MultiLevel_BayesianModeling.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# A Primer on Bayesian Methods for Multilevel Modeling"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Hierarchical or multilevel modeling is a generalization of regression modeling.\n",
    "\n",
    "*Multilevel models* are regression models in which the constituent model parameters are given **probability models**. This implies that model parameters are allowed to **vary by group**.\n",
    "\n",
    "Observational units are often naturally **clustered**. Clustering induces dependence between observations, despite random sampling of clusters and random sampling within clusters.\n",
    "\n",
    "A *hierarchical model* is a particular multilevel model where parameters are nested within one another.\n",
    "\n",
    "Some multilevel structures are not hierarchical. \n",
    "\n",
    "* e.g. \"country\" and \"year\" are not nested, but may represent separate, but overlapping, clusters of parameters\n",
    "\n",
    "We will motivate this topic using an environmental epidemiology example."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Example: Radon contamination (Gelman and Hill 2006)\n",
    "\n",
    "Radon is a radioactive gas that enters homes through contact points with the ground. It is a carcinogen that is the primary cause of lung cancer in non-smokers. Radon levels vary greatly from household to household.\n",
    "\n",
    "![radon](http://www.fix-your-radon.com/images/how_radon_enters.jpg)\n",
    "\n",
    "The EPA did a study of radon levels in 80,000 houses. Two important predictors:\n",
    "\n",
    "* measurement in basement or first floor (radon higher in basements)\n",
    "* county uranium level (positive correlation with radon levels)\n",
    "\n",
    "We will focus on modeling radon levels in Minnesota.\n",
    "\n",
    "The hierarchy in this example is households within county. "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Data organization"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "First, we import the data from a local file, and extract Minnesota's data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "%matplotlib inline\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt\n",
    "import seaborn as sns; sns.set_context('notebook')\n",
    "\n",
    "# Import radon data\n",
    "srrs2 = pd.read_csv('https://raw.githubusercontent.com/pymc-devs/pymc3/master/pymc3/examples/data/srrs2.dat')\n",
    "srrs2.columns = srrs2.columns.map(str.strip)\n",
    "srrs_mn = srrs2[srrs2.state=='MN']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Next, obtain the county-level predictor, uranium, by combining two variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/ipykernel_launcher.py:1: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  \"\"\"Entry point for launching an IPython kernel.\n"
     ]
    }
   ],
   "source": [
    "srrs_mn['fips'] = srrs_mn.stfips*1000 + srrs_mn.cntyfips\n",
    "cty = pd.read_csv('https://raw.githubusercontent.com/pymc-devs/pymc3/master/pymc3/examples/data/cty.dat')\n",
    "cty_mn = cty[cty.st=='MN'].copy()\n",
    "cty_mn[ 'fips'] = 1000*cty_mn.stfips + cty_mn.ctfips"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Use the `merge` method to combine home- and county-level information in a single DataFrame."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "srrs_mn = srrs_mn.merge(cty_mn[['fips', 'Uppm']], on='fips')\n",
    "srrs_mn = srrs_mn.drop_duplicates(subset='idnum')\n",
    "u = np.log(srrs_mn.Uppm)\n",
    "\n",
    "n = len(srrs_mn)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>idnum</th>\n",
       "      <th>state</th>\n",
       "      <th>state2</th>\n",
       "      <th>stfips</th>\n",
       "      <th>zip</th>\n",
       "      <th>region</th>\n",
       "      <th>typebldg</th>\n",
       "      <th>floor</th>\n",
       "      <th>room</th>\n",
       "      <th>basement</th>\n",
       "      <th>...</th>\n",
       "      <th>stopdt</th>\n",
       "      <th>activity</th>\n",
       "      <th>pcterr</th>\n",
       "      <th>adjwt</th>\n",
       "      <th>dupflag</th>\n",
       "      <th>zipflag</th>\n",
       "      <th>cntyfips</th>\n",
       "      <th>county</th>\n",
       "      <th>fips</th>\n",
       "      <th>Uppm</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>5081</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27</td>\n",
       "      <td>55735</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>N</td>\n",
       "      <td>...</td>\n",
       "      <td>12288</td>\n",
       "      <td>2.2</td>\n",
       "      <td>9.7</td>\n",
       "      <td>1146.499190</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>AITKIN</td>\n",
       "      <td>27001</td>\n",
       "      <td>0.502054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>5082</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27</td>\n",
       "      <td>55748</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>Y</td>\n",
       "      <td>...</td>\n",
       "      <td>12088</td>\n",
       "      <td>2.2</td>\n",
       "      <td>14.5</td>\n",
       "      <td>471.366223</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>AITKIN</td>\n",
       "      <td>27001</td>\n",
       "      <td>0.502054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>5083</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27</td>\n",
       "      <td>55748</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>Y</td>\n",
       "      <td>...</td>\n",
       "      <td>21188</td>\n",
       "      <td>2.9</td>\n",
       "      <td>9.6</td>\n",
       "      <td>433.316718</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>AITKIN</td>\n",
       "      <td>27001</td>\n",
       "      <td>0.502054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>5084</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27</td>\n",
       "      <td>56469</td>\n",
       "      <td>5</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>Y</td>\n",
       "      <td>...</td>\n",
       "      <td>123187</td>\n",
       "      <td>1.0</td>\n",
       "      <td>24.3</td>\n",
       "      <td>461.623670</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>1</td>\n",
       "      <td>AITKIN</td>\n",
       "      <td>27001</td>\n",
       "      <td>0.502054</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>5085</td>\n",
       "      <td>MN</td>\n",
       "      <td>MN</td>\n",
       "      <td>27</td>\n",
       "      <td>55011</td>\n",
       "      <td>3</td>\n",
       "      <td>1</td>\n",
       "      <td>0</td>\n",
       "      <td>4</td>\n",
       "      <td>Y</td>\n",
       "      <td>...</td>\n",
       "      <td>13088</td>\n",
       "      <td>3.1</td>\n",
       "      <td>13.8</td>\n",
       "      <td>433.316718</td>\n",
       "      <td>0</td>\n",
       "      <td>0</td>\n",
       "      <td>3</td>\n",
       "      <td>ANOKA</td>\n",
       "      <td>27003</td>\n",
       "      <td>0.428565</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>5 rows × 27 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "   idnum state state2  stfips    zip  region  typebldg  floor  room basement  \\\n",
       "0   5081    MN     MN      27  55735       5         1      1     3        N   \n",
       "1   5082    MN     MN      27  55748       5         1      0     4        Y   \n",
       "2   5083    MN     MN      27  55748       5         1      0     4        Y   \n",
       "3   5084    MN     MN      27  56469       5         1      0     4        Y   \n",
       "4   5085    MN     MN      27  55011       3         1      0     4        Y   \n",
       "\n",
       "   ...  stopdt activity  pcterr        adjwt  dupflag  zipflag  cntyfips  \\\n",
       "0  ...   12288      2.2     9.7  1146.499190        1        0         1   \n",
       "1  ...   12088      2.2    14.5   471.366223        0        0         1   \n",
       "2  ...   21188      2.9     9.6   433.316718        0        0         1   \n",
       "3  ...  123187      1.0    24.3   461.623670        0        0         1   \n",
       "4  ...   13088      3.1    13.8   433.316718        0        0         3   \n",
       "\n",
       "                 county   fips      Uppm  \n",
       "0  AITKIN                27001  0.502054  \n",
       "1  AITKIN                27001  0.502054  \n",
       "2  AITKIN                27001  0.502054  \n",
       "3  AITKIN                27001  0.502054  \n",
       "4  ANOKA                 27003  0.428565  \n",
       "\n",
       "[5 rows x 27 columns]"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "srrs_mn.head()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We also need a lookup table (`dict`) for each unique county, for indexing."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "srrs_mn.county = srrs_mn.county.map(str.strip)\n",
    "mn_counties = srrs_mn.county.unique()\n",
    "counties = len(mn_counties)\n",
    "county_lookup = dict(zip(mn_counties, range(len(mn_counties))))"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Finally, create local copies of variables."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "county = srrs_mn['county_code'] = srrs_mn.county.replace(county_lookup).values\n",
    "radon = srrs_mn.activity\n",
    "srrs_mn['log_radon'] = log_radon = np.log(radon + 0.1).values\n",
    "floor_measure = srrs_mn.floor.values"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Distribution of radon levels in MN (log scale):"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f38f7193f98>"
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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OcvW46xlGkuuSPJbk3nHXMowkZya5Lcn93f+jneOuaRhJTk3y5ST/1o1j3Z5mmeSkJF9N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\nqVU1cRTuVIAAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "srrs_mn.activity.apply(lambda x: np.log(x+0.1)).hist(bins=25)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Conventional approaches\n",
    "\n",
    "The two conventional alternatives to modeling radon exposure represent the two extremes of the bias-variance tradeoff:\n",
    "\n",
    "***Complete pooling***: \n",
    "\n",
    "Treat all counties the same, and estimate a single radon level.\n",
    "\n",
    "$$y_i = \\alpha + \\beta x_i + \\epsilon_i$$\n",
    "\n",
    "***No pooling***:\n",
    "\n",
    "Model radon in each county independently.\n",
    "\n",
    "$$y_i = \\alpha_{j[i]} + \\beta x_i + \\epsilon_i$$\n",
    "\n",
    "where $j = 1,\\ldots,85$\n",
    "\n",
    "The errors $\\epsilon_i$ may represent measurement error, temporal within-house variation, or variation among houses."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are the point estimates of the slope and intercept for the complete pooling model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/h5py/__init__.py:34: FutureWarning: Conversion of the second argument of issubdtype from `float` to `np.floating` is deprecated. In future, it will be treated as `np.float64 == np.dtype(float).type`.\n",
      "  from ._conv import register_converters as _register_converters\n"
     ]
    }
   ],
   "source": [
    "from pymc3 import Model, sample, Normal, HalfCauchy, Uniform\n",
    "\n",
    "floor = srrs_mn.floor.values\n",
    "log_radon = srrs_mn.log_radon.values\n",
    "\n",
    "with Model() as pooled_model:\n",
    "    \n",
    "    beta = Normal('beta', 0, sd=1e5, shape=2)\n",
    "    sigma = HalfCauchy('sigma', 5)\n",
    "    \n",
    "    theta = beta[0] + beta[1]*floor\n",
    "    \n",
    "    y = Normal('y', theta, sd=sigma, observed=log_radon)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 5000/5000 [00:04<00:00, 1144.80draws/s]\n"
     ]
    }
   ],
   "source": [
    "with pooled_model:\n",
    "    pooled_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "b0, m0 = pooled_trace['beta', 1000:].mean(axis=0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x7f38c7fd9198>]"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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v3ZfPTynu8V4xhYjdHYko780uj+CFf1iDA71RPLf7MM46ZW5BnqnHsbATUWi0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\nFDIs7EREIcPCTkQUMv8fELfl0I4uDmIAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.scatter(srrs_mn.floor, np.log(srrs_mn.activity+0.1))\n",
    "xvals = np.linspace(-0.2, 1.2)\n",
    "plt.plot(xvals, m0*xvals+b0, 'r--')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Estimates of county radon levels for the unpooled model:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as unpooled_model:\n",
    "    \n",
    "    beta0 = Normal('beta0', 0, sd=1e5, shape=counties)\n",
    "    beta1 = Normal('beta1', 0, sd=1e5)\n",
    "    sigma = HalfCauchy('sigma', 5)\n",
    "    \n",
    "    theta = beta0[county] + beta1*floor\n",
    "    \n",
    "    y = Normal('y', theta, sd=sigma, observed=log_radon)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma, beta1, beta0]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 5000/5000 [00:07<00:00, 626.73draws/s]\n"
     ]
    }
   ],
   "source": [
    "with unpooled_model:\n",
    "    unpooled_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x1512 with 1 Axes>,\n",
       " array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f38c652bb38>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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AeWk8zpPAcWVpAqsiYu4A41hEkkhwQZXntkbEhHonjlt1dZSRjKFpNC28XLXk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\nKyQXODMzKyQXODMzKyQXODMzKyQXODM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rM/OEccZyPPBD4Ji2ENRWEfw+8HuZeed4v4VR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ZEscJKkRrLASZIayQInSWokC5wkqZEscJKkRrLASZIaadQCFxHLImJtJw8YEasi4sAK5y2KiBsj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\n",
      "text/plain": [
       "<Figure size 432x1512 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymc3 import forestplot\n",
    "\n",
    "forestplot(unpooled_trace, varnames=['beta0'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "unpooled_estimates = pd.Series(unpooled_trace['beta0'].mean(axis=0), index=mn_counties)\n",
    "unpooled_se = pd.Series(unpooled_trace['beta0'].std(axis=0), index=mn_counties)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can plot the ordered estimates to identify counties with high radon levels:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "ename": "AttributeError",
     "evalue": "'Series' object has no attribute 'order'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mAttributeError\u001b[0m                            Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-19-911fc4b63752>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m()\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0morder\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0munpooled_estimates\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mindex\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mscatter\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munpooled_estimates\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0munpooled_estimates\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0;32mfor\u001b[0m \u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mse\u001b[0m \u001b[0;32min\u001b[0m \u001b[0mzip\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mrange\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mlen\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0munpooled_estimates\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0munpooled_estimates\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0munpooled_se\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0morder\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m     \u001b[0mplt\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mi\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mm\u001b[0m\u001b[0;34m-\u001b[0m\u001b[0mse\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mm\u001b[0m\u001b[0;34m+\u001b[0m\u001b[0mse\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0;34m'b-'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/usr/local/anaconda/lib/python3.6/site-packages/pandas/core/generic.py\u001b[0m in \u001b[0;36m__getattr__\u001b[0;34m(self, name)\u001b[0m\n\u001b[1;32m   5177\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_info_axis\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_can_hold_identifiers_and_holds_name\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   5178\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mname\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 5179\u001b[0;31m             \u001b[0;32mreturn\u001b[0m \u001b[0mobject\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m__getattribute__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   5180\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   5181\u001b[0m     \u001b[0;32mdef\u001b[0m \u001b[0m__setattr__\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mname\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mvalue\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;31mAttributeError\u001b[0m: 'Series' object has no attribute 'order'"
     ]
    }
   ],
   "source": [
    "order = unpooled_estimates.order().index\n",
    "\n",
    "plt.scatter(range(len(unpooled_estimates)), unpooled_estimates[order])\n",
    "for i, m, se in zip(range(len(unpooled_estimates)), unpooled_estimates[order], unpooled_se[order]):\n",
    "    plt.plot([i,i], [m-se, m+se], 'b-')\n",
    "plt.xlim(-1,86); plt.ylim(-1,4)\n",
    "plt.ylabel('Radon estimate');plt.xlabel('Ordered county');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Here are visual comparisons between the pooled and unpooled estimates for a subset of counties representing a range of sample sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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GLQda2dzUyr/8cR+56R7WOoF1dUUxM4syR+V9qsuL5PzBx4BlwAYAY8xeEZkc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\nSUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 864x432 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_counties = ('LAC QUI PARLE', 'AITKIN', 'KOOCHICHING', \n",
    "                    'DOUGLAS', 'CLAY', 'STEARNS', 'RAMSEY', 'ST LOUIS')\n",
    "\n",
    "fig, axes = plt.subplots(2, 4, figsize=(12, 6), sharey=True, sharex=True)\n",
    "axes = axes.ravel()\n",
    "m = unpooled_trace['beta1'].mean()\n",
    "for i,c in enumerate(sample_counties):\n",
    "    y = srrs_mn.log_radon[srrs_mn.county==c]\n",
    "    x = srrs_mn.floor[srrs_mn.county==c]\n",
    "    axes[i].scatter(x + np.random.randn(len(x))*0.01, y, alpha=0.4)\n",
    "    \n",
    "    # No pooling model\n",
    "    b = unpooled_estimates[c]\n",
    "    \n",
    "    # Plot both models and data\n",
    "    xvals = np.linspace(-0.2, 1.2)\n",
    "    axes[i].plot(xvals, m*xvals+b)\n",
    "    axes[i].plot(xvals, m0*xvals+b0, 'r--')\n",
    "    axes[i].set_xticks([0,1])\n",
    "    axes[i].set_xticklabels(['basement', 'floor'])\n",
    "    axes[i].set_ylim(-1, 3)\n",
    "    axes[i].set_title(c)\n",
    "    if not i%2:\n",
    "        axes[i].set_ylabel('log radon level')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Neither of these models are satisfactory:\n",
    "\n",
    "* if we are trying to identify high-radon counties, pooling is useless\n",
    "* we do not trust extreme unpooled estimates produced by models using few observations"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Multilevel and hierarchical models\n",
    "\n",
    "When we pool our data, we imply that they are sampled from the same model. This ignores any variation among sampling units (other than sampling variance):\n",
    "\n",
    "![pooled](http://f.cl.ly/items/0R1W063h1h0W2M2C0S3M/Screen%20Shot%202013-10-10%20at%208.22.21%20AM.png)\n",
    "\n",
    "When we analyze data unpooled, we imply that they are sampled independently from separate models. At the opposite extreme from the pooled case, this approach claims that differences between sampling units are to large to combine them:\n",
    "\n",
    "![unpooled](http://f.cl.ly/items/38020n2t2Y2b1p3t0B0e/Screen%20Shot%202013-10-10%20at%208.23.36%20AM.png)\n",
    "\n",
    "In a hierarchical model, parameters are viewed as a sample from a population distribution of parameters. Thus, we view them as being neither entirely different or exactly the same. This is ***parital pooling***.\n",
    "\n",
    "![hierarchical](http://f.cl.ly/items/1B3U223i002y3V2W3r0W/Screen%20Shot%202013-10-10%20at%208.25.05%20AM.png)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can use PyMC to easily specify multilevel models, and fit them using Markov chain Monte Carlo."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Partial pooling model\n",
    "\n",
    "The simplest partial pooling model for the household radon dataset is one which simply estimates radon levels, without any predictors at any level. A partial pooling model represents a compromise between the pooled and unpooled extremes, approximately a weighted average (based on sample size) of the unpooled county estimates and the pooled estimates.\n",
    "\n",
    "$$\\hat{\\alpha} \\approx \\frac{(n_j/\\sigma_y^2)\\bar{y}_j + (1/\\sigma_{\\alpha}^2)\\bar{y}}{(n_j/\\sigma_y^2) + (1/\\sigma_{\\alpha}^2)}$$\n",
    "\n",
    "Estimates for counties with smaller sample sizes will shrink towards the state-wide average.\n",
    "\n",
    "Estimates for counties with larger sample sizes will be closer to the unpooled county estimates."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as partial_pooling:\n",
    "    \n",
    "    # Priors\n",
    "    mu_a = Normal('mu_a', mu=0., sd=1e5)\n",
    "    sigma_a = HalfCauchy('sigma_a', 5)\n",
    "    \n",
    "    # Random intercepts\n",
    "    a = Normal('a', mu=mu_a, sd=sigma_a, shape=counties)\n",
    "    \n",
    "    # Model error\n",
    "    sigma_y = HalfCauchy('sigma_y',5)\n",
    "    \n",
    "    # Expected value\n",
    "    y_hat = a[county]\n",
    "    \n",
    "    # Data likelihood\n",
    "    y_like = Normal('y_like', mu=y_hat, sd=sigma_y, observed=log_radon)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma_y, a, sigma_a, mu_a]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 5000/5000 [00:10<00:00, 491.98draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with partial_pooling:\n",
    "    partial_pooling_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
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Ur+W1ug7cfqzrfQduP6bltR6LWIEEEPwgsPYiCmGV0o5SFCXG8zA1AQDyrlfBmDwbt9Ld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\nazt7cubd2jg3XIn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+i7LmpttCUgAIy/Hlxzb133HORX7S3NI/8zH83gbvZ9xF7t2+319U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\n8vt/TgAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 1008x432 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "sample_trace = partial_pooling_trace['a', 1000:]\n",
    "\n",
    "fig, axes = plt.subplots(1, 2, figsize=(14,6), sharex=True, sharey=True)\n",
    "samples, counties = sample_trace.shape\n",
    "jitter = np.random.normal(scale=0.1, size=counties)\n",
    "\n",
    "n_county = srrs_mn.groupby('county')['idnum'].count()\n",
    "unpooled_means = srrs_mn.groupby('county')['log_radon'].mean()\n",
    "unpooled_sd = srrs_mn.groupby('county')['log_radon'].std()\n",
    "unpooled = pd.DataFrame({'n':n_county, 'm':unpooled_means, 'sd':unpooled_sd})\n",
    "unpooled['se'] = unpooled.sd/np.sqrt(unpooled.n)\n",
    "\n",
    "axes[0].plot(unpooled.n + jitter, unpooled.m, 'b.')\n",
    "for j, row in zip(jitter, unpooled.iterrows()):\n",
    "    name, dat = row\n",
    "    axes[0].plot([dat.n+j,dat.n+j], [dat.m-dat.se, dat.m+dat.se], 'b-')\n",
    "axes[0].set_xscale('log')\n",
    "axes[0].hlines(sample_trace.mean(), 0.9, 100, linestyles='--')\n",
    "\n",
    "        \n",
    "samples, counties = sample_trace.shape\n",
    "means = sample_trace.mean(axis=0)\n",
    "sd = sample_trace.std(axis=0)\n",
    "axes[1].scatter(n_county.values + jitter, means)\n",
    "axes[1].set_xscale('log')\n",
    "axes[1].set_xlim(1,100)\n",
    "axes[1].set_ylim(0, 3)\n",
    "axes[1].hlines(sample_trace.mean(), 0.9, 100, linestyles='--')\n",
    "for j,n,m,s in zip(jitter, n_county.values, means, sd):\n",
    "    axes[1].plot([n+j]*2, [m-s, m+s], 'b-')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Notice the difference between the unpooled and partially-pooled estimates, particularly at smaller sample sizes. The former are both more extreme and more imprecise."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Varying intercept model\n",
    "\n",
    "This model allows intercepts to vary across county, according to a random effect.\n",
    "\n",
    "$$y_i = \\alpha_{j[i]} + \\beta x_{i} + \\epsilon_i$$\n",
    "\n",
    "where\n",
    "\n",
    "$$\\epsilon_i \\sim N(0, \\sigma_y^2)$$\n",
    "\n",
    "and the intercept random effect:\n",
    "\n",
    "$$\\alpha_{j[i]} \\sim N(\\mu_{\\alpha}, \\sigma_{\\alpha}^2)$$\n",
    "\n",
    "As with the the “no-pooling” model, we set a separate intercept for each county, but rather than fitting separate least squares regression models for each county, multilevel modeling **shares strength** among counties, allowing for more reasonable inference in counties with little data."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as varying_intercept:\n",
    "    \n",
    "    # Priors\n",
    "    mu_a = Normal('mu_a', mu=0., tau=0.0001)\n",
    "    sigma_a = HalfCauchy('sigma_a', 5)\n",
    "    \n",
    "    \n",
    "    # Random intercepts\n",
    "    a = Normal('a', mu=mu_a, sd=sigma_a, shape=counties)\n",
    "    # Common slope\n",
    "    b = Normal('b', mu=0., sd=1e5)\n",
    "    \n",
    "    # Model error\n",
    "    sd_y = HalfCauchy('sd_y', 5)\n",
    "    \n",
    "    # Expected value\n",
    "    y_hat = a[county] + b * floor_measure\n",
    "    \n",
    "    # Data likelihood\n",
    "    y_like = Normal('y_like', mu=y_hat, sd=sd_y, observed=log_radon)\n",
    "    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "We can fit the above model using MCMC."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sd_y, b, a, sigma_a, mu_a]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 5000/5000 [00:09<00:00, 546.29draws/s]\n",
      "The number of effective samples is smaller than 25% for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with varying_intercept:\n",
    "    varying_intercept_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x1512 with 1 Axes>,\n",
       " array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f38c579e320>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 26,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x720 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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y1B14+jPAfzQfMnkicCBgqrfUY/1w91/F05PtAmiXHbiEJ284rOvr254sS92B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\nZmZJcoIzM7MkOcGZmVmS/g8MR6h2F8YwiwAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x1512 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "from pymc3 import forestplot, traceplot, plot_posterior\n",
    "\n",
    "plt.figure(figsize=(6,10))\n",
    "forestplot(varying_intercept_trace[1000:], varnames=['a'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f38c3b20860>,\n",
       "       <matplotlib.axes._subplots.AxesSubplot object at 0x7f38c3ab89e8>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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chMg8sKRTr3x4sAAAsHxiiNQcluqeiaEAgI8O8Tg2IiKiN3d3l8GHuIpuFEb4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\n",
      "text/plain": [
       "<Figure size 993.6x331.2 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_posterior(varying_intercept_trace[1000:], varnames=['sigma_a', 'b'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The estimate for the `floor` coefficient is approximately -0.66, which can be interpreted as houses without basements having about half ($\\exp(-0.66) = 0.52$) the radon levels of those with basements, after accounting for county."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/stats/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.9\n",
      "  \"pymc3 3.9\".format(old=old, new=new)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd_3%</th>\n",
       "      <th>hpd_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_mean</th>\n",
       "      <th>ess_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>b</th>\n",
       "      <td>-0.663</td>\n",
       "      <td>0.07</td>\n",
       "      <td>-0.804</td>\n",
       "      <td>-0.541</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>2035.0</td>\n",
       "      <td>2035.0</td>\n",
       "      <td>2034.0</td>\n",
       "      <td>2584.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    mean    sd  hpd_3%  hpd_97%  mcse_mean  mcse_sd  ess_mean  ess_sd  \\\n",
       "b -0.663  0.07  -0.804   -0.541      0.002    0.001    2035.0  2035.0   \n",
       "\n",
       "   ess_bulk  ess_tail  r_hat  \n",
       "b    2034.0    2584.0    1.0  "
      ]
     },
     "execution_count": 28,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "from pymc3 import summary\n",
    "\n",
    "summary(varying_intercept_trace, varnames=['b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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d0/fOzVVa7Z49+HM7lpTj45psR0d1h8eZBnoPWLbQ/Dx+T9poTg6OmWyhhQXd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\nTTP9f30caBRzbXpjAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xvals = np.arange(2)\n",
    "bp = varying_intercept_trace[a, 1000:].mean(axis=0)\n",
    "mp = varying_intercept_trace[b, 1000:].mean()\n",
    "for bi in bp:\n",
    "    plt.plot(xvals, mp*xvals + bi, 'bo-', alpha=0.4)\n",
    "plt.xlim(-0.1,1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "It is easy to show that the partial pooling model provides more objectively reasonable estimates than either the pooled or unpooled models, at least for counties with small sample sizes."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pandas/core/series.py:1155: FutureWarning: \n",
      "Passing list-likes to .loc or [] with any missing label will raise\n",
      "KeyError in the future, you can use .reindex() as an alternative.\n",
      "\n",
      "See the documentation here:\n",
      "https://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#deprecate-loc-reindex-listlike\n",
      "  return self.loc[key]\n"
     ]
    },
    {
     "data": {
      "image/png": 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kuJ5GEfHhxtKFj4sI7KuqJnWNzOzsbJ01a1ZsT87Ph7vuch+YuXPdhyhgxAgI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\nv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f2SRdPY1RTlw0PddMeTuK6hsiTI/KlVLJtVp0uUVFE6/7Rafv3K+0RjSYx4F1aCthAO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\n",
      "text/plain": [
       "<Figure size 864x432 with 8 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, axes = plt.subplots(2, 4, figsize=(12, 6), sharey=True, sharex=True)\n",
    "axes = axes.ravel()\n",
    "for i,c in enumerate(sample_counties):\n",
    "    \n",
    "    # Plot county data\n",
    "    y = srrs_mn.log_radon[srrs_mn.county==c]\n",
    "    x = srrs_mn.floor[srrs_mn.county==c]\n",
    "    axes[i].scatter(x + np.random.randn(len(x))*0.01, y, alpha=0.4)\n",
    "    \n",
    "    # No pooling model\n",
    "    m,b = unpooled_estimates[['floor', c]]\n",
    "    \n",
    "    xvals = np.linspace(-0.2, 1.2)\n",
    "    # Unpooled estimate\n",
    "    axes[i].plot(xvals, m*xvals+b)\n",
    "    # Pooled estimate\n",
    "    axes[i].plot(xvals, m0*xvals+b0, 'r--')\n",
    "    # Partial pooling esimate\n",
    "    axes[i].plot(xvals, mp*xvals+bp[county_lookup[c]], 'k:')\n",
    "    axes[i].set_xticks([0,1])\n",
    "    axes[i].set_xticklabels(['basement', 'floor'])\n",
    "    axes[i].set_ylim(-1, 3)\n",
    "    axes[i].set_title(c)\n",
    "    if not i%2:\n",
    "        axes[i].set_ylabel('log radon level')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Varying slope model\n",
    "\n",
    "Alternatively, we can posit a model that allows the counties to vary according to how the location of measurement (basement or floor) influences the radon reading.\n",
    "\n",
    "$$y_i = \\alpha + \\beta_{j[i]} x_{i} + \\epsilon_i$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as varying_slope:\n",
    "    \n",
    "    # Priors\n",
    "    mu_b = Normal('mu_b', mu=0., sd=1e5)\n",
    "    sigma_b = HalfCauchy('sigma_b', 5)\n",
    "    \n",
    "    # Common intercepts\n",
    "    a = Normal('a', mu=0., sd=1e5)\n",
    "    # Random slopes\n",
    "    b = Normal('b', mu=mu_b, sd=sigma_b, shape=counties)\n",
    "    \n",
    "    # Model error\n",
    "    sigma_y = HalfCauchy('sigma_y',5)\n",
    "    \n",
    "    # Expected value\n",
    "    y_hat = a + b[county] * floor_measure\n",
    "    \n",
    "    # Data likelihood\n",
    "    y_like = Normal('y_like', mu=y_hat, sd=sigma_y, observed=log_radon)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma_y, b, a, sigma_b, mu_b]\n",
      "Sampling 2 chains, 11 divergences: 100%|██████████| 5000/5000 [00:13<00:00, 363.84draws/s]\n",
      "There was 1 divergence after tuning. Increase `target_accept` or reparameterize.\n",
      "There were 10 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with varying_slope:\n",
    "    varying_slope_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x1512 with 1 Axes>,\n",
       " array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f38ce15add8>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x720 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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pZt4wyzUWyyu27hm0RO+gltA9ObF77fLFJAxsancjW5Sa6ypN9I6IdwKXAd9r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\nKg08jYhlwGeB04BlwMWZ+fk21+gVnPqqWSvywR/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FssBJkopkgZMkFckCJ0kqkgVOklQk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\nnODMzKyS/h+0Dg81kjstwAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<Figure size 432x1512 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,10))\n",
    "forestplot(varying_slope_trace[1000:], varnames=['b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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atbdD4ImJenjMzAzprH4/RJKezj3U1vK53l7kmclJPb1LhtWUlWFMbr+d4/Pz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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xvals = np.arange(2)\n",
    "b = varying_slope_trace['a', 1000:].mean()\n",
    "m = varying_slope_trace['b', 1000:].mean(axis=0)\n",
    "for mi in m:\n",
    "    plt.plot(xvals, mi*xvals + b, 'bo-', alpha=0.4)\n",
    "plt.xlim(-0.2, 1.2);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Varying intercept and slope model\n",
    "\n",
    "The most general model allows both the intercept and slope to vary by county:\n",
    "\n",
    "$$y_i = \\alpha_{j[i]} + \\beta_{j[i]} x_{i} + \\epsilon_i$$\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as varying_intercept_slope:\n",
    "    \n",
    "    # Priors\n",
    "    mu_a = Normal('mu_a', mu=0., sd=1e5)\n",
    "    sigma_a = HalfCauchy('sigma_a', 5)\n",
    "    mu_b = Normal('mu_b', mu=0., sd=1e5)\n",
    "    sigma_b = HalfCauchy('sigma_b', 5)\n",
    "    \n",
    "    # Random intercepts\n",
    "    a = Normal('a', mu=mu_a, sd=sigma_a, shape=counties)\n",
    "    # Random slopes\n",
    "    b = Normal('b', mu=mu_b, sd=sigma_b, shape=counties)\n",
    "    \n",
    "    # Model error\n",
    "    sigma_y = Uniform('sigma_y', lower=0, upper=100)\n",
    "    \n",
    "    # Expected value\n",
    "    y_hat = a[county] + b[county] * floor_measure\n",
    "    \n",
    "    # Data likelihood\n",
    "    y_like = Normal('y_like', mu=y_hat, sd=sigma_y, observed=log_radon)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma_y, b, a, sigma_b, mu_b, sigma_a, mu_a]\n",
      "Sampling 2 chains, 30 divergences: 100%|██████████| 5000/5000 [01:02<00:00, 36.26draws/s] \n",
      "The acceptance probability does not match the target. It is 0.9151518603648835, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "There were 30 divergences after tuning. Increase `target_accept` or reparameterize.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with varying_intercept_slope:\n",
    "    varying_intercept_slope_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x2808 with 1 Axes>,\n",
       " array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f38c02f2f98>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "text/plain": [
       "<Figure size 432x1152 with 0 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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tzTOjajbc0G0j5WbDyH0Ds9/mgNnLgytTBN4FXDDIWJI0TOa+1d8o8uDOBT6bmXcX/ZYl\n1d2oVx5nfOBKvnt3Ly1uh5P7Bm5RzmWV5sFFxBHAfwaeNeA4kuaRUW9RAmzbOdnT9cPIfYPqf1a3\nKftXdR7cE4CfAW6JiNuAgyLiln7HlKRhMfet/irNg8vMvwcOa3wfEdsz82cGGFPSPDAbq45eT1Ka\n+1Z/lebBtXjNdk9RSpKGyDw4SVItmQcnSRovFjhJUi1Z4CRJtWSBkyTVkgVOklRLFjhJUi1Z4CRJ\ntVR5gYuIj0TErRFxffnn8VWPKUnSqAJP35iZnxrRWJLGXD8BqMMIP22wjdfcMFAnk4jYRJEisBi4\nODM/2OKajwCfH6DA2clEqqEqu/D3GoDaKvz0zi07+KUew08bqgxBBRMGpqmsk8nZmfkk4ASK6JzV\nba57W0R8OyLeXfawlKRK3LN9V8+vaRV+euSqg/jlxxw6rGlpFgy6grsIaOTBrQdOycyrpl1zOPAj\n4ADgg8C/Z+ZbexjGFZxUI1Xnp/W6eoNiBfe1C07iyGlF7o4tO3h6H6u4qldwzVzNVbCC6zIPjsy8\nOwu7gEuBp/Q7piRVIRPe+rnv7vf4ulUHmQ83j1WaBwfFCi4z746IAF4MfGeAMSXNc1WvOPo5YALw\nwMTugfLhmnnIZG6oPA8uIr4CrKFYRl4PvCYzt/cwlFuUkqR2zIOTJNWSeXCSpPFigZMk1ZIFTpJU\nSxY4SVItWeAkSbVkgZMk1ZIFTpJUS6PIg4uIeFtE3BwRN0XEhqrHlCRpFHlwr6SI1Dk2M6ciYu0I\nxpSkWddN27BecuhsAdabUeTBfQv41cy8pc9h7GQiaeSGkXrQKdmgVYrBTAkGg6YU1DR5YFbz4B4N\nnBER10TEFyPimAHHlKRaeO5xh+4X0TNTgkE/WXfjbNAtyg0R0ciDewRwDPCTadccCOzMzBMi4iXA\nh4GnDziuJFWqsdoZZCV3wMIFPLhnquVzEfD7zz9uv8fv3LKDzdtaF7IHJ1vfq1vTf5aarugeUnke\nHHAH8Ony688Aj+t3TEmaT9bMkCXXKkUc4C2fu7HngFW1VnkeHEWkzknArcAzgZsHGFOSRmrQVU67\ngyYBLfPntk5McuLRD297Pw+adG8UeXArgY8BjwS2U+TB3dDDUP5bRpLUjnlwkqRaMg9OkjReLHCS\npFqywEmSaskCJ0mqJQucJKmWLHCSpFqywEmSaskCJ0mqpcrz4CLiCmB5+e1a4FuZ+eKqx5WkYegm\n0w16y3VrxzZcwzXSTiYRcRnwd5n51z28zE4mkoDhZLT1qlOmGxTJAFdccNI+zZNnynVrZ9C8t27U\nMEGgmk4mEbEpIq6NiBsj4lUdrl0BPJuif6Uk1UarZICZct00GoNuUZ6dmfdFxBLg6oi4LDOn58E1\nvBj4v5m5dcAxJY2pUaw+pm9Jbt25u+Nrjj1sGZNTUyxasHfNcNf9E0zs3sPyxd3/mq3h6mpWjSLw\ntOHlwIcGHE/SmKt6m7KbLclmEfBHpz92n+I2uWeK1228jq0Tkz3dq8qfbRyLZ98Fblrg6Y6IuJzW\ngadExCHAU4DTWz0vSfNVq+3JRQsXcPt9O2ZpRmoYReApwMuAz2fmzgHGk6TKVyLdnppsaBdcevTq\npaxfvbSne3mKcrgqDzwtr70ceEdmfqmPoTxFKUlqx8BTSVItGXgqSRovFjhJUi1Z4CRJtWSBkyTV\nkgVOklRLFjhJUi1Z4CRJtTSKPLiTgXdRFNPtwCsz85aqx5U0t3XTMaTXjDU7gahZ5R/0joibgRdl\n5k0R8dvAUzLzlT3cwg96S3PQoI2BOzU17idjrao8tXFsVDyPzGoeXAIryq8PBu4aZExJ48GMNQ1q\nFHlw5wBfiIgJYCszN2WWNE/0u6ppbE12ylnrNWPtuMNXuEWpfQy0RRkRF7E3Amc9cEpmXjXtmk8D\n78zMb0bEG4H/lJnn9DCMW5TSLBp2Rlk3eWutticn90zx8r+8iqtv29LyNcPcnnRLcl5pu0VZaR5c\nRKwBjs/Mb5YP/S3QT6KApDFixpqGoeo8uC3AwRHxs5l5M/DLwE0DjClpxIa9munm9GQ/GWtuT2q6\nyvPgIuJ04K3AFEXBOzsz/6OHodyilCS1Yx6cJKmWzIOTJI0XC5wkqZYscJKkWrLASZJqyQInSaol\nC5wkqZYscJKkWqq8wEXEsyPiXyLiOxHx0YioPINOkqRKP+gdEQuAHwAnZ+bNEfFW4AeZ+Vc93MYP\neksaSDftwZr1GrQKtgqbRdV0MomITcAjKJosX5yZH5z2/Brgqsx8dPn904H/kZmn9TCMBU4aM7OR\nYNDQT9AqVBe22syUg5Yq62RydmY+CTgB2BARq6c9fy+wKCJOKL9/GUVBlKQ5qd+g1Xu27+Ke7buq\nnJp6NOj7YRvKZspQFK5jgIcCTzMzI+JM4N1lc+Z/APYMOKakGhj2Km0mByxcwIN7prq6dvP2nUzu\nmWLRwr3//p/cM9WxeD042d39NTp9r+Cm5cEdD1zHtDw4gMy8MjOfnplPAb4K3NzvmJLUjzUdVl/N\n1i5bvE9xgyKLbs2y7u+huaHqPDgiYm1mbi5XcBcCbxtgTEk1Mer3k7o9aNJPFl0zD5vMHaPIg3sX\n8HyK1eIlmfmeHofykIkkqR3z4CRJtWQenCRpvFjgJEm1ZIGTJNWSBU6SVEsWOElSLVngJEm1ZIGT\nJNXSUApcRJwbEbdEREbEIU2PR0S8t3zu2xHxxGGMJ0lSJ8MKH/068Hng8mmPP4+iAfMxwInAJeX/\nStLQjCLvrRXbcs1tHTuZdMp8m3btbcAJmXlv+f0HgMsz8xPl998HnpWZd/cwRzuZSDVSRYrAKPLe\nWqkyA87st64N1MmkU+bbTI4Eftj0/R3lY5I0K/rNe9P8002B2xARNwBXsTfzTZL6UsXK5ICF3R8n\naOS9Nesm7236eL2Mqdkx4/9D3Wa+zeBO9k3wXlc+JklDM+q8tzXLD+xpTM2OTodMusp8m8FngXMj\nYiPF4ZIHenz/TVINVbGKG1XeG3i4ZL6Y8ZBJD5lvG4ALgMOAzcAXMvOciAjgfcCpwA7grMy8psc5\neshEktSOeXCSpFoyD06SNF4scJKkWrLASZJqyQInSaolC5wkqZYscJKkWrLASZJqyQInSaqloeTB\nRcS5wHnAo4E1TXE5xwKXAk8E3pSZfzyM8SRpGLpt7zVofpytvWbHUDqZRMQTgC0UgafNeXBrgaOA\nF1P0tOynwNnJRKq5KjLiutFNjtww8uOqzI1rGOP8uP47mUTEpoi4NiJujIhXtbomM6/LzNtaPL45\nM68GdvcyW0maK9rlxx26wjSBua6bLcqzM/O+iFgCXB0Rl2XmT6qemKTxMVurj8de9OWO1+zYPcld\n909wxLRV2Kdf+4v87qe/zXW339/xHutWFa91q3K0Om5RRsRFwOnlt+uBUzLzqjbX3kbTFuW0e2x3\ni1JSL6reuuxmixLghKNWcfGZj+fIaSu5ubhV2UrNty/726IcQuCpJM171/xgCy+7ZP8DKetWHcRa\ng0/nrKoDTyWpb1WvPLo9RQkGpc5HVQeeHgZcA6wApoDtwHGZubWHObpFKUlqx8BTSVItGXgqSRov\nFjhJUi1Z4CRJtWSBkyTVkgVOklRLFjhJUi1Z4CRJtVR1HtyvARdSfE5hG/DazLxhGGNKqqdeuotA\nb1ltdhIZL1Xnwf0CcFNmbomI51F0QTmxx9v7QW9pjhhFblu3DZCh96y2YTc7rnkT4/mi7Qe9O67g\nImIT8AiKJssXZ+YHp1+TmdeV105//BtN314FrOtuvpLUXkSR0xZBy6y2tcsP5Mdbd83S7DRXjDIP\n7reAL/bxOklzRFUrluZtya07Z85HfuIjV/L2lzyOI1Yu4a77J7h3+y4OWba3AfJd908wsXsPyxfv\n/+vNXLbxMqo8uJOA9wO/1EdxdItSmiOq2qLsdluy1Zbk5q072b1niiNXHcQdW3Zw3sbrueYHW2a8\nT9W5bG5djlR/W5TT8uB2RMTl9JgHFxGPAz4EPM8kcEmDOHT54v22JNeuWMxT/+c/kcDmbbu6Dh9V\n/VWaBxcRjwQ+DbwiM2/uc46S5ohRbFHOpF0m2/rVS0kwl037qDoP7kPAS4EflJdOZuYJPc7Rf49J\nktoxD06SVEvmwUmSxosFTpJUSxY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4SVItDaXARcS5EXFLRGRE\nHNL0+Isi4tsRcX1EXBMRvzSM8SRJ6qTqPLhlwE8zM8uelJ/MzGN7vL0f9JY073XTjqyX8Faw5Vip\n/04m3eTBNV17Gy3SBMrnngZ8ODMf0+WkGyxwkmbVMFIUOiUmRMDXLjiJI7sMb4XqUhHmWRpC/4Gn\nDJgHFxGnA28H1gK/0u3rJKkO7tneXfDqc487dJ/iBoa3DqqbArehLFJQrOSOAboucJn5GeAzEfEM\n4A8p4nckac4aZu7dg5NTHa+JgN9//nH7PX7nlh1s3ta6uB2wcLAjFPNsldaXGf+GpuXBHQ9cR495\ncA2Z+VXgUc2HUCRJrXPuAN7yuRvbbk82Rwaptarz4H4G+PfykMkTgQPpYfUnSbNhmKubbg6XtMu5\n2zoxyYlHP7zlazxg0lnVeXAXAr8B7AYmgDdm5td6nKOHTCRJ7ZgHJ0mqJfPgJEnjxQInSaolC5wk\nqZYscJKkWrLASZJqyQInSaolC5wkqZYqzYNrev7JETEZES8bxniSJHXSTbPlbnwd+DxFHtw+ImIh\n8E7gH4Y0liTto5t2WM16zV1rZous+aPyPLiIOI+iVdeTgc9n5qd6nKOdTKR5aJgd+TvplLUGRcf+\nQ5cvZvP2nXz1jSft09y4U+5as6oy2JqNQ6f/IZqdPLiIOBI4HTiJosBJ0sC6zVhrePL6Vbz7jMez\nbtVB3H3/BIdPK1LmrtVT1Xlw7wEuzMypiLZFVlINjHLF1k3GWkMEDxU3gMNXLmFyzxSLmvLU7pgh\nd61h0Py1brhyG64ZC9y0PLgdEXE5veXBnQBsLIvbIcBpETGZmZv6m64k9aZV1tqihQu4+4EJDj94\nCXds2cF5G6/vuD1p/tr8U2keXGYe3fg6Ij5C8R6cxU2qoVGuPno5VNIua+38jddz8EEHcP+OB1m4\nINrmrjV4uGT+qTQPbto1H8FDJpKk4TIPTpJUS+bBSZLGiwVOklRLFjhJUi1Z4CRJtWSBkyTVkgVO\nklRLFjhJUi1Z4CRJtTSUPLiIOBc4D3g0sKYRl1P2svw74Nby0k9n5luHMaakeuk1063BbDe1M5RO\nJhHxBGALReDpCdMK3Bsy8/kD3N5OJtIIjTIVoFk3mW7TRcAVF8ztbDcwJaBi/XcyiYhNEXFtRNwY\nEa9qdU1mXpeZtw0wQUnqSQT8/BEH75cU0Mh2kyoNPC09LSJuAO6iWM3d2NdMJY3EbKUCbN25u+vX\nPfGRK3n7Sx7HESuXMDk1xaIFe/+tftf9E0zs3sPyxZ1/va1btXcF53Zl/XTcooyIiyhSuaFIFTgl\nM69qc+1t7LtFuQKYysztEXEacHFmHtPjHN2ilEZgNrYmh7Ut2QgwbWS7XfODLT3fd1TblQ1uWw5N\n2y3KSgNPM3Nr09dfiIj3R8QhjQIoSb1qF2D6/PdewY13b+3qvTeNh0oDTyPiMODHmZkR8RSK9/x6\n2d6UNCKzsaLo5+RkuwDTZQcu4inrZw4tnYlblPVTaeBp+fGB1wKTwARwfmZ+o8c5+u8xSVI7Bp5K\nkmrJwFNJ0nixwEmSaskCJ0mqJQucJKmWLHCSpFqywEmSaskCJ0mqpUrz4MrnngW8B3gYcG9mPnMY\nY0oaT/10PxkkMw7scjJfVZ0HtxL4BnBqZt4eEWszc3OPt/eD3tI8UnXT5l4bNA+aGQc2Yp7jZi0P\n7lcpUrxvL6/rtbhJ0kBaNWc2M248VJ0H97PAw8oUguUUcTl/3edcJc0DVa8+mrcov3v31hmuLOzY\nPcld909wRNMqbHJqimMPW86OB/d0Nea6VUvcppyHqs6Dex9wAnAysAS4EviVzLy5hzm6RSnNI6PM\nlet2u/LJ61fxif/6VBYt3LtpNde3KcGtyi71t0U5LQ/ueOA6esiDA+4AvpyZPy2L3leB43t4vSQN\n7If3TexT3MBtynFQaR4c8HfA+yJiEXAAcCLw7t6nKWm+GOWqo9sTle0y5I5evZT1q5d2dQ+3KOef\nSvPgyufeCJwFTAEfysz39KrM2KAAACAASURBVDhHtyglSe2YBydJqiXz4CRJ48UCJ0mqJQucJKmW\nLHCSpFqywEmSaskCJ0mqJQucJKmWhlLgIuLciLglIjIiDml6/I0RcX355zsRsSciHj6MMSVJmkml\neXDTrnkB8PrM7LWPjx/0lmqum5ZbvYSW2lZrrPTfySQiNgGPoGiyfHFmfnCGa2+jfYH7OPDPmfmX\nXU66wQInzVHDSg7olAoQAV+74CSO7DK0dFid/+3mPy8M1Mnk7Mx8EkXszYaIWN3z6BEHAacCl/X6\nWkn1ds/2XR2vee5xh+5T3GDmNIBu7qn66ybwdENENPLgHgEcA3QbeNrwAuDrmXlfj6+TNMuqznd7\ncHJqxucj4Peff9x+j9+5ZQebt7UuZJ3u2Q1Xb/PfjAVuWh7cjjKZu5c8uIYzgU/08TpJY+7Q5YtZ\nN231BvCWz93YdVipxlPVeXBExMHAM4Ff72N+kmZZ1SuZTgdM2mW5bZ2Y5MSj2x/K9qCJRpEH90rg\n1Mw8s885+m80SVI75sFJkmrJPDhJ0nixwEmSaskCJ0mqJQucJKmWLHCSpFqywEmSaskCJ0mqJQuc\nJKmWumm23FFEnAucBzwaWNOIyynbdP0N8MhyrD/OzEuHMaYktdLc+qtThpztvOqt0sDTiPg94ODM\nvDAi1lC0+zosMx/s4fZ2MpH0kE7pBo1suQi44oKT9mnUPD1DrlNunIkC80L/nUwiYlNEXBsRN0bE\nq1pdk5nXZeZtrZ4ClkdEAMuA+4DJ7uYsSb1pzoFrlUIwU4ac6qebLcqzM/O+iFgCXB0Rl2Vmt3lw\n7wM+C9wFLAfOyMzBg5okjaVOq7fmHLjN23cyuWeKRQv3/jt+cs/UQ0XwgIWdjyA0xnMlNz91c8hk\nQ0TcAFzF3sDTbp0CXA8cATweeF9ErOh5lpLUo7XLFu9T3AAWLVzAmmXFCm6NK7naqzrw9CzgHVm8\n0XdLRNwKHAt8q7/pShpnnVZSzQdM2uXIHb16KetXL/WAyRioOvD0duBk4IqIOBT4T8B/9D5NSeqs\nU9Fas/xANlrYxkanLcovAYsi4ibgHRTblPuJiA0RcQewDvh2RHyofOoPgV+IiH8F/i9wYeOEpSRJ\nVTLwVJI0nxl4KkkaLxY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4SVItWeAkSbVUdR7cKuDD5eM7KRo3\nf2cYY0rSsDS3+OqkU8bcTGwPNlpV58G9C9iemW8pW339eWae3OPt/aC3NCY6pQVUpZEh10k3GXMz\n6ZQ/NwxjmHwwa3lwxwFfKa/5HrC+7EkpSfPOYSvMmJtPqs6DuwF4CUWz5acAR1H0q/xxf9OVVGej\nXH00b0tu3bm74/VPfORK3v6Sx+33+F33TzCxew/LF3f+dbpuVbGCc6tyNLopcBsi4vTy60YeXLcF\n7h3AxRFxPfCvwHXAnp5nKWnsVL1d2e22JBRbk287/bEcMW2L8c4tO3jdxuvZOjHZ1X2+eet9wOi3\nYsdw2xKoOA8uM7dSZMIREQHcinE5kuaZQ5fvvzUJ8NJLvsGPtu6ahRmpG5XmwUXESmBHZj4InAN8\ntSx6kjSjqlcdvZycbBeeun71Uo5avbTnsd2iHI0ZT1FGxIHAJmA98H1gJXBRZl4+7boNwAXAYcBm\n4AuZeU5EPA34KMVJyBuB38rMLT3O0VOUkqR22p6iNA9OkjSfmQcnSRovFjhJUi1Z4CRJtWSBkyTV\nkgVOklRLFjhJUi1Z4CRJtTSsPLiPAScAu4FvAa/OzN1le66LgdOAHcArM/NfhjGmJFWpm04nvWbD\n2cFktIaVB3ca8MXy249TtOS6pHz8dygK3InAxZl5Yo+394PekroyzCbGnZox95MNN6w8uHFtntxG\n5XlwX8gSxQpuXfnUi4C/Lp+6ClgZEYf38QNI0pzSqgGz2XBzy1Dz4CLiYcArgNeVDx0J/LDpkjvK\nx+4eYM6S1NKwVjZnfODKjhlxxx62jMmpKRYt2LtO6JQNt27VErcpR2jYeXDvp9ievGIYk5Okbgw7\nX62b7ck/Ov2x+xS3yT1TvG7jdTNmw33z1vuGOle3Kmc2tDy4iHgzsAZ4ddPDd1IUxYZ15WOSNG+1\n2p5ctHABt9+3Y5ZmpFaGkgcXEecApwAnZ+ZU01OfBc6NiI0Uh0weyEy3JyUN1bBXMp1OULbLhzt6\n9VLWd8iHc4tydIaVBzcJ/ABonI/9dGa+tfyYwPuAUyk+JnBWZl7T4xw9RSlJasc8OElSLZkHJ0ka\nLxY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4SVItWeAkSbU0lAIXER+LiO9HxHci4sNl02Ui4tiIuDIi\ndkXEG4YxliRJ3RhK4CnwMeDXy68/DpwDXALcB2wAXjykcSTNYd2EhDbrNTC0mS2v1EnHTiYRsYmi\nYfJiisDSD3a4/vXAIZn5pqbHLgK2Z+Yf9zFHO5lIFRh2B37o3IW/WQR87YKTOLKHwNBmwwoPbbAz\n/7w1UCeTszPzScAJFNE5q9uOsjcP7ks9T1HSWHnucYfuU9zAwFANl3lw0pipYuXWcMDCBTy4Z6rj\ndRHw+88/br/H79yyg83bdlUxtY6a/15czdXDjCu4aXlwxwPX0TkP7vwhz1HSPLGmy9VXqzw1gLd8\n7sautielblSdBydpjql6ddLNQZN2eWpbJyY58eiHdzWOh0zUSdV5cIcB1wArgClgO3BcZm7tYY7+\ne06S1I55cJKkWjIPTpI0XixwkqRassBJkmrJAidJqiULnCSplixwkqRassBJkmrJAidJqqWh5MFF\nxMco0gZ2A98CXp2ZuyPi14ALKT6Itw14bWbeMIwxJY23XrPnGgbJoGtmq7C5byidTCLiNOCL5bcf\np0gUuCQifgG4KTO3RMTzKNp8ndjj7e1kIs0DVaYUtNJL9lxDBFxxwUn7NHq++4EJfvGdX2Gqxy66\nw86ja8dkg47672QSEZsi4tqIuDEiXtXqmsz8QpYoVnDryse/kZlbysuuajwuSbOhVYrB4Qcv4WsX\nPJsTjlrV073u2b6Le7bPTrSPutNNovfDM/O+iFgCXA08MzNb5sGVgaffBF43PRMuIt4AHJuZ5/Q4\nR1dw0jwzitXcPWVuXDf5cw2tVnANvaSJNxvVSq4dV3iD9aLcEBE3UKzAGoGn7bQMPI2Ik4Dfong/\nTpIGtmb5gV3nzzVkwnkbr+fuB/bf3jRNvH46xeU8C/gj4LllJtzltIjLKa99M/AE4CXNmXAR8Tjg\nM8DzMvPmPuboCk5SW/0cNlkAvO/XnsjqZfvm0f3Ox/+l5184HjaZdf3F5UTEi4BzMvMFZeDp9cCp\nLfLgzgHOpgg8nWh6/JHAV4DfyMxv9Dl5C5wkqZ2+C9yggacfAl5aPgcwmZkn9Dh5C5wkqR0DTyVJ\ntWTgqSRpvFjgJEm1ZIGTJNWSBU6SVEsWOElSLVngJEm1ZIGTJNVS1XlwLwL+EJgCJoHzMvNrwxhT\nkuaLbtqJ9ZtTZ6uw9qrOg1sG/DQzs+xJ+cnMPLbH2/tBb0mzYlipCJ2y61qlHHSbblBVmsE8SimY\ntTy47bm3gi7FYiVJ+2mVU2e6weC62aI8uzkPLiIu65AH9wrgdU2PnQ68HVgL/MoQ5ixJIzGMVcwZ\nH7iSrTt3z3jNsYctY3JqikUL9q457rp/gonde1i+eOZf0/NopTVy3QSeXgScXn67HjglM69qc+1f\nUmxJntfiuWcAf5CZz+lxjq76JI1EFUGt/WxPTu6Z4uV/eRVX37al4/2HuUU5T4tl2y3KGf9pUObB\nPQd4WlMe3OI2174ZWAO8utXzmfnViHhURBySmfd2OXFJqrVW25OLFi7g9vt2zNKM6qPTFuXBwJay\nuB0LPLXVRWUe3CkUeXDNYac/A/x7ecjkicCBQMvtTUmabVWsYDqdoAyKsNXmdPJ7tu3i6NVLWb96\nacf7e4qyvarz4C4EfoPi4wMTwBv7+JiAW5SSpHbMg5Mk1ZJ5cJKk8WKBkyTVkgVOklRLFjhJUi1Z\n4CRJtWSBkyTVkgVOklRLlebBNT3/ZOBK4MzM/NQwxpSkuWqm7iW95r7ZqaR/lebBlc8tBP4R2Al8\nuI8C5we9JY3MMBout2uw3E/um82UO5qdPLjS7wCXAZt7nLQk1Yq5b6NVaR5cRBxJEbVzEvDkIc1Z\nkiozjFXOYy/6csvHd+ye5N7tuzhk2d6Cdu/2XTPmvtV01TUS3RS4DWVoKcAjgGNonwjwfortySvK\n798DXJiZUxFtV5GSNGf1s2W5bedky8cjYGpq373Iqalk287JtluUw8qoG8dCWXUe3AnAxrK4HQKc\nFhGTmblp8KlL0vxy6PLFrF2x76/QtSsWs3b5gfx4665ZmlV9VZoHl5lHN13zEeDzFjdJ80k/K592\npyj7yX7zFGX/Ks2Dm3bNRygKnKcoJUnDYh6cJKmWzIOTJI0XC5wkqZYscJKkWrLASZJqyQInSaol\nC5wkqZYscJKkWhpKgYuIj0XE9yPiOxHx4bLpMhHxrIh4ICKuL//8wTDGkySpk6EEngIfA369/Prj\nwDnAJeX3V2Tm84c0jiR1pdEua6aAUdtg1VvHTiYRsYkiRWAxcHFmfrDD9a8HDsnMN5XNmt8wYIGz\nk4mklmbqtH/n/RMtA0bv3LKDXyoDRtuFiY5j5/15bKBOJmdn5pMokgE2RMTqtqPszYP7UtPDT4uI\nGyLiixHxc93OWJIG1Spg9MhVB/HLjzl0lmakUeqmwG2IiBuAq9ibB9fO9Dy4fwGOyszjgT+jaNws\nSZU7YOECfrxtJ3du2bHfc3/wguMworL+Zixw0/Lgjgeuo3Me3PmNxzJza2ZuL7/+AvCwiDhkOFOX\npPbWLD+QTHjr576733PrVh3E2qbIGtVTpXlwEXEY8OPMzIh4CkVBbZcGLkk96fRe2RkfuJIHJna3\nzWDb6CGTWqs0Dy4izgVeC0wCE8D5mfmNHufoIRNJUjvmwUmSask8OEnSeLHASZJqyQInSaolC5wk\nqZYscJKkWrLASZJqyQInSaolC5wkqZaGkgcXER+jSBvYDXwLeHVm7i6fexbwHuBhwL2Z+cxhjClJ\nw9bIkJvJTPly3TCDbnSG0skkIk4Dvlh++3GKRIFLImIl8A3g1My8PSLWZubmHm9vJxNJ+5kpC65f\nd94/MePzEfC1C07iyKYInju27ODpZb5cN9pl0A3LGGbZ9d/JJCI2RcS1EXFjRLyq1TWZ+YUsUazg\n1pVP/SpFX8rby+t6LW6SVLl7tu/inu27Ol733OMO3ae4gckEc1k3W5RnZ+Z9EbEEuDoiLsvMlokA\nTYGnrysf+lmKiJzLgeUUieB/PYR5SxoDVazSWnlwcqrjNRHw+88/br/H79yyg83bZi6OByys/rjD\nGK7cOuqmwG2IiNPLrxuBp+0ib6YHni4CngScDCwBroyIqzLz5gHmLEkj1yodHOAtn7ux4/bkGld4\ns2LGAjct8HRHuRLrFHj66qaH7wB+kpk/BX4aEV8FjgcscJI6GtWqpJvDJQEtc+W2Tkxy4tEPn/G1\nHiyZHZ3y4F4EnJOZLygDT6+nODBy+bTrzgHOpgg8nWh6/DHA+yjCUA+geH/uzMz8Tg9z9JCJJKmd\nvg+ZfAlYFBE3Ae8Armpz3V8Ah1JsQV4fEX8AkJk3lff4NkVx+1CPxU2SpL4YeCpJms8MPJUkjRcL\nnCSplixwkqRassBJkmrJAidJqiULnCSplixwkqRaqjQPLiLeCPxa01iPAdZk5n3DGFfSeOimlVYr\n/Wa32VqrHirNg5t2zQuA12dmr83l/KC3NE9U1f2/U05bKxFwxQUn7dMgudvstqoz28Du/0M0a3lw\nzV4OfKLbGUtSvyLg5484eL/u/2a3jZeOK7iIeHhzHhzwzA55cN8EXtcUmUNEHESRLPAzfWxPuoKT\nxtwZH7iS7969tatrn/jIlbz9JY/jiJVLmJyaYtGCvf+Ov+v+CU69+KsdV3D/etEpg0xXo9V2BVd1\nHlzDC4Cv+96bVD+jCiXdtnOy4zUR8LbTH8sR5RbjogULmNwzxaKFC7hjyw7O23g9Wyc632dUP9N0\nblsOV9V5cA1n4vakpIq1CiVdtHABz3/vFdx499aOKzfVS6cV3MHAlrK4HQs8tdVFZR7cKRR5cFPT\nnjsYeCbw60OYr6Q5Zj6Eki47cBFPWT9zKGkzT1HWQ6fA0wOBTcB64PvASuCiFoGnk8APgMb5209n\n5lvL515JEZJ6Zp9z9N9ckqR22r4HZx6cJGk+Mw9OkjReLHCSpFqywEmSaskCJ0mqJQucJKmWLHCS\npFqywEmSaqnqPLiDgb8BHlmO9ceZeekwxpRUT6POfmvHbibzX6V5cBHxe8DBmXlhRKyh6IZyWGY+\n2MPt/aC3NAtmq+HwqLPf2hlFJhzYYHkIZi0PLoHlERHAMuA+oHMrb0nqQasmy+tWHcShK8x+G2eV\n5sFFxHLgs8CxwHLgjMz8+x7n6ApOGiONLcpu89+gWMF96XXPeCgmp+Gu+yf43U9/m+tuv7/rex13\n+ArALcp5pP9elBFxEdDIg1sPnJKZV7W59i+Bn2bmeeX3LwN+ETgfeDTwj8Dxmdn9f7kWOGnkZmt7\nslmvW5UnHLWKi898PEdOW8n1ulVZ1dakW5GV6W+Lcloe3PHAdXTOgzu/6eGzKJIFMjNvAW6lWM1J\n0lBd84MtvOyS/Q+orFt1EGuXu1U5jqrOg7sdOBm4IiIOBf4T8B+DT1tSlebCaqOf05Tt8uCOXr2U\n9auXdnUPtybro9I8uIg4AvgIcDjFf3vvyMy/6XGOblFKktoxD06SVEvmwUmSxosFTpJUSxY4SVIt\nWeAkSbVkgZMk1ZIFTpJUSxY4SVItDaXARcTHIuL7EfGdiPhw2XSZiFgVEZ+JiG9HxLci4ueHMZ4k\nSZ1UnQf3LmB7Zr6lbPX155l5co+394Pe0jzVbbutXsNKbaelJgOlCWwCHkHRZPnizPxgh+tfDxyS\nmW+KiL+naM91RfncvwO/kJk/7mHyFjhphIaZJNBNIkA/YaXD6vg/F3puamADdTI5OzOfBJwAbIiI\n1W1HKbYmXwF8qXzoBuAl5XNPAY5ibxiqJLUNK50pAeCe7buqnpZqoFOaABRFrZEH9wjgGKBl4Cnw\nfortySvK798BXBwR1wP/ShG3s2eA+UqqWKtVTb+rugMWLuDBPVMzXrN5+04m90yxaOHef29P7pma\nsYg9ODnzPbvh6q3+Zixw0/LgdkTE5XTOg3t147Ey2PSs8vmgyIMzLkcaE2uWH9hxm3LtssX7FDeA\nRQsXsGbZgfx4qys19a/SPLiIWAnsyMwHgXMoVne9pHlLmgMGWe10OmjSb4abB03USdV5cE8DPkpx\nUORG4Lcyc0uPc/SQiSSpHfPgJEm1ZB6cJGm8WOAkSbVkgZMk1ZIFTpJUSxY4SVItWeAkSbVkgZMk\n1ZIFTpJUS900W+5KRPwVReJAADcDr8zM7WU3lL8GnkTRpPmMzLxtWONK0ih1m3HX0GvWXSu2JevP\n0DqZRMSKRp/JiPhTYHNmviMifht4XGa+JiLOBE7PzDN6uLWdTCT1ZZjZdg3dZNw19JN118qw8u86\nmacJC4N1MomITRFxbUTcGBGvanVNU3ELYAl7C9OLKPpRAnwKOLm8RpJqrZ+sOw1Pt1uUZ2fmfRGx\nBLg6Ii7LzP0y4SLiUuA04LvAfy8fPhL4IUBmTkbEA8Bq4N6BZy9J01SxamvWTcZdQz9Zd83jVGWe\nrtR61u3f4IaIuAG4ir2hp/vJzLOAI4CbgF62ISVpXljTw+prpqy7bsZp/FF/Oq7gegk9BcjMPRGx\nEbgAuBS4k6Io3hERiygy5tolgkvSQEaxOun2oEm/WXfgwZJh6GaLsmPoafme2qMz85by6xcC3yuf\n/izwm8CVwMuAr+Q8yOiRpHYGKT5rlh/IRovXSHRT4L4EvCYibqIIPb2qxTUBfDQiVpRf3wC8tnzu\nr4D/HRG3APcBZw48a0mSOjDwVJI0nxl4KkkaLxY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4SVItWeAk\nSbU0lDy4GbLgngG8B3gccGZmfmoY40kaX6PKY7NV1vw3lA96z5AFtx5YAbwB+GyfBc4PekvzSNXd\n/EeVx1Z1Btu4dPQfgf4/6D1IFlxm3paZ3wa6y5aQpCEyj228dbNFOUgWnKQxU8XKpHlbcuvO3V2/\nbsfuSe7dvotDmuJp7t2+i4nde1i+eOZff+tW7buCc8ty/ummwG2IiNPLrxtZcPsVuMw8KyIWAn9G\nkQV36dBmKWlOm0vbks0iYGpq373Iqalk287JjluU37z1vn2+r/pnBLcth23GLcppWXDHA9fRIQsO\n2Ai8dIhzlKS+HLp8MWtX7Psra+2KxW5RjolOK7hBs+AkjYGqVx69npxsGCRwdDq3KOefGU9RRsSB\nwCZgPUUW3Ergosy8vOmaBcAVFKclH8qCy8ytEfFk4DPAKmAn8KPM/Lke5+gpSklSO21PUZoHJ0ma\nz8yDkySNFwucJKmWLHCSpFqywEmSaskCJ0mqJQucJKmWLHCSpFqqOg/ufOAcYBK4h6Jx8w+GMaYk\njVIv3VT6zaBrsGvKcFSdB3cS8M2y1ddrgWdl5hk93t4PekvqSpUNkbtt+DxIBl1D1Vl0M5mHDZ9n\nLQ/unzNzR3nZVcC6XmcuSfOJGXRzxyjz4H4L+OJAs5WkGVS5+njsRV/u6roduye56/4JjmhahU1O\nTXHsYcvZ8eCeru7RnEXndmX/Om5RRsRFQCMPbj1wSmZe1ebaRh7c1Zl5adPjvw6cCzwzM3f1OEe3\nKCV1NJcy6Z68fhWf+K9PZdHCvZtkvW5TNoxqu3Iebk029LdFOYw8uIh4DvAm4IV9FDdJmnd+eN/E\nPsUN3KacDZXmwUXEE4APAKdm5ubhTl2S9ppLmXTm0M0NVefB/RPwWODu8vLbM/OFPc7RLUpJUjvm\nwUmSask8OEnSeLHASZJqyQInSaolC5wkqZYscJKkWrLASZJqyQInSaqloRW4iPiriLghIr4dEZ+K\niGXl46+JiH+NiOsj4msRcdywxpQkqZ2hfdB7hky45sdfCPx2Zp7aw639oLeknvXSWquVQUNLm9lu\nq1JtP+jdVaJ3RGwCHkHRaPnizPzg9GtmyITb2nTZUixY0tiquuN/s166/0+3YAG858zHP9RLcs3y\nA3nVMx7VVxoAjPbnnsepAEPXVYFjwEy4iPhvwPnAAYB/+5LmrCevX8V7z3wChx+8b0xNIw3gx1sN\nRZkvutqiHEYmXPncr5av/c0e5uiKT6qhqlc192zbxYN7pnp6TQRcccFJ+yVyQ+95bgc0xeWsqTgm\nZ8xXbf33ohxGJlyTjcCLO40pSYPqp6gcunxxy+J29wMTnLfx+p62J9csP/ChP5od3WxRDpoJd0xm\n/lt56a8A/zb99ZLGzyhWHb0eNGmV4/aT7bs4f+P1LFwQnHj0w7u+lwdLZl/HLcohZMJdTLEC3A1s\nAc7NzBt7mKNblJKkdsyDkyTVknlwkqTxYoGTJNWSBU6SVEsWOElSLVngJEm1ZIGTJNWSBU6SVEsW\nOElSLXWbJtBRRPwVcALFh+5uBl6Zmdubnn8p8CngyZl5zbDGlTS39NIea9DMNdthaSaVB56W3y8H\n/p4iLufcHgucnUykIauyk3+3OWytOvf32rH/yJVLOl80oDHv1D8fDNbJJCI2RcS1EXFjRLyq1TXt\nAk9Lfwi8E9jZ9ZQlzTv3bO8+K61V5/5G5po0DJUHnkbEE4FHZObfR8QbhzVxSb0ZRar0g5Pd569t\n3r6TyT1TLGrKTZvcM9V1kWzOWxs2V2310O1/IRsi4gbgKuARwDGtLsrMs4AjgJuAM8qUgT+lKd1b\nkgDWLlu8T3EDWLRwAWuWdbeCM2dNnXRcwU0LPN0REZfTIfA0IjYCFwCfBn4euLzYueQw4LMR8UIP\nmkijNdfy11plr92zbRdHr17K+tVLO77eAybqpJs8uBcB52TmC8rA0+uBU6flwU0PPH0XQGa+Ydq9\nLgfe4CETSdKQtD1k0s17cF8CXhMRN1EEnl7VZoCPRsQ+gad9TFSSpKEw8FSSNJ8ZeCpJGi8WOElS\nLVngJEm1ZIGTJNWSBU6SVEsWOElSLVngJEm1NJQ8uHZZcBHxSoquJneWl74vMz80jDElaS7qpV1Z\ns0Gz8VoZ93ZmQ/mgd7ssuLLAnZCZ5w5wez/oLWkoRpGo0G0eXrNhZOO1Moq8vH4NsTdq/x/0HkIW\nnCRpBmbjVaObLcq+s+BKL42IZ1BsXb4+M384jIlLUq9Gkajw2Iu+3PNrduye5N7tuzikKSro3u27\nmNi9h+WL+38nadxz7br5m9sQEaeXXzey4PYrcJl5VkQsBP4MOAO4FPgc8InM3BURrwY+Coz337ik\nSo1iG3Im23ZO9vyaCJia2nfja2oq2bZzcqAtytn+u4DZLbIzblFOy4I7HriODllwwEbgpeX3P8nM\nRjzvh4AnDWHOklQrhy5fzNoV+/5qXbtisVuUA+q0gjsY2FIGnR4LPHX6BS2y4F4IfK987vDMvLu8\n9IUUSd+SVJnZ3pbr5xTloOGv7XiKcob1b0QcCGwC1lNkwa0ELpoWdroAuALYJwsuM7dGxNspCtsk\ncF/5+Pd6nKMHViRJ7bQ9RWkenCRpPjMPTpI0XixwkqRassBJkmrJAidJqiULnCSplixwkqRassBJ\nkmqp0jy48rn/AlxE8Xm2GzLzV4cxpqTh6LbzRr95ZePeTUOzp+o8uGOATwLPzswtEbE2Mzf3eHs/\n6C1RXePcbvLLBskrG1Ym2Wy34NKcNWt5cP8V+PPM3FJe12txkzQHHLbCvDLNP1Xnwf1s+dzXgYUU\nfSy/NJypS+Nl2CuYxtbk1p27Z7zuiY9cydtf8rj9Hr/r/okZ88qOO3wF4BalZk/HLcqIuAho5MGt\nB07JzKvaXNvIg7s65SeTIwAAIABJREFUMy+NiM8Du4H/AqwDvgo8NjPv72GOblFqbFWZ59Xv1iTA\nnVt28LqN13PND7a0fe2wtianc6tS0/S3RTloHhxwB/DZzNydmbdSHEA5pqepS5o1hy7ff2sS4KWX\nfGPG4ibNBZXmwVFE7bwcuDQiDqHYsvyPoc1eqrkqVyvdnJ5sl1O2fvVSjuqQU+bWpGZb1XlwAfwJ\ncCqwB3hbZm7scY5uUUqS2jEPTpJUS+bBSZLGiwVOklRLFjhJUi1Z4CRJtWSBkyTVkgVOklRLFjhJ\nUi1VmgcXEe8GTiovOwhYm5krhzGmJEkzqTQPbto1vwM8ITPP7vH2ftBbUmW6DXyF/kNfp7ON2VD1\n38kkIjYBj6BosnxxZn5whmsDeD9wW2a+c9pz3wDenJn/2MPEwQInja0q0xQauklVgNbJCnc/MMEv\nvvMrTE31NmZVSQvt1DyBYaBOJmdn5pMotiA3RMTqliMUeXA/Ao6liMxpfu4o4Gig+v9aJakCrZIV\nDj94CV+74NmccNSqWZqVZtJNgdsQETcAV1Gs5FrG3WTmWcARwE3AGdOePhP4VBmnI0kdjWL11osf\nb9vJHVt27Pf4ESuX8J4zH0+0XUfMrpqv3mZUdR5cw5nAJwaaqSTNokw4b+P13P3A/lua61YdxNqm\nSCHNDVXnwVG+bhXQ/Tu5ksbeqFYevRwyATh/4/W879eeyOpl+2bkHb16Kes7ZOQ1eMhkNCrNgyuf\nvwhYnJm/2+ccPWQiSWrHPDhJUi2ZBydJGi8WOElSLVngJEm1ZIGTJNWSBU6SVEsWOElSLVngJEm1\nZIGTJNXSUAJPYcbQ00cCH6XogrIQ+N3M/MKwxpWkQXXbrmuQPDjbc43e0DqZtAs9jYgPAtdl5iUR\ncRzwhcxc38Ot7WQiqdJ0gW4y4RYsgK9f+GwOP3hvltsdW3bw9P/1z3Tza3QUGXBjmhwwWCeTiNgU\nEddGxI0R8apW1zQVtwCWsLcwJUWfSiiaN9/V7awlqQr3bN+1z59Onrx+FV+/YN/iBr2lCHQzjoar\nqxVcRDw8M++LiCXA1cAzM/MnLa67FDgN+C7wK2UKweHAP1AkCiwFnpOZ1/YwR1dw0pgYVQZctyne\n0DrJu6GXFRy4iqvIwL0oBwk9fTnwkfx/7N19uF11fef99zehEMgDhEAggJK00omZKiggOq2FYEep\no4NRO6C2HUDrrS2idTRoe+uNVm+d2haxdrxEb0Gn1kxHbKr1adoql6BEQQlWpD60VORBE0ggOZ6T\nQ07O9/5j7UP22dn7nLX3Xvs8rPN+XVcu91577bV+ATzf8/vt3/5+Mk+hKH7/s5FAIElzXrskb4AH\nHhnhdVu2ly5umnnTbjJpCT0djogbmSb0NCK2AJuB64CXAxc0XrslIpYAxwE7+h69pFqZixlwQZH3\ndnzTUuRDQ6O8fst2Fi8Kzll3bOlrudFkZpXZRdlv6Ok9wLOA6yPiiRTFcWclo5ekHvRbaFYtO4JP\nWKzmvGk/g+s39LSxc/JDwDKKz9M2Z+b/6WKMLgBIkjox8FSSVEsGnkqSFhYLnCSplixwkqRassBJ\nkmrJAidJqiULnCSplixwkqRaqiQPboosuFOBjwDHA7uA38zMe6u4pyTNNd20AIP+8uUm2P6rs0q+\n6D1FFtz/Bv4uMz8aEecDl2bmb3V5eb/oLaknM5VOMKHflIJu0wlgZhIKYE6nFPT+Re8+s+A2ABP/\nhX0ZuLCbUUtSXbVLKegmX07TK7NEeVlzFlxE3FAiC+6/NQ7fAbwQuAbYBCyPiFXt3i9JVZvpWcdF\nH7yF7z6wp9S5w/vHuP/hEU5qmoGNjY+z/sTlDD96oPQ95/DMataVabZ8FUVxgqLh8nMyc1uHcxcD\nfw7cmpnXRcRJwPuBdcBXgBcBv5SZD3cxRpcoJVViJpYsu1mmPHvtSj7xO0/nsMUHF9PmYojqhDla\nTHtbomzJgjsduJ1psuCALRSFjMy8PzNfmJlPAf6wcayb4iZJtfXjXSOTihu4TFml6ZYo+8qCi4jj\ngF2ZOQ68mWJHpSTNipmYgfQbprpz7yjrVi1l7aqlpa7hLsrOplyirCAL7sXAuyiWGb8C/F5mjnY5\nRpcoJUmdmAcnSaol8+AkSQuLBU6SVEsWOElSLVngJEm1ZIGTJNWSBU6SVEsWOElSLVWSB9csIt5H\n0aB5WeP5EcDHgDOBh4CLMvPfqr6vJM20Ml1L+sl8s0tJfyr9ondEnAW8FtjUVOB+F3hyZr4qIi5u\nvHZRF5f1i96SKldF4+XpGiv3m/lWdSPlOdosuV/9fdG7TCZcI0ngPcDmlpcuBD7aePxJ4FmNnpWS\nVGtmvs2uskuUZTLhLgc+nZkPtNSvk4EfA2TmWEQ8AqwCHuxz7JLUs35nMxd98Bb27Ns/5TnD+8d4\ncGiU45YdLGgPDo0ysv8Ay5dM/+P3lJVHukzZh7IF7oqImMiEexxwGsXnaQA0ct9+Aziv0tFJUh8G\nmf9WJvctAsbHJ69Fjo8ne/eNlVqi/Prdu/r+O9R0WbKUaZcoS2bCPQV4AvDDiPg34KiI+GHjtfso\niiIRcRhFBI+J3pJq74TlS1i9YvKPy9UrlrhEOUPKzOCmzYTLzM8CJ048j4ihzHxC4+mngf8K3AK8\nGPhSzoMIA0nz3yBnL2V2UJr3Nrum3UVZJhOuzXuGmnZRLgH+J8UsbxdwcWb+axdjtBhKkjoxD06S\nVEvmwUmSFhYLnCSplixwkqRassBJkmrJAidJqiULnCSplixwkqRaqrTARcT7ImKo6fmvRsS3ImIs\nIl5c5b0kSZpKZYGnjSy4lS2H7wEuAd5Q1X0kaUKZdlll9BNKOsGWWnNPmVZdWymaJS8BrsnMa9uc\nsxj4B+ClwA8m2nQ1vX498HeZ+ckexmgnE2kOGmSn/rLKdPSfSgScuHwJn3z1Mzi5x1DSCVWHk05n\nIacEtOjYyaTMDK6fLDhJGoidQ6N9vf/stSu5+qIzDgkkhYOhpD/d0989NLvKFDiz4CQ9Zi7M3AAe\nHRvv+b0RdCxuUMzgduwtX9wOXzzz+/V++d1fchY3jSkLXEsW3HBE3MjUWXDQyIJrisuRpDnlhOVL\npixur9uyvavlyePNd5uTppvB9ZsFJ6lm5sqsoZ8NJp1y2t669TvsHn6UxYuCc9YdW/p6bjCZm6bc\nZFJBFtzZwN9Q7K7cB/wkM/99l2N0k4kkqRPz4CRJtWQenCRpYbHASZJqyQInSaolC5wkqZYscJKk\nWrLASZJqyQInSaolC5wkqZYqy4ODIvCUIn1gopPJ64FXAGPAzsZrP6rynpJUtW7agPWTJWeLr8Gq\nrJNJI/D0tcCmpgK3Efh6o5flq4HzMvOiLi9tJxNJHQ0i3aBszlwE3LR546TGzQ88MsIv//cvMV4i\n7GAmMuTmSu/QAeq9k0lEbI2Ib0bEnRHxyg7nLAbeA2xuPp6ZX87M4cbTbcAp5ccsSXNbu1SCNUcf\nyc2bz+esU1dO+/6dQ6OP/VH1ynwGd1lmngmcRZENt6rNOY8Fnk5xnZcDn+9hjJLU1qCy6crmu/10\n7z7u3T18yPGTjjmS9158BtPlPz86Nv7YH1WvzL/FKyLiDooZ2ETg6WOaAk//vNMFIuI3KQrke3of\nqiTNjLL5bpnwui3beeCRQ5c0J1LBNXumi8s5D3gH8OymwNNJcTkR8Z+A/48iDgfg8cC/TmTCRcSv\nURS/czNzRw9j9DM4STOum40mi4D3v+yprFo2OV/uNX/1rdI/wNxw0rPe4nIi4kLgFZn5/Ebg6Xbg\ngi7y4J4CfLLxnh/0OHgLnCSpk543mXwBOCwi7gLeTbFM2Y33AMuA/x0R2yPi012+X5Kknhh4Kkma\nzww8lSQtLBY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4SVItWeAkSbVUaR4ctM2EexXwe8ABYAh4ZWZ+\nt+r7SprfZiKDzXZYC0ulX/TukAm3IjP3NB7/Z+B3M/OCLi7rF72lOWJQ3fuhvwy2e3cP88w//jLT\n/TgbVP7aAshcm8v6+6J3n5lwe5qeLsWCJakP7TLY7NyvdsouUV6Wmbsi4kjg1oi4ITMfajnnsUy4\naAlBiojfA14PHA74q440Tw1ypjKxRPndB/ZMed7w/jHuf3iEk5pmY2Pj46w/cTnDjx6Y8r3OtBaW\nUkuUEXEVsKnxdC3wnMzc1vT6ScBfA+dl5lhzokDLdV7aeO9/7WKMzvikOWa2lyrPXruST/zO0zms\nKZi0zDJllUuUFss5o/clykYm3K8Bz8jM04HbgSUtpz0FeALww4j4N+CoiPhhm8ttAV5QbsyS1N6P\nd41MKm7gMqUOVWaJ8mhgdyPwdD3w9NYTMvOzwIkTzxszuInA09OasuD+E9BrLpykOWImliqnEhSB\nos3J2zv3jrJu1VLWrlra8X3uolxYpl2ijIgjgK0US5PfA46hJdW7zXuaQ0+voZgB7gd2A5dn5p1d\njNElSklSJ70les8Rc36AkqRZYx6cJGlhscBJkmrJAidJqiULnCSplixwkqRassBJkmrJAidJqqWB\n58E1HX8R8Eng7My8rer7SlpYynQ86TY3zk4n9TLwPLjG8eXAZynSBC7vssD5RW+pJqps0jxdU+Ze\ncuNsxjwvzV4eXMMfAf8d2FfmfpLUL3PjNPA8uIh4KvC4zPxsRLyxmmFLmo+qnNVc9MFbpsyOG94/\nxoNDoxy37GBBe3BolJH9B1i+pP2PPmdd9VK2wF0RERN5cI8DTgMeK3CNPLjfAM5rflNELAL+DLik\n34FKqocqlyn37hvr+FoEjI9PXoscH0/27hvruERZ5dgslrNv0Hlwy4FfAm5sHH868OnGZ3WSNDAn\nLF/C6hWTf1StXrHEJcoFZOB5cMBxTcdvBN7gLkpp4ap6mbKTXjLj3EVZLwPPg2s5fiPdFzh3UUqS\nOjEPTpJUS+bBSZIWFgucJKmWLHCSpFqywEmSaskCJ0mqJQucJKmWLHCSpFqqtMBFxPsiYqjp+SUR\nsTMitjf+vKLK+0mS1EllgaeN/pIr27z0vzLz8qruI2nhKhNy2qzbwNNmtu2a/8q06tpKkSCwBLgm\nM69tc85i4B+AlwI/mGjTFRGXAGf1WeDsZCLNI1V25G81Xchps0WL4KtXns+aow+GmE4XeNqsyvDT\nViYNVKqvTiaXZeaZwFkUsTmr2pzzWBZcm9deFBHfjohPRsTjyo1Xknp39tqVfHXz5OIGBp4uNGWW\nKHvKgmv4DPCJzByNiP8L+Cjgry5STQ1y9lZWBFx90RmsaTMDu3f3MDv2jk75/sMXD27vnTO3mTXl\nv8k+s+DIzIcyc+K/pg8DZ1Y3dEk61AnLl3DKyqMOOf7AIyO8bsv2aZcnj19+xKSIHc1f083g+sqC\ni4g1TcuW/xm4q5phS5qLBj1DKbPJpF0O3ENDo7x+y3YWLwrOWXfslO93c0l9TLnJpN8suIh4F0Vh\nGwN2Aa/OzH/ucoxuMpEkdWIenCSplsyDkyQtLBY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4SVItWeAk\nSbVkgZMk1VJleXBQBJ5SpA8sazr2X4CrKL6wfUdmvrTKe0qqr27z36C/DLgJtuuqh8o6mTQCT18L\nbGpq1XUa8NfA+Zm5OyJWZ+aOLi9tJxNpDpiNpIBu8t+gSBK4afPGSc2W79s9zK+UzICbMMgsuFYm\nDPSt904mEbE1Ir4ZEXdGxCs7nLMYeA+wueWl3wH+IjN3A/RQ3CSptHZJAievPIr/+MQTZmlEmk1l\nEr2PzcxdEXEkcCtwbmY+1HLOa4FFmXl1S7PlrcD3gV8GFlM0av5Cl2N0BifNotnMeOtlBnfz5o2c\n3FLkuknyhpmdwbVyRte1vnpRXhERdwDbOBh4evDKBwNP/7zNew9rnH8e8BLgQxFxTLkxS1J3MuHt\nn/nuIcdN8l6Yptxk0hJ4OhwRNzJ14Ck0Ak8bmXD3Al/PzP3A3RHxfYqCd2ulfwtJAzObM4peNpk8\nMrL/kDy4nXtHWbdqKWtXLS11DTeZ1MN0eXAXAq/IzOc3Ak+3Axd0kQd3AfCSzPyvEXEcRSL4Ga1L\nnNNwiVKS1EnPS5RfAA6LiLuAd1MsU3bji8BDEfFd4MvAG7ssbpIk9cTAU0nSfGbgqSRpYbHASZJq\nyQInSaolC5wkqZYscJKkWrLASZJqyQInSaqlgebBRcTVwMbGy0cBqzPTXpSSplSmRVcvuW+24FpY\nBpoH1/L6a4CnZOZlXV7aL3pLc1zViQPTpQi0y30rkxgwyJQAUwBmzazlwTV7CfCJ6e4nSdNpl/tm\nYoBalVmivKw5Dy4ibmjTT/Jy4NOZ+UAjUWCSiDgVWAfMXrCUpIGpevbypKu+OOXrw/vHeHBolOOW\nHSxoDw6NMrL/AMuXdP6xdsrKI12mXEDKFLgrImJT4/FEHtxjBa4pD+68Ka5xMfDJzDzQ4zglzVGD\nCETdu29sytcjYHx88lrk+Hiyd9/YlEuUX797V2XjdUly7ptyibIlD+50iribqfLg/o1GHlzLORfj\n8qSkipywfAmrV0z+UbR6xRKXKDXJdDO4o4HdjbDT9cDTW0/IzM8CJ048b+TBPaHp+XpgJdB9cqGk\nOW8QM5npdlEG9Bxq6hLlwjFd4OkRwFZgLfA94BjgqrKBp43nVwFLMvNNPY7RXZSSpE467qI0D06S\nNJ+ZBydJWlgscJKkWrLASZJqyQInSaolC5wkqZYscJKkWrLASZJqqdI8OGibCfd44KMUXxJfDLwp\nMz9X9X0laRCm66rSbS6dnVRmTqVf9G6XCRcR1wK3Z+YHImID8LnMXNvFZf2it6S+9NNgeapsul5y\n6arKpLPZ82P6+6J3n5lwCaxoPD4auL/MPSVprjOXbm4rNYOLiGObM+GAc1sz4SLitcCizLy6uR9l\nRKwB/g9Fw+WlwK9l5je7GKMzOEmz5qIP3sJ3H9jT9rUI+NJ/O++QXLrz//TGjjO4DWtWuExZrY4z\nuLKfwfWTCfcS4PrM/NOIeAbwPyPilzJzvOS9JalnVeS/dcqn6yWXzky6mTPtEmUFmXAvB/4aIDNv\nabz3uCoGL0mzyVy6ua3MDK7fTLh7gGcB10fEEykK3M6+Ry5JJVQxy+m0k7LXXDqXKGfGtJ/B9ZsJ\n19g5+SFgGcXnaZsz8/90MUY/g5MkdWIenCSplsyDkyQtLBY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4\nSVItWeAkSbVUaYGLiPdFxFDT81Mj4h8j4tsRcWNEnFLl/SRJ6qSywNNGFtzKlsN/AnwsMz8aEecD\n7wJ+q6p7SlKvpgsynUq3IafTsXXXYJRp1bWVIkFgCXBNZl7b5pzFwD8ALwV+0NSm607ggsz8cUQE\n8Ehmrmh9/zTsZCLVUFUd9Xs1VZDpVNqFnD7wyAi//N+/xHiPGSlVhaCWUcMEgr46mVyWmWcCZ1HE\n5qxqc87lwKcz84GW43cAL2w83gQs7/B+SZoX2oWcrjn6SG7efD5nndq6iKXZVGYGdxVFcYKi4fJz\nMnNb0+snUcThnJeZYy2Nlk8C3g+sA74CvAj4pcx8uIsxOoOTFoiZnNVVOYObcO/uYZ75x1/umAXX\nyUzO4KYyT2d3vc3g+s2Cy8z7M/OFmfkU4A8bx7opbpI0p2TC67Zs54FHDi2Qp6w8yiy4OWTKGVxE\nXAi8IjOf38iC207xmdqNU7yneQZ3HLArM8cj4p3Agcx8a5djdAYnqXL9bDKBYnbw/pc9lVXLJmfB\nveavvtX1Dy03mfSlt7icCrLgXkyxczIplih/LzNHuxy8BU6S1Il5cJKkWjIPTpK0sFjgJEm1ZIGT\nJNWSBU6SVEsWOElSLVngJEm1ZIGTJNWSBU6SVEuV5MFFxPXAucAjjUOXZOb2RkTONcBzgeHG8W9V\ncU9Jmk29tPrqNUfOVl69qaSTSaPA/V1mfrLl+HOB11AUuHMo8uTO6fLydjKR1JWZSCXoNo0gAm7e\nvJGTm1IIyqYPzETawDxNEoB+OplExNaI+GZE3BkRr+zyxhdSJHpnI2LnmIhY0+U1JGnee/aGEyYV\nNyifPrBzqNsWvoLqAk8B3hkR346IqxtNmgFOBn7cdM69jWOSNDAzMRs5fHH5LQwR8JbnbTjk+H27\nh9mxd/ri9ehYj1HhXfjld39p1lPWq1bm39AVEXEHsA14HHBam3PeDKwHzgaOBa6sbISSNAcd30Xu\nW7sUcIC3febOrsNRVd6Um0xaAk+HI+JGDg08JTMfaDwcjYjrgDc0nt9HURQnnNI4JkkDNROzuLIb\nTYIiK665KO7cO8qekTHOWXdsqWu40aR70+2iPBrY3Shu64GntzspItZk5gONXZMvAL7TeOnTwOUR\nsYVik8kjTcVQkua1forO8cuPYItFa6CmK3BfAF4VEXdRBJ5u63DexyPieIpfVLYDr2oc/xzFDsof\nUnxN4NK+RyxJUgkGnkqS5jMDTyVJC4sFTpJUSxY4SVItWeAkSbVkgZMk1ZIFTpJUSxY4SVItDToP\nbj1wHfBU4A8z80+quJ8kVamXbDfoPd+tmS24BmfQeXCrgVMp2nft7rHA+UVvSYeosvN9t9luUCQE\n3LR546QmymXz3ZrNRNZbJ/M4A67Z7OTBZeaOzLwV2N/N+yRprmuXEFA2300zo8wS5WWZuSsijgRu\njYgbMvOhNue9MyLeCvwj8KbMNKFP0sBUOfu46IO38N0H9nT1nuH9Yzw4NMpxyw4WtAeHRhnZf4Dl\nS8p9+rNhzQqXKAeozL+FKyJiU+PxRB5ca4F7M/AT4HDgWoo8uLdXNUhJajaIYM69+8a6Oj8Cxscn\nr0WOjyd7942VXqK8d/fIrIWM1mR5ckpTLlG25MGdDtxOhzy4LIxSbCp52gDGKklzxgnLl7B6xeQf\nh6tXLHGJcg4ZdB6cJFVuELOPbndSdgoxXbdqKWtXLS11DZcnB2vKXZQRcQSwFVhLkQd3DHBVZt7Y\nct6XgEl5cJk5FBEnArcBK4BxYAjYkJndLHa7i1KS1EnHXZTmwUmS5jPz4CRJC4sFTpJUSxY4SVIt\nWeAkSbVkgZMk1ZIFTpJUSxY4SVItDToP7mUUfSkD2Au8OjPvqOKekjTTOW52HplfBp0H9x+AuzJz\nd0T8OkUXlHO6vLxf9JbmoZloIjzTOW4zld22EBohV2jW8uC+lpm7G0+3Aad0835JqkoEnLhiCSeu\nMMdtoZh2BhcRxzbnwQHntubBNWZwzwBG6ZAHFxFvANZn5iu6HKMzOEmPaV6WLJvh9tTHH8O7Xvhk\nTjrmSO5/eITDD1s0Kcft/odHuOCar0w5gzO7bc7qvRdlRFwFTOTBrQWek5nbWs5Zw+Q8uH/JzLc3\nvb4R+B/Ar3QIS52KBU6a42Yy06zbZcl2S5I79uxj/4FxTl55FPfuHuZ1W7Zz2492T3GVmVuenOAy\nZWkdC9yUm0xa8uCGI+JGOuTBNR6ORsR1wBuarvFk4MPAr/dQ3CSpLycsP3RJcvWKJTz9//0HEtix\nd7R0QKnml4HmwUXE44FPAb+Vmd+vcNyS5pCZnG1Uldu2dtVSEsxuq7FB58F9GHgR8KPGqWOZeVaX\nY/R3K0lSJ+bBSZJqyTw4SdLCYoGTJNWSBU6SVEsWOElSLVngJEm1ZIGTJNWSBU6SVEuVFLiIuD4i\n7o6I7Y0/ZzSOXxgR324cuy0ifqWK+0mSNJ1B58EtA36WmdnoSfnXmbm+y8v7RW9J0+rUwqtsuKmt\nuOat3potQ5EHBzyOosnyNZl5bdm7ZuZQ09OlWKwkTaPXZIJ2KQMR8Gf/5fTH+lAev/wIXvmrP982\n3LTX+9r1f+4qs0R5WWaeCZwFXBERqzqc987GcuTVjR6WAETEpoj4Z+CzwGX9D1mSJts5NNr2+LM3\nnMDJhpsuWGUK3BURcQdFIvfjgNPanPNmYD1wNnAscOXEC5n5N41lyRcAf9T3iCWpxaNj44cci4C3\nPG/DIcfv2z3Mjr2TC+Lhi91vV0dT/lttyYM7HbidDnlwWRgFrgOe1uacrwA/HxHHVTFwSZpKuxw4\ngLd95s5DliePd0ZXS4POg3sCRbp3RsRTgSMAQ08lddTLZ1rtNph0yoHbMzLGOeuOnXSuG0zqadB5\ncFcCvw3sB0aAN2bmzV2O0Y0pkqROzIOTJNWSeXCSpIXFAidJqiULnCSplixwkqRassBJkmrJAidJ\nqiULnCSplixwkqRamjYup4xGHty5wCONQ5dk5vam188GbgEubs2Mk6SZ1ik7rlXZLLlmtv2aOwYa\neNp4bTHw98A+4CM9FDg7mUjqOa+tnXbZca0WLYKvXnk+a44+8rFj9+4ebpsl1+zkY47s/GKPzJyb\nUu+dTCJia0R8MyLujIhX9nDz1wA3ADt6eK8kVWbn0GjH7LhmZ69dyVc3Ty5uYJbcfFNmifKyzNwV\nEUcCt0bEDZnZLhHgnRHxVuAfgTdl5mhEnAxsAjZSZMVJUleqnLm1y41rFQFXX3QGa9rMxO5tkyU3\nE9r9M3BWN71BB56+F7gyM6f/r0qS5oBOOXIPPDLC67Zsn3J5UnPLlDO4lsDT4Yi4kQ6Bp42HoxFx\nHfCGxvOzgC1FTBzHAc+NiLHM3FrN8CXVXZUzlTKbS9rlyD00NMrrt2xn8aI4JEuulZtM5o7p8uAu\nBF6Rmc9vBJ5uBy5okwfXHHh6NbAvM9/Ucs71dNiIMg1/X5IkddJxk8l0n8F9AXhVRNxFEXi6rcN5\nH4+ISYGnvYxSkqSqGHgqSZrPDDyVJC0sFjhJUi1Z4CRJtWSBkyTVkgVOklRLFjhJUi1Z4CRJtTTQ\nPLhGq6+/Be5uHP9UZr69intKWnjK5ri16iXXrR3bcM0vA82DaxS4N2Tm8/q4vF/0luagKrv8l1Um\nx61VBNy0eeOkBsplct3aqTrrzUSASsxqHpwkzZp26QDmui0MA82Daxx/RiNu536K2dyd1Qxd0mya\njdnHRR+8he8xl+73AAAgAElEQVQ+sKer96w/cRlj4+Mctujg7/P3PzzCyP4DLF9S/lOaDWtWuEQ5\nz0y7RBkRV1GElgKsBZ6TmdtazlkD/AQ4HLgW+JfMfHtErADGM3MoIp4LXJOZ7fLkpuISpTQPzNSS\nZTfLlO2WJ8cOjPOSD23j1n/b3dV9q16eLMMlzFJ6W6JsyYM7HbidDnlwWRgFrgOe1ji+JzOHGo8/\nB/xcRBzX699CkrrRbnnysMWLuGfX8CyNSDNpuvn50cDuRtjpeuDp7U5qyYN7AfCdxvETgZ9mZkbE\n0ygKarvlTUnz3EzNNrrZSdkuvHTn3lHWrVrK2lVLu7qvy5Pzz3SBp0cAWymWJr8HHANc1Sbw9EvA\npDy4xrLk5cCrgTFgBHh9Zn6tyzG6RClJ6qTjEqV5cJKk+cw8OEnSwmKBkyTVkgVOklRLFjhJUi1Z\n4CRJtWSBkyTVkgVOklRLA82Da7x2HvBe4OeABzPz3CruKWlu66bjSD95bXYYUSeDzoM7BvgacEFm\n3hMRqzNzR5eX94ve0gANqkly2abI/ea1DbIJss2O54VZy4N7KUWK9z0APRQ3STVnXpsGZdB5cL9I\nkSBwI7CcIi7nY1UNXlL/BjFLueiDt7Bn3/5S5w7vH+PBoVGOW3awoD04NFoqr82MNk2lTIG7IiIm\n8uAeB5zGoYkAb2ZyHtyVwNsb1z8TeBZwJHBLRGzLzO9XMHZJFRjEEmW3mW3j45PXIsfHk737xqZd\norx398iM5NC5VDk/DTQPDrgX+GJm/iwzHwS+Apxe4fglzXMnLF/C6hWTf6ysXrHEJUr1baB5cMDf\nAu+PiMMoZnfnAFdXM3RJVRjUEmVZ/WS2uTypqQw0D67x2huBS4Fx4MOZ+d4ux+guSklSJ+bBSZJq\nyTw4SdLCYoGTJNWSBU6SVEsWOElSLVngJEm1ZIGTJNWSBU6SVEuVFLiIuD4i7o6I7Y0/ZzSOv7Hp\n2Hci4kBEHFvFPSVJmspA8+Baznk+8PuZ2W1fIL/oLWlgumkr1qyfkNYJthqrRO+dTCJiK0WKwBKK\nuJtr25xzPdMXuL8CvpyZHyo56AkWOKmGZiIFoIxukg8m9BvSOsGw1kr01cnkssw8EziLIjpnVYfz\n3hkR346Iqxs9LA/ePeIo4ALghrIjlqS5ypDW+WHQeXATng98NTN39TdcSXUx1QxjJmd3hy8ufs9/\n9MB46ffsGNrH2IFxDlt8cI4wdmCcnUOjXd+3Sgto1lbKoPPgJlwMfKKSEUtShY5ffsSkqJ4yVi9b\nMqm4ARy2eBHHLyt/nW7vqe4NOg+OiDgaOBf4zYrGLKnmZmMmMlMZdhPcYDJ4M5EHdwlwQWZe3OMY\n3WQiSerEPDhJUi2ZBydJWlgscJKkWrLASZJqyQInSaolC5wkqZYscJKkWrLASZJqyQInSaqlMs2W\np9WIyzkXeKRx6JLM3N5o0/WXwOMb9/qTzLyuintKUq+6zYDrJ/vNllyzZ6CBpxHxB8DRmXllRBxP\n0e7rxMx8tIvL28lEWqAGlSrQTQZcu+y3+3YP8ysls98GmfnWyQJLFei9k0lEbI2Ib0bEnRHxyi5v\nnMDyRhPmZcAuYKzLa0jSrGmX/XbyyqP4j088YZZGpLLKJHofm5m7IuJI4Fbg3Mx8qOWc64FnAKPA\nPwJvyszRiFgOfBpYDywHLsrMz3Y5Rmdw0gIz6Dy4nXtHS+e/RcDNmzdyckuRK5vgPRMzuAU2Y2vV\nVy/KKyLiDmAbBwNPW72ZooidDRxLEXgK8ByKdIGTgDOA90fEivLjlqTqdZPFlglv/8x3Dzlugvfc\nN+Umk5bA0+GIuJEOgaeNh6MRcR3whsbzS4F3ZzFN/GFE3E1RCL9RzfAl1dFMzEi62WjyyMj+nvPf\n3GQyewYdeHoP8Czgpog4Afh3wL9WM3RJ6l2/hef45UewxeI1p01X4L4AvCoi7qLYAbmtw3kfb+yS\nfCzwtHH8j4DrI+KfGq9dmZkP9j9sSZKmZuCpJGk+M/BUkrSwWOAkSbVkgZMk1ZIFTpJUSxY4SVIt\nWeAkSbVkgZMk1dKg8+BWAh8BfgHYB1yWmd9pfxVJ6l632W4T+sl4a2Yrrrlr0Hlw7wGGMvNtjVZf\nf5GZz+ry8n7RW5oHBp0A0Ek32W4T2mW8lU0HaDXTeW8LPDmgnVnLg9sAfAkgM/8ZWNvoSSlJs+bE\nFYdmvJkOUD9lligva86Di4gbWvPgGt4ZEW+lKQ8OuAN4IUWz5acBpwKnAD+taPyS5oiZnFk0L0vu\n2be/q/c+9fHH8K4XPvmQ4/c/PMLI/gMsX1Luk5sNa4rkL5co564ygadXAZsaT9cCz8nMbS3nrAF+\nAhwOXAv8S2a+vZH9dg3wFOCfKKJyficzt3cxRpcopTlktpYim/WyLAntlyYB7ts9zGu3bOe2H+0u\nfa2ZXpoElyc76LhEOdA8uMzcQ5EJRyNK526My5E0S05YfujSJMCLPvA1frJndBZGpEEaaB5cRBwD\nDGfmo8ArgK80ip6keWouzCJ63TkZ0Da4dO2qpZw6TXBpK5cm574plygj4ghgK8XS5PeAY4CrMvPG\nlvO+BEzKg8vMoYh4BvBRimXGO4GXZ2b5NYCCS5SSpE46LlGaBydJms/Mg5MkLSwWOElSLVngJEm1\nZIGTJNWSBU6SVEsWOElSLVngJEm1VFUeXADvAH4DOAB8IDPf1zh+DfBcYJgiJ+5bVdxTUj2161Iy\nXXabXUXUTlV5cJcCGykK2HhErM7MHRHxXOA1FAXuHOCazDyny8v7RW9pnuumQXNrI+Uy2W3dNj6e\nC+3GVJmB58G9Gnh7Zo4DZOaOxvELgY9lYRtwTCN5QJJKadcg2ew2lVFVHtwvABdFxCZgJ3BFZv4A\nOBn4cdN59zaOPYCkBaPsjOmiD95ySL7b+hOXMTY+zmGLDv4+3prd5oxM7ZQpcFc0ChfA44DTgNYC\ndwSwLzPPiogXAh8BnlndMCXNR91mx7VbnnzHpidNKm5jB8Z57Zbb2TMy1vN9wKK4EEy5RNmSB3c6\ncDtt8uAoZmafajz+G2AiLvc+iqI44ZTGMUmaVrvlycMWL+KeXcOzNCLNJ5XkwVFE6mykCDQ9F/h+\n4/ingcsjYgvFJpNHmsJRJdVct7Ok1h2UnfLb1q1aytqm/DZ3UaqdqvLgjgE+DjweGKLIg7uj8TWB\n9wMXUHxN4NLMvK3LMbqLUpLUiXlwkqRaMg9OkrSwWOAkSbVkgZMk1ZIFTpJUSxY4SVItWeAkSbVk\ngZMk1VIlBS4K74yI70fEXRFxReP4+oi4JSJGI+INVdxLkqQyKgk8BS6h6Dm5fiIPrnF8F3AF8IKK\n7iNJs6JdEGs704WzdmK7sepN28kkIrZSFK8lFIGl17Y55xvASzPzhx2ucRUwlJl/0sMY7WQiqaNe\nkgR60Zp00E4E3Lx5IydPEc7aSbehrWUtgNSEvjqZXJaZZwJnUUTnrGpzzkQe3G0R8fmIOK3HgUrS\nvPXsDSdMKm5gOOtsMg9O0rzWOkOZqRldqwh4y/M2HHL8vt3D7Ng7OuV7D188uP1+E/88FsBM7hCD\nzoOTpAWhXXYdwNs+c+e0y5PHO8MbiEHnwUnSjBrUTGW6TSadsuv2jIxxzrpjp3yvG0wGY9B5cCcC\ntwErgPHGaxsyc08XY3STiSSpE/PgJEm1ZB6cJGlhscBJkmrJAidJqiULnCSplixwkqRassBJkmrJ\nAidJqiULnCSplirJg4uIAN4B/AZwAPhAZr4vIl4GXEnxRby9wKsz844q7ilJZZXNcmvVa7bbBFtw\nza5KOplExKUUvSgvmQg8zcwdEfEfgLsyc3dE/DpFm69zury8nUykBWJQSQBlstxaLVoEX73yfNYc\nfTCnrWy224RBZbxNWIgJAW303skkIrZGxDcj4s6IeGWH014NvD0zxwEyc0fjf7+Wmbsb52wDTulu\n3JLUn51DU0fVtHP22pV8dfPk4gZmu803ZZYoL8vMXRFxJHBrRNyQma15cBOBp5uAncAVmfmDlnNe\nDny+/yFLms9mOq/t0bHxrs6PgKsvOoM1bWZf95bIdoPB5rs1W8hZb2XMSOBpRGykKHC/0v+QJWlw\nOuW6PfDICK/bsr3U8qT5bnPDlAWuJfB0OCJupFzg6XVN13gy8GHg19vM/CQtMDM92+h2g0m7XLeH\nhkZ5/ZbtLF4U02a7gZtL5oqBBp5GxOMpCt9vZaYhqJJmXBXFZtWyI/iERWveGXTg6YeBFwE/apw6\nlplndTlGd1FKkjox8FSSVEsGnkqSFhYLnCSplixwkqRassBJkmrJAidJqiULnCSplixwkqRaGnQe\n3IXAHwHjwBjwusy8uYp7StJsmar9V68Zcrb3qt6g8+CWAT/LzGz0pPzrzFzf5eX9orekSvWbaNAp\nXy4Cbtq8cVKz5rIZclVmxy2wdIFZy4MbyoMVdCkWK0k11i6J4JSVR/FLa44mOv4Y1qBMO4OLiGOb\n8+CAc1tTASLiIeDPgEPy4BpRO+8CVgP/KTO7zY63KEqaU5501RfbHo+AL7z2VzmpaTY2Nj7OYYsW\ncf/DI7zpU9/m9nsebvveDWtWAC5V9qD3XpQRcRVF4YKi6fJzMnNbyzlDwP+TmX/ayIP7/cx8Zss5\nvwq8NTN/rcvBW+AkVWpQS5QAZ526kvdefAanrDyKsQPjHNYUflpmudKlyq71tkTZkgd3OnA75fLg\nntx6QmZ+Bfj5iDiu3Jglaf657Ue7eeYff5nnv+/mScUNiuXK1YahzphB58E9AfiXxiaTp1Ikfxt6\nKmlW9TuzKROi2i44defeUdatWsraVUs7vs8lyuoMOg/uSuC3gf3ACPDGHr4m4BKlJKkT8+AkSbVk\nHpwkaWGxwEmSaskCJ0mqJQucJKmWLHCSpFqywEmSaskCJ0mqpYHmwTW9fjZwC3BxZn6yintKEpTr\nKtKq18w2sNPIfDLQPLjGa4uBvwf2AR/pocD5RW9pHui3gXGvpmp83E4/mW1QbTPkbi2Q5sndmp08\nuIbXADcAO9q9UZJmUqfMNpsg10+ZJcrLmvPgIuKG1jw44BeAixrZb4/lwUXEyRRROxuBsysduaQ5\nZaZnFxNLk3v27e/qfetPXPZYRtuE+x8eYWT/AZYvmf5H4ikrD87gXK6c28oUuCsahQvgccBpHJoI\ncASwLzPPauTBfQR4JvBe4MrGsmVVY5Y0x8zG8mS3S5NQLE++Y9OTJhW3sQPjvHbL7ewZGSt1ja/f\nveuxxzP593Z5sntTFriWPLjhiLiRcnlw1zUenwVsaRS344DnRsRYZm7tf+iS1J12y5OHLV7EPbuG\nZ2lEGqSB5sFl5rqJEyLieuDvLG5S/czG7KKX3ZO9ZrR14hLl3DbQPLiWc66nKHDuopQkVcU8OElS\nLZkHJ0laWCxwkqRassBJkmrJAidJqiULnCSplixwkqRassBJkmqpkgIXhXdGxPcj4q6IuKJx/LyI\neCQitjf+vLWK+0mSNJ1KAk+BSygaMa+fyINreu2mzHxeRfeRpEqVbfnVa0iq7bxmz7SdTCJiK0Xx\nWgJck5nXtjnnG8BLM/OHLcfPA97QZ4Gzk4mkgXXuL5NKsGgRfPXK81lz9MGonLIhqVUEpJokMKW+\nOplclplnUiQDXBERq9qcM5EHd1tEfD4iTmt67RkRcUfj+L/vbtySNLvOXruSr26eXNzAkNT5oEyB\nuyIi7gC2cTAPrtVjeXDAhyjy4AC+BZyamacDf07RuFmS5oUIuPqiM1jTZhZ27+5hduwdbfu+wxcv\neuxPFWYjb68Opvyn35IHdzpwO+Xy4J4MkJl7MnOo8fhzwM9FxHHVDF2SBqtdfhzAA4+M8Lot2zsu\nTx6//IjH/mj2DDQPLiJOBH6amRkRT6MoqK1p4JI0rUF9DjXVJpN2+XEPDY3y+i3bWbwoOGfdsW3f\n58aSuWGgeXARcTnwamAMGAFen5lf63KMbjKRJHViHpwkqZbMg5MkLSwWOElSLVngJEm1ZIGTJNWS\nBU6SVEsWOElSLVngJEm1ZIGTJNVSJXlwERHAO4DfAA4AH8jM9zVeOw94L/BzwIOZeW4V95SkmTBd\nXly3OXG28Zo5lXQyiYhLKXpRXjIReJqZOxotvL4GXJCZ90wc7/LydjKR1JMquvBPlRcXATdv3sjJ\nTQ2Zp8uJqyIfrplZcX10MomIrRHxzYi4MyJe2eG0VwNvz8xxgKYi9lLgU5l5T8txSZrzdg61j8OZ\n8OwNJ0wqbmBO3Fwy6MDTXwRWRsSNjSL52xWNW5KmVMXs7dGx8Y6vRcBbnrfhkOP3dciJqzIfboKz\nt6mV+QzuiojY1Hg8EXjaGnnzWOBpRLyQIvD0mY3rnwk8CzgSuCUitmXm9ysZvSTNkk5ZcW/7zJ1t\nlyfNhpt5Uxa4lsDT4Yi4kXKBp9c1HX8oM38G/CwivgKcTiMvTpIGpYrZTbdZcTv3jrJnZKxtTpyb\nS2beQANPgb8F3h8RhwGHA+cAV/c9akmaAd0WpeOXH8EWC9mcMV2B+wLwqoi4iyLwdFuH894NfDwi\nfp8i8PQVAJl5V0R8Afg2MA58ODO/U8nIJUmagoGnkqT5zMBTSdLCYoGTJNWSBU6SVEsWOElSLVng\nJEm1ZIGTJNWSBU6SVEsDzYOLiDcCL2u61xOB4zNzVxX3lVQ/0+WvTTCHTdMZaB5cyznPB34/M7tt\nEOcXvaU5rIqu/c2myl+bEAE3bd44qdmxOWwL1qzlwTV7CfCJMqOVpKm06+RvDptalVmivCwzd0XE\nkcCtEXFDZrbG5UzkwW0CdgJXZOYPJl6MiKOAC4DLqxq4pLmhqpnMxNLknn37pz13/YnLGBsf57BF\nB39Hv//hEUb2H2D5kvY/1k5ZeaTLlAvMoPPgJjwf+KqfvUn1UuXyZJmlSSiWJ9+x6UmTitvYgXFe\nu+V29oyMdXzf1+/eVfly6gSXK+emKZcoW/LgTgdup1we3JNbXr8YlyclVaDd8uRhixdxz67hWRqR\n5qpB58EREUc3jv1m/8OVNJdUOXMpu3uyU9DoulVLWbtq6ZTvdYlyYZlyF2VEHEFRvNZS5MEdA1yV\nmTe2nHcM8HHg8RR5cK/KzDsar10CXJCZF/c4RndRSpI66biL0jw4SdJ8Zh6cJGlhscBJkmrJAidJ\nqiULnCSplixwkqRassBJkmrJAidJqqVKClwU3hkR34+IuyLiisbxoyPiMxFxRyON4NIq7idJ0nQq\nCTwFLqFoxLx+Ig+ucfz3gO9m5vMj4njgexHx8cx8tKL7SlqgBhWM2sr2XvPXtJ1MImIrRfFaAlyT\nmde2OecbwEsz84ctx9/ceO/vUbT7+nvgFydy40qyk4k0Dw2qc/+EMukDixbBV688nzVHHww7nS4Y\ntVXVQanNTCGoRMdOJoPOg3s/8GngfmA5cFGXxU2SHrNzaLT0uWevXcn7Ln7KpOIGB4NRf7qn/LU0\nPw06D+45wHbgfIoi+PcRcVNm7qlk9JLmlEHP2h4dK/f7cQRcfdEZrGkz+7p39zA79pYrbocvdh/e\nfDboPLhLgU9l4YcUcTrrKxi3JHXULjMO4IFHRnjdlu2llyebI3k0/ww6D+4e4FnATRFxAvDvgH/t\ne9SS5qRBf6bUT2bcQ0OjvH7LdhYvCs5Zd2yp67jBZH4baB5cRJwEXA+sofhv7t2Z+ZddjtFNJpKk\nTsyDkyTVknlwkqSFxQInSaolC5wkqZYscJKkWrLASZJqyQInSaolC5wkqZYGnQe3MiL+JiK+HRHf\niIhfquJ+kiRNZ9B5cH8AbM/MTY1WX39B0bpLUg1MtM5ql7n29gv9fVaza9B5cJ+laM91U+P5vwD/\nITN/2sUY7WQizaKpEgLue3iECLh580ZObmpufO/uYS7+4LYp/89rFpoq0lcnk8sy80zgLIronFVt\nzpnIg7stIj4fEac1jt8BvBAgIp4GnAqc0tXQJc1JE9lsz95wwqTiBkXmWnT8sSPNjDIF7oqIuAPY\nxsE8uFaP5cEBH6LIgwN4N3BMRGwHXkMRt3Og71FLmnWPjo0TAW953oZDXrtv9zD3TpG47exNM2HK\nz+Ba8uCGI+JGyuXBXQfQCDa9tHGtoIjTMS5HqolOuWtv+8ydpTPXpEEZaB5cI0ZnODMfBV4BfMU0\nb2l+6TTbuuiDt7TNXdu5d5Q9I2Ocs+5Y89Q0qwadB/cM4KMUG0XuBF6embu7HKO/B0qSOjEPTpJU\nS+bBSZIWFgucJKmWLHCSpFqywEmSaskCJ0mqJQucJKmWLHCSpFqywEmSaqmSPLiIuAlY3ni6GvhG\nZr6g0X/yGuC5wDBwSWZ+q4p7SlKvJnLsWrXLtfveT/Yecp4tyOaHyjuZRMQNwN9m5sci4rkUKQLP\nBc6hyJM7p8tL2slE0iGmyqmbzn1tkg4i4KbNGyc1j7539zDP/OMvH9I4+uRjjuz53mCaQsV672QS\nEVsj4psRcWdEvHKac1cA51P0rwS4EPhYFrZRROes6WLgkjQj2iUjnLLyKFY3NZLW/FJmifKyzNwV\nEUcCt0bEDZn5UIdzXwD8Y1NiwMnAj5tev7dx7IGeRyxJ9DcLetJVXzzk2PD+MR4cGuW4ZQcL2oND\no4zsP8DyJZN/VDoDmx/KFLgrImJT4/FE4GmnAvcS4MNVDEySptLPEuXefWOHHIuA8fHJa5Hj48ne\nfWOHLFH2c2+L48yZcomyJfD0dIpE7naBp0TEccDTgM82Hb6PoihOOKVxTJLmlBOWL2H1isk/3lav\nWOIS5TxWVeApwIuBv8vMfU3HPg1cHhFbKDaZPJKZLk9K6ls/M6F2uyg7hbeuW7WUtauWTjrXXZTz\nQyWBp41zbwTenZlfaDoWwPuBCyi+JnBpZt7W5RjdRSlJ6sTAU0lSLRl4KklaWCxwkqRassBJkmrJ\nAidJqiULnCSplixwkqRassBJkmpp0Hlw64HrgKcCf5iZf1LF/SSpX50y4VqVzYhrZqeTuWHQeXCr\ngVMpUgZ291jg/KK3pEn6aXY8oV0mXKtuMuKa9ZsX145NmjuanTy4zNyRmbcC+7scsCTNOjPi5rdB\n58FJUuWqmM1c9MFb+O4DU/+o6iYjbsKGNStcopwjzIOTNC9VsUzZLheuWTcZcRPu3T3S99hcjqzG\noPPgJGneMiNufht0HpwkDURVy5RT6SYjboLLk3PHoPPgTgRuA1YA48AQsKHLz+jcRSlJ6sQ8OElS\nLZkHJ0laWCxwkqRassBJkmrJAidJqiULnCSplixwkqRassBJkmqpkgIXETdFxPbGn/sjYmvj+Msi\n4tsR8U8R8bWIOL2K+0mSNJ1KAk8z85kTjyfy4BpP7wbOzczdEfHrwLXAOVXcU5K6UTbgtJNegk87\nsZ3XzJi2k0ljNvY4iibL12TmtVOcuwL4EXBqazuuiFgJfCczT+5yjHYykWqoijSAbpQJOO2k1+DT\nTgYRiDqVmqcT9NXJ5LLMPBM4iyI6Z9UU506VB/dy4PMl7idJc4rBp/PTjOTBRcRGigL3K70MUlL9\nTMwqZmomd/jiRTx6YLyn9+4Y2sfYgXEOW3xwTjB2YJydQ6Ndj2Em1XzmNq2B58FFxJMpit6FUySB\nS9JAHd/HbGv1siWTihvAYYsXcfyy7q55/PIj+hqHujPQPLiIeDzwKeC3MvP7fY9WUu3M5Cyj140m\nveTCtePmkpk16Dy4DwMvoth4AjCWmWd1OUY3mUiSOjEPTpJUS+bBSZIWFgucJKmWLHCSpFqywEmS\naskCJ0mqJQucJKmWLHCSpFoadB7chY08uO0RcVtE2ItSkjQjKv+i90QeXGZ+LCKWAT/LzGz0pPzr\nzFzf5SX9ore0APTSRqvfjDZbZ9VC751MKsyDewbwkcx8YhcDBwucNKcMqvt/t3ltEXDz5o2c3EdG\n20zksi30jv4zYPby4CJiU0T8M0XKwGUlByxpAek2dgbg2RtOmFTcwIw2TTbwPLjM/BvgbyLiV4E/\noojfkTQPzFRW26Nj3eW0RcBbnrfhkOP37R5mx95yxXImstmcvc2ugefBTcjMrwA/3zhPknrWLmEb\n4G2fubP08qS5bPU36Dy4JwD/0thk8lTgCDrP/iTNMTM1A+l2g0mnfLY9I2Ocs+7YUtdwg0n9DToP\n7krgt4H9wAjwxsy8ucsxuslEktSJeXCSpFoyD06StLBY4CRJtWSBkyTVkgVOklRLFjhJUi1Z4CRJ\ntWSBkyTVkgVOklRLZZotTysibgKWN56uBr6RmS9oev1s4Bbg4sz8ZBX3lKRelWkN1m/W3ARbgs2e\ngQaeNp4vBv4e2EeRB9dtgbOTibSAzESCwXTZcxFw0+aNkxo6d5s1N2EmMudgQScX9N7JJCK2RsQ3\nI+LOiHjlNOeuAM6n6F854TXADcCOkoOVpFnVLq3ArLn5p8wS5WWZuSsijgRujYgbMrNTIsCkwNOI\nOBnYBGwEzq5kxJJqreqZSLvlyD379k/5nuH9Y9z/8AgnNc2+xsbHWX/icoYfPdDV/U9ZWVzDpcqZ\nN+0SZURcRVGkoEgVeE5mbutw7ueBD2fmDY3n/xv408zcFhHXU8TpuEQpacbCVKdbjuzk7LUr+cTv\nPJ3DmoJRe12mhJlbqoQFt1zZcYlyyhlcS+DpcCMSZ7rA001Nh88CtkQEwHHAcyNiLDO3trmEJM0Z\nP941Mqm4wcFlyp/uKZcartk10MDTzFw38bhpBmdxkzRnw1QndApVXbdqKWtXLe36ei5RzryBBp62\nvH49LlFKkqpl4KkkqZYMPJUkLSwWOElSLVngJEm1ZIGTJNWSBU6SVEsWOElSLVngJEm1NNA8uEar\nr78F7m689qnMfHsV95SkmVC2E0oV+XF2O6nWQPPgGgXuDZn5vD4u6Re9JU1pkI2byzRrrio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KmULHCSpFKywEmSSskCJ0kqJQucJKmU2lbgIuKMiLg9ItZFxM0R8Z+mPP/qiMiIWNWua0qSVE/H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\nkg1OklRJNjhJUiXZ4CRJlWSDkyRV0v8D7PQyZYDpTsUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x2808 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.figure(figsize=(6,16))\n",
    "forestplot(varying_intercept_slope_trace[1000:], varnames=['a','b'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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/CI2FOIelcmaz+qwEHqRBgIvC2RICe2Wln0u0jAoKdEz5wSCZQv7escTxH2At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\nEQIRjgJVU3oV7DlA96inRxXPQw+52Fx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2N4Z88muvxadFkXhgwXV7u/5cW1M18Pzz+j0y\nRlgiKE3W1/vUKWUrQ004IC5YFm83N7vsBDj/2lqc7kmwARaC/UOWC1aK8wMqClkbISwEtISeObAB\nx4wkBpouHR16DgqenC/YTo2N+pxXr8Z7AtXVDh9QdVDlkNX29Oh3r19XEHj1VafZMmiE7AUT1lwX\nVDU0G5kuXlryhjFUXBxUOEVcU6P37+jQ/09PezbK60MpDemiUEVD5x8u+SFI1NXp8/f2KnsPlwiF\nks63bsVx/ZISv44mJ+NwTnW1HB29q+LiOIYfzgeAqZu5BDTGdDYVwX730EG0UXZKk9FTbVC10CC+\n0/YsAjDvgxAeVTRJC2KH6BdNTvouZhYqMdH+8MN6z//+35VUrK7qezx3zuwTn3gLNHcP4fg/aWYn\noyj6mdf/fcPMFswsMrN/H0XRZw936EeL8QMrIPRVVqYvELzPzB1/iHeiMz8wIGnfRx+NN98OsiiS\nkxka8gXXOFAwRqYW4elvbankffllNbPYh0qPIoQOzJwKB/sH2IBGIswGRM0aG/U6IR0OTSEyToap\n2EAEXAQsES4SZ6MYTefw3MEWgkkBfx45Bo63qEjHBURGMAwbdEAfiOFNTMhxkJGC6UKThd/NYN6p\nU66tHy6YHx2N6+/znXA+mB5FMmFjw2mqSCtAmSUIh8GYc0EgaGvTZzRzsTRE9YqKHDdH6gBNGwIr\n55SgYObSHASCnh5fukMgwMlyzCH2XlzsFU4IjULDpGl+8qTeK1zKEiZTSDGgFRVW2nV13iTeDxYK\n9wDvRxtF44mGbyiQVl/vkNDtZLex7e04Kyl/LSpJGbDQ4KAek5M+PZ/LeQJQUuJaRmZmH/yg2T//\n57d///thR+L4U6nU+8zsN83sySiK5l7/WXsURWOpVKrJzL5kZs9GUfQXd/F+nzKzXzYza21ttfHx\n8QOP8Y3Y5z+vpergtawv/OQnzZ56SosUvv51BQduflgXRUVx3XWyYsSqHn9cNwSqhwcZYlzXrysI\nwCxh6QtZMFo8yDagY3P1qk9JwiYJVySikAlrB145Nxh9BHRsmpsVCGpqfGaAaoChJJQ+mSSlyQie\nD+SBZj0QFFRSnkMTkxF9NHfAT8l2gSSoWHDm6BixdH593YMvMEq4LAbYaXNTjqilRZnhQw8pk6XC\nMJNDHB7W7ACyw9BmqVzoaQCN9fTo7zs7CgBsy6IqYN8AjdyQ1UO/hWy/qck1/Tl39FLyzzE9GK5l\nZgbCZT/IciDHweKVM2dUGRAI4ObnSzbQ+0G9c3LS7wEWrZw+rcDS0eFKo/spgpLU0EAPFwyF/P9w\nIxxGcCcQ5NNG2fUAVBf2VICEkBW/k4XLeJBnwdgnwJDj/Lzuw1deMfvsZ+OV2YkT+p1MRsKQD9Ie\nuONPpVIPmdkXzexHoii6epvnfMrMVqMo+tW7O2zZUU3ufuITar4yuXv+vNm/+3fxcmx9XV/m176m\nLJBNR+DSlP7QMoFhYOX096tnwMg+yzZuZ7mca5/cuOFOendXFy7lPDAC2CMNX9gYNGJx6jgTM91s\nMH7QsyGrpKnK5G5zs467rs4lqXE0DDCB64JV19S4UyZIEXxwUDg9JjSBlUJYqLp6r+ZOuLaxpMSn\nRDHUQBlc472o6qgiqOBoqDJwBFvokUfimC2SCNevKxAg7cxn5tihzLa1KQvu6tL74/zZnzs6qtdg\neI2AwGc180AVzmWwxzds9IZwGaJj8/Pe9A+X3ZMIoDuEM0MdtatL56Cvz1lDYX8g1KqhQkPyGhox\n8x49PQoqp07pmKen96d2ZjIe8On9YAQUoKH9uPZ3ctAsyOGaJ1AVFroS6t1CtndiJTU1+ZzCj/2Y\n62gx4EhV99WvHvw+b8QeqONPpVJdZvYVM/vfoyj6RvDzSjMriKJo5fW/f8nMPh1F0Z8c5uCPwvH/\n8i+b/cmfKHPhxiouvnM5tr6ujPziRfHA0apJpXwMHgfFRiouNAa1BgaUWYKz75fRYLmc3uP6dWWe\nwCVwyCk5ucDgbJMlsxGIZururm4EftfMfw57haYkpbOZ7+atrdUxUw1wTqgGgMvMHKvmgg+XydB8\nBo4h+0VLfX3dJRJCBhCBi+lbVC3NvCHd1eWDO2HvZm3NaXscJ1pJqZT+b2bGM/rGRgXsD39Y1UD4\nHUWRnNjIiKCdEKrjuLNZl9To6hIUeOyYjjNsLvIYGfHKhSlm+jS8JtVmuB+iqUmOs63NM1gw9aUl\nl1UON7FREYZzHeHuBzNXIO3o8NWKra16XwJByI4iEAPDMdOAcF5dnTeK+/r0M5q0+U40hIVWV+OO\nvLbWg0D4mUMLmUiTk3F9LII51z3fK5IqQEIHGX2ZkJXEtfi5z+k7DWdgzHQ9/bf/dvBrvxF7o6ye\n3zOz95pZg5lNmSCYYjOzKIp+O5VK/Qcz+1/MbOT1X8lGUXQhlUr1maoAM7MiM/svURT9ymEP/igc\n/9/6W7oxLl92Z1dUJOfyS7+kGxXdk/1sfd01yl96KS6XS6+Am5asEz41Cort7boZBgZ0k7FIZT+a\n2O5uPAiEdMTWVh9OgYLIzYdMAQEhFP0CtyZ7DKWIcZzcLGTLND2ZIiZ40ewEFiIDZrcxmWImowdZ\ne0hXBKrhvOFEQn47kr1UMTSFob6GC16YhiUQ0lxdXZXzWlpy54/cxdaW6wLRKG1sFHz3gQ8oCOQz\nu1ZWlMEPDysQhHIDVGZIQvf2+rrHykpfXkIVQEBBQ4ogh5ggwT8cUgJ+o0/T0eEBkMY9ex2mp32R\nC/AX/SG09KnOmN3gOmOT3PHjfs3SeM+ne8IGW172oT7YU0h8HDumaqC1Vb8HfJO/hIZlRdms0yx5\nj3CIbL8k6k60UcgbDL2RtFRWxiGhu1nuvrXlx/8bvyGNKb4regMf+chbAON/M+0oHP8P/qAuxqkp\ndxyUzqdOubga05OnTuliP3Zs70YgggAYPUJboXwxQmtmDtVQ2paVOd0NnZrWVs+u8y+83V2HDUZG\n/EZgujVcej0youNhOpX+AdkyzoWl8SyKCVUnw8UYsIO4EZEwgLdONcDnY/WimWP5ZHEIwlVWupYR\nlDlKfiAJgsrcnDNswMRpgJvptUOHhrwziplFRe702FvMkFVBgcsSpNM6Z9ev6xohoDQ0iC75xBP6\ns6Ul/t3s7Lhe0/XrcgYomQJTAbkMDPhroYoaNhdHR30XxMSEq8hSiYV/p8lPsAXrJovt6XEWDMNX\nyC/PzcW3haEqyRYzzhPXj5n+n2Tl2DF9loaGeCZMsA97NuE0cbjIh3mL/n4d9/a20ztDeAl5cjNf\nZIOVlcWVOfcjWtyONgocyHeI/lJRkQdSgulB9rnPiSX23HO615qa1Pc4fToRabujHdUGrvy3yOXk\nOD/2MZ/qZawbTnpFhS72gQHdTP39+hORqDAIjI35IBAsDFg1oTMFA+fiS6flRDs7nbpGIGhujo+S\nZ7M++DQ66jcvg089PbrYx8bUfEIhM9yGRMCjtEZHvarKYSDwY6qXbNZlpHG+ZHMMnLW16TgIFDjz\ncAiI5iSvl8nEWSk0zhkaQ14Zeh0aPXxHSCPDggJyYhAHNhMrH+kz0ABeXPQAxfrFggKxN2D5sAEN\nCh+aQKdOxQf+okjHSAZ/86bO/ciIZ7VM/fb1qcp8xzv0PadSce1+AjjDTCylgZxAYgG8Re+AyWq2\nxjFL0NTklQT0zXBHLxWfmTtnej0MpBFAzXS9NDfr2Pv6lCwRzGZm4rAQx8WcxfKyXmttzSfKm5pc\n1I/92AyjhQyxTMYr1rW1/Ruwd1rons9ooseCXhTHyoxCU5MCQE/P/jIVZsnqxXu2o8L4/+APXNsD\nGYOPfczsX/wLPWd1VRfbyy+LR8+mKfTlCQRVVZ4pEgyQ3GXZNzMDoYgWGXWo+Y6hxc7FzYAXEAaB\nINR439mRgxgaknPgxmXhdX+/njs+rsD2wgtqIMP4IfsBTkH8C/lcM181iVMFyoCNgnNloxdNSWSJ\nkZoGD6Y3QPbOnl2CSHW1NwxpzIZZO/RItp/BmIFjHVYFodQFOv3otISS1qxL5LpA76WrS8d37ZpL\nAYSLUsjiH35YRAGomdjamksR3LwpB0s2v72tc8XU9cMPq8HMPmOzOHbNcBs0Rzj+VHPhecCB8XnQ\nrQ8XmEBn5TzMzuraACcPs+5wcriuTkF1acmvCzO9B8SAnh5VBeFCnxAWYj4CWQlIANvbroVEQOF6\nX13du4SGSoXKkf4R91Nzs3/e/aidIW00fO2NDZ8PiSKvUtNpr6haW70yT0Ta7tGOwvF/7nPKfv/0\nT32Aiszg6addAI3hKHT0x8Z007JkhOlNMk7ofdXVvvO1p0d/0ghlyxCYOnz05WX9G4kAM8e1zfQe\nOKK2Nj0Q9CIQgPejUwOLhJujsVEXX1+fLtyVFfUoLl5UMMDxQrGDvQRNtKrKtzuRdW9tObuIBm5F\nRZx7Dh2WzBAYgeGyVCo+CYqjX1x0OicLaIB5aB7D3zZzOGVlxZ0LUBFOjeoGvXQ+Vybj/RmwcbLf\nsjL9HyV/aanTHpFGNnPoC6E+9PcZCsSyWVdvHR3V32/c0DUFjRdm2MCAegtAgGTLNEfpLzB9G+5n\nDhfHmHmwpLdC4Kur86nacBcE3z+wVxgIwlmEujrvMRQW6r1hcEEWaG7Wo6tLVQfXFfpBZh6kqJ5X\nVnzKvKDA51SARumJLS7uXUJTXu46Uuw9xkpLHRYi8OXbfrRR6KdURKHmVUeHD4594xvJ6sVD21E4\n/rAcCxdbmKnEpCw18wsuDAasWKP8RF6WLAz2CCP2JSU+ks9SCSQPGBGvrHQ63s2bzorIXz5dVubl\nPPg1Ny0Osq3NIaKiojj8xNff3OxBgC1Vly5pUvjVV31UHf4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4Zjw46LooSBzTsGxt1RcP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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "xvals = np.arange(2)\n",
    "b = varying_intercept_slope_trace['a', 1000:].mean(axis=0)\n",
    "m = varying_intercept_slope_trace['b', 1000:].mean(axis=0)\n",
    "for bi,mi in zip(b,m):\n",
    "    plt.plot(xvals, mi*xvals + bi, 'bo-', alpha=0.4)\n",
    "plt.xlim(-0.1, 1.1);"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Adding group-level predictors\n",
    "\n",
    "A primary strength of multilevel models is the ability to handle predictors on multiple levels simultaneously. If we consider the varying-intercepts model above:\n",
    "\n",
    "$$y_i = \\alpha_{j[i]} + \\beta x_{i} + \\epsilon_i$$\n",
    "\n",
    "we may, instead of a simple random effect to describe variation in the expected radon value, specify another regression model with a county-level covariate. Here, we use the county uranium reading $u_j$, which is thought to be related to radon levels:\n",
    "\n",
    "$$\\alpha_j = \\gamma_0 + \\gamma_1 u_j + \\zeta_j$$\n",
    "\n",
    "$$\\zeta_j \\sim N(0, \\sigma_{\\alpha}^2)$$\n",
    "\n",
    "Thus, we are now incorporating a house-level predictor (floor or basement) as well as a county-level predictor (uranium).\n",
    "\n",
    "Note that the model has both indicator variables for each county, plus a county-level covariate. In classical regression, this would result in collinearity. In a multilevel model, the partial pooling of the intercepts towards the expected value of the group-level linear model avoids this.\n",
    "\n",
    "Group-level predictors also serve to reduce group-level variation $\\sigma_{\\alpha}$. An important implication of this is that the group-level estimate induces stronger pooling."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [],
   "source": [
    "from pymc3 import Deterministic\n",
    "\n",
    "with Model() as hierarchical_intercept:\n",
    "    \n",
    "    # Priors\n",
    "    sigma_a = HalfCauchy('sigma_a', 5)\n",
    "    \n",
    "    # County uranium model for slope\n",
    "    gamma_0 = Normal('gamma_0', mu=0., sd=1e5)\n",
    "    gamma_1 = Normal('gamma_1', mu=0., sd=1e5)\n",
    "    \n",
    "    \n",
    "    # Uranium model for intercept\n",
    "    mu_a = gamma_0 + gamma_1*u\n",
    "    # County variation not explained by uranium\n",
    "    eps_a = Normal('eps_a', mu=0, sd=sigma_a, shape=counties)\n",
    "    a = Deterministic('a', mu_a + eps_a[county])\n",
    "    \n",
    "    # Common slope\n",
    "    b = Deterministic('b1', Normal('b', mu=0., sd=1e5))\n",
    "    \n",
    "    # Model error\n",
    "    sigma_y = Uniform('sigma_y', lower=0, upper=100)\n",
    "    \n",
    "    # Expected value\n",
    "    y_hat = a + b * floor_measure\n",
    "    \n",
    "    # Data likelihood\n",
    "    y_like = Normal('y_like', mu=y_hat, sd=sigma_y, observed=log_radon)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma_y, b, eps_a, gamma_1, gamma_0, sigma_a]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 5000/5000 [00:16<00:00, 306.29draws/s]\n",
      "The acceptance probability does not match the target. It is 0.7008977953489228, but should be close to 0.8. Try to increase the number of tuning steps.\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with hierarchical_intercept:\n",
    "    hierarchical_intercept_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "Text(0, 0.5, 'Intercept estimate')"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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atGnDXXfdFbBXQsxWuP1gwfmRrh+ekyisSsqUVl5KGm963GaMZ3njHkqPgoF0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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "a_means = hierarchical_intercept_trace['a', 1000:].mean(axis=0)\n",
    "plt.scatter(u, a_means)\n",
    "g0 = hierarchical_intercept_trace['gamma_0'].mean()\n",
    "g1 = hierarchical_intercept_trace['gamma_1'].mean()\n",
    "xvals = np.linspace(-1, 0.8)\n",
    "plt.plot(xvals, g0+g1*xvals, 'k--')\n",
    "plt.xlim(-1, 0.8)\n",
    "\n",
    "a_se = hierarchical_intercept_trace['a', 1000:].std(axis=0)\n",
    "for ui, m, se in zip(u, a_means, a_se):\n",
    "    plt.plot([ui,ui], [m-se, m+se], 'b-')\n",
    "plt.xlabel('County-level uranium'); plt.ylabel('Intercept estimate')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "The standard errors on the intercepts are narrower than for the partial-pooling model without a county-level covariate."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Correlations among levels\n",
    "\n",
    "In some instances, having predictors at multiple levels can reveal correlation between individual-level variables and group residuals. We can account for this by including the average of the individual predictors as a covariate in the model for the group intercept.\n",
    "\n",
    "$$\\alpha_j = \\gamma_0 + \\gamma_1 u_j + \\gamma_2 \\bar{x} + \\zeta_j$$\n",
    "\n",
    "These are broadly referred to as ***contextual effects***."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# Create new variable for mean of floor across counties\n",
    "xbar = srrs_mn.groupby('county')['floor'].mean().rename(county_lookup).values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as contextual_effect:\n",
    "    \n",
    "    # Priors\n",
    "    sigma_a = HalfCauchy('sigma_a', 5)\n",
    "    \n",
    "    # County uranium model for slope\n",
    "    gamma = Normal('gamma', mu=0., sd=1e5, shape=3)\n",
    "    \n",
    "    # Uranium model for intercept\n",
    "    mu_a = Deterministic('mu_a', gamma[0] + gamma[1]*u.values + gamma[2]*xbar[county])\n",
    "\n",
    "    # County variation not explained by uranium\n",
    "    eps_a = Normal('eps_a', mu=0, sd=sigma_a, shape=counties)\n",
    "    a = Deterministic('a', mu_a + eps_a[county])\n",
    "\n",
    "    # Common slope\n",
    "    b = Normal('b', mu=0., sd=1e15)\n",
    "    \n",
    "    # Model error\n",
    "    sigma_y = Uniform('sigma_y', lower=0, upper=100)\n",
    "    \n",
    "    # Expected value\n",
    "    y_hat = a + b * floor_measure\n",
    "    \n",
    "    # Data likelihood\n",
    "    y_like = Normal('y_like', mu=y_hat, sd=sigma_y, observed=log_radon)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [sigma_y, b, eps_a, gamma, sigma_a]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 5000/5000 [00:19<00:00, 260.96draws/s]\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with contextual_effect:\n",
    "    contextual_effect_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "(<Figure size 432x331.2 with 1 Axes>,\n",
       " array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f38b5c75e48>],\n",
       "       dtype=object))"
      ]
     },
     "execution_count": 51,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<Figure size 432x331.2 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "forestplot(contextual_effect_trace[1000:], varnames=['gamma'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/stats/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.9\n",
      "  \"pymc3 3.9\".format(old=old, new=new)\n"
     ]
    },
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>mean</th>\n",
       "      <th>sd</th>\n",
       "      <th>hpd_3%</th>\n",
       "      <th>hpd_97%</th>\n",
       "      <th>mcse_mean</th>\n",
       "      <th>mcse_sd</th>\n",
       "      <th>ess_mean</th>\n",
       "      <th>ess_sd</th>\n",
       "      <th>ess_bulk</th>\n",
       "      <th>ess_tail</th>\n",
       "      <th>r_hat</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>gamma[0]</th>\n",
       "      <td>1.427</td>\n",
       "      <td>0.049</td>\n",
       "      <td>1.331</td>\n",
       "      <td>1.516</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.001</td>\n",
       "      <td>993.0</td>\n",
       "      <td>986.0</td>\n",
       "      <td>992.0</td>\n",
       "      <td>1438.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma[1]</th>\n",
       "      <td>0.701</td>\n",
       "      <td>0.087</td>\n",
       "      <td>0.549</td>\n",
       "      <td>0.872</td>\n",
       "      <td>0.002</td>\n",
       "      <td>0.002</td>\n",
       "      <td>1458.0</td>\n",
       "      <td>1458.0</td>\n",
       "      <td>1453.0</td>\n",
       "      <td>1501.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>gamma[2]</th>\n",
       "      <td>0.397</td>\n",
       "      <td>0.204</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.770</td>\n",
       "      <td>0.007</td>\n",
       "      <td>0.005</td>\n",
       "      <td>913.0</td>\n",
       "      <td>913.0</td>\n",
       "      <td>915.0</td>\n",
       "      <td>1122.0</td>\n",
       "      <td>1.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "           mean     sd  hpd_3%  hpd_97%  mcse_mean  mcse_sd  ess_mean  ess_sd  \\\n",
       "gamma[0]  1.427  0.049   1.331    1.516      0.002    0.001     993.0   986.0   \n",
       "gamma[1]  0.701  0.087   0.549    0.872      0.002    0.002    1458.0  1458.0   \n",
       "gamma[2]  0.397  0.204   0.004    0.770      0.007    0.005     913.0   913.0   \n",
       "\n",
       "          ess_bulk  ess_tail  r_hat  \n",
       "gamma[0]     992.0    1438.0    1.0  \n",
       "gamma[1]    1453.0    1501.0    1.0  \n",
       "gamma[2]     915.0    1122.0    1.0  "
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "summary(contextual_effect_trace[1000:], varnames=['gamma'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "So, we might infer from this that counties with higher proportions of houses without basements tend to have higher baseline levels of radon. Perhaps this is related to the soil type, which in turn might influence what type of structures are built."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Prediction\n",
    "\n",
    "Gelman (2006) used cross-validation tests to check the prediction error of the unpooled, pooled, and partially-pooled models\n",
    "\n",
    "**root mean squared cross-validation prediction errors**:\n",
    "\n",
    "* unpooled = 0.86\n",
    "* pooled = 0.84\n",
    "* multilevel = 0.79\n",
    "\n",
    "There are two types of prediction that can be made in a multilevel model:\n",
    "\n",
    "1. a new individual within an existing group\n",
    "2. a new individual within a new group\n",
    "\n",
    "For example, if we wanted to make a prediction for a new house with no basement in St. Louis county, we just need to sample from the radon model with the appropriate intercept."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "69"
      ]
     },
     "execution_count": 53,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "county_lookup['ST LOUIS']"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "That is, \n",
    "\n",
    "$$\\tilde{y}_i \\sim N(\\alpha_{69} + \\beta (x_i=1), \\sigma_y^2)$$\n",
    "\n",
    "This is simply a matter of adding a single additional line in PyMC:"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "with Model() as contextual_pred:\n",
    "    \n",
    "    # Priors\n",
    "    sigma_a = HalfCauchy('sigma_a', 5)\n",
    "    \n",
    "    # County uranium model for slope\n",
    "    gamma = Normal('gamma', mu=0., sd=1e5, shape=3)\n",
    "    \n",
    "    # Uranium model for intercept\n",
    "    mu_a = Deterministic('mu_a', gamma[0] + gamma[1]*u.values + gamma[2]*xbar[county])\n",
    "\n",
    "    # County variation not explained by uranium\n",
    "    eps_a = Normal('eps_a', mu=0, sd=sigma_a, shape=counties)\n",
    "    a = Deterministic('a', mu_a + eps_a[county])\n",
    "\n",
    "    # Common slope\n",
    "    b = Normal('b', mu=0., sd=1e15)\n",
    "    \n",
    "    # Model error\n",
    "    sigma_y = Uniform('sigma_y', lower=0, upper=100)\n",
    "    \n",
    "    # Expected value\n",
    "    y_hat = a + b * floor_measure\n",
    "    \n",
    "    # Data likelihood\n",
    "    y_like = Normal('y_like', mu=y_hat, sd=sigma_y, observed=log_radon)\n",
    "    \n",
    "    # St Louis county prediction\n",
    "    stl_pred = Normal('stl_pred', mu=a[69] + b, sd=sigma_y)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "Auto-assigning NUTS sampler...\n",
      "Initializing NUTS using jitter+adapt_diag...\n",
      "Multiprocess sampling (2 chains in 2 jobs)\n",
      "NUTS: [stl_pred, sigma_y, b, eps_a, gamma, sigma_a]\n",
      "Sampling 2 chains, 0 divergences: 100%|██████████| 5000/5000 [00:18<00:00, 269.28draws/s]\n",
      "The estimated number of effective samples is smaller than 200 for some parameters.\n"
     ]
    }
   ],
   "source": [
    "with contextual_pred:\n",
    "    contextual_pred_trace = sample(2000)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/anaconda/lib/python3.6/site-packages/pymc3/plots/__init__.py:21: UserWarning: Keyword argument `varnames` renamed to `var_names`, and will be removed in pymc3 3.8\n",
      "  warnings.warn('Keyword argument `{old}` renamed to `{new}`, and will be removed in pymc3 3.8'.format(old=old, new=new))\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "array([<matplotlib.axes._subplots.AxesSubplot object at 0x7f38b56184e0>],\n",
       "      dtype=object)"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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IurxyuyOJtAoVnHidh9/bRJ3L4p5pgwjyd9odxyPFRnbgsdnJ1LksfvZKOpU19Se+kUg7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\nxxEfNW1oNwKcDt5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      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plot_posterior(contextual_pred_trace[1000:], varnames=['stl_pred'])"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "** Now I want to make predictions for all other counties which do no exist in this dataset.\n",
    "e.g. : check rest of data file **"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Benefits of Multilevel Models\n",
    "\n",
    "Accounting for natural hierarchical structure of observational data\n",
    "\n",
    "Estimation of coefficients for (under-represented) groups\n",
    "\n",
    "Incorporating individual- and group-level information when estimating group-level coefficients\n",
    "\n",
    "Allowing for variation among individual-level coefficients across groups\n",
    "\n"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 1
}