW0caPfe2WzcWPuREecF7pYSg5aYuYniGh3AOOY+REi6gsg5SKIitL1YAa+/GWJ8X3wwdwS\nxkr5mDBB1sw5/XSZtbzmmtxQJaX7QETPAagHcDuAjzPzu2m2z8yfTLDNpUnaMkaQT9QAuY/nzg1e\nsw1mOxQLCBY/tdsgCtbrMV4b24hyjSxfiE2UyDJGuTGOzXiMwVJbK6LL5A35FoP1iayJE4PcpNpa\n4J135HFDQzD2KVMkpNIVWf36Saibbdy7fRriBJE5d6efHrQT58lqafGX13f3cb17Q4aIUHa9kePH\ny8LO9qK2rifLjM1ur7XV7z065JDcha03bZJZe9tz5hNZRBIiaPJXwkSWfd3Yx2iqwrliwt7HFlk2\nUUavO2FQqIFsQvjq63OPP8yL8vzz4d/V1avl8xg1So6lvT03fM6+/o0ny61ECASFLozI8glJlyhP\nljtOW6iPHCnLoNjt+MIFfbl4PuHliiwbY/dEfUauyLLvTzlFvIGvveYXWYsXyzW/ZYu8fv/9wTH5\n2jcYz+OKFfHjK4WSPVlE9DkAd0Bm8QCprHR3+B6K0v3JZIBLL5X1R+6/vzxuaCWckSMl1KKlRUIr\nlmvGaHfl08w8mZmvSFtglQs3n8T32OALdfMVv7BhDpY0MIn1YYuo+sIF7XZ8mHEar7xZANSudrfr\nriKSiCQvx/z+uTk+NraHzj7G+no57h13DDxLrsgaPlyKXthhba4AMLhCx0dDgwhFnzfMN/aHHsrf\nzsYWRz7jz7cmWm1tYDi7nizjeQFy22tvD8rv25+fuxbb9u1B2LodYmkvGN3RIQaoXY1x553F22i2\nd9twBdXgwbleIxtXZBVi5EZVy0yC/bm659GXD7luXXh+VFOTCGJz/oxYMm3bn62pZGi3ZReRsSdF\nbNEUJrJsFi3KX5vM3mfcOJlszGTEM2anLbieLHNsYTlZ5rHblyuy9t1XxNz06clFlivIBw3KHwsz\ncOihQZXCbdvk98MVpmGYJQ3syKKqFVkAvgTgcAAbAYCZFwAYFrcTEZ1MRG8R0TtE9K2QbRqJ6GUi\nep2IHvdtoyjVRkeH5GC9+irwyCPyI6F0Pv36SZGRU06RGXA7vl3pHjDz25UeQ1KOPlqMAt9sLBAv\nsox3opCiOW1twYy0MUDsEtKu4ZLEk2X2GT1a1qgzXmLbWDdhYbvuKgLrtNNy9/UZQPZYjEAy58sO\no3LH5wtrM2XS7ddWrhThl6TyWJQYTPqajTF+t2wJz+lycb1xtncqTGSZ52FFE8y+tsgyDByYKwo2\nb5b+7HDKAQPE42j6MeLNCGTjySISw9oYyD5PljmWsLDOKKPXPV+u4R+Hr3Kk7fH1TYT4rjN7PEZk\nuZ4s2+tmi1iD8aTcc0+uJ8uU0jf7RV2zgwfLubbz0lyRVVcnIjlMLBZSXRAIxmOLStfzvssuudeG\nzbhxUiTHbsvuw/f7aH/nBw4MBPq0aflCMcqTZX4D3PLy5SANkbWNmT/S3ERUByDyUieiGgC/BXAS\ngImQBYwnONsMAvA7AKcx8z4APp7CWBWlrLS1Af/2b5L4+cADuUmvSudDBHzve8Af/gCcey5w+eXJ\nSgQrStrsuqsYrMV4ssx7STxZQDBD29YWGI8dHWKEvfJK7rpMvvwQ1+jyUVOTKwRskWU8V8aIco/R\nZzC6RTIACcEyRm+YkenLEzGV7+zX5s+XtYbiwgXtfew+fOM0jByZmzNz0EG54Vj2mj6+/X2/ScOs\nqWozniiRNXYscMQRwWf64ov5bZp9163LNTAnT5br0xYBW7eKx8OU6HbHUlMTlPy3PZW+ym4+T5Z7\nHRcS0h3myUpSYdDu1+ROmXEaQ90nRHzfW9fDac5fWLig/X7Ycfm8VnEhkURyvdjre/lC+8y14fMq\nJhFZvsIXricr7PfN5aCD5PtttrNFW9gxuqHW5lodMEAmBf75z9xj8o3DvkZtD281i6wniOg7APoQ\n0QkA/g5gdsw+UwAsyFaGaoMkLJ/pbPNJAHcyczMAMHNIQVlFqQ42b5aFhjdulC+75mBVD6edBrzw\nguTGnXgi8MEHlR6R0hOJyo2KE1nMyUVW375ieJjqZaZfkyRuV7OzZ55t49FXfQsIn6QwbdfWyuTS\nySeH59n4hIZ9XEa89e8v/dmG+9ix8tsaVrDDjMH1+BlB4K5NlATXG2Fz661y7LbIGjdOPD5mFt/u\nz94/KlzwoIPytzPHbIcdmvd2313EnmvoHnlkbrtPPimVDk3uGSAluU1YqWHbNn8lXNtb2KePFLRw\nQ/58Rq17fQ8cCFxwQfC8oUEW191///w2XMI8WWHX5uDBwWN7nTNbcBuR5QsX9PXpjtEnstxwQZ8n\nyxQ5MX34xE2ScEGfUPKN1/e6CWO097WFj/267fkzYw4LF4ybRLKvF1u0hY3TVBK0w2bDcIW+jTnP\n9sLD1Syyvg1gFYDXAFwC4D4A343ZZwSA963ny7Kv2YwHsAMRPU5Ec4nowhTGqihl4YMPZBHcXXaR\nCk5aaKH62G034LHHJGzrgAOAm29OHl6iVCdE1JeIvkdE12WfjyOi0yo9rjBcQ8g10nzbG4zIShIu\naAxm48kyuSKukWIeu94HItnXzscxhBmygwblLqrr29c10AynnZYrUozgGjAg8GSZ8zNlSn4Jd5/I\nMgLBbGf6DAvZswkLbfONnVl+/32fizkHJnnf3d8Xima/d8wxudu5Zdnt91xB3ru3hFHZ5xUIxLOd\nA+e2aQhbeBkQoUsUiCJ7LK5xvXp1tJFt6Ns3f7y+/QoVWW4ZdYOdn2cXnIgTWWPHBmGTQOARs0WW\nLdoMtsjq21cKkpg8Q9OHLajMuShUZBmhGBaa6rblij930sUu6+8LpbXFYSEiy75mzXfe52kDxPtq\nCv2YbQYMyBVKQH74sg9zbuzfqHKJrDSqC2YAXJe9pUkdgMkAjgXQD8AzRPQMMy/0bTxjxoyPHjc2\nNqKxsTHl4SiKn9deEyPhC18Avv3t8n1ZldKprQW+/30xej7zGeDOOyWUcFhsFqlSDE1NTWhqaipn\nFzcAeBHAodnnzZBoin+G7lFBbKPLNSaMIWgbKq63IpNJ5iFvaREvg52T1dGRL7JMXz6RBYgRs25d\nbtth4TwjR8otijBPllsYqKEhuLmeLIPvPJrXTKW8M86QvFhAzoUpoV2KyAoLNTRr+fjo21c+N7e0\ndBy2d88Oj/KNwxY45py4ImnEiGAh6SlT8vtzhaIrVG1816Hv862pkTA2Ow8qCvs4jjvOX2I/TGT5\nPDkHHpjrlTWhtDvtJOGztlg130/fNW6/NmiQhIMuXBj0ZSYzXE+Wjf3+HnsEAuuYY8SOcEXWvvtK\nLmHUtWWfA1/In02Yh8gnsuzrzfw2+XKyTL+2B879/TJ9u9ivTZ0qIirJxKcZx4EH5noCe/WSZVye\neipa4Blx3a+fTBK88koViywiWgxPDhYzf8yzuaEZwCjr+W7Z12yWAVjNzFsBbCWiJwHsDyBWZClK\nZ3HbbVJF8OqrJdFX6RocdJDkLMyYIX+Wv/qVhK6oQE4Xd8Jr5syZaXcxlpnPJ6LpAMDMW4iq91O0\nQ7lcY6JfPzFqhw0Lkt59nqx+/cSwCMu52WsvMZZXrJAwNjvXxC0jb4yuNWtyPRvmDLqzxEBpOY1R\n4YI2ffsCxx8fGL1uiJ8vPwMQT9rRR+fnYwFy7CNGyJqFcd7AKJFlhIdrsMblefm8eHFVZ13PUJTY\nswX5M8/4qygOHRqIrDCj1whRIDo01bfmY5gnCxAPYhLsfcMmv4xH14S4heXzEEk5/CVLgAUL5LVD\nDpGxLFyYK7KMkAnzZPkw/ZscOV9Olo0tZux2jWfWFVlmLayamujoGCPyXA+1S1jopk9k1dQEIcD2\n9ed6sowYMyLLtx6f+9hgX7M77yyRQKaPMLFl54C59Onjv2bdbW0v35gxIrLKRRrhggcBODh7OxLA\n1QD+GrPPXAB7ZBeRbABwAYBZzjb3ADiCiGqza28dAuDNFMarKCWzdassMvy//yvle1VgdT169wau\nuELWj/nJTyQfoNmd6lGqne1E1AfZiT4iGgtgW2WHFE5UuCAgxVlsI8GXk1VbK4ZBmFCYNClY1Nd4\nbaJE1iOPSNW9sWPz2/J5K5IUFwjDF2oUhqnKaooHuN4RnyHc0BCUdTbY+RujRwPnn1+ayDLn5JRT\ncreNa9MnsiZNkmIVScZhC3QgX+TYXgSz2LBr5PfuLddOFLbYjvqcoozZMA9GEi+FT6i5ZDK5AnXC\nBDk2X8gbIJ+7mevp1UvCxIyXz14ny3xPkhZvMP3Z4YJ2jpIrjOrq/IUvbA9aTY2IYbt6HpHk3J3p\nVi5w2kjiyfIRFi54yCHiTfRNaAwbJuOzPVkDBkg7xvsdJ7LczzpKXBnMYs5h7cV5zMz3yP0+lmtq\nrmSRxcxrrFszM18F4NSYfToAXArgIQBvALiVmd8kokuI6PPZbd4C8CCAVwE8C+BaZp5f6ngVpVTe\nfFPWaFizBnjpJcnvUbouU6aIV+CAA8ToueEGzdXqQvwAwAMARhLR3wA8CuCblR1SOFGFLwym8p/Z\nHggMACOyTDs77SSeK4PdZkODGCSDBgXGn20U2u02N4thZzCv+2bP0xBZhYTMZTLAhg35Br+vKmIU\n27eLMEjSd5TIMuLCeDFMiKRPkNjt+ESWL6TPt7/Pk2Xn8uy/fyBK7bA8d0z19fJ7F2Ws22MuVmTZ\n1435nKZODW/L10bUZ8osouO444Kx7LSTFDfytWWPwxAmstzCF0mxv5fmmrSrXAJB2K6LMfyN8d+7\nN3DqqYF3zXi3fHl0vrajvD2mPxsj/gxm3/r6/GqMZt9ddgHOOSfXk1VTI95i4wlNKrLs37k4T5Yt\nYn3nIE5kmTZ8fZeDNMIFJ1tPayCerdh2mfkBAHs6r/3Ref4LAL8odYyKkgZtbcCVV0po2Y9/DFxy\niYaXdRd69QJmzpQ/jc98BrjjDuC66/JnxZXqgpkfJqKXAEwFQAC+Us2VaOM8WUDuIqTGO2J7suyE\n+poaCbN50xPjYTwdgwYFBpgr8Oz+fSLLZ0h3RrigzdChwPvvizfCbicst83XHyC/30kqM7r7AfnC\nctKkQNTYCfuFtGmIOhe24DAGaG1tsP6UYe+9g8d21UB7G1N8I85Y94ks37ElFVnm3PkqFcb1H4b5\nHtjhhB9+6BcK9nMbtxCJERotLcnDBW2MSLPDBe32gfxwQrsPX26keS+J59cWWVGl4H24VRDDzp1v\nfLYnC8gtMlJIuKC5j6ouaMYQVtQjiSfLPc9V78kC8Evr9lMABwL4RArtKkrVMHeu5PE8/bR4Pb7w\nBRVY3ZH99weef14+60mTgL/9rdIjUnwQ0WRzA7A7gOUAPgAwypn4qyrcwhc+bJFlG6bGODCz277Z\navuxMZqM98bnyQrDNRBtg6bUdebMjHdSRo3KL1aRVGSZ9wH/ArxJcUXWXnvlGr7TpvmrKSYhyoD2\nebKGDQNOOinZWO3z4gqzuD7jxhYlsuxQxkK9Qkk8WXYJe4O53sO+X+7zXXaR8Fzbk9W/v1SKLMaT\nZYcbhoksk+/27rv5Xs4okRX3fTGiw60uGCay3Nd9peV924a1aYssX7izr08gGK8t+uPOfZSXjkhE\n3vDhua+76/V1pshKo7rgMWkMRFGqkWXLgO98B3j4YeBnPwMuvFDFVXenoUG8WmeeCXzqU8D99wO/\n/70uLF1l/DLiPYZUpS0ZIjoZwFWQCcnrmflnzvtHQ/KH382+dBcz/zi8vVxDyPdbss3KKLOLLABB\nuKDdVtjv0cSJuSWgbZFljwfIz70yr9fWSr7pE08Ea8uVEi5o2i5EZBmviO0dsc+jPV5fX4aknqyx\nY/MFU5SwZA7WYUoi9lySeLLM46hFmdPC9bwA/rH7QknNeUqyzEAYSf5fTdVMm8MPl0nQ7dtFzERN\nQBgaGoJjq62V0M/165PnZNnU1QWeFHvxZft8NjQAhx0m3ycbe9LE5ymK+8z79UsWLhjlybILfvi8\nbKZdX5v28dqffdy5699fPNR27lmYl8oQFS5IJOf4WOfX3x6Te57Lbc+lES74taj3mfn/Su1DUTqb\nDRuAX/4S+N3vxGv19ttqZPc0Jk8Wr+XXvhasq3XIIZUelQJ0zuQeEdUA+C2A4yBesrlEdE82X9jm\nSWY+I0mbScIFp0yRkK9XXsnPh7BFljGqwoyEvn2DGeK4nKwwz4jp68gjxYBtbi7dk5XEaLQxBpgt\nBInE0G5tldLX9ppFLnZ1wiT9+kqbp7GwfNh5S+rJSiqyzjkHeOCB5NX8wvq0xzZ5cq7QOuccfy6Z\nT4Cn7clqaAiElM3IkVJ4YevW/MWRAQn9PuGE/PbscEHbE5WU+vpcAW++lz4vsBmHi/lsfcVKfG3Y\nnHGGCN733y8+JwsIvFm+MENbZMWFC4aJLF+fvXtLfru9jRlDMTlZSQRTmMewXHnYaVUX/CJkMeER\nADtyc7MAACAASURBVL4AWd9qQPamKF2GTZuAyy+XNSyWLAFeflkqz6nA6pn07Qtccw3w85/Ln9lV\nV2lRjGqCiHoT0deI6C4iupOI/ouI0loKfAqABcz8HjO3AbgVgK9kQOK50CSFL0aNkt8fABgzRgoc\n2J4sewY2zCjz9dvRER4u6BqstifL7G8ed7Yny/z22uXke/eWioh33y3PTanpMArJx3I577xcQzCK\nffbJFWm+8E2XKJHlnqckRT569UqWwxOGT2QNHSqFJew+fPiEZNoiyy04YlNXB9x3nyxf4PZLlJt3\naLDDBV2PTtQ4DMbbbMSFyW/yebJs7D7sghuFhgv26xcU3TDnf8kSvxCJaidMYMaFC27eLAVHihFZ\nPuJysuLCBZO07xNZpf6uhZGGyNoNwGRm/jozfx2SkzWKmWcy88wU2leUsrNpk4QD7rEH8MYbMmt7\n001i8CjKOecAzz4L3HijhBAmXVhTKTs3AZgI4DcQr9NEAH9Jqe0RAN63ni/LvuZyKBHNI6J7iWhv\nz/sfEVZ63MW8PniweE+N0eF6spJW1nNLU8flhbkiy9desRAVJgL69pXvnx3CZ4SXMejCBIw5jvb2\n4kPY6uuTj3fQIH8pfCDck1Vo4YtyhzclzcnyESeydt89vphQEhEZ17/Ja0z63QByC1cUEi7oiizX\nwxz2+bp9GOPfF46XtCKm2b+tLfpa8b3uyyczJKnk6cvJcvPOkhxDnCiP8mQlvV47I+zWUHK4IIDh\nAKxUXWzPvqYoVc+6dcBvfiO3E04AHnssOvRE6bmMGQP8618SPjp1KvCPfwQeB6Vi7MPMtrB5nIg6\nc6mPFyGTiluIaBqAuwGM9204Y8YMtLRIFbTa2kYwN4Y2Wl+fH9rU2ioeG98ioHG44YKGOJFlGyJm\nW3v9nmIwHoNCcPszayTttZeEC9rFQlzCPASdTakiy7RRipcqCcV4Hwxx4YJ77ZW75EBU/2F977VX\n/O9ulCHuw6xzWVMjYXc77JA/HjfPxzBwoNgRdrhgc7OUMjfPfbiTLXYJd5ukIsuIu/p62WfVqiBX\n0D2WOJEVVrAiSQhimCdrr71yvaFhbRghN3So/1q3S+TbnHhisrDefv3y958/vwkPPNCUlyuXBmmI\nrJsAPE9E/8g+PwvAjSm0qyhlY+1aCf363e8kDGzOHFkZXlGi6NMH+POfpRDGEUcAf/+75KsoFeMl\nIprKzM8CABEdAuCFmH2S0gzA9mXvln3tI5h5s/X4fiL6PRHtwMxr3cZmzJiBtWulemVjI3DrrdFG\noFtSfeVKuf7MzHlcTpaNW/giLmQxypN18snx/UUxbVrxVf4MZn93zaowOnPm2mb06OBxkpysqEIF\nhYSHlhLSbPdZqJhOM1zQR20tsOOO4ULT9rgUu9YVIPaBi1uxDgDOPlv2Wb062NeErra1yf3AgbKm\nZthYgdKrC5o27PWqNmyQc+VuE0ZtrUzk3HtvbrU/t/CF28bQoXL85jtofzZu0Y8kS6IYITdypD8k\nNExAu8fqY/Bg/6TL3ns3orGx8aN112bOTC8Ir+SfHWb+CYCLAazL3i5m5stLbVdRysG6dcD3vgeM\nGyfVsubOlcVnVWApSSECvvQlCSc991zgL2kFpynFcCCAfxHREiJaAuAZAAcT0WtE9GqJbc8FsAcR\n7U5EDQAuADDL3oCIhluPpwAgn8Ay1NXllpouxFPQ3p5r6BXiyQrLyYrLQ7ANJrsKWynelFIFFhAY\nSGZMxqB1MeemUiJrt91kMgaQCIl9983fxuctNLieh6THkcZaZtOnBx7DpJQ7J+sTn/DnVRnMAs3m\nui7UExe29lIYvXuL0D/DKntj+jYh5b5CKkC+JysNkbVunVQnNQua2x45IL9aqbv/hg3y2Fyz7lh9\nv1nG427EZZ8+Upl3+vTCz7/xZPkwHtC4oh5RmH07s/BFGp4sAOgLYCMz30BEOxHRGGZeHLVDXGlc\na7uDAfwLwPnMfFdK41V6GFu2AFdfLRUDzzhDxJX5QVaUYjjxRODxx4HTTgMWLJCy7+XOl1DyKNGv\nEg4zdxDRpQAeQvA/9SYRXSJv87UAziOiLwJoA9AK4PyoNm2RVQhGULmzxElzdGprJaQuabig3W81\n09EhC/FGiQGTy1bpcEF3rZ4kuDlZSY+jmGvM7bMYfAbykCGB8V5u9t5bxE2xnqw0rxE7fNBH2uGC\n7kSDb922KM9kTY2Is2HDgoW2Tf9xOVmm8IYharHrKExfvj4mTZLrqNBQUBtmiQgA8ouZlavwRRol\n3H8AqTC4J4AbANQD+CuAwyP2SVQaN7vdFQAeLHWcSs+kvR34f/8P+OEPZXbm6aeBPfes9KiU7sLE\niVIQ4/TTJQ7/j38sbY0YpTCY+T0iGgJgJKz/M2Z+KaX2H4D8t9mv/dF6/DsAv0vaXn29/CYtXVrY\nOIhkPze0zIS9xCWM19SIcWE8WnGFL8plcKRN797hhSaAwBBbs6Y8ImuHHWRR23Lhy8lKUiUxzLNX\nSJ/F4LtujjsuOmcuzf6B3AqehbZlf7/69pXJ2WLGs8su+V7LsGISQDrhgraX+7jj/BWRzdpmYZ6s\n1tbwSqNmzL59TzklnQmZKJFlxljsZwsE53zlyvx8tXJNwqRhDpwN4AAALwEAM39ARHFO5o9K4wIA\nEZnSuO76I5cBuAPAwSmMU+lhPPSQrHE0bBgwezZw4IGVHpHSHRk+XAqmnHuuVEG79dbiZ/KUwiCi\nHwG4CMAiyCLEQIqLEadNXZ0YwHPmFLaf8WLYoXZ2KXdjnAwb5t9/5EhZd6tvX+k/TmT17Qvst19h\nY+xszj03meBglqU4ykHY+mJp4eZkFRL2WGxIZynG5uGH55fTr6nxL1xcLqKq5CXZ1zBtmtwX+l0F\nZLmBKFHlPk8jXLC+PsiPCvsdiPNkbdni9wpH5WQBucsrlEJUuKAZY1oVNt02yvWfnYbI2s7MTEQM\nAESUZNk+X2ncnMhVItoVwFnMfEw21l1RErFgAfDVr8oCwr/4hYQHVnvYi9K16d9fhPxnPysx6v/8\npz9cQ0mdTwAYy8wFzJVXjlJ+h9rbJd/BbcuILCA8BLpPH1nvKZMBbr89WQl3t8rq+PHpGVNpkEZu\nV7URVvjC9mQlMbj79St+AeVSrlF7AexKUcyCwva+gOR+GZE6bBiwcWPyNqZOBXbeOX47n8jasiX/\n862rSx4dEXdtmHbCQv62bMnPeUtaXTAt4ioYJs1DDWvb4J6rcq2FmobIup2I/ghgMBF9DsBnAVyX\nQrtXAfiW9TzytM6YMeOjx42NUilE6Vls2QL89KfAH/4AfPObwJ13llZqWFEKoaFBimF84xvA0UeL\nJzXJn213pqmpCU1NTeXs4nUAgwGsLGcnadOnT5CcnoSwnCzzXtI2zP5JC1/YDB/ur7BWzSRZd6ea\n8XmyknioSgnfqpYJyWI/t1I8Wb6qmhMnFrasy5gx0W0bfN+9bdvyvbNHHJF8Ie36+miRG7cYcWur\n3+uYZJ2sNEgS9lyKyLKP33588sm5eWhpUrLIYuZfENEJADZCYte/z8wPx+wWWxoXkud1KxERgKEA\nphFRGzPPggdbZCk9j3vvBS67TCr5zJsnVZ0UpbOpqZHiKj/5ifw5PvJIbhnnnoY74ZVmadwsPwXw\nMhG9DmCbeZGZzwjfpfL06iUFUwrBzcmyRZYxPgql3GsuKYURV10wqSerlLzQahFZxeYF1tQEhT8K\nPZZyCvKocEHDkCH5HsikAguQcM0ooiZmamok1NOXkxVVXTBNkuRklSKyRo0CXn89aMtQzqiTkkQW\nEdUCeISZjwEQJ6xsPiqNC2A5pDTudHsDZv4o8IGIbgAwO0xgKT2X5mbgK1+RfINrrwWOP77SI1J6\nOkTAd78ribVHHgk8+KBUvVLKwo0AfgbgNQBdpFyDzBgXYgiHFb4AisuhMQbsIYeUViSh2qkWwVAK\nZ51VeHXBUqiWc1ZIsQwbU0mzGMHUv7+/zH458I3vgANKazNu0iTqszXXVTGFL9IkyltWisi64ALZ\nb8gQ4KmnOq/aaEkiK1viNkNEg5g5cZHOhKVxc3YpZZxK96OjQ8ICZ84EvvhF4K9/7dzkWkWJ49JL\nJQTh2GPF06qFV8rCFma+utKDKIRilo4gEsPRJ7LsnKxC6Ql5g10pXND3OZo8vEILXxTL6NGllYBP\ni2LHYM5TsYUv9tmnuH6TjMvGd12W24aJ8mRt2iT3vnDDuMIXaREXLmg+22J+79xQ0C4hsrJsBvAa\nET0MoMW8yMxfjtoprjSu8/pnUxin0k145RXg85+XHJgnnlAvgVK9XHihVGuaNg244w7gqKMqPaJu\nx1NE9FPIIsF2uGAqJdzLwSGHFL5PezuweXNuCJVZ76W2tjCjY+ede84yA9XilUlKXDGPzvBk7bST\n3CpNsR7WUst8l4u4cMHjjy9fXpAh6tpZv17uXZFlhM+2bfIbVO5wwThPVnt7aWMwIquzro00fmrv\nyt4Upay0tMh6VzfcIDkv//7vlV9gUlHiOOssEVrnnQfceGNQGlhJBRNgM9V6rWpLuBeLCZ0aNSr3\n9UGDgnWyknLMMemNqyvQlTxZI0eGv9dZ4YLVQrHhgkZkVfu5cq/LzhC2UZ6sAw7wVw+trZVzuWaN\nhBKWs3pkba3khYVVMa2rk1DrUgSSOQdV78kiolHMvJSZb0xzQIriY9Ys4MtfBg47DHj1Va3apnQt\njjtOruEzzwSuugqYPj1+HyWebD5wt8cYnG4SvDF4qmnGXimcY45JVoSkM8IFq4ViS/TX1ooXbPv2\n6irznyRcsLPG4Ot7wgT/PrW1sn1rqyyyXM7fGpMPNmKE//26OvlcS/kOdKVwwbsBTAYAIrqTmc9N\nZ0iKErBkiRS2eOst4PrrxVhVlK7I1KlSbXDaNGDtWuBLX6r0iLoHRHQqgIkAPspoYOYfVm5E5cEV\nWAcdVB1hXdWMbRD6FlmtFpJMGvYkT9Y55xRf+bJPH+D996XCcDUt4ZKkumBnUWjfzMDzzwN77FGe\n8RjMb1zY52Y8WaWI584WWaV0Y+vZIlJ5FSWclhbg+9+XYgEHHyzeKxVYSldn332Bp58Gfv1rYMaM\nrhXKVI0Q0TUAzgdwGeQ/6eMAdq/ooMqEK7LGjZMKloB6sqIw37GTTqrsONKgra1n5NP16lX8cQ4f\nLvu3tFSXJ8ulK4ksw7Zt8duUghE+YQLbiKxCytqH9dEVRBaHPFaUoslkgJtvFtf1woWy5tV3v1td\nM1KKUgqjR4vQmjUL+M//rI5KXl2Yw5j50wDWMfNMAIcCGF/hMZWFqMpjKrKiIer64sRUmKxm4VAt\n1NdXn8hyv6OVtGmKFVmliJs0MCKrlO+yOYbO+s0sRWTtT0QbiWgTgP2yjzcS0SYi2pjWAJWew8MP\ni9fqV78CbrlFxFZUIrCidFWGDQOamoBFi4CzzxaDQCmK1uz9FiLaFUAbgF3SapyITiait4joHSL6\nVsg2VxPRAiKaR0ST0urbZYcdosZZrl67NnYOSnc5R5U2dLsCRBIyWC0i64ADcqsgn302MHly5cZT\njMgaPlxClMvJLrtEV4uuq5OJ+FI+V7Nv1YssZq5l5oHMPICZ67KPzfOBaQ5S6d489xxwwgmSo/Lt\nb0vs7xFHVHpUilJeBg6U9bOGDgUaG4EVKyo9oi7JP4loMICfA3gJwBIAN6fRMBHVAPgtgJMgOV/T\niWiCs800AGOZeRyASwBck0bfLkceCey/f9RYy9GrUk2Yz1hFVjybNlWX12/CBPmdN/TuXXzOWRoU\nI7J22qn8Y+7VK/p3zniwSvkOmO9RZ0WQ9IAUSqVamTNH4uQ/8Qkpb/3GG8DHP64Gg9JzqK8H/vQn\n4NRTgUMPBV57rdIj6low84+YeT0z3wnJxZrAzN9PqfkpABYw83vM3AbgVgBnOtucCeCm7FieAzCI\niIan1P9H7LZbtMGov5nRdIfzY4xCFVnJ0TQDP/Z6e0k455zyLdJcCObzTGPR5mLXYSuUiomsuDAM\nIvokEb2SvT1NRPtWYpxKumQywH33ScnaCy8UUbVgAXDJJfrnofRMiKQIxo9+FJR6V6IhooOJaGfr\n+acB3A7gR0QUEVhXECMAvG89X5Z9LWqbZs82Zac7iAglGlNiWz/r5FSLJ6vaKNST1atXdVx3AwfK\nhHwagq+z7M2KpIJaYRjHAfgAwFwiuoeZ37I2exfAUcy8gYhOBnAdchecVLoQra2SY/V//yc/fF//\nOnD++SqsFMXwqU9JxbhzzhGv7re/XR1/bFXKHwEcDwBEdBSAKyAVBicBuBbAeZUbmp8ZM2Z89Lix\nsRGNjY2ptT16tCwWqvjpDt+jsWO7fvGOzuL442W5jEqG5FUzXbmqbRo247nn5rbT1NSEpqam0hv2\nUKmv7EdhGABARCYM4yORxczPWts/iwrMDiqls2QJ8Ic/SEjUlCnA1VcDxx7bPf70FCVtpkyRHMWz\nzwZeeEG+N4MGVXpUVUktM6/NPj4fwLXZkME7iWheSn00AxhlPd8t+5q7zciYbQDkiqy0iUoWV7rH\n/01NDTBmTKVH0TUw68dpuKCfQsMFuxuuh9Od9Jo5c2ZqfVUqXDBJGIbNfwC4v6wjUlKjvR245x7g\ntNOkGk17O/DMM5Lkf9xx3eMPT1HKxYgRwFNPyQKlBx4IvPxypUdUldQSkZkkPA7AY9Z7aU0ezgWw\nBxHtTkQNAC4A4AZzzgLwaQAgoqkA1jOzljBRlApzwQXVvQB1JenKnqyuRtU7n4noGAAXA9B6c1XO\nokXADTfIbfRo4HOfA26/Hejbt9IjU5SuRa9ewO9+B9x6K3DiicAPfwh84Qs6QWFxC4AniGg1pIz7\nUwBARHsA2JBGB8zcQUSXAngIMiF5PTO/SUSXyNt8LTPfR0SnENFCAC2Q/yqlytDvTc9DP3M/hxwi\nE3lK51ApkZUkDANEtB8kvv5kZl4X1WA5492VcFpagDvvlLCm+fOBT34SePDB6qhEoyhdnQsukDVW\nPvUpYPZs4PrrZS2RrkK5Yt2Z+SdE9ChkTayHmD+am62B5Gal1c8DAPZ0Xvuj8/zStPpTyoMa3Ioi\nfOxjlR5Bz4K4An5DIqoF8DYkzGM5gOcBTGfmN61tRgF4FMCFTn6Wrz2uxHH0VDIZ4IkngJtuAu6+\nGzj8cOCzn5XwQK3moyjp09YG/OQnwDXXSF5jV13qgIjAzF1w5KWh/1GV45ZbJMn9vKorhaIoSjWS\n5v9URUQWICXcAfwaQRjGFXYYBhFdB+AcAO8BIABtzDwlpC39A+sE3noL+MtfgL/9TZLxP/MZ8Vzt\nvHP8voqilM7zzwMXXSSVxn7zGwnL7UqoyFI6m1tukcm/c8+t9EgURekKdAuRlSb6B1Y+PvxQ8kL+\n+lfggw9EVF14YfSq3IqilI/t24Ff/EKWQ/jGN4Cvfa3reJBVZCmdzS23SI7jOedUeiSKonQF0vyf\nqthixEr1smmTeKxOOgnYay+pbnb55cD774txpwJLUSpHQwPwne8Ac+cCc+ZI+e5bb9WyvIqiKIpS\nTajIUgDI7Pjs2ZJov9tuUhXwoouA5mbgxhulwpku7Kco1cOYMfKdve468WoddBDwwANanldRXLpi\n/qKiKF0fFVk9mEwGePJJKQ29667Az34GHH20lGKfPRuYPl3LrytKtXPMMbKA8Xe+I+GDkydLiFR7\ne6VHpijVgU48KIpSCTQnq4fBDLzyCnDzzRJiNHiwlIe+4AJg990rPTpFUUqBGbj/fuDKK4ElS2St\nuosuqp51UTQnS+lsbrlFPFkXXFDpkSiK0hVI83+q6hcjVtJh4UL5s7nlFmDLFilgcd99up6VonQn\niIBTTpHbCy9IKOG++wKHHioFa045BRg4sNKjVJTOo65OvbqKolQG9WR1Y5YuBf7+d+C224D33gM+\n8QkJAZw6FajRQFFF6RFs2QLccYd4rp9+GjjiCOCss4ATTpC8rs5EPVlKZzNrFtDSIv99iqIocWgJ\ndwf9AwtYsgT4xz9EXL39NnD22cD550veRp36LRWlR7Nxo3iwZ80CHntMci6PPVYWFD/kEGDChPJO\nwKjIUjqbp5+WpUh0MWJFUZKgIsuhJ/+BmRyre+8F7rpLvFdnnCELLx5/fNdZP0dRlM6FGZg/X8TW\nM89I8YzVq6Vwxv77y22//WQZh7QK4KjIUjqbTEZuOsmoKEoSVGQ59LQ/sJUrgaYm4JFHZFa6d2/g\n1FMlBOjII/XPRFGU4li9GnjxReDVV4PbO+8AO+8sYmuvvYA995TbhAnAsGGFlcdWkaUoiqJUM91C\nZBHRyQCugpSRv56Zf+bZ5moA0wC0ALiImeeFtNVt/8A6OiTs7/nn5fbUU7Io8JFHSpjPqacC48dH\nt9HU1ITGxsZOGW9XRc9RPHqOoumu56e9HVi8WLxeb70lv0fm1tYGjBsnv0Hjx8tj83zw4Py2uorI\nIqIhAG4DsDuAJQA+wcwbPNstAbABQAZAGzNPCWmv2/5HpUV3/f6kiZ6jaPT8xKPnKJ40/6cqUv6A\niGoA/BbASQAmAphORBOcbaYBGMvM4wBcAuCaTh9oJ5HJAMuXS7jO3/8OXHEF8JnPAAcfLIbKGWcA\nDz0khsuf/iSzzbNnA1/9arzAAuRLpUSj5ygePUfRdNfzU1cnwunMM4FvfUt+g+bMkd+hd98Ffvtb\n4KSTRIzNmiXr7v33f1d61CXzbQCPMPOeAB4D8D8h22UANDLzAWECS0lGd/3+pImeo2j0/MSj56hz\nqVRg2RQAC5j5PQAgolsBnAngLWubMwHcBADM/BwRDSKi4cy8ojMGeNVVInza28WblMn4FzQkyr8Z\nmGX/9naZ8d22TaoctbQAmzcDa9bIbf16YIcdgJEjgVGjpOLXUUcBl1wi4TlDhnTGESuKohTGjjvK\nberUSo8kdc4EcHT28Y0AmiDCy4VQoclKRVEUpbqplMgaAeB96/kyiPCK2qY5+1qniKy+fUX41NbK\nrabGL6J8N3ubujqgvl7ue/UC+vWTtvv3DwyUHXaQbRRFUZSqYJiZ0GPmD4loWMh2DOBhIuoAcC0z\nX9dpI1QURVGqmorkZBHRuQBOYubPZ5//G4ApzPxla5vZAH7KzP/KPn8EwDeZ+SVPexrsriiK0gWo\nlpwsInr4/7N35mFyVFX//57JZLIvJCQBErJABGSTsAkEZAATFtlVNpVNERX1/bm9vvqqBJEXBH1f\nFVcQERdANlkEISAEiQIJECBAwk5CEgiBhOyZmcyc3x+nD3X79q2le6qne2bO53n66e7qqlu3blVX\nne89554LYIy7CCKavgPg98w8wln3HWYeGShja2Z+g4hGAbgXwBeZeXZgPXtGGYZhdBPyek7VypO1\nFMB45/u4wjJ/nW1T1gFQPw9twzAMo3vAzNPifiOi5RqeTkRbAXgrpow3Cu8riOivkIiMEpFlzyjD\nMIzeR61iyecCmExEE4ioCcApAG731rkdwOkAQET7AXi3q8ZjGYZhGL2a2wGcWfh8BoDb/BWIaCAR\nDS58HgRgOoBnuqqChmEYRn1TE08WM7cT0RcBzESUwn0BEZ0rP/MVzHwXER1FRC9BUrifVYu6GoZh\nGL2OHwK4gYjOBrAIwEmAhAcCuJKZj4aEGv61EArYCODPzDyzVhU2DMMw6oseMRmxYRiGYRiGYRhG\nvdDtUs8S0RZENJOInieie4hoWMx6rxHRU0Q0j4jmdHU9awERHUFEC4noBSL6Zsw6PyOiF4noSSLa\no6vrWGvS2oiIDiaid4noicLrO7WoZ60goqsK41GeTlin115Dae3T268fACCicUR0PxE9S0TziejL\nMev1iusoy325pxN3TSQ9z4noW4XrYwERTa9d7bsWImoo3DtuL3y3NnIoTOdzY+GYnyWiD1obRRDR\nV4joGSJ6moj+TERNvb19Qs/tStqEiPYstOsLRPSTTDtn5m71goRx/Gfh8zcBXBKz3isAtqh1fbuw\nXRoAvARgAoC+AJ4EsJO3zpEA7ix8/iCAR2pd7zpso4MB3F7rutawjQ4EsAeAp2N+7+3XUFr79Orr\np9AGWwHYo/B5MIDne+u9KMs9pze84q6JuOc5gJ0BzIOEYU4stCHV+ji6qK2+AuBPeh+xNippn98D\nOKvwuRHAMGuj99pmm4Lt21T4/hfImNJe3T6h53YlbQLgUQD7FD7fBcmSnrjvbufJgkwSeU3h8zUA\njo9Zr7dNEvneBM/M3AZAJ3h2KZrgGcAwIhqD3kOWNgLk2umVsKSfXpWwSq++hjK0D9CLrx9A5pVi\n5icLn9cBWACZ49Clt1xHWe85PZqYa2Ic4p/nxwK4npk3M/NrAF5E6VyaPQ4iGgfgKAC/dRZbGxUg\noqEADmLmqwGgcOyrYW3k0gfAICJqBDAAkpW7V7dPzHO7rDYhyTI7hJnnFtb7A+L1x3t0RxFSNEkk\ngLRJIucS0TldVrvaEZrg2Tds4iZ47i1kaSMA2L8QwnQnEe3cNVXrNvT2aygLdv0UIKKJkB7ER72f\nest1lPWe02twrolHAIyJeZ73luvD5/8AfANivyjWRhGTALxNRFcXQiqvIKKBsDYCADDzMgA/BrAY\ncqyrmfk+WPuEiNMScW0yFnL/VjLdy2s1T1YilDxJpE9c5o6p7EwSSUQLODBJpGF4PA5gPDNvIKIj\nAdwKYIca18noPtj1U4AkvflNAP6j4L0wejn+NUGlkzT32kxcRPQRAMuZ+Ukiak5Ytde2EcRm3RPA\necz8GBH9H4D/Qmmb9Mo2IqLhEA/NBACrAdxIRJ+AtU8WqtImdenJYuZpzLy789qt8H47gOUaVkIZ\nJ4kEoJNE9mRyneC5h5LaRsy8jpk3FD7/HUBfIhrRdVWse3r7NZSIXT9CIVTlJgB/ZOaSOabQe66j\nLPflXkHMNRH3PO8t14fLVADHEtErAK4DcCgR/RHAm9ZG77EEwOvM/Fjh+80Q0WXXkfBhAK8wk4ND\nywAAIABJREFU80pmbofYvgfA2idEuW1SUVvVpchKwSaJDGMTPKeT2kbuuBAi2hcy4HFl11az5hDi\nxxX19msISGgfu37e43cAnmPmn8b83luuoyz35d5C6JqIe57fDuCUQma0SQAmA+jRWYKZ+dvMPJ6Z\nt4NcJ/cz86cA3AFrIwBA4R7xOhFpdMBhAJ6FXUfKYgD7EVF/IiJI+zwHax+g9LldVpsUQgpXE9G+\nhbY9HQH94VOX4YIp2CSRAdgmeE4lSxsB+BgRfR5AG4CNAE6uXY27HiK6FkAzgJFEtBjA+QCaYNcQ\ngPT2QS+/fgCAiKYC+ASA+UQ0DxKG8W1ICEuvuo7i7jk1rlaXk3BNBJ/nzPwcEd0AMRDbAHyBCym9\neiGXwNrI5csA/kxEfSGZ9M6CJHvo9W3EzHOI6CZIdry2wvsVAIagF7dPzHP7Ekg4ZTltch4ku2V/\nAHcx892p++6B7WkYhmEYhmEYhlEzumO4oGEYhmEYhmEYRt1iIsswDMMwDMMwDCNHTGQZhmEYhmEY\nhmHkiIkswzAMwzAMwzCMHDGRZRiGYRiGYRiGkSMmsgzDMAzDMAzDMHLERJZhGIZhGIZhGEaOmMgy\nDMMwDMMwDMPIERNZhmEYhmEYhmEYOWIiyzBygoheJaJDa10PwzAMwwhhzynD6DpMZBlGjbGHnmEY\nhlHP2HPKMMrHRJZhGIZhGIZhGEaOmMgyjHzZl4ieJaJ3iOgqImoCACI6mojmEdEqIppNRLsVlv8B\nwHgAdxDRGiL6emH5DUT0RmH9WUS0c9qOiehqIvoVEc0slPUAEY2v5sEahmEY3Q57ThlGF2AiyzDy\n5TQA0wBsD2BHAN8hoj0AXAXgHAAjAPwGwO1E1JeZTwewGMDRzDyUmX9UKOeuQhmjATwB4M9l7P8C\nACMBPFXGdoZhGEbvwJ5ThtEFEDPXug6G0SMgolcB/A8zX1n4fiSAywHMBLCCmc931l0I4Bxmfqiw\n3aeZ+f6YcocDWAlgGDOvTdj/1QD6MfNphe+DAKwGMIGZl+ZykIZhGEa3xZ5ThtF1mCfLMPJlifN5\nEYBtIGEWXyeilYXXKgDjCr+VQEQNRHQJEb1ERO8CeBUAA9gyw/5f1w/MvB7y0AvuxzAMw+iV2HPK\nMLqAxlpXwDB6GNs6n8cDWAp5oPyAmS+O2cZ3J58G4BgAhzLzYiIaBmAVACpn/0Q0GBL2sSxj3Q3D\nMIyejz2nDKMLME+WYeTLeUQ0lohGAPhvANcD+C2AzxPRvoCERxDRUYUwCQBYDmA7p4whAFoArCqs\nczFKH3BxHEVEBxQGMl8I4GELwTAMwzAc7DllGF2AiSzDyA8GcC0ktv0lAC8CuIiZHwfwGQA/J6KV\nAF4AcIaz3cUAvlsI0fgqgGsgg4yXAngGwL/LqMO1AGYAeAfAFACf7MwBGYZhGD0Ke04ZRhdRF4kv\niOgqAEcDWM7MuxeWXQpxRbcAeBnAWcy8pna1NIz6pjCg+HVm/l6t62IY3QkiOgLATyAdj1cx8w9j\n1tsHYkyezMy3lLOtYRj2nDJ6F/XiyboawOHespkAdmHmPSA9Ld/q8loZhmEYPRoiagDwc8gzaBcA\npxLRTjHrXQLgnnK3NQzDMHofdSGymHk2ZMCku+w+Zu4ofH0EkuXGMHo1RPRMYQJHfa0tvJ+K7PHw\nhmFE7AvgRWZexMxtkPEpxwXW+xKAmwC8VcG2htFrsOeUYQjdJbvg2ZCHl2H0aph514Sfr+uyihhG\nz2EsnJTSkPTW+7orENE2AI5n5kM0MUDWbQ2jt2HPKcMQ6sKTlQQR/TeANma+ttZ1MQzDMHolPwHw\nzVpXwjAMw+g+1LUni4jOBHAUgENT1jP3s2EYRjeAmbPMo9OVLIXMFaSMKyxz2RvA9UREkMlWjySi\nzRm3tWeUYRhGNyKv51Q9ebIIziR2hYxN3wBwLDO3pG3MzPaKeZ1//vk1r0O9v6yNrI2sfar/qlPm\nAphMRBMK8/acAuB2dwVm3q7wmgQZl/UFZr49y7ZOGfZKeNn/x9rI2sfaqB5eeVIXniwiuhZAM4CR\nRLQYwPkAvg2gCcC90nmIR5j5CzWrpGEYhtHjYOZ2IvoiJKOtpmFfQETnys98hb9J2rZdVXfDMAyj\nfqkLkcXMpwUWX93lFTEMwzB6Hcx8N4AdvWW/iVn37LRtDcMwDKOewgWNKtHc3FzrKtQ91kbpWBsl\nY+1jGJVTrf/Pk08C991XlaK7HLvHJGPtk461UddCeccf1gIi4p5wHIZhGD0ZIgLXX+KLqmPPqNpx\nxx3AunXAqafWuiaGYXQH8nxO1UW4oGHUKy0twK23Ao8+Cjz7rLzWrQOGDwe22AIYOxb40IeAQw8F\npkwB+vSpdY0NwzAMpa2t1jUwDKO3YiLLMAIsWwb8+tfAFVcAu+4KTJ8OHHYYsPPOIrBWrZLXa68B\ns2YBZ5wBvPkmcNppwLnnyjaGYRhGbWlJzU1sGIZRHUxkGYZDezvwv/8LXHIJcPLJwP33i7Dy2WIL\ned9rL+CjH5XPixcDV10FHHEEMGEC8LWvAccfDzTYyEfDMIya0WiWjmEYNcDGZBlGgZdfBs48U0L+\nfv97YOLEysrZvFnGAfzgB0BHB/D97wNHHw1QrxuJYhjF2Jgso6u57jqgXz/gxBNrXRPDMLoDeT6n\nrI/dMADcfDPwwQ/Kg/j++ysXWID0mp5wAvDYY8D55wPf+Q4wdSrw+OO5VdcwDMPIiOlbwzBqgYks\no9fz618DX/oSMHMm8JWv5BfeRyThgvPmAZ/5jHizPvtZYMWKfMo3DMMw0jGRZRhGLTCRZfRamCWU\n77LLgIceAvbcszr7aWgAzj4bWLAAGDhQkmL88Y/24DcMwzAMw+ip1IXIIqKriGg5ET3tLNuCiGYS\n0fNEdA8RDatlHY2eBTPwjW8Af/0r8K9/AdtvX/19Dh8O/OQnwF13ibA75hhg6dLq79cwDKM3Yx1a\nhmHUgroQWQCuBnC4t+y/ANzHzDsCuB/At7q8VkaP5aKLgHvvlfFXW23Vtfveay8Zr7X33sAee8jA\nbMMwDKM6mMgyDKMW1IXIYubZAFZ5i48DcE3h8zUAju/SShk9ll/8QrIH3nNPlIq9q2lqAmbMkDrM\nmAGcdZZMcmwYhmHki4kswxBeftnmjutK6kJkxTCamZcDADO/CWB0jetj9ACuvVbmwLr33q73YIXY\nc0/JOkgkn+fNq3WNDKP3QURHENFCInqBiL4Z+P1YInqKiOYR0Rwimur89pr7W9fW3MiCiSzDEObM\nAV57rda16D10pyn6Em+TM2bMeO9zc3Mzmpubq1wdo7vxwAOSPfD++4FJk2pdm4jBg4Hf/U7CBqdP\nl8mQP/WpWtfKMDrPrFmzMGvWrFpXIxEiagDwcwCHAVgGYC4R3cbMC53V7mPm2wvr7wbgBgDvL/zW\nAaCZmf1oDKNOMJFlGBE2Z2fXUc8iazkRjWHm5US0FYC3klZ2RZZh+CxcCJxyigiZXXapdW3CnHoq\nsNtuMsfW3LnAj38M9O1b61oZRuX4HV4XXHBB7SoTz74AXmTmRQBARNdDwtXfE1nMvMFZfzBEWCmE\n+o4KMXoAra0SgfGRj9S6JkZ3J69paox06qmpqfBSbgdwZuHzGQBu6+oKGT2DFSvkwXTJJcChh9a6\nNsnsuqsIrJdfBqZNA1aurHWNDKN7QEQDiGjHCjYdC+B15/uSwjK//OOJaAGAOwCc7fzEAO4lorlE\ndE4F++80S5dKR5LRc1m5Elizpta16B50dEiH6oYN6ev2RsyT1XXUhSeLiK4F0AxgJBEtBnA+gEsA\n3EhEZwNYBOCk2tXQ6K5s2iQTAp9yiiSX6A4MHw7ccQfwn/8JHHCApHzfbrta18ow6hciOgbAjwA0\nAZhERHsA+D4zH5vXPpj5VgC3EtGBAH4AYFrhp6nM/AYRjYKIrQWFZE5FVDOk/amngNWrgZ12yq3I\nHgdz9zYubRxNNpYtAx58UD5v3ChzUxrFlPs/YAYWLQImTqxKdWpONcPa60JkMfNpMT99uEsrYvQo\nmGUS4HHjgAsvrHVtyqOhAfjRj2Ts2NSpMp/XfvvVulaGUbfMgIT9zQIAZn6SiLKOvFwKYLzzfVxh\nWRBmnk1E2xHRCGZeycxvFJavIKK/FuqRKLLyxsYcJdPQ0P1F1ooV8t7RYeFeSbiZ8zo64tfrzZR7\n/SxbBjz8MDB2bM8cwlDNsHb7qxo9lu9/X8Lufv/77vtQOu884MorZeLiu+6qdW0Mo25pY+bV3rKs\n0mMugMlENIGImgCcAglXfw8i2t75vCeAJmZeSUQDiWhwYfkgANMBPFPpQcRx++3Aq6/G/24iK4y2\nC1H9G9x33y3eyDgaC13i7e1dU5/uinueW1trV496ppzOho4O4JFH5HOt23PdOuC224AXX6xtPcqh\nm5qehpHMdddJxr7bbgMGDKh1bTrH0UeLkXXWWcANN9S6NoZRlzxLRKcB6ENE7yOiywH8O8uGzNwO\n4IsAZgJ4FsD1zLyAiM4los8WVvsoET1DRE8AuBxR+PoYALOJaB6ARwDcwcwzczwuAMD69RISGH8M\nee+xZ6GerHpm1arIWxVC628iKxkTWemUI7JaW6N2bGurTn2Ujg7gjTfif1+7VsbZdXas+j//Cbz7\nbufKyEpdhAsaRp48/DDw5S8D//hHfcyFlQf77y+ZpY48Um40n/50rWtkGHXFlwD8N4AWANcBuAdA\n5iBhZr4bwI7est84ny8FcGlgu1cB7FFZlbPTr5+ML3H5978lnHjrrau99+4NkbzqXWRlZfPmWteg\nvnFF1iOP1Md0La2t4onUiJoFC4DRo4GRI2tTn3Iie1xBVm2RtWIFMGsW8NGPAk1Npb9v2iThip2d\nTHnpUmD8eBn/Xm3Mk2X0KF56SVKg//73wO6717o2+bL77nIDuvBC4Oc/r3VtDKN+YOYNzPzfzLwP\nM+9d+Lyp1vXKi0GD5N3twV20SO53QM8REHnTXcIFs2TB602erFmzKs+W2dEB7LCDvOqFm28Gnngi\n+v7kk8Bzz9WuPpWOTay2Z1DFU5yXadMmYNgwea8U7awKibhqYJ4so8fw9tvi6Zkxo+fOJfK+98kD\n6JBD5EZ53nm1rpFh1B4iegCBMVjMXHeTNqiR3KdPedsNHixe7BEjomXas2wiK57u4Ml6/vls6zU2\n9g6R9cYbIpYqyZbZ0SHejkmTkkPPupr164u/1zIJS2jfc+ZIgoujj47G/wHF/5ulS4Fttqle3bWz\nwffaK5s2ifepM+dV75ld1eliIsvoEWzcCBx3nLiZP/e5WtemukycCDzwgAgtwISWYQD4uvO5P4CP\nAqjLwKr775cH/VFHZd+GWQwfP1TMRFYy2i71PiYri3CKuwZ6Kv36Vbadm32xns+5L1RuugnYZx9g\nwoTq7TNJWLS1iR21cSMwZEi0XNtw5Ehg8WJgl10iz3reqIfKF6RKR4dcF53paNA26JYii4h2Y+b5\neZZpGGm0twOf+hSw7bbA//xPrWvTNbhCq6EB+Pzna10jw6gdzPy4t+hfRDSnJpVJ4e23y9+GWXrn\nfeNCDe5yjMn77hNjPcdpuuqeeg8XzGo09unTOzxZQOdEVt+++Xlb1q+XrHZjxuRTnuKPi2prA+bP\nl7FCbt2XLxfvdR6p0/U/ELpf6D7jrq9DDpEMmNUUrh0dQP/+8WOuVEBXUoeWFmlDvWd21f8o7zFZ\nvySiOUT0BSIalnPZhlECs3iu3n0XuOaa7puqvRImTpRe8YsvlmM3jN4KEY1wXlsS0eEA6vYZVIkB\nGPJirFlTfjkrVgBvvVX+dt0RnRtr/fr6TvucxTvFLCKrnsVinlQ6Zqa9XeyAvEJE58yR52ze+PcA\nIvEi+f/p++/PHk6aRtK1o23lX4vMMqFz377SrtW+/pJEVEeH3AcrOa+33ALMmyeiVcvqCnL1ZDHz\nQUT0PgBnA3i80JN4NTPfW2mZRPQVAJ8G0AFgPoCzmNkScxoAgG99S1Ib/+Mflfd8dWcmTQJmzpRe\npkGDgI99rNY1Moya8DhkTBZBwgRfhTw36pJyO4M0VMztfR00SMRDW1v5Rkd3npS3EoYOjR/nUQ9k\n7VXvCiO3o0PCtgYOrO5+0mis0DpVb0e9j8ML/QcHDgzXOa/jSPJk6W/+teiuW+02TZswvKNDOhoq\nrcPGjcALL0RldQW59/sz84sAvgPgmwAOBvAzIlpIRCeWWxYRbQNJzbsnM+8OEYWn5Flfo/ty2WUy\nf9RddxXHEPc2dtoJ+PvfZWyWTVhs9EaYeRIzb1d4fx8zT2fm2bWuVxzt7TKXX1Y0XNDtZe7fP/rN\nRFYYNdp22KHrsolVgp7XpPPSVZ6sZ5+V+SVrTaXXaN5jsqolKvyOFj2/1RRZWk7SPkIiS89FtcNu\nmdM9WXn9B7qlJ4uIdgdwFoCPALgXwDHM/ERBLD0M4JYKiu0DYBARdQAYCGBZXvU1ui8//znwy1/K\npHJbblnr2tSePfaQB+Oxx8oA2g99qNY1Mozqk9Z5x8yVPHOqRmeSFvieLDVEOjqiz0uWAOPGpZel\nRtPrr0vvbj2lu87KnXcCe++dbaxMnz71nTAia+KLrkjg0Zn02HnSGZHVp0/l269aJZ22lXrS5s2T\nMg5NyWvq1k+FTLVFTFLZKk5D16LWtdrXX7U9We617R7nunUSGVCNzqe8PVmXA3gCwAeY+TxmfgIA\nmHkZxLtVFoXtfgxgMYClAN5l5vtyrK/RDfnNb8SLdf/9kuzCEPbbD7j2WgkZdOfkMIwezDEJr6Nr\nWK8gq1dXNm40FC7ohv64IisOd1s1JubPBx73U4Z0E9asyZbKmaj+U59nFYBZE18wx881lGXbSlm4\nUKYYqSWd9WTdfbf8L5Ryy3j7bRn3k3ZOXYO+o0O+x4WD5iVs9NqJCxfUiX513JK/blckkMniyaq0\nPdyEGu5x3HGHTBBdDfJO4f4RABuZuR0AiKgBQP/CRJF/LLcwIhoO4DgAEwCsBnATEZ3GzNf6686Y\nMeO9z83NzWjuTamTehFXXQX84AdyI6+HmdzrjQ9/GPj1r2WesAceqGyeEcPIi1mzZmFWFa0uZj6r\naoVXgY4OGXexbl1526nIWrGieJm+pxkdr74KPPJIlFFQDbykjGXLl+efUS1v0gSHtktv82S98ook\nbDj11PLr0hmDfsmS4msUEDG8YgWw/fad3//GjcCAAcnbu2OyKmXDBuDllyv3ZmkZQ4dG3/3j8kVW\n0jiySs5JyCuU9B/QkORnnpF2dq+drvZkhfbx5ptyLXVGZLn4YrHSTok08hZZ9wH4MAB9hAwEMBPA\nARWW92EArzDzSgAgolsKZSWKLKNn8rvfAeefLx6srDfs3siJJ0qP+fTpwOzZkhLWMGqB3+F1wQUX\nVG1fRPQRALtA5skCADDz96u2wwpgFiPxmGPKG5MFSFj0008Dra0yvigULhiH9uD++9/yrkZTnBG5\nYYPcZ11Dq71dyql1QgSXLL3q3d2T9fDDwP77y+esiS9Wr86nXuUS8tLOny/zK5UrskLX9K23Agcc\nED+XVFtbPtkFN28WkQoAo0aVt21Hh/w/168vFlk+frhgQ0O8iMl6HOvWybpLlgBPPlkqspPm1VNP\nlt8B5I/JylNktbRI5sTddy/dl88DD8i7TuKeFlqYhn8/0ImQ8ybvcMH+zPzeKSp87swteTGA/Yio\nPxERgMMAVMmpZ9Qzv/oVMGOGPPi74/iBruass4CvfAWYNq3Y9W8YPREi+jWAkyGJkgjAxyEREHWF\nGlOVbDd4sCS7UOMgKVOYj67b6uXljfNkher4+OP1kRDBpTd4sl57LRLSWQf9x03mmgUtf8mS8kPD\n1AB2UcMekGNIKzNJZAHxcygBMh552bJI3JQrCLTs1tYosUy5dHRIR0pSPYHi/1jamKysx/HYY8Df\n/lbqTVTcc+HT0RH2sKeFC153XeU2xvLlkmjF3VeatyyPzJGh46hagpOcy1tPRHvqFyLaC0DFiVOZ\neQ6AmwDMA/AU5OF5RWcraXQvfvpT4NJLJUTQBFZ2vvIV4JRTgMMPr54r3DDqhAOY+XQAq5j5AgD7\nA8h8tyCiIwpZcF8gom8Gfj+WiJ4ionmFuSCnZt3WRcdeyHbpD3ZmYO3ayAhzPTKu0Z1mmPoGhVsH\nIN7Id5enGY1ZyXOOrizeqVp6spiz7TdOAPrnM6snK49xMw89VP7E2Wkia84c4K9/TS4jj7oPGVKZ\nl0PPw6ZNUViinoN580rXD9VV53JKO464MVmVGvsrVkRjFOOup6TJy5nFvpoypbSTJS1c8M030+u3\nZo1411xCGRbTzltnRdbo0ZIwJ+6emDd5i6z/B+BGInqIiGYD+AuAL3amQGa+gJnfz8y7M/MZzJyg\nxY2exqWXApdfLgJru+1qXZvux4wZkmnw6KM717tpGHWOduZtKGSzbQOwdZYNC2OHfw7gcEi44alE\n5I9mvI+ZP8DMUyDzb/22jG3fwzci0gyFV16RnmnXI+OLrCxjstrbgZ13do+5eP++hytuYtI8mD07\nvzmrNm6ULIM6941PtT1Za9YUl+uLqvnzgRtukM9Llsh4l1Ad4wxyP7lJVk9WZ3rl3W1DoimJkAfU\nvbZWrSq91uL231nPQiWGeHu7hMNu3Fh67MsCea3/8pdSL07W5AyhcMFKPFkbNki7hkJEV60q/p7m\nyRo/XoSWu78sKdxDHjB/2SuvlCaXCF1f1fRk6f811FlRSYRBFnItlpnnAtgJwOcBfA7A+5m5m+Yu\nMmoJM/C97wFXXw08+GB8DLaRDBHwk58AkycDxx9fP+l5DSNn/lZIlHQZJMPtawiM3Y1hXwAvMvOi\nQife9ZCES+/BzG7E/mAAHVm3dXEzn2XpOXWNIqJikaVlJRkb2rGi40RGjCjed9LcOKHleZAlZCwr\nK1aI4ZTWk963b7KBWSl33inj5JRnnolEFSB1U159tThrnZKWjMAlqycrL5GVR7hgueK20rrr+XVz\nnpVb1ubNQL9+4onSZ6WWEffsXLMGuPfe6Ht7u2xfjsjS/3IlY7L++U/JiOiG/ra1Sfm+JzLJkxWX\nMMRdN65+ixdLqKLLHXcUXz+h7eI8WWkiK1SPO++U8V1ptLaGU9V3F08WAOwDYHcAe0J69U6vwj6M\nHgwz8LWvyZ/0wQeBsWNrXaPuTUMD8NvfioH1sY+l9yQaRneDmS9k5neZ+WbIWKydmPl7GTcfC+B1\n5/uSwrIiiOh4IloA4A4AZ5ezbVTPbJ6sjg4ZX+Jv53pksng2br9dDC7tXddEF1lFVshA/sc/xLCr\nlKwhdFkYPFjeVTyGIBLDubW1OuMu3GNxRZVPXBKE0Nxniu/JyhJOtnlz50SsW37ceXrnnfByFVmd\nOb+VerLuvlve3Y6ErGWoF0gF0tChpZ6YuOfm22/Ly+38cD1Z7pgjF1dgaLigW+e1a6Pfk45D6+WW\n19oKbLVV6XZp4YJxXqIskxEvXRp91qQ+vkfMx78PdWZMVjlTOoTum9USWXlPRvxHANsDeBKA/s0Y\nwB/y3I/Rc2lvB77wBeCppyTJxRZb1LpGPYPGRuBPfwI+/nHgtNOA66/vXHpaw6gniOhpiBfpL8z8\nMoCcRhBFMPOtAG4logMB/ADAtHK2nzFjBlavFoOuvb0ZRM3B9draxEjSTGmyb3mPCxcM4Rp92kut\nvd2dEVlvv915I76c7V94QcZRDB8eLVOj+JhjZJxHXKiPHgeRHPujj0pUxNaZAklLy1A2b47un0lh\nRmlGppaVtn3o/Mdxyy35iBwgvpyZMyUEfciQ4uUqsl5/HZg4UT6Xa7xmGaeo05O451FFkdahnP3e\ndRdw0klyLvr0kaQXmjwirT4qONvaIuPdNeJff714/VtuKa2fn/iCWcKETzghve7qwXPPVWurdCz4\ndU86FtfL7tYpiycLiLKO+p5QNxugj3uf6du3uBOqrU3GkvvZHTub6j40H9lzz83CzJmzqjLHW95m\n1t4AdmauVp4OoyezeTNw5pnSI3LvvaU3cKNz9O0rMeQnnAB88pMiukxoGT2EYyDZBW8gog7IeOAb\nmHlxhm2XAnAnOhhXWBaEmWcT0XZENKKcbWfMmIHXXpOxHQccIGFloSflAw9EhpsbohQXLhgnWLSH\nu709WrdcT1ZoAuN+/To3pqpckfX44xLqeNhhkdC6777ieiVZHG69X30VWLQIOPnk7Pu/7TaJpthn\nn2jZPfcAhx5aXD5QmacsSRC5Ikt7+dPCHvMM8dSy1q8XsTtlSvTbpk2lz+hyQmHjSPNkzZsnv22z\nTVgsuyGLWc6HXoubN0eerHLGomlCmLY2EWea+CL0H2ptjdZPSuGu62Tx6qlIb2+Xa7ylJV1kxYUL\n+kl52tqi0EN3eYimJnl371lpnQy+yHL38eyzMobLT0Pve/xC5aXhhwvuvHMzpk9vxkEHyfc8pxrJ\nO1zwGQBb5Vym0QtoaREvy8qV0qtkAqs69OsnPWlr1kjmwWqMUzCMrqYwJupSZt4LwGmQkPVXM24+\nF8BkIppARE0ATgFwu7sCEW3vfN4TQFNh/sbUbYvrmW6wuALENbZ8kZXmyXJ7uHXuoDhP1ksvFY8X\n8j1Zr78e9cj36xd3dNkoN1yQSCaef9U5m2rQ6e9J+1K03h0d5d33Nm4sTSDQ0hKVQSShnaHsi1k8\nWUltERqcX07WukoIjcl64QVg4cLi9ULhc+VMK5Bl/3G/DxwY70H0M2e6hNpal7W1RZ6skHCOa1dt\nB/2v+OGC7rUWl6HTDRfs6IjmbPI92XHbqmhQ0dmvX/haSSpHhR4QHevMmRJR5GYX9Mvs21cyMYaO\nN21Mln+fcesQV9fGxnw9WXmND40jb5G1JYDniOgeIrpdXznvw+hhbNgAHHec3JhuvTV9Rnejc/Tv\nL2l0W1tF2OaVmtkwaklB6PwnJGxwJwD/mWU7Zm6HZMGdCeBZANcz8wIiOpeIPltY7aOJtaB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lzuvlvuZ77Imj27tA1coRnqAEqiW3iymPkd57WUmX8C4COdLPMpZt6Hmfdg5hOZeXVO1TWqREeH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\nwzAMwzAMw0iQ/wUrFlLsigMRSgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x124d8ceb8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "pm.traceplot(m1010_traces);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "\n",
      "alpha:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  0.947            0.386            0.019            [0.196, 1.686]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  0.155          0.709          0.969          1.200          1.650\n",
      "\n",
      "\n",
      "beta_p:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  0.263            0.037            0.002            [0.196, 0.341]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  0.194          0.238          0.262          0.286          0.340\n",
      "\n",
      "\n",
      "beta_c:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  -0.139           0.783            0.050            [-1.479, 1.291]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  -1.552         -0.709         -0.134         0.468          1.266\n",
      "\n",
      "\n",
      "beta_pc:\n",
      "\n",
      "  Mean             SD               MC Error         95% HPD interval\n",
      "  -------------------------------------------------------------------\n",
      "  \n",
      "  0.048            0.086            0.005            [-0.119, 0.193]\n",
      "\n",
      "  Posterior quantiles:\n",
      "  2.5            25             50             75             97.5\n",
      "  |--------------|==============|==============|--------------|\n",
      "  \n",
      "  -0.108         -0.018         0.051          0.111          0.213\n",
      "\n"
     ]
    }
   ],
   "source": [
    "pm.summary(m1010_traces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "m1010_traces_df = pm.trace_to_dataframe(m1010_traces)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "def traces_to_dotplot(traces_df):\n",
    "    fig, ax = plt.subplots(1,1, figsize=(6, 1.5))\n",
    "\n",
    "    param_qs = traces_df.quantile([0.055, 0.5, 0.945])\n",
    "\n",
    "    for index, col in enumerate(param_qs.columns):\n",
    "        col_qs = param_qs[col]\n",
    "        ax.scatter(col_qs.median(), index)\n",
    "        ax.hlines(index, col_qs.min(), col_qs.max())\n",
    "\n",
    "    ax.set_yticks(range(len(param_qs.columns)))\n",
    "    ax.set_yticklabels(param_qs.columns)\n",
    "    ax.grid();\n",
    "    \n",
    "    return (fig, ax)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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rz4go5RdwIfCKZPsG4IsN2rwC+B+gFzgc2AUs6XDONwJvAH5A7ePrm7X7KXBcjv05bc6C\n9OffAZ9Jtj8L3FCE/mylb4B3AHcl28uBrTn8nlvJeR5wZx73w0k5zgX6gD1Nri9Cf06XsSh9eSLQ\nl2wfAzyUxf2ztM9AIuKeiPhtsrsVOKVBs7cCj0TEaES8CPwb8O5OZQSIiIci4hF+dzGtRsYX4MpF\nizlz78/kfOOfTrABeE+Tdp3uz1b65t3AbQARcR+wUNIJHcwIrf8O23pVTpYi4kfAL6Zoknt/tpAR\nitGXP4uIXcn2r4AHgZMnNZtxf5a2gEzyZ8DmBpefDPxv3f7jvLzTiiKoreS4TdKH8w7TRBH6c1FE\n/BxqfxRAs+UAO92frfTN5DZPNGgz21r9HZ6dDGPcVbemT9EUoT9bUai+lLSY2rOm+yZdNeP+TLse\nyKySdDdQXwFF7YHhmoj4dtLmGuDFiPhaDhFJMkybswXnRMRTknqoPfA9mPx3U7Scs26KnI3Gj5u9\nDn3W+3MO2w68JiKek/QO4JvAqTlnKqtC9WWygN+/A59MnomkUugCEhErp7pe0gDwTuD8Jk2eAOqX\nwj0luSxT0+Vs8TaeSr5XJd1Bbagh0we8DHLm3p/JhOUJEfFzSScCB5rcxqz35ySt9M0TwO9N02a2\nTZuz/oElIjZLWifp+Ih4pkMZW1WE/pxSkfpS0mHUise/RsS3GjSZcX+WdghL0sXA1cC7IuL5Js22\nAb8vqVfSEcCfAnd2KmMDDcdCJR2d/GeApFcBfwg80MlgkyM1ubwI/XknMJBsXw687A8hp/5spW/u\nBD6U5DoLODg+HNdB0+asH/eW9FZqbzjOq3iI5vfHIvQnTJGxYH35L8C+iLixyfUz78+8Xx2Q4lUF\njwCjwI7ka11y+auB79S1u5jaKw4eAf4yh5zvoTauOEZt+d7Nk3MCr6X2apidwP1FzVmQ/jweuCfJ\n8H2guyj92ahvgI8Af1HXZi21V0HtZopX5eWZE7iSWsHdCdwLLM8p59eAJ4HngceAK4rWn9NlLFBf\nngP8pu7vYkdyP0jVn/4oEzMza0tph7DMzCxfLiBmZtYWFxAzM2uLC4iZmbXFBcTMzNriAmJmZm1x\nATEzs7a4gJiZWVv+H3wVthOU0llsAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x12a6add30>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "traces_to_dotplot(m1010_traces_df);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True     0.956\n",
       "False    0.044\n",
       "dtype: float64"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "cfact_log_pop = 8 \n",
    "\n",
    "lambda_high = m1010_traces_df.apply(\n",
    "    lambda row: row['alpha'] + row['beta_p'] * cfact_log_pop + row['beta_c'] + row['beta_pc'] * cfact_log_pop, axis=1)\n",
    "\n",
    "lambda_low = m1010_traces_df.apply(\n",
    "    lambda row: row['alpha'] + row['beta_p'] * cfact_log_pop, axis=1)\n",
    "\n",
    "lambda_high = np.exp(lambda_high)\n",
    "lambda_low = np.exp(lambda_low)\n",
    "\n",
    "lambda_diff = lambda_high - lambda_low\n",
    "(lambda_diff > 0).value_counts(normalize=True)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "There is a 96% plausibility that a high contact island has more tools than a low contact island.\n",
    "\n",
    "You can't just inspect the marginal uncertainty in each parameter, which is what is shown in the table of estimates,\n",
    "and get an accurate understanding of the impact of the joint uncertainty on prediction -- the correlation between beta_c and beta_pc is strongly negative, so when beta_c is small, beta_pc is large = inspecting just one parameter (beta_c) doesn't explain the joint impact of parameters on prediction.\n",
    "\n",
    "A better way to assess whether a predictor is expected to improve prediction is to use **model comparisons**."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": []
  }
 ],
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