{ "cells": [ { "cell_type": "code", "execution_count": 12, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/html": [ "\n", "" ], "text/plain": [ "" ] }, "execution_count": 12, "metadata": {}, "output_type": "execute_result" } ], "source": [ "%matplotlib inline\n", "import pandas as pd\n", "import numpy as np\n", "import matplotlib.pyplot as plt\n", "import warnings\n", "from pandas.core.common import SettingWithCopyWarning\n", "warnings.simplefilter(\"ignore\", SettingWithCopyWarning)\n", "\n", "from IPython.core.display import HTML\n", "def css_styling():\n", " styles = open(\"styles/custom.css\", \"r\").read()\n", " return HTML(styles)\n", "css_styling()" ] }, { "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": { "collapsed": false }, "outputs": [], "source": [ "# Import radon data\n", "srrs2 = pd.read_csv('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": 3, "metadata": { "collapsed": false }, "outputs": [], "source": [ "srrs_mn['fips'] = srrs_mn.stfips*1000 + srrs_mn.cntyfips\n", "cty = pd.read_csv('data/cty.dat')\n", "cty_mn = cty[cty.st=='MN']\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": 4, "metadata": { "collapsed": false }, "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": "markdown", "metadata": {}, "source": [ "We also need a lookup table (dict) for each unique county, for indexing." ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": false }, "outputs": [], "source": [ "srrs_mn.county = srrs_mn.county.map(str.strip)\n", "mn_counties = srrs_mn.county.unique()\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": 6, "metadata": { "collapsed": false }, "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": 7, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 7, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "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": 8, "metadata": { "collapsed": false }, "outputs": [ { "name": "stderr", "output_type": "stream", "text": [ "/Users/fonnescj/GitHub/notebook/src/ipython/IPython/html.py:14: ShimWarning: The IPython.html package has been deprecated. You should import from notebook instead. IPython.html.widgets has moved to ipywidgets.\n", " \"IPython.html.widgets has moved to ipywidgets.\", ShimWarning)\n", "/Users/fonnescj/GitHub/notebook/src/ipython/IPython/utils/traitlets.py:5: UserWarning: IPython.utils.traitlets has moved to a top-level traitlets package.\n", " warn(\"IPython.utils.traitlets has moved to a top-level traitlets package.\")\n", "/usr/local/Cellar/python3/3.4.2_1/Frameworks/Python.framework/Versions/3.4/lib/python3.4/importlib/_bootstrap.py:321: RuntimeWarning: numpy.ndarray size changed, may indicate binary incompatibility\n", " return f(*args, **kwds)\n" ] }, { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 1000 of 1000 complete in 2.2 sec" ] } ], "source": [ "from pymc3 import glm, Model, Metropolis, NUTS, sample\n", "\n", "with Model() as pooled_model:\n", " glm.glm('log_radon ~ floor', srrs_mn)\n", " pooled_trace = sample(1000, NUTS())" ] }, { "cell_type": "code", "execution_count": 9, "metadata": { "collapsed": false }, "outputs": [], "source": [ "b0, m0 = pooled_trace['Intercept'][500:].mean(), pooled_trace['floor'][500:].mean()" ] }, { "cell_type": "code", "execution_count": 13, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "[]" ] }, "execution_count": 13, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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E9sOoincppfY7HBMAvAbgOzCq9R/ZEE+uCjXGzbJzjOcqpzGec1JXGZYOEJFL\nAMwHsBrGf6DdAE7N9DNExA/g60qprSLynYnX5MWKuKa8rhlGFfF+vnFNcSqHWHI5t1AxAbDtvTEV\nkx3jKN+YJo6fBvAnMP7/6heRFyeqUUdiEpGLANyklPrWxL/3icj/KKVGLY4pF4Ua4zkrwBjPJZac\nx3i+ywRMOgrjcgoTv3SxUupcn7jLAXhF5HkAjQDcItKnlPqVRfGYjQsicjWAG5VSGxyMJee4CxCT\nne+N2Zhm3ThSSsVE5BMA9UqpT0UkbHEsOccEozqvAgARKYGRTBM2xTXpi5JPocb4VF+YEAs0xqf9\nyi/4fu5j3MLG/60ADsG4zLv1c9/7JoA/mOF1d8OmG1xm4gJwDMArAPoA7CxELDPEMWPcDsZk23tj\nNianx9EM79MFAH42cf76WRLTIwBeB/AGgO/YGFMHgJ/DWJL76S+IqVBjPJeYCjXGs45pyveyGuNc\nJoCISCN8+IiISCNM6kREGmFSJyLSCJM6EZFGmNSJiDTCpE5EpBEmdSIijTCpExFp5P8BqhGNfIur\nv64AAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "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": 14, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from statsmodels.formula.api import ols\n", "unpooled_fit = ols('log_radon ~ C(county) + floor - 1', srrs_mn).fit()\n", "unpooled_estimates = unpooled_fit.params" ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": false }, "outputs": [], "source": [ "unpooled_estimates = unpooled_estimates.rename(dict(zip(unpooled_estimates.index.values, \n", " [x[10:-1] or x for x in unpooled_estimates.index.values])))\n", "unpooled_se = unpooled_fit.HC3_se.rename(dict(zip(unpooled_fit.HC3_se.index.values, \n", " [x[10:-1] or x for x in unpooled_fit.HC3_se.index.values])))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can plot the ordered estimates to identify counties with high radon levels:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "order = unpooled_estimates.order()[1:].index\n", "\n", "plt.scatter(range(len(unpooled_estimates)-1), unpooled_estimates[order])\n", "for i, m, se in zip(range(len(unpooled_estimates)-1), 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": 17, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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Jx/4KqCIYHvKxoVyv67TT6DrttOCXffuI1tWRU1sL0eQzbW3XLry8HFTJJMva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0mSJGlITK4lSZKkITG5liRJkobE5FqSJEkaEpNrSZIkaUhMriVJkqQhMbmWJEmShuR/uBIV1lCL\nu+QAAAAASUVORK5CYII=\n", "text/plain": [ "" ] }, "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", "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", " m,b = unpooled_estimates[['floor', 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": [ "## PyMC 3\n", "\n", "![pymc](http://pymc-devs.github.io/pymc/_static/icon.png)\n", "\n", "We can use PyMC to easily specify multilevel models, and fit them using Markov chain Monte Carlo.\n", "\n", "Features: \n", "\n", "* Fits Bayesian statistical models with **Markov chain Monte Carlo** and other algorithms.\n", "* Includes a large suite of well-documented **statistical distributions**.\n", "* Uses **NumPy and Theano** for fast numerical computation.\n", "* Creates posterior summaries including **tables and plots**.\n", "* Several **convergence diagnostics and goodness-of-fit** procedures are available.\n", "* **Extensible**: easily incorporates custom MCMC algorithms and unusual probability distributions.\n", "* MCMC loops can be embedded in larger programs, and results can be analyzed with the full power of Python." ] }, { "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": 18, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pymc3 import Normal, Model, Uniform\n", "\n", "with Model() as partial_pooling:\n", " \n", " # Priors\n", " mu_a = Normal('mu_a', mu=0., tau=0.0001)\n", " sigma_a = Uniform('sigma_a', lower=0, upper=100)\n", " tau_a = sigma_a**-2\n", " \n", " # Random intercepts\n", " a = Normal('a', mu=mu_a, tau=tau_a, shape=len(set(county)))\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " tau_y = sigma_y**-2\n", " \n", " # Expected value\n", " y_hat = a[county]\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, tau=tau_y, observed=log_radon)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 2000 of 2000 complete in 7.9 sec" ] } ], "source": [ "from pymc3 import sample\n", "\n", "with partial_pooling:\n", " \n", " step = NUTS()\n", " \n", " partial_pooling_samples = sample(2000, step)" ] }, { "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": "code", "execution_count": 20, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "sample_trace = partial_pooling_samples['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", " s.sort()\n", " axes[1].plot([n+j]*2, [m-s, m+s], 'b-')" ] }, { "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": 21, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with Model() as varying_intercept:\n", " \n", " # Priors\n", " mu_a = Normal('mu_a', mu=0., tau=0.0001)\n", " sigma_a = Uniform('sigma_a', lower=0, upper=100)\n", " tau_a = sigma_a**-2\n", " \n", " \n", " # Random intercepts\n", " a = Normal('a', mu=mu_a, tau=tau_a, shape=len(set(county)))\n", " # Common slope\n", " b = Normal('b', mu=0., tau=0.0001)\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " tau_y = sigma_y**-2\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, tau=tau_y, observed=log_radon)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can fit the above model using MCMC. Here, we use the No U-turn Sampler (NUTS), which is a gradient-based method for MCMC simulation." ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 2000 of 2000 complete in 6.1 sec" ] } ], "source": [ "with varying_intercept:\n", " \n", " step = NUTS()\n", " \n", " varying_intercept_samples = sample(2000, step)" ] }, { "cell_type": "code", "execution_count": 23, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 23, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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J3vcy4+MbGB/fwKJFN7rTMuuYVN9hCdhD0l7AVuBgSXtExI7Cdmup8tJjnincrMuSdFgR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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymc3 import forestplot\n", "\n", "plt.figure(figsize=(6,10))\n", "forestplot(varying_intercept_samples, vars=['a'])" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[,\n", " ],\n", " [,\n", " ]], dtype=object)" ] }, "execution_count": 24, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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dTrCwzlNxIb/5ZBE8CJwHfAT4ILBGVQ8UuVxVqdDr3Tyxb5Bo0uLNK5sKet18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\nfGaenzxzil8eGODq9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NVFrjq6HPCKyA+B1YBTRPYqpZ4vsZzlppBzZ9EhIhcCr1dKfSK6\nyFY/0SlgS1VvSdcGhidC6ylKimeRPpfisev7aR3FYw7s5aSXfPRVcQNLKRURkTuAX2FMO7nD+ruI\nXA+MK6Xutyz7LrAeGANuLKO4FSFXHSmlXopmOXkC40T4mlJq0XeM8zmXMLwMv1BKLQUDNF8d/T3w\nnego672LyXuVijzvSz8GOjGmCv5NGcWtCHncl+4H7o/+9m4gtAiNq4x6WYLcCxyLjqY/q5T6qIh8\nngT9LGW9pbg2ntV6SsL6LPqpUmpS62iBFH0/rSNARD4FvBloF5E6pdQHc9FLPvqSaHYMjUaj0Wg0\nGo1Go9EUyFLKeKXRaDQajUaj0Wg0JUUbWBqNRqPRaDQajUZTJLSBpdFoNBqNRqPRaDRFQhtYGo1G\no9FoNBqNRlMktIGl0Wg0Go1Go9FoNEVCG1gajUaj0Wg0Go1GUyS0gaXRaDQajUaj0Wg0ReL/Ay+Q\nNB1duD9qAAAAAElFTkSuQmCC\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "from pymc3 import traceplot\n", "\n", "traceplot(varying_intercept_samples[-1000:], vars=['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": 25, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "b:\n", " \n", " Mean SD MC Error 95% HPD interval\n", " -------------------------------------------------------------------\n", " \n", " -0.662 0.070 0.002 [-0.798, -0.519]\n", "\n", " Posterior quantiles:\n", " 2.5 25 50 75 97.5\n", " |--------------|==============|==============|--------------|\n", " \n", " -0.807 -0.706 -0.662 -0.619 -0.523\n", "\n" ] } ], "source": [ "from pymc3 import summary\n", "\n", "summary(varying_intercept_samples[-1000:], vars=['b'])" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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anZfLhVv6g4uYLICd8Eyp5Prqma0tvp9g928Q/1yvaO3sDR74XgvPHBy0q34i\nPHPy4qZM5nfe+WEsLf0YHEeD7fwOgATy+Ydx333/G7SmQdTYmOMhB8rLHnsshtlZboG3thTqdYVs\nlnrzRIL+5TMzro8Zgnjm8NDgmbk5G7OztAhoNKhmqdfhJfFW9QxRQzIpem9q2C2L39n4OJOiNDcJ\nnmlVz4jhVywm6hmqQFoTcTodxjMyhJmWt/wcymXuPjj4gsm5p0d7g625aHUaHFGtEs/MzRHPLC4a\nPDM8bEbzDQyYz60TnllfN+oZWRSHhohnRD0ji5TjtB/0cpJReBFzHKpnuGvgQrq7G07gtB1g4g8e\nWt9IzCGdva1DSoLXm8kY9Yy8Thbm1gPwKH5w4yZN5r+KlZWXoNF4ceBfv4F8/jF85CPvRTLJKqhc\nZgu/Uny4i0WaMyWTGlorrKwAjz4ax8oKufnWFl/b1cWqOJt1MTYGX6o4Pc2DwlTKdBnOzSm/el9Y\nCOMZHqjycJULj/KSifKtBcRISyr5TEb7zU1TU9wxdHWFBy4H5X+ZjNvW3NTKarUO/6x0Q+bzxDP0\nZSF/PzjgfysWmcCzWb7HZrN9cEQqxZ8NqmdWV6mvJ9ri5zY5GZ5f2notnIlq8IzjsMIeGHC97lKD\nZ67mzU5FTvsi1opnpO9Afjaddn0uH/SsaVXP3Cg8ExxSEkZunZu5WlVFEZ75wYmbMpnfeuuHsLb2\ndmjdhNYKgIbWGaTTf4/XvvadSKeZhDIZYHjYQT7Pn5MJOM0mQF05K8q+Pge2zfFvFy/aeOKJzngm\nkWD1KnhGKuq+PlaLzWYQz9B7ZXVVeYOl29UzlEoSo1QqxBGplMEzMiKur68dz8Ri4YHL8kCnUtrb\nBfD31GpAo6FCyb2nx8XhYeduyFRKo1rlzmV5mf7vrsv3wOpde6+xkEq1D44AgniGXuXb28wopVI7\nnhH5Y+u1LC/TE8eytI9n+vqIZ9gXQPVMudy5VT+Xu3pLvyyArsvrCCZwwTONhlHP3GjMcXTUfs4S\nHGYieObgIHy9+/thVZFgqyi+P+OmTOZ33vkhrK29Es3my0HMogB8DYXCN/Ebv/EuHBwo7zCQUsRm\nkw9rJgN0d9OCNpOBP6B4a0t5v4OJcGyMC4BSlAwG8Uy5zEopm3V9/t7fL3iGqOTUqTCeWVkJ45mt\nrXY8E4/DTyJiU1uptOMZpcJ4ZmqKw58HBsz1tD7QV8MzweacdFp7Y/aM+iaZbMUzlEdublLhI9y+\nu5vJsVq1bHCYAAAgAElEQVTt7Kgoh5qinllcpL+84JnJSV7H4GAYzwSvZX2d36dlcQFwHH4ulFS6\n/qJAPNO5VT8W69zSXyy6ofOJ3d1wAqeuPYxngBuLOVo7ezsd+Gaz7c1NnVRFsmOK4sbGd53MlVI/\nDOBjAP5Ra/3eZ3jt7wM4B6AK4FNa6z+82muvRzL/iZ/4OGZn70GlUoXr2nBdB5aVQbH4GH7mZ/4t\ncjntHSDyBteah0ridLi9zYqvqwtIp5mMSyXK4eTAjE6G2h/2zGHN3K634plyma/N5VhNZzIuRkeB\nmRkHk5NMtkE8s7enMD9P/fvsLKvXSoXfodas4G2b+EVrvgfLCuMZUc8kEvzvqZTBMzMzYTzTiS9L\ndQrw4HZ/vx3PAIJDwt2QPT3teGZ/n1VvqcTkns3CxzOtgyPSaX4Gq6vGe2ZlRXYm8JubBM/IgIzW\na6FzJHwJouMQNQwNuZ78U/CMWZxaD3qlcal1Ecvn2VegtfKrdMAkwkyG6hnBMzcac4gMtrVLuXVH\nwe+0XS3Uiq0iPHP943tJ5vcCyAF42bNI5r8H4ANa68VnekPXI5nfd98f4UtfSqNczoI2NE0Ui/u4\n/fYm3vzmt2NuzsLSEgcrkw2zSkmlgEyGiezoCP5hoLDiVIqvy2aBoSEentq2QQCNBqAUE/fwsEZ/\nv+vhFY1Ll4hnymVu2/f2iEqIZ1jBEpWE8UwsZvDM3JyFS5eIZ1ZW+DAqxWrd4BlKF22biaZSUd58\nUYNn+DsVensdzMxo3z3y1CnimVZvc8EzcnjrutTb1+vhRJzPu6hWg9t90w0ZxDMrKxaWl00VSPkk\ndxa1WmdHRYCJ+soV5alniGeUou78anim9VqWl1ltczQfdyKinuFiDF/aGBydJ+8nlwuqScKLWFeX\n66lyuKhubZkEXipx8EcQz9xozHG1LuXg+ykWWSR0Ugu12kdEcbzxPWEWpdQrALz2WVbmH9Razz/T\n77weyfzXfu0P8Ru/sQHHeR1kOIVt/1e8+939eO973+6/bmUFuHAh5m/tV1ctZDIuenqAXM71Ei28\nipo3tVSbKyvKr/TS6c54ZnubeEbUM6OjwS25wqOP8m/v7hJR0OPc9fl7qaRx+rQxyTp1yjgJVqvw\nKlcbc3M2Ll0K4hkmWqV4aBiLGTxzdEQ8I9iG6EgcIIGxMeM9c+aMi4EB3dEyVqY0CZ5xHGKGVild\nJmOmMwW7IWUi0d4efDyzsUFs1NdHjJXLuYjF+Ll0clQUKd/sLDt4FxaIZ2ybi+nEBBepwUEzIKN1\neLTgGaVMpa6UwTM8dOW1BRen4FmADJpuXcRkNydNU3t74QTOg9Nwc1Mr5qB/z7E+LqFonSHb6cA3\nm9W+Xj+4m2v15InwzHMb1yuZ/xaAFwIoA3i31vrS1V57PZL5vff+Os6ffxOq1Sko5UIpF/H4Ms6c\n+XN88YvvuerPNRrA3Jzh14uLUnW5XuVFGVgiwUpMfMppR2ujXA7jGXkABM9sb4sXDKvmnh7imUyG\nVeLaGvDYY3EsLRk8A/DvplKsrkdG6DA4MUFHx9FRYgnBMwsLBs+Iekba66W5SYZTuC4T3+EhGXAm\nw8Qdi0nDlEIiof2qXayBczkzcDnY0CJ4RpqmHIfJq1VKp5TBM8FuyJ4eNsnIecaVKxYqFQv5PJNm\nPk805DjwmHe4OgzimUuXiGd4UAqk01fHM/RNacczgpmCeKa7mwnYcZRnutV+vlAqaf93BhexZJKL\nCvEY/+72djiBZzIc/CHoRzxrgtd6PTFHJxlscJiJfPbs1m1XC7XiGdkxRfGdx3VJ5oHX3wniljde\n7TXXI5k///m/jsPD9+HgoAHXVZ77YQq2/Sd461t/GqdPMynNzJBVX6uC2N8HLlyw/K390pKNZpO8\nU/BMMmnwTL3OhLK1ZVix4JlMBhgcdNDTY/BMuWx5h5xMHENDlNwRhWjMzlre8GImvZ0dopJsFojH\nmVympgTPMOEODLDqdRyDZ0Q9s7zMh1GamxyH7yWVIp6JxUwSpuc7E3wyCQ8TEM9MTWk/wU9NESEE\nBy7LA51IhNUz9Tp3DUFWWygInmnvhmTjEpPe8jL/h41PTP75PPHM0ZGFeLz98E6pMJ6Zn5dFkgeb\nExO8BsEzIn9s9WlfWgrjGcdhgg3iGUEora36nfBMcBEL4hlBUZLApbqnodf3B+boJINtHWZSKmlP\nERVWC0V45ruP5yKZv05r/UvP5o8ppc4B+FWt9Vuu9prrkczPnfsw9vZ+Ac1mHlorT55YRTz+u3j9\n69/tDWRQfmU6MkKkMDNjWPW1Kp/VVeDixZi/tV9dtZBKEc90dxs8091NPHNwEMYzRj3DqpvVueAZ\neFI9SuNk2LPgmWpV4bHHbFy8aPtKm2pVIZMxeKa3N4xnJieNk2CtBk/3bXt4gr+j0eC1CZ6Jx1nF\n1+sGz+ztUaVCXxUzoMN1+R6lW/bMGaINoN08a2+PVW48btwVq9V2KV02G8Yz0g1ZLBJrEAcQz6yv\nE8+UStK96iIe56LVyVFRpHxzc7aP2CgP1Z53OxeooSGDZ4LDo8vlMJ4RzGRZ9J4pFg2eEYTSOjqv\nVKJCJjisW15XLLq+MslxiMWCCbxQ4L1QqxnXScEc8ruvN+boJINtHWaSy7Ximc6qItkxRRGO7+UA\n9N8D+GcABgB8SWv9c96//xSAA6315wKv/QyAIQAVAO+6Fju/Hsn8xS/+AGZnXw3gJwP/+rcYGvoK\n3ve+92N+3sbSkrgj0k/l6Ej5bDOTged46PqKE9GidwrHMXhmdtb2RsMpz3PctMYnEso3gRL1zMqK\n7TUjkc2nUmTl/f0Gz+zsKOztWX5129PjYnjYDGrY2KB6hniGD7fWYTwzOqoxM+N4laiLsTHz83t7\nwMKChUuXuPuYmzPOiY7Tjme0bsczrksZZjJJ18dEwqhnpHs1nzcDl4MKkUZDeeoZvh9pbmpNxJal\n/URQLptuyJ4eDdfVXrJlct7bs9DdzcSWzxMNBfFM6+CIvT1gddWM5ltetryDY/jNTadOMeHI/NLW\n6USrq/z8Bc9Ik9fgoOv5vhg806lVv1QyM2BbF7GeHu19/mb6U5BTZ7PEM/K7g942cq3XE3MInuk0\npCS46Nh20Aq5XVUU4RkTN6XO/E1v+m187WsTqNcnobUFpVzY9hW84AXL+MM//DcoFvnQkK2SL8/O\nWiiXLc8nxEWtxsod4Pa3WHTb8My1KoiDA+KZS5e4tV9astFodFbPZLNGyre1ZYy8gs1Ng4MOCgUe\npgnOEDyjtfaGGLu++mVuTnl4hrYCu7scSpHNUj2Ty2mcOsWE2wnPlMvKT2yzs1z8BM80m+14Rpqb\nDg5Y5adSxDPsXmUSLZWIZ/g3Wf0mEu1Io1zme6UDJRePoyO0TR4qFFwcHYV5bq2m/ORWrdL7XfBM\nowGUSvy5fJ545OiofVcgHjxbW2H1zNaW8juFZVEcHQ3PL229lpUV2kIInmk0mMAHBsxgbPGob23V\nl4PeSiU8eFwmNOVy2mua4nWLjFCqYWkqE/uG7wc802lISaubZbWq/OQuaqGwqZzZMd1McZMm89/D\n7OzLsLp6Ea4bg2U10dV1Fv39T+C++97i2ajq0Pauu5tbd/H1lgq1UhGZH3w84zj8t6EhF2fPMhHS\nEvbaFcT6OnDxoo1Ll2wsLLB7Mpk0eIYc3OCZw0O2qK+vU87XaChPGsmqm3ppVkFUhRDPaM0qbmyM\nW3Ju9xWeesrG+fOWZ00AX5MuzU29vdofk0dFi/a29MQza2thPEPVBj8TaW4S/XsQzwTVM1ozido2\nEcLoqMxe5U5oeJj3ZVBxsrlJTBXEM7JwtCbiri5j/ysVvG3Da/yRsX0KV64Qz8iAZsEziUQ7npHB\nEcKK5+e5SC8uUrJqWdofrTc1xdF8ojoKKoHKZfrOrK4aPOO6vN6hISNf1NoglE6j85LJds24tPQn\nk653j14dzxwdmUpYMEfwWq8n5gjimeCQkuCCFuEZxk2ZzN/2tk/g618v4PDwh+C6TG62/U+YmKjh\nbW/7d9CaB0+xmDm4isXab45Egg/N5cuWr44QPBOP8+EO4pl0OoxnTp16ZjwzP2/hwgWjntnaMuqZ\nXI6HqvE43y/AjtOtLYXVVUr5lAK6urTnV048I1YA1LNbfvXW3U31jAxq2NwEHn005mOhrS0Lrmu8\nZ5JJwTM0F5uZacczi4tWoLmJf89l7wlqNeMcGVTPVKvccot6hgOy4U9x4oGuMRfr6bn6wOVsNoxn\n9vfDzoiCZ+TwMNgNWSgQzwibp3rJQi4XxjNUAnUeHLG3B6ythfFMswlfikr+zntKPrfWa1lb4+5J\nOLvcS0H1jNbKk7C27yRKJf5M66FkLIaQvLLZJAYKJsKurjCeuZq3zfXEM1cbUhLEM/E4QveC4Jng\n8xs80D4JcVMm83/+z38TDzzww2g2XwRAe/LER3H77V/Cr/zKe7CyIq3fgLDNeFz7XYEcIdfesVcs\n8qFZW6O+e3aW1fvmplTrxDOOY8y0CgWyaknwo6PXriAOD4GLFw2euXKFzoOFAh9sJm4mi64ug2e2\ntw2eodoljGds2wwoPjqCXzUODBDPSEPLwgLtCTrhmXg8jGdEzTI4yJ2A2OLOzlqesRYHW7B6ZRJr\nNo33e6PB5O66TMKCZ1yX6hkO3bZQLLqhvzc1xQUr7G1u+HIqFVbP1GrhZFAsuqjXO3dDZrOud07B\nndOVK8QzxaLgGXrLHx1ZflUfTKqxGLypT8r/Djc2qJ7p6XExPm7OLILzS1uvZXnZCuAZNnkVizxY\nTqU4GFukjVcbndeqGZfXCZ4BWNFvbYUTuKhnBM9czdvmemEOkcFey3aA3brPPJ/1BxnP3JTJ/DWv\n+V089dSPolLZBGBDKY1EYhTDw9/ARz/6Jr9bEQD29niDLC3xyw9O+OnqModdjqP85Nxq/XpwEK5Q\n5+YoSRQTqGoV3pZaFBNh9czAwLUrn40N4MIFG5cv21hY4KFpIqF9W1rBM7mc9pKcxs6OuS4eMBr1\nzPAwq0pq0+EdmPLQLhYzeIYNLQbPbG9z53B4yHmo6TSr7lLJ9ap37XevCp45OjKLn3Swbm4KRyaO\nAdqbm+p1Dta2bfiVJZubmNhGR2X2KhfKkRHtfZ/tD3QrnhH2H6z0cjntV6fBbkhKA7kjkuamtTXi\nGTEX6+pykUoZG+LWwRGSjObnzWi+gwMu+IODRnVEm1+DZ4LXsr7Oua+ADo3mGxw0fFzwzOZm51b9\nVKrz4PFikQuE4Jn9/XACLxblu5RF88Zjjk5dyq22A93d2rNTCM9nDT6/0p/wgxA3ZTJ/2cv+Iy5d\n+hE0Gq8EO0ABpb6M/v6v4T//5/egq4tyuFa/jGyWW1E5eFlcVP6QZ9fVHfGMbYc7AgXPbG+bCnV+\n3sbiovK9vRsN+HNGm01uqScnKenjwaBhrp3Cccj22dxEeWS5bKG7m8kll2PTksgjxRBse5sNMevr\nVhueYcs9vMM4DpqQ7X1Xl8boqOM7AW5tAd/6VhDPMAnIoW4yyQ5MOjgy2Y6NGbxTqQBXrgQXP/49\n6b6s13nQK6P55IyiVmMFn05zkbQs8bNhchX2LnimULj6wGXRdtNcjHw56IxIK4UwnpFuSM5ONWye\nn0NnPNOJeQueWV8P45lGA56Rm+uNGeRoPvncWq9lbY1ozLbh2ThzcR0ZCeMZWaRaW/V7e80M2NZF\nrFBwPU8bg2fqdXOvd3VxdyDj8G405ghKR69lO5BIhNVCneazBg+0O8XCwioefHAVjmPBtl3cffcg\nxscHj/0ab8pkPj39y9jefguAce9f6gD2kE7/Fd75zg9ibc1CNkt9d18fH3qpWoLyqWJRI5HQvt/I\nyoryDq/k4SGC4LY1jGdab2rX5fDoIJ5ZX2cCi8UMngF4Y/b0hPHM2Ni1K59qtR3PcManwTOUKXLH\nIQZTW1uWvysRPCO8tlDQbXiGodDfT/sCwSvz88QzGxvEMzs7gme0j7BOnYKv4ZZKVH5+ayvoPcP3\nf3go8kgmFFHPNJvG5OzggCglnSYCE+/3ZpOdo9PTRq0zPW3wTGt3ZiwmeAa+93vr5KFi0UWj0bkb\nsqsrjGc4NzWonuF7lB1Ja1KNxeAZvYXxjBQQ0r06Ph6eX9p6LfJ3ZacneIbqGaPtl11W6/lCT4/2\nm9laF7Fczni/12psYjLdr/xsm034EtEbjTlaO3ulS7l1mAnHG7arhVpVRUoxkX/uc2tIpe72/06t\n9iBe85qBY0/oN2UyHxt7Lw4O/kcApwDEQfvaMmKxL+MXf/E+nDvnwLIUdnf58K2uMqn191O/TekT\nK49W+VRPD/FMpcIvf3mZX74xbqLUULZurqu8KTftN/XBAbC0ZPkIYm6OB4iU+cFj28qXAQ4MGDwz\nM0P1zLUqiHIZOH+e6pOFBSKCRII3Zj4v2nf4ib5aNTa3S0tktiKP7IRneGAKcL6q9mV6lsXDz29/\n28bTTxs8s78vnbLwGoBcr7lJ+1JFaVWv14PqGVawou6wLPLRTuoZwTNS2WsNpFKuj2dGRszs1dOn\neYahFDrK/zIZJk3h77K4hKV92j+YDHZDtuKZ5WXiGUnkMptV1DOdHBXFYG1+nvLQ+Xlx6zR4RtQz\nwQEZMp1oY4NJdXWVfQcymi+IZ+RwWvBMp1b9TKZzS7+M5iOeoXVyMIFLMSCDQb4fMEerdLST7UA+\nr9HqRSQ7rMce+wb29p6Hzc0d2DZlzBMTeUxOfhtvetMdx/reb8pk3tf3C3Cc9wA44/2LC+AygN/G\nT/zEb6BWI34oFlktjY1RPXF0ZKbVUJWgMDzsYHDQ9Spcg2eC8ikObDZ4ZmGBeEY8SlrxjAx9br2p\nZXCyNCDNzxtvb0nw/L/hKyYmJohnpqf5P8+EZ65coXpGBlNvbho809UFP8HLIdnBAfHM2powW0n+\nxDMDA0Y9w2Edln/429WlMTbmIJslPtneJp5ZWLD87bngmXSaeCY4mm9mhpWo4J39fVn8jPf7zo5R\nz1AmyeSuFCv4eJx2AJWK5bfdB/GMbcPvXBU8UypdfeByNqtD5yrSNBVMBvF4GM9IN2ShwIYxwTNX\nrhDPZLOsjHt6jGti66GtOCrKoiMDTngmwmtuxTPyubVey/q62Y3IlKZkEhgeDt8/lUq4Vb/VxbJ1\nIIZSYTzjOMQzwQTOyVBccL9bzPFcRicTuU4HvoJnPvGJr+KRR25DszmA0VHXO+eZw4te9G3cd9+P\nHOt7vUmT+S/Bcd4O4CXevygADwL4An7yJ98P19W+ZDGZZFXnOMo3c8pmgdOnHZRKLioVC9vbwMaG\njdXVMJ7p6SHv3tkJy6fopEfGu7lJtrmyYvCM45CdB1vF5ZCy9abWOlyhCp5pNrk4tKpn8nntV+6S\nDK9V+dRqgmeYIAXP9PSwY1Nkiul0GM/s7EinJbs9JSEPDrr+wArBU0dHPFwFyFwHB12vU9SoZwTP\nbG/zs+nq4qKSzbqYnGzHM4mE6TKcmzOfj7TmS5KSil3UM7KD2t+nRl6830U902xycQs2U01P8zxB\nXBqDlR1lldpfuJtNop9W9UyzGdbNC87r6qKfz/Y2K2iql7iTKxZZcafTfO9AO56Jxw2ekf6I9XWq\nZ7q76RwpeCY4v7T1WlZWLK+Pgv/dcYjoBga4gxM10va2WZyCeIaTjNoHj7fiGfGHlwTOg1Pt45mg\nZ03QCuBaRcpzHVeTwfb2uvj0p/8SjcZbkUwiJFooFD6Dj3709cf6vm7KZD44+Cuo1+8DcAiZEASU\nAPwXvOpV/6s/BELMpqTrUabTxGJAtUq/j2KRFVGh4OLsWQfxuMEzKysGzwwNud7gBRkoHPbLKBSM\neoZsk8lLbnLXpaY8iGeaTbLz1i3g4SErbDHPmp9nciUOgMe2aWnLz4NOi6dPGynhtSqfrS1Rz3B3\nsLxsIxYT9QwTt+AZzlPV/o5GpJRBPDM05HpDQJSPHRyH75F4hklBDj+fftrgGZ5jcDEJ4pmZGRcT\nE0Y9I3inXufZxOXLtl+9rq8LnjHqGduGL8ekBJI6bqnsZUQfD6wVhoZEscPqfXycf6/TRB85fJZz\nlWpVtQ1Y7u6WBqZwNyQ9W8yB9dISRwsG8Uwu5yKZ5O/tNDhCLAGCeEZmz/b3u6HmpuCAjNZrkYEg\nUnAYPKO9oSdsQCqX21v1r4ZnZKEL4pnDwzCnLhZd/7uSz6fTQbLo9q9HyLnRJz7xRTzySD+azbsx\nNuZ6/kUP4O67N3Hffa881vdwUybzkZFfQrX6bwHcFfjXR2Hbf4a3vvVDXiVtwXG015nIm5Ot8fBv\nYMcx0+EB+HimUGBFNzpKU6YgnllZIWseGQnjGWGSwYevqyuMZ65cUd7hlfKbbMJ4Rnlb3nbr12CF\nOjdnDkDpPcMDK2luSqU4+u7sWe3rtkVK2Cm0BhYXFS5cMNXvxoaFXE683w1/FxVFpWJhZwc+ntEa\n/oSnnh4m+KB6hosR4LrUtI+PO76KY3eXzU3z82Y0X7Op/LOJZJLt8WfOuH6z0fi4QRZBPDM/z+5V\nwTPS3Srs3bJ4SBmP8wxB8Ax3VfxbSjG5Cp6R0XyteEYSUbWqvB6GMJ5pTcSJRDueyWa1Jw00zU1X\nrljY2rK8g3bX8wCSe7Rzy/7+flg9Q/08MRSbm7gTuRqeKZe5w5TdiBykEs9wR8sOX0obg2dNwZ0E\n0L67AVgscdfA+357O5zAu7ulaS7sWRO0Hg7q9o8r/uIvHsH8/Djm51d8ldXExBAmJxcjZn4cceed\n/wFLS8+H49wKGU4BPI10egHvfe970NfHCm97W2FhgTfHzo6FgwOybEnulHzBxxhMsPAlYLSQZaUh\nXttkrtqbMwqsr9tYWbGQybTjmd3dsHxKKp4gnlleFmklb/JYTLatRj2TTnd+aNbWZHg0q7O1NeIZ\n2+ZDT3bPhzafh4dnDKu+VuVzdARcumQSpOANsaUV0zCO5nO92Znc0ZAVG/VMKgVv4dNeEmUVxElK\nrOh7e3k4nUzy/S4tEc+srSnf18S2g3hG+5W7VNPDwwbP8GyCFbwsUHK4SEMuLqqplOurZwAe/NVq\nRj1Da2ANx7HQ1SXad+P9nk6bgcvBKtyygGTS9RduUc8EE3GpxM8tiGcE5+Vyrt80tLYmZyvEM4WC\n9gZTcyFv9T8h1+dnsLxsvN/X1qieyeWonpFFMTi/tPVaVlb43ATVM4UCz1KyWZP0xZ+/00FvJ2+e\nbFb75mTiX1MuM4FTSkttvHD5YFNUa/PUc4lnOqtZHsBrXnP88sSbMpnfe+/H8O1v34tmcx9AzEMq\nefT2fhOvfvX/goMD5bkj8oYZGXG9wynaw165YvuTgo6OWJlLyzkAfwsoplZaK39SDVv9uV3u6mLF\nce6ci3hc+6x5dZUPQ18fE5SwesuiZrvZVAEW6XpqC1HPiLbYWKSm00y8svA0m/AUBeGbuloNHyDO\nzRk8w2k6Mrga3pZc48wZJqWpKSbDZ4NnZG7p0hLxDIc6m0Qr6hnBM5ubyt9JZDIGz3CAMx/mSgW+\nERrAz3t0lNcneObCBQtPPmkH1DOsfqV6LxTcttF8gmcaDeKZS5eIZ+bm+D1xsLQoi+AlYWHxrOIF\nYYjMUvBMs6kwOOj6fjfPBs/I4GhRzwh6ke8yn9d+5RvshuTsVBYR7EDlaEFR1hSLVM8Inuk0OEI0\n5+JPND9v3DP7+416hlOYnhnPBJub+vv598Qfv15X/tlB60FvNtt58HgQz7gu8UwwgReL3B0E8YwY\nrwUXSNnxfbexsLCKhx5aQ7PJ4upFLzp+WSJwkybz973vj/DZz7qo1X4U8uAnk/fjLW+x8eEP/6uQ\nG97Fi1QEiJ91JkMJ4OAgk/HBAbC8zK5LWtEqTxsuMzddH8+IhFBmcga1wLkc1TOZDBtqpqcd1Oth\nPFOrUT0jGu9cTqNeb/fLyOWIZ2QLvLho+YZXsk0lV4X3vvj+ggdWwhx3dxVmZ8MVarXK7XezqVCt\nwlfPsKEljGekO7BTaA1cuUJtvfiGr69byGZdFApEMiL/41kD5W3b24Jn2DUr3u/5PBN8JsPPWIZ1\niGFVJsP3J63mu7vAY4/FvHmh4ttu8EwiYfCMjJibmDDIgt+9WfwEzziOOcwT9m7bTOx0gSSeEd26\nUtyl8F4knpmcNHimr6994LLIBDvhmdZEnExqv/U+2A1JmafpbKX3j+U1ilE9093N91itdsYzBwfE\nMyIPpY6dSWx01Hjo9PcbrBW8FvF+39hg0SA7n3iceKanpx3PtLbqB4eMtC5ixaLBM1KlBxN4LieF\nSth4LbhTCer2v5/jpkzmv/M7/4jPfnYBly/bcJw4gAaKRYV77hnDW9/6qjY1QK1mhhXMzlK6t7VF\nZidTgkR/nkxSYre4SKOrnR0L+/vUg8diGvE451YG8QyrE/H85hBhxwGKRfjqmZkZB/39cvAFbG7a\nWF62PC9yg2ckAQflU3xf2m+3Xl3l4GJA+R7asRhnavLBkUab9gYKpaRCtbwDUBtra5wtys+KSUUe\nylyO7/3MGbMtv1blc3QEXL5sEqRMY+rpEXmk9ipULkiuSzwjh4HBZqR0mslYBlbUau14plQyeEZr\nYGmJ3u/0HmeStyxzqJvNaoyPm8Vqepo7Evn5nZ3w4sfRdny+iL2M90yzCcgh7/6+DBHh90Hv93Y8\nMzXFnVAm03ngslLciQmeqdcNngl+l67buRuyu9v1FkKDZ6pV+GimUNC+wsdxOpvP7e5yh8gdDA9o\ntVYe2uLnNjFhnhf53lvVMwcH5jyq2eQBKIsok/QFz3Q66A372ZjX5fNmAWTjUDiBp1IutFa+E+N3\nimeiDlAvrkcyv+++P8LTT78I1eqLPXWKhlIP4syZb+CXf/nt/k0V7IAzTUFmG7y6avkt+Zcv29jf\nl6YgVs1Bi1k+GBw0werA4Bm5oYPqmXY8Q+dG+oQAPT0unvc8Np7InNHVVerChR+XSlLZhO1M6QnC\nxMz8MZYAACAASURBVM1RZdz6yuGVqGdSKSYNURU0myqEZ+TzqNXCFargGQBQyvXUGuYe6+/Xvve7\nJMNrVT47O/C072Y0n2WZ5qageiaTETxjtNqi6iCeobmYuFVWKmxu4gLEz3t4mMmJW3KNCxdsPPWU\nja0ty9PKcxEX9YzgGTnwnJkxnueNBgsBuUfm5rij4IIi33NrcxMZueCZRIK7KeIZ/s6BARczM9rX\n209MyPfZPnA5iGcch/deayLO54lgOnVDplKmn2BlhaMFuZMTewiiqlqts6OiGKwZPEN7BkE84j0z\nMhKeX9p6LcvLBs/ITndgwOAZgBizXO7cqt/V1XnwuDQ3iS1HK56RIRlHR2Y0X6u3jWDTqAM0ENcj\nmb/jHZ/B+fNvRLVa8jswG419jI39Bd7//rf4X5AY8bR2tsmXKNswGSIcdMMTbFCtsrLLZMgVBwd5\nOFWtsnpZXrY9rxPlOwZS9+z680lFVSEPvnQu1mphPCMSQ84ZNXimWg3jme5u7THJsF9GVxd55daW\n5bNRqlzMVCHhqjKQmYdn4c+Dk3lMhSr+MIeHymfFtZr2jZukoUW834Odnp1C8Ezwc15bYwWbz7fj\nmXicla8Mgl5dJZ4R58h8ntLRdNq0m7MiV56/OjA66qC7mwlxb4+Hq7OzxnumXieeSaWYfIPNTdJR\nKnjm8LAdz2xv8/BZKeP9LniGqhIzmo8zUwFA5ovyPpmYCDc39fd3Hrgshl+2ze+g2SS+ak3EqVQY\nz0g3pPQJCJ65coX3WioFf2GQQ/hqtfPgiGqVeEbmzxIF8v4YHjaj+QYGzOfWei3r6zQYE/WMKMvY\n8UpZoNbwF6nWVn3aH3du6S8UXK/I0t7hfDiBi6eR4Bk5tH766W9gf38U29tLSCRYmU9ODkdqluOK\nX/ql/4onn3wlnnpKw3HisCwHIyMJTE39I97xjn+GRoOreydnuXi8c2dbawecjHQLtlufP2/5MzmT\nSaOx7u/XnvcLsLAQxDOUuFmWRiJB33JKI0U9A6/Byahnmk3imZ4eJqfpafJ9zhlld+DyMtv2R0Zc\nDAywSs1mNfb2wu3WpZIMQzbOfEtLrLJF5WLbCDV91OuUNrZ+HpzObvAMt9/EM9TiKt9AS/DM9LSD\n06cNqxZJXKeo14HZWZMgxe5X1DPC1RMJ4hmt4Y/mu3LFDjQjITROLZGA7zPCZiNWyYJnODFJYXk5\njGe2tgye4UBv4hkO9TDqGelp2N0Nq2cWFgyeoSEXk3siAZ/JSweuDBEhpoOPZ7LZsDXw9DQ/w04D\nl7UmnonFjHrm4CCM6np7udi3DmEWd06xW15fZ4KXn6eaS/vvsROeke5mTvfid7iyQhTIz87xzhLC\n80tbr2V11UKlYvCM47DCHhwUPg6vsa1zq36xqH17gdZFrKcnfJ9vbYXNydJpF3/8x/+Ir341j93d\nO9HdXYdtu8jnn8DLX16JdObHEe9735/ir//6+YjHfxgAvEaah3HPPU/jDW94k38yHtTGyureyQSJ\n3XLtnW2tVqeCZ2RYgcgCKxVW5ZkMK9/RUVamgmeuXCGe2d5WvuY5FjM3tByq2rZo35l0RGVh2zRT\n6u5mFXr2LJUNgmfW1qgLlwQl+CQWY9VydKT85C5VmbRyLy/z0Mh0BjIpsEXf4JmgMZF8HkdH8KRv\n9IeZnVXesGp6WlSrfJh5KzIBiHpmZsZ0el4t9vaA8+eN8mJpyQag/d1JMNGSQWt/CIfgGTkTyWSA\n4WGDZ8RsSri3ZWkMDXH4B78P4pknn7w6nqHRl5lAJMPC5UB5Y0P598nsLNkzD+KZxATPiF2C7Hoq\nFX5mySQXnmRS++iuv18UO47nWskKttPAZUpHjXrm6IhS16ALaE9PK54xOC+VogJqe5sS2pUVHkrK\nz3V3E4/Uajz7aTWfA3j/0T6aC5zcH4JnpqbonxMckNF6LUtL3ImJ5bTjEPX190v/CIuJcpnfUdjG\nmliz0+BxyjsNnqlWLfzmb/4N1tdfjWQyh2xWe8VJGc973l/i4x//F89RBuscN2Uyv+++P8KXvmRj\nbQ1QKgnbPkKhoPGqV2l8/ONv6ziLUE7QMxmjja1UOjvLiblS69a2k9WpnOwvLytvZJxxBLQsVon9\n/SLD40zLK1fILre3DZ6Jx7Wve+aNazpWZSYnLWNZaWazHKiQzWpfYthoEM/Iw3dwIN4zlHXl89pz\nBQz7ZfAgEr5HumiaeUAkUkiaRgmeAdD2eQiekQp1bo4SRsEzjqNQrYbxzMgIpZ2tUsKrxdIScOlS\nDJcvMzmsrVnIZExzE10cDZ5hP4DBM82m8tl8dzfxTCbDz5hDQES+qX11Tz4P32Y4iGeCdrvpNL/D\ngQHtM3CZRhXEMysr7Xim0eiEZ4z3e63GXUgiIXrvoMWAwTNTU1wsBc90kv9dDc+EfcuNIVvQ/pbf\nDYuIctnyJ2clk3y2yN+ZHKvVzo6K1Sp3lzKXV7yJngnPBK9lfV2Gzxg3U8uCJ6lsxTOdvdml0Gld\nxD796T/GwsLLUa/3I5l0YFka6fQabr31K/jkJ/+nY8tpwE2azN/4xt/CAw90o16/DYANrR0AT2Jk\nROMXfuHfYGqKrDNoqN9q+ykn40Qq4l/O1b1T4hYjntbOttYqX/BMcFjBhQvGUS6R0IEGI+15vwDz\n8zY4C1O259o7VDPqmWZTvNfDeKbZZKVXLMI7DOKkoKEhF4eH5JTlMivbeFzwjFGX7O0Zvwyzbda+\nVpjb7jCesSz4qgJRz8hDHfw8OJ09PJpveVn5B8VHR8rflXBgCDA15fgHrJOT18YzjQZ8hZLgGVZn\n5KLd3cHmJraoC55ZWrJ9tUsQz8j3LQdmbDbidRYKHM0nrHtlhXhmZUX5ygylyJzjcVo4jI5SESRO\njjIsXAZUzM+rwGi+MJ6p183hqpi6WRYrZsEzsjDG4/zvqZSZFCVNYoJnOvFlqU6D3jPBeyHc2Rke\nwpzPi3rG4Bmql3TIC8lxqGhpNZ9LpbiItuIZYiO04Rl5nluvZXXVwu4u7ylRmmWzxmpC1DNyTtDp\noPfoCPi5n/tTPPnkD+PwMOdPtEqlKrjttn/CJz/5L5/7ZBaImzKZnzv3f6BSeRsajRd7Ol8AeADZ\n7KfxkY/8n5iftzx0wC+Jk9bD2znXvfrJeBDPHB52xjOlkgwAbu9sa+2Asyye7Eu7tSgj9vZ4g2cy\nlBWOjPD3KqWxvh5Wz1SrvFEtS7bOUrVLS7/BM3LYZllGPZPPs3onWzfV6vo6x7aNjrp+d2E8bvCM\nXKvgGXqvEM/QmQ+QAQfptPZ2Pp3xjHwe9Tr8nYyoZ7a2wuqZIJ4plcJ4Rjo9rxZ7e1TPBPGM62ov\n+Rg8IzJJ2jWwSl5YaMczQ0M8PLVtgwAajXb1DFGIxqVLNh5/nHiGc1qlG5aj+fJ57Tc3yYGxDAsX\nPGO835nceBBv8Axnr3LBlV3P/r7y7Bz4/6dS/C6bTZkWpX21zuRkGM8EEWMqFfaeqdeJMYKJuKfH\n9Z8NSfKC89JpmrDJAf7ysml8YnMTF9hqNbgrCDs2Cp4R/6DtbZ5tFYvXxjPBgo1FQ9C+Wvt4JpUS\nPMOfkcXpU5/6U8zPj6PROO3ZOmgkk+dx110X8fGPv+24UhqAmzSZ33nnf8LGxi+iXi/6ZlNaV5FO\n/y5+7ufeiXPnHIyPc3LO5qbytvu2z6uHh00zBPEHf0dwFqH8bzHTEjzDqeidneXyeR0YBRbubAsu\nBLmcOdkXN7xLl8KOgOk0b3LaljLBLS0Z9czenqhniGeSSdeTQjKRMjGIRQCTf7UKr2uViWVggJVi\ncJAF9cEKQ0MGz3R3MzkE/TK4bXb9wyjBM3LIKBN+8vl29Uynz2NvD/5ORvDM/r5JVLWa6YiNxzlM\nWYzFglLCq8XKCnDhQsxXXqyuBvFMeDRfPM7KV6rNlRXlV3rpNF8/PEw8IwhA8IzW2h/23NPDc5OD\nA4XHH+ffFvVMtUr1TCYDH3lJkp2ednDqlHESrFbZuUxfHhuXLvG7Ip5hou2EZ46ODJ4R9UwQz4yN\nuf6B7pkzdFDsZBlbqfDaKQE25lnBe0GekZ0dK1TBJ5Mm4XKEIXdEGxvEM319xFi5HAUCh4edB0ew\nV8TgGSq1WMjI8zw1RbWZuJW2FmyCZ5QyeEapMJ751Kf+Bv/wD3s4OOhCMhmDZTWRze7gzW/O4Vd+\n5X841rx2UybzH/qh38Lq6rtQqTSgdQxaW0gkUkinP4tXv/pfYGdH+V7WhQLbrc+dczAwQLe2pSWz\nnXMcblXHxlxfZxzczrXafsrJeKlkWpcbDT6gV8MzV+P3YRMmc7IvSe3iRaOJTSa1310qk+Cp5OBN\nKnhGa+1XbaII4E0r8kSjmpABzGwm4UHi5CSr9IMDY1kqroojI+wE5GJAU6Tt7fDDJ1a0YTwDr0Wb\nD093NxOD4JlEovNkns3N4PBo4hmxvD06Uj6CoGc68Yw0N01Omo7FTtFowPeVFzyzsxP2nqE7IpGD\n+JTv7PC8o1xuxzN9fa6fRLe3uRgBvM6enjCeWV8HvvWtOJaXjXoGCE6M0hgZoVR1YsL15qCSzQfx\njKhnZPGT9nqxo5DZoTKfVtQzMppP1DNaEwEGvWdOnyaeaR24LI6hmYzbZg3celCulMEzQfvbnh7X\naxpSnkjAQqXC6VGCZ0QyTPuLdvO5vb12PMMDfPiTm1rxTGvBJnjGtvn5f/rT/y9WV8eh9V1IpRwP\nszyCO+98NKrMjyN+5mf+b/zt394N4MdgLHD/Hj/2Y9/EBz7wLqytKd8adHeX3PPgQBppqFo4c6aJ\nmRlu+2o1Muu5Ocvb7hMHyHZubMzMO7zWLEJpXXZd+F7fQHui4g0VxjPidR5keJYVdsMjorGxuwsf\na3R3a7/ByLI0ONvU8hUYz4RnHIfNTa6rvUk+TPwcNMBdy7lzDrq6XN/9UIYPFwraQ0NMgMkkF65g\nu3WpZPCM+HpQWwyIBlhknsHmpqCaSD6Pet1UqGxAYmLhOsXRfEbbTzwj7H1mhtvya+GZ/X2DZ6S5\nqdnUHnozeCabZSIL4pnFRct3ShR1zfBwGM+Uy5b/+QK8DwcGDJ65fNnGE0/YftIzZmUGz5w6JeoZ\n3psDA9q3eBY8I+qZ5eUwnhGbCpGrxmJM8pWKJEF+9oJZiFY4s1YOqE+d4oLVqchJJrXvTBnEM8FE\nXCi43rNhnh/Bedms9s54iGaWlmRnrP1Flu897JceNJ/b2lJYXFR+gxoXSarB5FBampuk2Aley4c+\n9P/h4sV7Ua9rdHUdep5NLm677f7oAPQ44u1v/118+cv9ODg4DcCCUg7S6Qt4+cs38Qd/8O/81wVN\n6K9cUT5/NI0iTG5dXVQEnD1LPJPL8aagYsL2/UuGhoJ4xmznxF86yA/lBF2M/13XNAK1cvV8Xnud\nnO0LRKuXhuAZJjUmd2noETxTKhk8c3Rkmpu2t3ntfKiZPNNpg2fEcVHwDMdmcZufySjfxKi/n0lS\ntrHb20zSlYqFoSEevIrxEy2ATbu14Bn+LK9VNM309uCBqDQ3ScKnT0f757G3x+HXYg28sMAKVc4R\npGlKKtORETOaT6SE18Izq6vEM7K1X121kErReyaXE0wSVs/wQM+oZ4S9B/EMiwJ4Uj0upokEMD5u\n8Ey1qvD44zYuXrRDeEZ88YU3czQfq+nJSdOqXqtx8ZOzicuX+V10wjPSmSrqGQ4lCeMZOXwfH3d9\nt8ozZ/gsAJ2LHJkRK8+J4BlxRqQqTJr7wva3knDJ9Yln1teJZ0ol4/0ueKZTy770ivD6Dcq0bTaG\niXpmaIjP8zvf+Rk8/PDd2N7uAqC9TuVDvOAFD0XJ/DjijW/8A5TLb/I8hy0o5SKZHEGx+N/xa7/2\nekxNOX4jT2uI38P6OjskZ2d5A4lMkDIn5eOZs2fpWx6Lsetvbs7G0pLyD5jIHVmx8PCHf6eT7afI\nu9ioYvBMJ66eSnVWHrRanYrDX7Dd+sIFVs/VKgLqGYNndnfhe5Zvbxs8E49TERHEM+Ky2KqeaTQM\nnkmnuYsZG6N6xuAZC5ZF73fBM11dBs8EHz6ZthPEM2xq4v8O4hnx5IjHO1u/Cp6R5qalJXZ4SoKX\nQRZEBcCpU46f4CcmXF+L3ikcBz76mZ01eKa72+AZaW4Sj+5Khd/zygoVS5YF/xCwVKK2XdQzPA+x\n/Oq2p8csAACwsUH1zNKS8rzfOf9TBonIdy3XMjNDbCY/37r4zc1R/SPpQszFguZWlkXb5v197iB5\nAKs9hQ3va0Ea09Nc6Lu72wcuiyUF1TP8e9Lc1JqILUuH7n0ZbtHTo+G62m9uonqJeEYKCCl6uLNo\nd1QUKw/xfl9etvw5APff/3tYXn4lEomzAWXMk3jhC/8On/rUz37XOevZxE2ZzN/0pv8HlcrPo14n\nLjg6YjUB/D5e8Yp/5RtoDQ3J9HZWLMGtlYTwR8qbDJ7hYY1wTzO/8syZJk6fdn0p0/w8Xx804Z+Y\nYIIfGzPzDq81i1BalwXPiBVsK55xnPbONjkoDeII2dYHhxVcusQTe/qjGzzDz0T7Dwabmyx/NyLe\nM0rJ4ZpJivRrMSZYVM8YPHP2rINczvWkgAbPiC1xX5/rJTW0dezyczMNLSsrZKtBPJNIaG+WqXiU\nd8YzzSawusoKVQ7QZFi1ZRk8w+BCLuxd8Iw0eHWKgwPimUuXjHqm0WhXz2SzHJMnnZblsjHyEu+Z\ndJrqmZ4eg2e2tgye0Zr3oRQYzSYwN8cDVhYlTHwc9Udpay5HPBMclRfEM+VyuLlpeVn5fRJyriJ4\nRhZFmSrFjmEm+ERCOpkVSiXBM0axE493LnLicd4DIv88OoKHXoJNatxldhrCnM26qFbh7RCZnBsN\n9kEUClxkqVqi+qrVUdGy4Dutvv/9f44LF6ZRrd6BdPoAtu2iu/spvOhF5/GJT0TM/DmPj370L/H5\nz2eRSLzZ/7ejoz/Hj/94Ff/6X7/Z56oXL/LGPjxkddfVFfa6HhkxqCQYzSa/XPHhlhtctrqNBl/H\niTms3icnqZ7hRCDiGUEHgmdkOycqhU6zCOt1yruk+yyIZ1qd5QoFo54JdrZdDc/IsAImd1ZmMpFe\nOvhGRmidWq9TPSNOhjs7Ug0Tz8gDLHhGuG8nPFMo8DCrr4+fFWDwzPIyK9HBQVagIg113XZJaD7v\neouiwTOVigpZyOZyLlKpznhGmka6uykVlQp1fp4VKu0XeF2cl6n8aTPDw643WFssYY0krlOsrxv1\nzMICk0wyadQzXV0INTdVq/DOIyjnk5mxYvoWxDNyDiTqmXgcIVO4alXhqadoP8HDVfhmZdK9KuoZ\n6V49dUr706hqNQ4+4eLHzl5KD/mZCJ4Mm4sZ9YyoauiLo/3D79FRw/pnZlwMD2v/XmgtcoJ4xnFY\nvcdiYW+Wri5jyCY/H4tRvhiP8zsWu4f1df68MRdjE1wrnvnoRz+Dhx/OoFzegFJJKHWEQqEPL33p\nQYRZjiMWFlbx8Y9/FU8/nUCzaSEWc3Hu3BHe9a6XhZzNgtXwlStULszOks8eHPCm6+nRfqee+DZ3\nGpAsA3LX1y0PZ8gEI8OhbZvbYlHPDA1xO7myYhYEOWAy6hnXxx+AmUXYqftOEmizyUWlE1fPZK4+\nrDbc5WdO9gXPXLzIyrlW4wMfVM/I9vTKFb5G8IywXtoD8xrMgAkmeKnapLkpiGcmJmirW62aanVp\niYlKRvNJc9PBAXcOweo7k9F+s5fgGdNcxUovOJqPzUqdrV/lnESam5aWlDeMhIevQTyTTofxzOTk\nM+OZVvXM1pbyPMcNnonH+X45Qo3f8+oqpXw839H+uUh/v+tjNt4PlrcYEfuMjBi74o0Ner8LFuLO\nxOCZZJL+5WIuNjPDnWUQz7At3wwe5/dvvGdEPSOe+53wjOz0BFNOTZlzqJkZ7kiuVuRks64/HazR\n4O9tdUW1rPBoPsF5hUJnPNPdrb1eDC7yH/vYx3D58jCU+lHvb1Fc8ZKXLOHP//zd33XOejZxUyZz\nAPja1x7DX/3VLOp1G4mEgze84RRe+tLbnvHn5EahZlXhwgVK76pVeHiGFqvEM+SAgkpaY2+P2ldR\nz8zNKb/VeX/f8MT+fo2zZ9nVKKqM/7+9Nw+TK6uvBM99L3KP3FO5SLkpM6WUVEVh05QpytANlBl3\nlzG2wdCGb9p8bnvsNh57xmMMGGYMxt3FZmObZgobY1MNbgyYMqv1VRmmWFwLlGSgFqkkZaZSyn1X\n7nu8O3+c+L1748WLyEURmVmpd76vvqJEpPLFixe/+7vnnt85AwPsjIWeqaryksNN6fSM0a6b6bvK\nSmODCxh6JugsV1cnCTPp/H2QjnDd9LACoWfW1viFjMe17z1TUED1zMCAoWeWlw09I+Pn8uWjjFD7\n9IyYYHEwiHxneTlw8mQCVVUe5udV8svHaL6KCkPPUNnAIra8bM4camuNTtymZ+Qgz/OEgjA7Hzmk\nDN6PRIIdak8PP6v+ficZVq3gulRl2M6Y1dVsDE6cMPRM2LmNYHkZ6O01u6ShIebLyvSqyBRLSoB4\n3NAzop5ZWDDRfKWlfG6rq+F/jkY9w+eooYH0jARdDwzQnkDombk58ZKnesamZ2SatKFB+4lL09Op\n0tHhYZXcjabSMyJXdV3e/8VF7vJS6RmNjQ0HNTWkZ+T3dXR4yUCQ9CaHnvHw/971ddr42q6oNTXc\nZdqdv9B5ZWUeVldT6Zl//Mf/iYWFewA0Ixbzkpr0S+js/Ac88sjv7axI7RC3ZDEfGBjDBz7wMH7w\ngwQ8rwCOs4EXvcjFO9/507vyHJYHZWyMndnly24KPVNWRnpG7Embmw1VYsMOyB0ZYTEcGTGDIhJN\nVlpq6Jnjx/mluXFDJRUTpGeUSqdnRKVg00CiALDlXSKPXFgId5arrmbXJ4dS9nh20OoUQFJbbdQz\n4rfCkWsWvmPHvORoN88eJJpvdla04dxuizGSfOFl6tHzZBEQSoDb5bIyLk6nTiWS6ULsKsfGqK1v\naDDqmaoqKnPECdMMc3kASFdNTioMD/P9ptMz4mSp/OJsTz1WVGgsLaV3qDLuD5CeYTKSKCaMeqar\na2t6ZnKS0XxXr7oYGOChaWGh9p0N7eEmLobap2fIFaukNJKLwdGjpHTYFCB5YMrFNBYz9IzjpNIz\nEs23vMxDVSY3ySSph/Z2I1cUemZtzdAzMsEqXbXjmGi+WCxVPbO+zuQmSfeiLw7VM5ubpGcoi0wk\n9fY6+XmmNzlCzwD8HJeWVIqSSugZGeu37W9raz387u/+NRYW3oLV1UW47gocx0NpaS1qa/8Kjz32\n2zuuLTvBLVnM3/nOB/C1r5XAcX7NH+ff2PgkXvvaVbz//W+56b/f7oYlFq2/n19acb2rqjJpNWIM\nFBaQLPTM1JTjD3lMTzNt6MYNJ+lzwm6so4OBFU1NCRQUGHpmeJj0DLfCRj1TX29+J0OSTXEXMy2h\nZwD4UXRhznI7pWfMuLWLnh6F8XHubgoK5BDPRI0JPTM66vjDTaJrF3pGulsJwWAHL5axvI+0Y4U/\n5NXeTvWM2KGOjrJQHT3KATHh6ldW0iWhkggUpGckf9KmZ0htkbqxHQdtekZ2Mgy/Vr6OW7TWsmiV\nlADt7Qmff+/o8JI+6+HPYiJBbp/0DHdB09MOKiqE+0VyuAm+RzfTrCiPnJzkzk/omZoa0jPFxaRn\n6AZp1DPl5RrNzQnfD2dmBnjqKUPPTE9zEZegbloxi7kYi21Li6F3FhbgPyc8fObvE4WS2CbzGdD+\nGYXQMzLcJBm9MtEsxb2jgwtldXXmJkfoGUAlJ7jTD8odh97vv/RL/x3Dw28AcAKFhXK4fgXHj/89\nHnkkollyjp/8yT/D0tIfJikK7XN1VVXvw9mzv5vi15AryIMigxk9PVQtrKxIQks6PSOTjEFIQO74\nuETZKZ8vXlw0fKK4IZ44QWphY8MMN4mHdWWl56fUt7YKzWAWJD7YqfIu8VnhqHh6ipEUKnpfp/P3\nQavTWIy7Gxm3ZgdPvlLUM2VlXIjk+oSrn57mIJLQM0ohOXIugR4qmUyjkx2z9mkCxsaxY43HkaSx\nPCwsMGd0cpKe69KhHjnCLpLe8ywWsiWvqaHhmgx7jY6yGCplPEoKCox6hhFyXCCC98Pz2KFK997f\nz6LK3QfVM+I8qbU5txF6pqVla3pGdkkcbqKfjFgv2PRMWZnnO0LOzpLKmZsz9ExJCdDY6PnfGVGb\nrK/Lb1PJUBbPX1iFnpmcNOoZifqTe9TeboabOjtpdyz0zMyM7T1jXEYB+ENjrsvnQLxVtGaXLfRM\nIkFjN2bZOqiq8lLUOp2dPE8Ia3JiMe3nt8q0rFAv99//KVy82I319ZcmF1iNoqJHcffdz6TMsOQD\nt2Qxv/vu+zE//zbMzgKJhJPkLRVc94v4qZ/6ef/LceYMJYmiYMg15EGR+LnLlx0/BIEaZp2UKRp6\nJix7UOiZqSluleUBJ6Wgkrwy1TNM9BFrVZ3MrCQ9I9v9hgZzqMRQXeMrY4cK2/KueNzzi9TiYjiv\nXl1NqWAYfx+0OgVYQISekanKpaVUeuboUXaYiQQHXAYHU+kZ2Xob9UxqsLZNz6yu8syjpobFvbaW\n98pxJGeU9MyNG6RnRJpZWcnQblkgZVGrqjL0DIdWUumZjY10eoYpN+n3Q+gZM37PDlWmcEXaKe+t\nsdHzi7vQM2GNgWB6GrhyheqTgQGqkGx6Roabyst1ssgZm9vhYXL12egZkXJK5qkszI7Da3/uOReX\nL4t6RmFxkXQiaSGe73C4iY2HnUa1vo4kxen6O5zJSaFn2KULPSNTyjY9I5291oxK5C5I4dgxk70q\nbpVKpdIz0uRIstWDDz6M732vFsvLKmmB6yEeX8TrX7+Ed73r3pzXEBu3ZDG/554/Q3//b8NxagDI\nIdYc6us/gde97ncwMOD4ST9MGOGX4dSpBE6dMgEO2bqf3cDuhgcHjYGW0DOOk0rPHD/Ojicsrs8L\nYQAAIABJREFUINkOyL1+nQes7IQoYZNtf0UFvxynT3s4diyBwkLSM1RMsDMWekY6pfp68zttGkiK\nvEzo2fSMDFXZyTVHjvDLz+DcdP7eNmGSSDfbDa+nx8HYmJu0HBCHQnN9i4tGPTM7S7VGIiE7MRla\nkX9UcpsO3xJWovm4G5G0IKpnOIrPRWtkxEl++Q09U14eTs+UlRl6hoe/YuGrkoNVKhkMYtQzrpt+\nPxgcbjrU69eNt7c93CT0THEx0NaWQHe3dJ9e6LmNIJHgvWP2Kv/uqSlDz8TjSA43IbnbMPSMuGkC\nSHb5fB4aGjw/SIPPg+M3APG4RktLwn+uZmeBH/2I9Ax3neb8SaZXGZNIeqari5+L0Dvy2cvhan8/\ndxZcUMxwk9Azm5vKl3guLDhJDxyxsOXzEYvB91/q6PCSOzmjtZ+aUrjvvi/jypUXYXx8HEVFCq6b\nwPHjjbjjjh/iAx947c0XiSy4JYv5O9/5AL785QJsbv4yANG8PoBf+AUP73//W3zJ3eiogwsXHFy6\nFPP1zOvr8LMmW1pYBGnoHz5UdLOQbnhiggZapGfYvQs9U1+fQFeXTqaeJ/xJxiBseoZRdkZmtrAA\n3yzpyBHSMydPeqir4zZ7cFDCiPklrajQ/li2JK3L75TfE5R3yYARwC54etro4oP0TBh/H7Q6FXpm\nasqoZ2Q2gF22Uc/I9Qk9I+qZpSXTmRcVmdF8cq9iLGb02ELPSEdeVmboGU6mGnqmrEzUM+Rki4uR\nXFRUinY9FmP3KJ/NyIiTPOQ1BlcVFYaeocwu/X5onUrPXLvGokodv/bpGTlfqKy06Rly1WGyWsHK\nCnwK7No1F0NDXDwqK438s6jIqGfECCsTPSOZtK5r6Km1NfFK4nPR2OglpYjA4KDC00+Tnpmd5XPl\nuto/zI3HPbS3wz/0F3qmsDCVnpFBONtlNJEgJSPDTRsbcihNOm1tDSne74WFjOarqDDde2dnAp/8\n5AP40pcmsbZ2BkAMwCaKii7ijW88gg996JdzUxQyYNfFXCn1MgAfAfBtrfXbt3jtPQDeC35K79Va\nP5LptXtRzL/whafx+OMLeOSRHqyvF8J113HmTDde+tJyvOlNL0gpTAIx0+G0nIueHvpNz80BAB/o\n6mp2zbfdlkBbm9kiZ+p+dgvphiV+jtmipCBS6Rnjw15Zme4hIg+4mPNfvWq+dPQjhx983Nys0d29\niePH+cVlYDPpmfl5fgEbGrTfJQk9I7pqm56ZmqK8S8y45DUyrRnGqwunHuTvgx41QKobnhQ2MUor\nLeV1cbiJBXB01OSAzs4qv2sTblSoGAnBYI4lOVOhZ4qKSM+Ul3OK99SpBAoKlO+fMjbGRbO+3vON\nzST0OOiEWV0dpGe48Ag9ww7VFF7PU757ZfB+LC+bDpXTydIR62RcIp9f+bo3NXl+ce/spI1xtgZl\nZkbUM9wdjIy4cN3UaL4wekZop7U1nonE4zolDEImRKUjN/QMdd1y+HnpkotLl6ieuXFDYWGB9IwM\nN9XUpKpnOjoMvbO+DkxMcAcsE6wTEyo5D8BpVSCVnhEP+Pl57pRloSgu5oL50EP/L5aX1wDckfSr\n96DUj9DdPYlHH/2j3BSADLiZYn4PgHIAd2cr5ooWb48CuAc06nhYa/1vM71+L4r5gw/+CAsLP+H/\n9+oqsLiooPV5nDnzojTfDzHdsYuyuB9SSuXg2Wdd3wR/aYkfclUVf/bUKXbwR48ayiDXkG5YUuv7\n+qj6EHqGgQZGHtnQEJ7Ak5meMcNN9AahZWx3t4fmZtIz4+NOit5ZQqNtekZ+pxgY2c55rkuemveH\nXZDol4O8elmZTkudF/4+OARl0zNy+Dw6ykM/KdiNjeaeLC3R5nh01PG9TuTglPp3nZQPmsgxZq+a\nIGGhZ8QauLmZpkw2PTM6yvskw01Cz6yupk/sxuOp9MzQkJmoFP27Pdwkypow61ehZ3p7WYClw3Zd\ndqT8e+H7jbS2JnDypPYPBsPObQRas4Pu6XH97ndy0kF5uVHP2PSMOGIKPTM2lqqeqa5mgRd6Rjp9\n7lJ08hzIqGdmZ4Gnn44lqVLeL84BeGn0jJwLtbYau+PFRX72MpyViZ4Rd0fRwi8vk5559NGPQ+uf\nAHAngE0AGkqdQ2XlZ3H16vtv7ku+BW6KZlFK/TsAP7NFMT8J4J1a6/+c/O+/BXCf1ro37PV7pTM/\ne3YcxcV3+n+2uvok7r23Ea2tjSkdqwwaLC+nfzGCXLVI7kZHHVy8aOgZHsaxw62s1BY9wwKXaajo\nZhCkZyS8YmWFXXFhId0Lu7pEPZPwpXJBLCwYczEZfmGgAj1oOEgDP9Hn5EkqP7Q2w03j4zwcLC8n\nPXP8eMJX7MjvzEbPiPZX6JkwXt14X6fz90GvcxqmqWRYA7+8DMw29AwpEnboN26QnuHULhdsHpqL\nplnuu/ILjUw3ysi65xl6Jh5nFFxdHemZ2Vn4w00mFjCRnHQ19IwtCS0sTKdnAKOeicVM9y/qmZKS\ndM8eraVDNQfN4+OOH1KyuiqySz5XlZVIHqwaKWGYrFawtgb/HlN6SXrD9n430XySJ8vna3jYeMWw\nwCN5LsHFlSICPtfizVJXx92P0DNDQ/SeGR9PpWdk1xCPa1/R1d6emkYl13LtmkLQWVPULBKaXlzs\n4Ytf/ASA3wRgy+HWUFDwdoyPv++mv9fZsBfF/KUA3gghwojPaa2/H/b6vZoAHRgYw/nz49jc5EP/\n4hc3ZB0YsjtWe1Ag+MUI0jPC6V67pnDxoovLl10/BVzGpqur+SDdfruhZ7IdTu0W0g3LhOaVKzzU\nEnqmpER4cG6xW1oMVWJDbHQnJ7lwCT3D6VWqZ7Tm4nX0qMapU5tJPTQdACW5SeiZ+nrjecPUFsMP\nB9UzIgFj8C9fQ4VMOK8eNGbKtOsCUukZcvBuCnVVWan9BCCbnpGkIBlJl5FzgF2cqGrEXEwpWVDM\nIsgEJ9IzhYWkZ2ZnSc9MTzs4csQcvFdUMNQhOLFbXc0FbWHBSQ6ekdoResbzgJISFl7xLGGaU/r9\nWFkxHarQM+yIaRVAKSAfUKWQIoPt6CBXvV16ZmCAMt1YjPe4spIH48XFRo++umroGdlJiHqmvFwC\nz/k+Fxb4HBpbCO6M6uo8f/iop8fBxYuuP9wkmnQON+mk62mqF5PQMxsbXPz6+lLpmdVVha9+9e0A\nPgDAdlZbRSz2NkxM/Leb/xJnwV515n8ALlcKwMcB/Nf97MxzBelYpVAEfT/ki2EXQ6Fn+DCQnrl2\nzUkmy4je3fO/HFSZGMog15BueHiYw022ekZsY216prExnJ6RlKOpKSo0+vvdZCfEQiedXUUFFQGn\nTiXQ3JxAURHH/69d485BZGPHjqUON8k2ONuiWlJiJlxnZ8N59Xjc0DOy6xL+3nbDkxDh6Wnle9n3\n9prD51jMdImNjbw+0jOcupRoPgl04AGrl0bPsMDDbwJWVpD0AoG/GHZ2JrC+nkrPrK1xuKmpSegL\njfX19IndeJxduiyKg4NOGj3DA0TtyyO1hm/5atNVc3MK/f2mQ01Vzyg/VnFzkxpum54RKWE2emZo\nKJWemZhwEI+LuZjo0PlMMvWIB85jY9yZaK18eqaqivRMcbE8D3wWef+pfGppYfaAUqRnnn02lvwu\niiGeoWcKC3kmdPIkRQadnbTPEMmyUHOvetW7sLz8iwBeIu8MwPdQWfk59Pd/KHdf3BDkopi/Rmv9\n+1le4wD4Lhjr4wD4Z631yzK9fi8783PnxpBIOHBdD3fe2birUX4bdscqxcb2/TBfsNSfE053bIz0\nzHPPuX4c2OoqO9yqKk7WnTmTX3rG7oavX2dnJtti6STr6nhIZsfkhdEzEvYr9AwzLCWkmF2qeIqf\nOEH+vb7eS26NWTDGxkjPxOOp6hn7d2ZaVGWQh1thQ88E6TLXRUpxt/n74K6LWZImrKC310laLZgQ\nZw4Y8fpu3KASSPxLFhdJz3By1UMsJn7vRmXCASegoICOkhJ7JuqZri6qp8g1A1NTLkZGHBQXc+dg\n0zNzc8YqWd5HURGTgiT2bGSEXbbjkJePxeDvfCSar6Qk/X4oBb8pkenVsTGqZ3ivuIjLc1VezmuX\ncO3W1q3pGbnHop5ZXFS+La3IHouLFeJxWjFwHsC4dcowUkkJd4AydGbTMzJUVFvr+QuA5wEjI/R+\nHxtLp2cKCrjYtraaxaqrK4E3vOEP0ddXAuAo2J2vARjGiRNr+P7335uz72kYbuYA9B0A/gOABgDf\n1Vr/RvLP3wBgSWt91nrtqwG8B1ym3qe1/kamv3f/OPNzuPfe7FTLbmB3rFIobN8Pw3+m/pxNzzz3\nnIMrV2hoNDdn6JmqKsoRb7st4WcVZjuc2i2kGx4fJ/3Q08NDrZUV8rDi4tjZaegZoUpsCP8o9Iyk\n74i2XkyzSko44t3dTXqmspKFS6yB5+YMPUNzMXKcMkQStqhKvmpFhRQp+FF0Ybz6dugZUQjZYQWi\nGllcZCETC1rbYnZszMHQkIuZGZWUUabTM0HvGaFnXFccBlUKPXP6tIeCAqqMZmdZpKemHJ8/Fm9u\n0jOpE7tiuMa0KhZ3pjsZ9YyhZ5SvxbfpGQ5JMUJxZCT1AHFuTrh8mouJ5YJS8GWwPLvh5xgmqxXM\nzppoPvF+Z5qP8X4XHry0VOgZSQtzfCvfsjJq5RsbE75b5cICfOqKShTj+km6TKOnx8Vzz7l+rOL8\nvKFnCgo0zp17B1ZWKgDYtiAPoKurD08++bGb/i5mwy2pM3/wwR/h+vVWfOc7Y3BdB8XFCXR1NeH0\n6UG86U0vzOvvBkzHarsQBl33gsXQtuPt7eWBDg8iqREvKOBo/pEjGt3dHs6cSeSVnpFueHjYeL8v\nLLB7B7gtFu9poWfCApIl5WhqyvEHpYSemZkx9Ex5OdDe7uH06QRaWhIoLjbj/0IdxGLw1TPHj1Od\nItvgsEUVMPSMFM+5ufDCXVGRqp6Zmko9FBd6RkKEZ2ZUyr2RkXnHYZHhiDsL/fIyMDJi6Jm5OeWr\nJAoKGBAhBdCmZyS5SYabbHqGig3SM+JnPzLCnZ7QMyIfXF9Pl4TG49zRiB3swIBNz/A9MpoPSdpI\nJadf0+kqyliVf7gqMYWxmNAzkt/K98MpZTNWvx16RvyPBgd5eCv0TEUFu3KhZySwRIKgx8aUL78t\nLeV3qKnJDKkJTSieO6WlQHNzIumHw8Xz6adJz8zOKnz3u5+F570OwByAJQCbiMWqEY9/GFevvieH\n38B03JLF/P77v43z54/Ace70U0mWls7j6NEpvPrV92x5qJlr2B2rFBvx/bA7+GAxDNIzly+7GBpi\nJ7SyQqpBuMPTp0ljNDQYf5NcvwcpdgMDPFwdGLDVMywU4j1z/Dipgkz0zPR0qnpGutjZWeWrZ2pq\nSPd0d3Pykl9sfqnHxhx/srC1lYVBhpuk+820qIoNrkTzSYpRsFDFYlsfitfWGqveqSlRFrHAS3i1\nBFLLASflg1QCGXpGRtJJzxQUKJ/jFota21xsY4PPR00Nz2BKS+H77S8v84B1ctLxXRVteqa0VGN+\nPlUSyoles0ubmOBCLr7zYiPAw1nuJOiDkn4/HIdUlRw0X7tGFY+ElKyt8WdFPVNeDnR2Jvxw7ba2\n8Klnwfo6o/ls73cqgYz3jETzlZfzuWGalZk3ECtfWx4qNJvMdMhQV20tdz/FxRpvfvOfYH39LQDa\nfSdMoA+lpfdjcPC9uf3SBXBLFvN3vOMrmJ19E+bnxS+ZD2J19efw7ne/No1/DRrYhyk8cg27Y5Vr\n0TqVngnjqiWjdGBA4cIFB5cvx/z0Fc8z6pn2dtIzHR35o2ekG5b4OckWXV5GSsiGHLC2thqqxIYE\nP4fRM9PTtFnVmuqGpibSM2KturQk6hnuYgAuKhJgLEnrNj1jF2jJV62s9PzrkuGmMF6dRXt7h+Lz\n8/AHv0QWKIempaUsjOL9DuhksAmLjahnOLhkrCXs4SZq3416hnSOGGqxC+3u5s5kft5ovScnHb9A\n1dXppH4d/tmAFHcxXFtYkMxWc18A+PRMWZnQM+zE7UNp0jyMUBweNtFz/f1cxDgJ6/nqGZYlXoMU\nd5ESZmtQ5ueBK1dS6RkgfbhJOnShZ2ZmDD0jZyKlpcDRo4aekeZjcxP48Ic/gETi/wYZZc///WVl\nv4fBwQOsZskH9qYz/xecP9+N+fnjWF1VSYe3Cbzwhc/iV3/1rhSaI9OhZrBrDlN45Bry0NidZGlp\n6hcjWAzF74UHVYaeYdKPoWdqa5m5eeZMwpdxZet+buY9BOmZ+Xnlu94JPXP8OL+olJyl/z1iuSCD\nUlevusmDKhNRB1A909bGnUlzM70/JieVH6YsCoxjx0ygcJCeybSolpYaA7JM9Ex5uU6LNRP+Pngo\nLofPcm/6+owjoOPAP8TjPWGm5dAQ6RnxvtnclFBthaIiL+VgVWR1PFzl+1tbo5lVTQ0LVUMD6ZmN\nDdIzDJJmJ8rhJpOLubFBjl2SrPh+RSfu+OoZmoBxwaUU0kNREWkLcX8Mm+GYn0/Xd2ejZ5qbvaT3\nDJ+dsMbAxvAw0Nsb85sDWjB4qK6GldzEswGqZ3iPhZ7Z3FTJyVUeGDc1efjDP3wbZmdfBuDN1m/6\nDJqaHsOFCx+8uS/PFrglizk581O4fn3e71waGqpQVXUJP/ZjL9qS5lhfT1c/KBW+vc4n7I5VCkXQ\n90MyPG2IHe/YGMMELl2iqZbQMzLyfvRoKj2TD8rJpphs3+2VFRZ4OZyU4aaODqpnwgKSJR3HHpQS\n7n1uTiVtaJHUEFMe2djI7ml4mB3h6Cj9S2j8lDpQJd2vLEiymMiiatMzm5uya0jn1QsLM/P3wUNx\noTWuXxfvd2NGVliorQEjXt/cHG2OZbiJgeJiLkb1jMg3HUeoGu3z7xLNV1ND98aSEu2feSwvUz3D\naD7Xn/Ctr+dhfFlZOj0j6hny8sb7XWsToScTyhL0vL7O3XLwfojqSHYy169T9SU7kY0NQ89sbgLx\nOKeUpYNvb8/edG1swD/gt+kZieYT/p30jIbW5sB5eJgL6te+9udYXb0bWveB4r1NFBV1oK7uLJ55\n5g9y+t0J4pYs5ltNgAI7pznkJNzumu3ttWwn803P2B2r/DuRSP9iBIuhcLqDg45Pz0xMkJ7Z3KT3\nTGVlKj1TX58fyknuvT3cND5O9cz6uqFnpLgLPRP0oBdNv3jPSAcm1sBCz5SU8MDQpmdWV4Fr17gl\nn552oBSLtahnmpvN75QFyS7Qsqja6hmJogvj1UlJbe9QXOIGRT1DeoYLiNAzomARekbUM/Zwk1J8\nDkxyk/ItdWnIZeSYrquSWZcsvN3diSS3bg4TJyZIzxw7JslNqfSM/T2QMX7xfp+cdPzMTPHjLy2V\nzpu7gODMQHU179vIiKQTMXqRYdXp6hnGC3q+esae9MyE+flU9czQkAut+d5EHllUJPSMxtvf/hGM\nj78QnvcaOA7DPpT6Erq6zuGxx96d2y9KALdkMQd2PgEKZKc5pMhnksdNTaWGGewlPSMdq30t9sGO\nfd025uc50NPXp3DhApPixWExFuN2ua6OroG33WbomXy8J7n3IyOkVK5cSaVnyspS6ZmmpnB6ZnMz\nlZ6RblxUC0LPlJczmu/UqQRaW+n9wfF/doS03QWOHjXe7zYlZC+qsouTRZVFitciVEaQV6+o0JZv\ndip/bz8/5eXmWRseNrbJtiOgfNZNTYzmW1nha0dGUtUzBQWMWisq8pJSyFTvd61lEaB0lqZipBka\nGlgkxSlxZsbx6ZmmJk6E0oiMxVokocazXVwWHb+pIL1kovmEntGaf4fWCL0f8/PwD5rt8ftYjD+3\nsmLomYIC0jOS3NTVZQ5pM2F0FOjp4fdhcJD0TEkJ6ZnPfOZPMTX1Gmg9D8dJAPDgOCXo7v4avvvd\nrH6EN41btpjnAtloDruDD5PHyb8lzCCb5jzXsDtW+7rF9yN43QKR3I2OKly54uLCBapnZmdT6Zmm\nJhbB7m4WuHy8J/veDw4a321Dz8APNLDpmTAPetGUCz0j6hmbnonFzN8n6hnHIT1DNQbpGYmksweq\n5HeK86b9DJSU6CQlZ9QzMzPhvHphYfpu0XZbtHeLQgXy/fBsYnKS6hmhZ0RDXVqKpJKD98CmZ2gq\nZYbTJKaQ/1v7/LsEMFdVGXOx48fZpS8tyc6FroqxGNUzNj2zsJA+sStBztulZyQTNPh9EtWR7GSu\nX+fntbbG16+tkdqRQ+OyMqOe6ewkPRMmqxVsbMA3Lvv93/8IJiZeCK1/MmnGBTjOo+jsPI9HHnlb\nbr8EAUTFPMeQjszuhLPRHLvRnOcDdsfKf6vk5GHqdQeLodAzQ0Op9MzcHE/3Zbiprc3D7bcnkuP5\n+XlPcu8nJuj4eOUKJW+rq/AnNMUmgFLFzPSMLBSiNqELH/wkKPqckJ45eXITXV2er8qQaD5u97Wv\nHuro4ECV+N5nW1SrqtLpGSD9OSIllb5bFH7e3nUtLBh6hoWN9IxE81VU8P7U1pIemJxk5ykDMrIb\ncZxwekaGm4SjX1+nikWsjisqgFOnEojHPT+Gbnyc/1RX07aitpbPiyxcq6tGElpbm0rPjIwYeoYu\nm0ZxIvSMHFIGd6Hr6/TWEXqmv5+7CSq6GM1nZJ8qGURN7xmh2cIalJ//+U+hr+82TE31ACgAsIG6\nuhPo7LyAL3/5V3L7wAcQFfM9wFY0h6hQbP51O9vrfCM4BRkWBRdWDIXT7eujuVhfHyfmKAVVqKxk\nQktQPZOP9yTd8Oio8g8QZ2fZvYtNgBRa+rB7vl+HDdH02/TMyIjy+XcWLh66tbWl0jPT08b7fWWF\nHWBTk03PGN97cd409IyZ1mSRYvcog0DBhb+yUicnObfedQk9MzJiTKOuXxcHQvi7hmPHjHpmZIT0\njFgiCz3jOHQNJD2jfMfFjQ12za7Lwr+yApSWsjiWlXF4SuiZuTnKEUdHFRYXHTQ2ki4jV2/omVjM\nLGoVFV5yl8b3OjRkNOA2PVNYyEUmkeBCHPw+VVTwuR0YMPTM9es2PYNkzqzyA0OOHUsdbjpyROMX\nf/FP8eSTrUgk3ug/O677Bdx11yC++MX/K/cPuIWomO8Dgh3Z1FRq4n2Q5gjyr2Hb67BDzXxcd5BW\nsn0/jhwJz0sVemZ8XOHyZRcXL1I9wyBmlWKM1N1Nc7GGhnAdfS7eg9x7oWeuX2cBsOkZWz1TX5+Z\nnrHVMzxTMN7vUsSqqvj3dXdTPeO66fRMcbFYA/OfI0eM732mRVWi+Wx6JmzhLy7OfChud/BFRYYK\nvH6d1yezASsrsNQzhp6ZnWXEIS0PqP6QVCZKJPkexMGQ/ztVPbOxQXqmqooLyPHjtNVdWoI/ij8y\n4sBxTDSfJBsx3SlVElpSkk7PkPs3fvzl5ZwGFbmk0DP2/YjFuLDa6pnhYXOALNF8ssCWlgKPP/4J\njI3dDq3Lk4efHoAJvOQl38PXvhbRLLcEwmgO6cjCaA7pOO0v+HYONfNx3ak8bqrvh8jTgsVQJHfD\nw4aeEb9pm55pbSU9I8NN+XhPcu+FnunpIbe7smLomaYmLzm9ypDvsIhA0fRTPaOS1rFMo5qZcZIB\nKEylEXrmxAkqP2x6Znqab7C62vMTo1pajLFatkW1qsrzXyNRbGG8OhuEdP4+SM+4LqlAGfwS3pmH\npoaeEfWM61I9Mzgo7oNcCOzhJqWMBW+QnhH1jARrCD3T3Z1AebmXHG7iYNPYmOOnRh05QrVVURH8\niV05c+B90/6w1+goP2s+R+zWJc5OePONjXB6ZnOT4dFiH9Dfz89Law43ff3rn8bq6k/D86pRULCS\nVARNoqHh8zh3Lirmtyx2QnPs9lAzX9dtaKXwKDh+8VN/Tux4w+gZhk+TnhH1TEtL/t6T3PvRUTPc\nRN6Y3Z1Nz3R2ku8NiwgUTb+cKwg9I/p3oWfKyox6pq2N9MyNGyqpmHB9ZUeQnhHf+2yLammpofCE\nngny6tXV6eqZbPTM7KzQM0a2J8qi0lI+l4zmM/SMaLHn5nhYGYvpZKiDThZDukSy05X801R6pqaG\n9MyRI9zpyMI2O+v4Ob2NjaTLRBrqeemS0MpKL/mzhp5h4IShZ8rLPRQXh6tn5Fm26ZmrV1389m9/\nFGtrv4dEYhWFhRtwHA+xWCni8T/GM8+8M/cPqoWomD+PEOzIxEUxE80R5F9le73VoWY+rtsUCh5a\nhUXBBYuhTEQKPXPhghluWlpiV1hZyYnIU6doDyzDTbmmnOx7L6n1167xOpaWjNqlq0vCfanWCIsI\npP2qSo7ns9vlkI+J5nNd5dMzp07RGCsWM/TMyIhKsUSw6RkxVsu0qNr0zOYmF5Wwwl1aGpRXZt4t\nChUoRa2318wGBNUznO5kNun4OG0WGNbCnQf9Z+BPrgo9Y3vPyHATD4tJz7S10VZ3ZcXQM8PDDpRK\npWfKy+mFHpSElpZq34uHuwvzWXgeKZmqKqOeoZdM6i70DW94P/r77wTw0/LkQKmH0dHxJB577F25\nfSgDuGWLeT78zPcDO6U5gt1+MMwg06FmPq5bOtbJSTPVKL4fhv9M/TmhZ0ZGHDz7LK2BhZ7Z2GA3\nVVkJtLXxcLWri+qZfNEzksnZ359OzxQVAU1NCd9crL093INeFjv6iyt/+IXeM/RA15q7svp6Duyc\nOJFAbS3pGYnmE8VLVZWXHG5Kp2cyLapigwuQnrF18fYcRSKx/d3i0hL8wS/xJZ+bY4RiaamJ5hMa\nZGrKSebokkrhgaPkriI5VEQKhHSI9ukZMTPjYBA78vJy4OTJBCorPSws8BmZmCA9U1FBeaSoZ4qL\nkSYJlYleURONjlLdJPQMDd/4PmTh+djH/gZ9fT8Jz1uVTxcFBR5e/vJH8fnPvzW3D2AAt2Qx30s/\n8/3AdmiOoDzO7sDsw1h7O5lvSMcqxT3o+2H4z9SfEzteoWd6ew094zhGPdPVRXqmtTUVaUR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2bUMzL009Xl+UU+k+mdWC4IPXP1qgRMp9IzEvV36hRj5ZRCMgzExeioQiLBM4yWFjNQZUuFg4vq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\nydAzS0vp9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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "bp = varying_intercept_samples['a'].mean(axis=0)\n", "mp = varying_intercept_samples['b'].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": 27, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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lWm4k2emJJMTYo/beNB2jLcv19cCzrZx7sZXjQSEihwEPAZ8rpW5qp+9zGEE2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\nC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"text/plain": [ "" ] }, "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": 28, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with Model() as varying_slope:\n", " \n", " # Priors\n", " mu_b = Normal('mu_b', mu=0., tau=0.0001)\n", " sigma_b = Uniform('sigma_b', lower=0, upper=100)\n", " tau_b = sigma_b**-2\n", " \n", " # Model intercept\n", " a = Normal('a', mu=0., tau=0.0001)\n", " # Random slopes\n", " b = Normal('b', mu=mu_b, tau=tau_b, shape=len(set(county)))\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " tau_y = sigma_y**-2\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, tau=tau_y, observed=log_radon)" ] }, { "cell_type": "code", "execution_count": 29, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 2000 of 2000 complete in 7.6 sec" ] } ], "source": [ "with varying_slope:\n", " \n", " step = NUTS()\n", " \n", " varying_slope_samples = sample(2000, step)" ] }, { "cell_type": "code", "execution_count": 30, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 30, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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vlcDR3Xab+ftdlf8MFje87ZBq0sM3AMdHxOn56/WS7oyIZ1PUb4vnA74agxDT7nRWMzW1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\nW2yH+xabWQnKuJLaQSGCvm6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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,10))\n", "forestplot(varying_slope_samples, vars=['b'])" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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W6f9//ryJ6WnDq2BNU0IIfx2iUsK9P4KxadKILpWSWFgALl0yceGC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\nSHNzDnl5y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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "b = varying_slope_samples['a'].mean()\n", "m = varying_slope_samples['b'].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": 32, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with Model() as varying_intercept_slope:\n", " \n", " # Priors \n", " mu_a = Normal('mu_a', mu=0., tau=0.0001)\n", " sigma_a = Uniform('sigma_a', lower=0, upper=100)\n", " tau_a = sigma_a**-2\n", " \n", " mu_b = Normal('mu_b', mu=0., tau=0.0001)\n", " sigma_b = Uniform('sigma_b', lower=0, upper=100)\n", " tau_b = sigma_b**-2\n", " \n", " # Random intercepts\n", " a = Normal('a', mu=mu_a, tau=tau_a, shape=len(set(county)))\n", " # Random slopes\n", " b = Normal('b', mu=mu_b, tau=tau_b, shape=len(set(county)))\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " tau_y = sigma_y**-2\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, tau=tau_y, observed=log_radon)" ] }, { "cell_type": "code", "execution_count": 33, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 2000 of 2000 complete in 9.5 sec" ] } ], "source": [ "with varying_intercept_slope:\n", " \n", " step = NUTS()\n", " \n", " both_varying_samples = sample(2000, step)" ] }, { "cell_type": "code", "execution_count": 34, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 34, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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3JuA7+dcHkT2j6kTS10o6MCLWOt1nNp57921r8oBC/wm9pjwXs6lVFZy4E9gL\nmJ8P7Q5skHQxWRx9Qz62tor5zdpuEHr3NTnFN9tjc5FLp5IiFRELJB0OXAMcB6wji51/iKxIXZGP\nmdmASnEid0Jv8KmERb7uAPYDzomI5ZL+AjgC2AH4RUQcLWkO8C9kz53uBt4YEfPz918AfBi4JCI+\n1b3/9evX+wazDZ3R0VHGxsbqPoxWaGNrozYec5VGRkYm/Aso60rq6vxzUJA9fwqyUMZTABGxRdJX\ngA8Avwss7rwxfyZ1ZEnHYWZDppPQa4vxV38rfPU3iTKK1GbgVEmrImJ5YTmOsyl0Oo+Iz0j6Z+Ad\nEfHNznh+JXUwcGsJx2JmVpvpP+vyQovTVUm6r0dwYkJO95mN59591WtysGMyVR13U4tfquCEmfWh\n7cm+NqjrpOywR3+qbDD7I7JnU938L2FmQ8vtmPpTRpFaAJwmqZPuW012q+8XwLs7G0m6D3gtsKOk\nvSPiPfn41nQf0P2BYDOzZFKl7toW9qhTFW2R5kXEKPA7wHsK42/O2yWdQPZh3iK3RTKzWrnFUjOl\naotUVFwM0cEJM6tUf0EDp+6aJlVbpKKtiyGaWW/D2LuvrWm7jhTHP4yFMGm6r9diiGY23iD07utX\n3Sdgp+6aKVm6b6rFEM3M6uTUXTOVvuihpNWSxoAHgCWF7SZaDNGLHppZI6RaBHE2CzUOm5TpvnGL\nIRY43WdmQ8Epwv7Uke7bZtzpPjNru/5DEzNPEUL9z+9SSpru66enn9kwc+++2Wt7WnAyVf9sTSqC\nSdN97ulnNj3DluyrQpNOtEVOEfanjt59E42bmQ08pwj7kyzdJ+m6fBXfR4B7C+NO95lZ68wmoZcq\nRTgIUqb7TgFuBG4GftK1D6f7zKw1nNBLJ1m6T9LOwNuB64FdOuNO95lZnWYeQnBCL4WU6b4zgcuB\nPauY02yQDGPvvqkMWlov9c/T1qKYJN0naS5wVERcJGkRXvjQbFLD2LtvKk06yTqhl45mex81D0Ps\nB3QWPfwL4AhgB+AXEXG0pOOBK4Ed8z/rgBMiYk1x0cOI+FT3/tevX+8bvTZ0RkdHGRsbq/swGivV\n4oRNP4ZBMTIyMuFfXllXUldHxPL864PIIuZzgKcAIuImSbcC5wPHALtExJr8tfMkHVnScZjZgBt/\nFbOilqsYr66bRhlFajNwqqRVEbE8T/Eh6WxgS2E7AXMi4prim/MrqYOBW0s4FjNroVRthZp0y9Cm\np5J03wTjTbV6AAAgAElEQVTBiY3AMknrgLMi4jFwus+sTdoeXqjy+F0Aq5GsLVJEnAkg6VCyX4NO\nqmJus0HQ1N59TTgRO7QwXOpoi7QZeKHCec1az8m+ibmt0HBJ2RZphaT1wD3As4Vxt0Uys74MYlsh\nL4TYW1nBiW3aIgHkib33A3fmL20Cjo+Ie8ftwW2RzGyINSWx2ERlfE7qfODb3W2ROum+iPicpDnA\n/RFxeD/7AH9Oyszap66ASROeGc5Eis9JbaNHum8P4GWSbgDmkqUBb6hibjOzbm1PJU7XIBbHVOm+\ndWTPod6Vz3mPpFsi4vkq5jdrO/fuK1fTrzCcWJxYknRfRLwo6Ulgr4h4WtLmyd9qNtzcu2+4OLE4\nsTKK1ALgNEmd3n2ryW71/QJ4N0DeYHZf4CFJ2wM7dq6iir37gHHPpMxssLjnXW9us9RbkkUPI+K5\niDgiIl4J/Bbwt137cLrPbAh4sUDrV7JFDws+AlzW+cZtkcwGw/Qf2vffd6/pz5SsOikXPUTSKLBP\nRDxcxbxm1r82JN/KPEYXvHZJ1rsvdwbZulJmNomUvftSnrSdYrN+JevdJ2k74ETgqArnNBsIg5rs\nc4rN+pWsdx/weWAf4C5Jx3QG3bvPbLgMYt+9DvffK1+SdF/uKLIY+vHAhV37cLrPzFrNycVqpEz3\nPQy8DXgVcEtn0Ok+M2uimYU1ZrZicIdDHeOlTPfdDSwiu3q7top5zWzwtSGNOFMpf7a2FMQk6T5J\nBwDHRsQpAJJWSrotIjZVMb9Z27l338SaenJ1crEaZSzVcQewH9Bpi/QXwBHADsAvIuJoSQcBNwAb\ngZ8CvwQcFhGbi22RIuJT3fv3Uh02jEZHRxkbG6v7MKwPndDEY489xgEHHDCQwZCqpFiq4+qIWJ5/\nfRBZ9HwO8FQ+9hTZEh0bgRHgZxGxGbY+kzqypOMwM0tu26uo7XnrW7/Bl7/sPnxlKGtl3lMlrYqI\n5YVbemcDW/JtBPyYLK6+BVgpafu8O/oFwMHArSUci5lZafp7RjTz0ERTb2E2QSXpvu7gRERsknQh\nWapvI7Ab2RXVM073mVm/Bi08UdXPMwjFL1lbpPx24HIASQ9ExDNVzG1mg69pJ1+HJqqTrC1Sh6Tj\ngYcqnNes9VL27rPZc7un6lSR7rsO2AN4M7Ckk9iTdBNwJNliiIsj4sZ83Ok+MzOGd0HIydJ9VbRF\nOgW4EbgZ+AmAsr/pXYE9gb2Bs7v24bZIZjbU3Fapt9KDE5J2Bt4OXA/skm9zEPBoJ3Yuaa2kAyNi\nrYMTZjbIUiUEO5r2vG62qngmdSZwOdlVU8fuwAZJF5PF0TfkY2srmN/MbEYGITWY4mdIWQhLLVKS\n5gJHRcRFkhYVXlpHFjv/EFmRuiIfMzNrjDqvQpwQ7K3sK6n5wE6SlgH7A9tJ+kfgEbJbfpAVqQMj\nwldRZhNw777h44Rgb6Wn+/KxHYGngdsj4tR87KPABcCzZOm+b+bjTveZdXHvvsE2rCm+iSRN9+U+\nCNyV/+lYBbwPuLZToAqc7jOzoeAUX39SpfuIiNslLeh+s9N9ZjZIphdc6C/FN2iJvX6kSveZmTVS\nGxJ9ZR5j2wpe1em+4b7RamaNl/qk7RRff1Kk+1ZGxJrCNv6XMJuCe/cNLqf4+pMy3Xcf8FpgR2BF\nRLwnH3e6z8wazWm8ajUi3RcRb46IEeAEso4TRU73mVkjOY1Xr2TpvoKNFAqS031mltLMQgjuqVeX\nOtJ9pwOXVjCvmbVIG1J1Zarr5217cUya7pN0Alk39EfKnNfM2qctJ0+n8eqVLN0n6TDg6Ij4WMlz\nmg0c9+5rjpRpPAc0xkuZ7uv82hRk6b4P5ONO95l1ce++4TPMV2yTpfvKuJKabrpvBEDSkcD7u7Z3\nus/MBlKqRQ/bcvu0X3Wk+94EfKfzjdN9Zla3QQhxVP0z1FUEk6b7JN0J7EX27MrMrBGacBUyzLf7\nJpM03RcRCyQdDlwDHFfm3GZmbeZ2Sb2VUaQWAKdJOofs2dROkv4OOAn4YbF3Xx6oWA4813lzMTgB\n3FTC8Zi1nnv3VaupKTpJzJs3r+7DaJQy2iIBXB0RyyPipoj4beBbwMPAfYUCdR3Zc6ftges6b4yI\n84AHSzoOs4Hg+Hl13OaoXcpK950qaVVELC8EJy5j2+DEacDX6ApU5FdSBwO3lnAsZjbkqlh0EJrx\n3GoYlZ7uY+LgRM9xp/vMhltbknVVHaeL3+SSBCe8GKKZTcSLDtpkkrRFAvbtNd61GKKZWeWcomuX\nMoITC4AvSHpnIThxGnAA8FhErMlvBT5F1j5pLrCmEKi4APgo8IYSjsVsICxZsqTuQxhonRTdvHnz\nehaoiGD16tWsXr3aoYqaJVv0kKxn38kRcUhELOra3m2RzAqWLl1a9yEMLaf/miVlWyTRoyg6OGFm\nKTn91y4p2yJtBJZJWgecFRGPVTC3mQ24pqYByzouF7ttJWuLFBFn5tscSvZrykllzm1mw6Hqk7jT\nf82SbNHDwjabgRdKntfMrBRO/zVLknQfgKQV+cKH9wDPdt7sdJ/ZeO7dl14x0QdMmv6zdJIteghs\nAo6PiHt77MPpPrMC9+5La/wtvhW+xdcQZSwffz7w7a5039YefRHxRUlzgPsj4vDp7KPIy8eb2UwN\n6kKAg6bq5eO79Ur37QG8TNINZB/mvTwibqhgbjNroaYm9qZSxXG78G0rVbpvHdlzqHflc94j6ZaI\neL7M+c2sneo+MTvR11zJ0n2SngT2ioinJXU/wzIzq02vRB+wNUTRpIURh02SdF9+hbUv8JCkZ4HD\nOldRTveZjefefekV+/kBbo3UEGUEJ24iaxz7pxGxPB87k6x43R4RX+za/vXARyLi9/PvLwBOBy6N\niIu69+/ghA2j0dFRxsbG6j6MgVDX8666b2G2SdXBien27uv4CNmqvYB795kNs7YGJqajzp9tkApk\nyt59SBoF9omIhyuY18xapqknUwcpmiNZ777cGcCVZc5pZlY2t0ZqjjKK1ALgNEnnkHWe2EnS35E1\nkP1hId23GPhTsvDEWESshK3PpD4MXAKM+zCvmVlZIqJQeCZP7HWCFFavMtJ9AFdHxPJCuu9bwMPA\nfYXmsucDFwLH5/8LZM+kgAdLOg6zgeDefeXzYobtVHq6r1dbpHy7rwLXAK8CDoiIT+bjTveZ2ay5\n+0N7JU33MXFw4m5gEdnV27WdQaf7zIZTG5J9XsiwflUHJzrjBwDHRsQp+fcrJd0WEZvKnN/M2iP1\niduJvXZK0RbpH8kWOdwVQNIOwG7AlpLnNjObkBN77VRqui/vOHGTpB2Bp8k6TnQWPXxe0kbgF8B/\nj4jN+bjTfWaWRF2JvX5ShbatMtJ9Uy56mIcp9oqIV5D19Htj1/Ze9NCswL37BodThbOTatHDl5MV\nrCPIbvOtBI6JiBd77aPI6T4bRu7d1z5lBkGGLWhR+6KHEbFJ0oXALcBGsmdSI8AzFcxvZjYjTUkc\nOlX4kmRtkfLnVZ0u6Q9EhAuUmTVKFSd1pwpnJ9mih50NJB0PPFTyvGZmjeRU4eyUnu6T9LvAwcBc\nsudMnXTfTcCRZOm+xZ03O91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ZtVjdJ2Kn/5opWVukDknHAw+VOa+Z2Ww5/ddMpbZFyhc3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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(6,16))\n", "forestplot(both_varying_samples, vars=['a','b'])" ] }, { "cell_type": "code", "execution_count": 35, "metadata": { "collapsed": false }, "outputs": [ { "data": { "image/png": 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wPW16S3/48gPNzVzik4urfJ104st0NlqLzC5pngMDXFHMzBiIRICDB/lYtcoA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rW8TEdEMkkoSKqqInulrc2Plquu3rurzud9b//iTSCZJFYrlNeyMuDkyQLOnNmbilm8ZKA+OcnP\n1d3Ngl9Xd/v30XX55ycnFUZHAxgf55C2tJSinro6UgO3tpQx6FpZUSYRqrPTxeBgAVqTBpnJEPqS\nYI22NtckUhUKGqOjHJbn89wMk0kyTEIh4vaPP14wpny7nQbjcb/o88RgGTxf4KGaGo1kEp61se2d\nAEiprKvjcyfU2vl50jbHx8naop6AJ6RAAJ5gS6GnhycEgdckRH1zk8wYZgRTOCWmazSwo2vnygq7\nfTpQai+hinOPjQ3LuHU2N7OB+uM//k+YmnoTtD4JAFDKgWVdxJNPPoMvfen/vP1DcRfrsMjfxyUW\ntdIVS/efSCjP66W4+D9cvN9xOLgVT52yMt8Xv6pq9+dgL2EXsN3L52FAPtLlT09bJt7Ptnm87+sT\nYZA2Xiyjo8SDk0ni3a2ttJXIZtU23/D6+ttTMyXYRYo+IwBJg2xqYpGkeMpn/ux14ltfV144Nx0u\ne3pY8A9i8RCLKUxPK4yMcEi5tsYiLENB26YXS1mZi/V1nnIKBW569fXa8OR7ehwkk/7vyWSUEY7V\n15PlMz1NSGxri//O0HUW7fZ2QkrHjpFltLPRkSjC0VHLuE3G48xS5UyJzJZgkL7zsRjdPPkdeK1d\nF+Z5C4ddzxqa13593fIiHBl6ns2ySenvp7Zg5wbsujzB+R0/g10AbFOr06KC3kOi+rVtNn5LSwpb\nWxY+//nfxubmcZBdAyiVh20PYWDgMr75zV/a9728k3VY5B/CkiLgF0f+Z2dnXFXlekHRD/bziXhp\nZoadUyDAjmq/vvgvR8gnFqN4Znra8rp8bqihkPbyWbWnrAQuXbJx9WoAhQKNyDo7uSGkUn4m6O1C\npHdbmQyZKJcv0yu+ro6FK5NRnrMn73kx/l8861ldlYJvG+uEnp69N+G9VjJJyG5khDCHeNKUlfnx\ngfX1GqmUxsqKbWwBRKD25JOkSSYStP69fp1Rk0rRI6a5mTbHW1t8posD67NZdruFAnnqvb3c9Pr7\nb55hSCbu6Khv8kZuuk+FjUR8g7zTpzlYluLMTZZzFa1pQZBIwFgkWxafgdJSFuWODuLrzAje+/ql\nUvAKv2Vgn0TCtyuR9DARmq2vW/i1X/sAMpl3AEgBUF6IeSmqq5/G8PCvHOj+HXQdFvmX0crnYbr9\nYuhH+LfFg97q6r2TbO7l0loEJBxkuS5FRwf1xX85QT7S5YtP0MaG701eWkocuqWFdMSREbJTHAdo\naNAe1ixHfOLcpaXadPpNTfsLVikWWjU0+IPwRMIPdqHIqXjo65oZQDpNHH562kZJifY6/DuLn8zl\ngLk5ZULAJyd9iEfyTiMRDkQtC55QjXDMa15TQE8P6YMLCzw1SVIUTwjcyCT8o7SUvvh9fQ5mZwnR\nTE9zniJpVv39BXR3M4mq+NSUz/O+jYzw75ifJ0OppIQFn7YPnMmcOUPTNenOJTuB7xUhGXb3fM+2\ntviMZrP83oODLk6eLODUqf3BZI7jd/3FsI/4N/3sz34Qmcy/glKc9zEL+HlUVn4aw8O/dvCbdoB1\nWOS/A1bxAyqdSTTKB7q48Avef7dKz1st8cWfnia2SQO17SKfg6ydG9vDgHyky5+f52xCbBRcV6O0\nlPme4quyskIoi77jHBSKGCubJeVPDNik09/Lihi4vdAqnd7J+OE1yuV8mwfJhY1GFWprtef4eece\nR7IJsmAT45YsV2Gm0ImS37e+XuPxx8XJkjAMbQcszzqaXz6TUUinNTY3Kdo6e7aAN76xgIEBF8kk\nRVcUHhGmCQbpPdPfT3itvn47BTKdBhYXLZOxurqqvPg/nppyOeYTPPqog9On+dl23odUis/f8jI5\n+5OTthfbxxhB1+Wc5swZdvkdHe5Nm8+tFiM5Fd72to9hbm4QrtsCJkO5UGoe/f0X8fWv//s7u1H7\nXIdF/jt4yQMkx8Zo1A/0fhCwCJ0nycXf3FTGra+t7dbioP2shwX5FHf58/Pi+669fFz6yRcKykv+\ncY34anWVmx7ZISx02SyHvPE4C2FxPNxuGHwspoy68nZCq1zOL/6yAUSjtHkQ862GBt/yorn5zof9\nssGNjFi4eJFQ1uIiRVqVlYSyxEOnpcU13uptbYSy2IGLhw9PTtksqZUrK6Qbftd3Ofjn/zyPo0dp\nARGPs4CPjpKams0S4ggE4Llw0lZBCr9tc/61sEAYanSU7pRiAQIATU0ajz7K7ry5ee/QD8klHhmx\njTvm+jp/D+cULrq6SPns6aHQq6bm1tfwwx/+Ej796UpsblZAaxtKOaiujuOHf3gL7373v7yzG7PP\ndVjk/ydbrksvkJ2wSCp1s8WxBCrfiyVcfImba25mwe/ouDe2wMDe3+1+Qj7xOEzBX1mxPGtZ7WWx\n2gZSIe+8gECAitWlJUIejY1kcAQCNMySYHAJv9gtT/ROhVYANykp+DduCBxCeKWjg2ZrTU3bOf93\ncjqKRjm7eOGFAC5fDniZxsSjJfiksREmGLyjw58dyDVdWLA8nxn+M5nkfTxzxjHBKfX1hAQ3N+mn\nMzfHmUSh4MOVtk2RVX29NlGL1dXaY7so7zRim/sSCPCE0NKiPQsHXxW+W9GXTWpkROHcuQCmpixY\nlkJFBbH7WIzD4ZYWnjh6elzDCpJn/9vfHsJ73/tNzM93QesAlCqgtXUaH/zgq/Hkk6cOfgMOsA6L\n/D+RVfzy+0wfuvMJFFIMjex3mLjbEi7+9DQVmsLF5wDz3n0nWQ8K8tnZ5dP4yzXhImNjNsrKgFOn\nCnj88QKamqjklOIiHX1DA03G6NhoGYx7ZxD0TqFVOAzPxOxgG6fjwBhrjY1ZCAb9fNNMhjRfgX6K\nPX4O8gxsbgLf+lYA//iPAbz4IjUIoRDQ3e3gsccKaGnxbaQ7OvgdLYufTZKoLl+mTXIiobzsVd6/\ngQGxK/AH/8JRX1wkdz0Y5GBYDO1SKQ7IpejX1movWN3Ciy/auHQpgLU1+ss3NZFNVVEhMY/aM8vb\nfeYUjwOXLzN7d3TURl0dv1NlpYtUipuXwFu1tcxMuHDhq7h6tQTZ7BEoxVNJVdUYXve6zGFoiKzD\nIn9/Vjbri7uKoR/bJt6/vUM+eIEULv70NAvjXlz8+7HuN+Szs8tn3irTnmZnafN79ChdHn2PeAp8\nlpYsw7BpanJRVuZCa1L0lpd5OmlocI13fH29NvF5BxVaFS+JN5S0q/p6et5UV5M9VIz/i71zsc/P\nbsEuO5ekb335ywE8+2wIExPsfNvaCjhxwp8hDQ6yOLa1+ZtWMknzs29/m/z7igrqGyg8IwNIQt+b\nmigWE08aKfrCgIpECKXl87z3pMey8Itr5NSUheefD2By0kZpKTtzcdMsLQX6+2+d7ZvPA5cvW3jp\nJRb8khLgxIkCjh2j9bUwop5++mtIJB5FOj2HYNBCU5OD2tpWtLX9A37rt77/QPfwoOuwyB+uXRdF\nLWQi7BZpuHPYu58CKVz86WnylvfDxb/X635BPju7/FyOQ7vlZV+BWl7OTralhZ1iVRWl+lL019eV\n8Y+vrmYC0cYGBTfr68qLqOOf29oi40mpWyda3e4zC1SyuEjhkEANoZA/lNzcVJ7oyzJcdOn6i31+\nyst313nEYsAzzwTx5S8HMTlpG6qmXOvSUo2TJws4e9bdtvlvbgLPPRfEpUukcbquNjbEtbX8uUCA\nWHtzs2uG3aQAW1hcZOFPJpVJ8iopof0vA0SoWmboh4ulJdI0Z2YsBIOcN2jN+ya+9wMDrse+ulko\nl8sBo6MWzp8PYHKSfvzt7dzk//N//jxGRhqRTtdDawvhsItweA2nTk3jYx/74YPduAOuwyJ/uPa9\nRNwVjVrb4BFRTxarendzASxeu3HxpeDvh7J2r9e9hnyKu/yJCQqEUikOa8nWoQ9SUxOHgK2tpBoW\nd/pra8oz2WLHatsasRg7/dVVKkNDIUI6yaRlmDl7JVrd7vsXxxs2N7Pgd3TcHC6fydzM+BGbh52w\nj4RnSBMwP6/w138dxPnzAWxsKCNySqVoIRyJUJn72GN5vPKVPMlkMsD164RyJChFfPRdl+EzTU2E\ndxIJf6Nk4ScsJlYTi4tkPzU3kyZbW+sil+MJiu6X3NASCc4Acjkq36ur/Q2mvJywEE8V24u+rFSK\n0ZKXLvHk9Zd/+VdYWGhHScmrEAjQtqFQ+AYee+xF/Nmf/dTBbtYB12GRP1x3vRzHx/t9qidf+mJe\n/17dcTEXf2qKUn4RXzU2Hrxg3ct1LyCfYvXt5csM6wiFNAYHKfnP5/3iIzF7LS300fGLPgt7WRkL\nWFMTO+B4nLROoYCm0/xsZ8/SUuBOefNyL8TQrqeHQ8Vbsaby+e3FX04BqRQLY7Gvf0mJxtSUhb//\n+yDW1pSX7cprmMnwRLS5qVBdDQwOOnjiiQJe8YqCyREOh9klOw7hnRs3OCPh7KeA2loORFdXxYKa\nwSaNja4ZpC4uckOzLI2WFm2uvWUR8xffm5ERDntldkEBFe91IqFQVsZ/Lyvb3unL6TQWU/jJn/wb\nXL78L5BKBaCUg3A4jaqqPB599Kv42MeeOvhNOsA6LPKH676tXA7bin5xd1xc9P2Aaf65aNQXX6XT\nymTb7sZzfhjrbiGfeBwYGbFw7lzQDO4eeaSAwUEHjsMh7dISXTQF2pEADjFbW1z04w8llamy0sXW\nFlk5Q0M2pqZstLa6OHWKtEFJnDrIolXB7vGG+6VkisJ7p8ePDFjTaXbN8Tg7c62VB205cF1uOOPj\npDF2dLg4dqyAvj6GoGgNLxWNcIsMbyWZ6+RJbqS5HDdK0TnwmrLo53LKQDtLSxYiEW1OV83NhK6S\nSeDaNQtDQ/QDyufpcx+J0KNIwk9yOSASYVKX+Om3tbn4yEc+g4sXX4e1tQq4rgXbLqCuLoknnvg6\nPvaxtx/sphxwHRb5w/XAVzpd7OTpQz/SKRXDIpalsbBAGmAs5nPxW1vvnot/r9edQD65HHDxoo3z\n5xkpV1dHG+RTp8g/FxbJ8rIUdBYfuknC48ZzY1hZoYBIin5VlYsbN2xcuBDA0pIywdc9PT5n/yCd\n/s54Q6ELSrzhQZfritaD91YsiefnLcM+KhRoXUC/H8fj63PImcnQZrqqiorj7/7uPB55hLOJaFTh\n4kWenCYmuJGeOOHg7FmebsRgbGXF8oJ1hNJKy2AWfGWcLaXLF8x/asrC8DA/a2kph7jr61S55nKC\n4/NnKyoUPvOZP8Ls7KOwrFJYFpO6lIrhySfP4XOfe9fBL94B1mGRP1wviyV4f/GgVwZ+ctSnfwyP\nv8mkhdbWe8/Fvx9rv5BPSYnGxARTluhgCi/Mg4UUgMGVV1aYlUq+N4uPbfvqzaUlbgy2zeCMsjKm\nZU1MMMy7vJwOnRI1KJz92tr9nZZSKXb4U1N7xxve6drcVHjpJQvDwwEvTFxjcpIbi2VxjsH8WseE\nfS8u2uaanT6dx2tfKxGH3EivXGHk4PAwdyOJDTx61EEmw41SvOCDQV4zzkKYRCVd/vo6abBS9MNh\njelpmqm5Li0V6IZpmbzZZFLha1/7U8Tj1QC+F5bFDd6ynkFv7zD+/u/fc3cX7DbrsMgfrpf1Esn+\n9g6Zxb9Q4DAzk1Ho7KS74bFj94eLf6/X7SAfcWScn7dQUUFYoKKCOHRbGwuM2CTLkLauzi8+wkOP\nxbYXfcdhTq7I/3t7HVRVsRAuL1PAVazObWi4fSbCQeIND7IyGVodXL9uo6KCnykW48lHrB0KBWW6\n5pISDnbHx2kRUVLCwejp044J7G5s1JiaUnjpJcYVxuP8vKdOOTh+3EFjozZDV3b7/ALC3qmv5yBY\n6JqJBAVvra2ka9I1lIrl3l6mfkWjwBvf+AlEo+9EJpMC4CAcTqC0tA51dZ/Ac8/9uzu/SPtYh0X+\ncH1HLoFGNjfpnzI+bptwiMZG1zBNmPd5d+KuB7l2Qj6rq0xCYrGhmpSbgPgGuSbQW4r54iLhj8ZG\n4s4tLWQsKeXH3S0vW5iepg2vpGU9+ijnArEYC9zKis/wKbZbvpVK+qDxhvtZAp+Pan8AAB/dSURB\nVI9cu2Yjm+XpJhLRmJtjBw3weohZWTjMU8v164w4tCzi4yUlYi3MoJjBQQe2DVy5wjDzaJTe/4OD\nLPgikCq+ZsvLCvm88obf5PwzEYr++7kcr7tSnDVsbnJw/Su/8nuYm3sDXPe0cUC1rEvo63vm0LtG\n1mGRP1z7Wckkh5rXrzMe0HGAcJgCl7Y2dxvHv7r6/pq53ctFSh4HqqOjtgnDLinRyOUIU3Bjo3Uv\nsJ0rnkopM8BtbfXpfltb/LmhIQtXrgSwsmLhyBFi14ODvF7RqCQj8Z+BgO+62djIa7mXMnRnvGF3\n990xplZWaG+8uGihv58d+uYmWTDCWgoGaRZH2MXF7Cyv2+Ki5Vn88hTF4SmZXAMDdNO0bdI1V1ep\nQm5rY6YrT0/as1D2i/7SkjKZA83NGhUVrgkVWVykpbJSwO/+7icxOflGAI733R0EAmm86lV/h89+\n9mfv7GLscx0W+cP1P+0SLv70NC0HslmKeMSDPB7fjotL8a+sfHmwePZahQLhkdFRG4uLHD4Gg34g\n9dqaL2zq76cjJbtby+v0t9M1m5v9AezGBnD+fAAXLtiIxRRqaqjg7OjQnqBImyLHbn+7Olcgnp2b\nZyzmp10VCvuPN9xrJRIsxjdu2Ghupu1BTY32YCNeA/rykJKZTHKwv7ICbG7a3kyC0BVPg/TQES1D\nayttDQoFjUyGYebFCti2Np8imUr5g1yJK2xoYNEvLSV75+d//r/g6tUB5PPfA6UUgsE8Skr+Hq98\n5QQ+9amfuJvH4bbrsMgfrn8SS7j4QgfUGl4cHguSb+vAglBs5iZ0z70UnQ9zxePErcfHWbhodeBi\naoqbwPi4hUSCHS7Tnaj8DIV4AkilWOBsWxtop7mZeb/LywpXrtBPPxQi5CU5rP5gUiOfh+n0V1fJ\nMKmp0Uak1Ni4fU5yN/GGO1c+D4yNkelSUkKjuO5u1zCBZE7Q3Ox4Kl6JOiQ9tL2djKfNTTKbIhGN\ntTWNyckgbtywPHsHbeynmajF4t3cTMy/r881VEuAs4Tioh+PK3z843+CWOx12NqaBGAhEHBRVdWN\nzs6v4AtfeOe9eRj2WIdF/nD9k1zRqF/wObj1ufjF/uzFHP9cDtsUvfLvL4dBr+vC+LcvL1vo7qa3\nTUODNurbiQmyYUSiHwxqOI6Eg8DktIq5V2srRT21ta73u22kUjC+MLEY6a/19dpg1I2NEmDNgi8Q\nT0mJNgVfXDCBm+MNu7t5AjlIvCEAzxWUuH08rnDsGKGccHg7bJTP040zHKavzLlzVN4eOcIZTjDI\nYXcwSOVtRYX2LKAZVLK8THhGKZ4GS0u5+YXDZNZ0dzNTtrvbbwpyOeBf/+tP4sqVLgBvM2KqQuEL\nOHt2Ep/61M/c68dh27ovRV4p9XoA7wegAbxfa/31W/zsnwI4BiAN4Gmt9Z/v9nOHRf5w3a8VjwMz\nM+Tix+N7c/Gz2d3FXUo9/Ezb4pVKAePjDL+wbXLMe3tZ2ER9KwEp+bxCTY2LsjKxSPAHvo7Dwp/L\n0R+mt9dBdbX2AtNtAwmFQtrr5NnF19b6RV/sBoTaubpKiCefV9s6/bo67QWQc+O1bdxxvOHGBnH7\nmRkLPT2EcuR3RKPK2+yIuff0uCgtdTE0FMD58wEEAgxA6e7mCUXmGe3tVPyWl2vMzorXvG3SqQIB\nGp9VVHDjTKctlJVxMN7T4+KP//iLuHy5ArHYNJQqgVJZ1NS041WvWsNHP/qO+/EYmHXPi7xSSgH4\nJoDXA1AAvqK1fs0tfv5PALxPaz17q997WOQP14NYySSMn876OnHrri6+4HtRCXfy4AX6CYe3G7kJ\n3n+n4R13shYXFW7coCGchG4Xe9vsdNKkNS7pgpYFk2EqIigmJolTI39PeTlM5xyJcDgqg8m1NVpb\nNDWRzy+BKckktnX6sRgpoELdVErcS+883jCVggkQqa0Vu2K/pq2scFOZmrKNWV4qpXH+fBDr6/Rj\nOnHCQX09NQpiC93YyOeho4MGZjMzFq5csfHSSwHMzipksxba233n0WRS4dlnv4ShoSgKhdcDAGy7\ngHD4q/jBH7TxW7/1HWZQppQaAPBLWut3ev/9TwB8UGt9Y4+f/1Ow25++1e89LPKH60GvTIZGWDMz\nvi++iK9uB9GIuKtYACVmbuXl2wv/7czc7sXK5cjOkQE0sWRnGx1yZ5fvOAptbWQltbb6zpRra1Sn\nTk3x9LO4aEEpDctS6O2lz8zJkxxcui6M06Z08hUVUvT9IPR8nj8nw1zx6WlspDHb1hawtmYjEmHB\nP0i8oePwu1+7xgD3wUEHfX3+Kc11uRnK96mrI+YejZJiWlHBOlhdzZmFhJTPzdECQTzy6+oo1puc\ntPDccwHPnIwWxi+88BdIJF4HoBVKaQQCLixrHEeOfBZ/93c/f29v9o51P4r8dwF4OwjVyC/+jNb6\n+T1+/vcBPAZgHcC/11qP7/Zzh0X+cD3MtdMXv7ZWo7PTQWfnrXnjO5eweooLf7GZWzHmf78CzYtD\nxOvrXRw5QlhhJ6Nory6/rW17SlUmA4yP08jr0iV6s2ez7PZPn6YISb5TVRUdJ4tN18QrRrxkIhEW\n3mhUmU5/ZYWK0mBQm7lBczMhpK4umrntZy0sEMpZW7MwMOB4nHv//2fAik/JLC2lH43QJMvKtAdl\nKbS3k7WUy5Ejn88r0+HLZhCPAxcu2PjxH/8Eksl3AQgZMzPXTaKu7j/i3LnvMJ6818n/MoB/Axb5\nPwLwm3t18kV/7iwI27xlt///sMgfrpfL2umLX17Oo35n55374ktm607fG61x06C3utqPvrubJVTM\nsTHCML295Nnv9h320+XLSqfZOb/wQgAvvWQjn1dobSUDJRCgF03xdwIY8r22tt1LRlSmsokmEjAF\nf3GRhbVQYAFua2NYd3+/u6+NMR4Hrl2zMTFho6ODUM5Odk8ux5PcxISF2VlfYXv6NDcW8fSPRqlB\nqKmhhfTqKmGq5mYW/PZ2F294w+9hff3nsbWVhdYWbNtFJFKC+vr/G9/85s/d8T3cz7ofRd4C8I8A\nvheABeBZrfWr9/HnjgH4da31rpZsh0X+cL0cVzEXf2aGVEMp+PfCF7/YzK0Y8w+FsK3wS3jLnYq7\ndqNidnff7CVf/PP76fK1BsbGFF54gZTEQACorydUI3F96bTaplkQv5psVhn6pwSDNDX5oSLZrJ8I\ndf26jbExMqUkqOPMmQLq62/9vbNZsU6wUFZGCmZnp3sTdCaUTLJsbORy5My/+tUF1NXRq2Z2lt2/\nWBszkJwb48c//vu4caMRSp0AS6QL4AqefHIWn//8/3FnN22f636xa94A4H0gZPPrWuuvev/7DwJI\naq2fKfrZzwBoAZAA8K69sPnDIn+4Xu5rNy7+/fDF19p3byy2QIjHlUlcKi7+B4k2vBUVc6+13y4/\nnSbr59IlG7EYO3rLgsHoKyu3M3w2Nym0CgSYCpXPE9aShC1xhZSTh+NwmCrc/slJG9XVLo4epeVw\nR8fNaU7F33tmhi6YmQxx+/7+3YftW1v8Ht/6Fk8CLS0uXvOaAh55hErjxUWF2VleC6Womv3EJz6H\nv/u7JHK57wFANW4w+DW8/e02PvShH93fzbnDdciTP1yH6z6tW3Hx74ei1nV9vL+4+KfTvriLxZ8n\ngNvNEoqpmIEAQ8SFi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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "xvals = np.arange(2)\n", "b = both_varying_samples['a'].mean(axis=0)\n", "m = both_varying_samples['b'].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": 37, "metadata": { "collapsed": false }, "outputs": [], "source": [ "from pymc3 import Deterministic\n", "\n", "with Model() as hierarchical_intercept:\n", " \n", " # Priors\n", " sigma_a = Uniform('sigma_a', lower=0, upper=100)\n", " tau_a = sigma_a**-2\n", " \n", " # County uranium model for slope\n", " gamma_0 = Normal('gamma_0', mu=0., tau=0.0001)\n", " gamma_1 = Normal('gamma_1', mu=0., tau=0.0001)\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, tau=tau_a, shape=len(set(county)))\n", " a = Deterministic('a', mu_a + eps_a[county])\n", "\n", " # Random slope\n", " b = Normal('b', mu=0, tau=0.001)\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " tau_y = sigma_y**-2\n", " \n", " # Expected value\n", " y_hat = a + b * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, tau=tau_y, observed=log_radon)" ] }, { "cell_type": "code", "execution_count": 39, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 2000 of 2000 complete in 7.8 sec" ] } ], "source": [ "with hierarchical_intercept:\n", " \n", " step = NUTS()\n", " \n", " hierarchical_samples = sample(2000, step)" ] }, { "cell_type": "code", "execution_count": 40, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "" ] }, "execution_count": 40, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "trace = hierarchical_samples[-1000:]\n", "a_means = trace['a'].mean(axis=0)\n", "plt.scatter(u, a_means)\n", "g0 = trace['gamma_0'].mean()\n", "g1 = 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 = trace['a'].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": 41, "metadata": { "collapsed": false }, "outputs": [], "source": [ "# Create new variable for mean of floor across counties\n", "xbar = srrs_mn.groupby('county')['floor'].mean().rename(county_lookup)" ] }, { "cell_type": "code", "execution_count": 42, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with Model() as contextual_effect:\n", " \n", " # Priors\n", " sigma_a = Uniform('sigma_a', lower=0, upper=100)\n", " tau_a = sigma_a**-2\n", " \n", " # County uranium model for slope\n", " gamma_0 = Normal('gamma_0', mu=0., tau=0.0001)\n", " gamma_1 = Normal('gamma_1', mu=0., tau=0.0001)\n", " gamma_2 = Normal('gamma_2', mu=0., tau=0.0001)\n", " \n", " # Uranium model for intercept\n", " mu_a = gamma_0 + gamma_1*u + gamma_2*xbar[county]\n", " \n", " # County variation not explained by uranium\n", " eps_a = Normal('eps_a', mu=0, tau=tau_a, shape=len(set(county)))\n", " a = Deterministic('a', mu_a + eps_a[county])\n", "\n", " # Random slope\n", " b = Normal('b', mu=0, tau=0.001)\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " tau_y = sigma_y**-2\n", " \n", " # Expected value\n", " y_hat = a + b * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, tau=tau_y, observed=log_radon)" ] }, { "cell_type": "code", "execution_count": 43, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ " [-----------------100%-----------------] 2000 of 2000 complete in 7.0 sec" ] } ], "source": [ "with contextual_effect:\n", " \n", " step = NUTS()\n", " \n", " contextual_samples = sample(2000, step)" ] }, { "cell_type": "code", "execution_count": 44, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "array([[,\n", " ]], dtype=object)" ] }, "execution_count": 44, "metadata": {}, "output_type": "execute_result" }, { "data": { "image/png": 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6K9mO7/kzV+qmy2Dmk0R0NYBL3I9edBWiujDz5wF8PuTzb4Z8di+Ae6O022za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\nCnAyXQffxbmwzHGHC14BfDCJ10UnBgOIyBYRSXjnT0QqgTc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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "traceplot(contextual_samples[-1000:], vars=['gamma_2'])" ] }, { "cell_type": "code", "execution_count": 45, "metadata": { "collapsed": false }, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "\n", "gamma_2:\n", " \n", " Mean SD MC Error 95% HPD interval\n", " -------------------------------------------------------------------\n", " \n", " 0.375 0.266 0.020 [-0.190, 0.846]\n", "\n", " Posterior quantiles:\n", " 2.5 25 50 75 97.5\n", " |--------------|==============|==============|--------------|\n", " \n", " -0.144 0.188 0.378 0.558 0.907\n", "\n" ] } ], "source": [ "summary(contextual_samples[-1000:], vars=['gamma_2'])" ] }, { "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": 46, "metadata": { "collapsed": false }, "outputs": [ { "data": { "text/plain": [ "69" ] }, "execution_count": 46, "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": 47, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with Model() as prediction:\n", " \n", " # Priors\n", " sigma_a = Uniform('sigma_a', lower=0, upper=100)\n", " tau_a = sigma_a**-2\n", " \n", " # County uranium model for slope\n", " gamma_0 = Normal('gamma_0', mu=0., tau=0.0001)\n", " gamma_1 = Normal('gamma_1', mu=0., tau=0.0001)\n", " gamma_2 = Normal('gamma_2', mu=0., tau=0.0001)\n", " \n", " # Uranium model for intercept\n", " mu_a = gamma_0 + gamma_1*u + gamma_2*xbar[county]\n", " \n", " # County variation not explained by uranium\n", " eps_a = Normal('eps_a', mu=0, tau=tau_a, shape=len(set(county)))\n", " a = Deterministic('a', mu_a + eps_a[county])\n", "\n", " # Random slope\n", " b = Normal('b', mu=0, tau=0.001)\n", " \n", " # Model error\n", " sigma_y = Uniform('sigma_y', lower=0, upper=100)\n", " tau_y = sigma_y**-2\n", " \n", " # Expected value\n", " y_hat = a + b * floor_measure\n", " \n", " # Data likelihood\n", " y_like = Normal('y_like', mu=y_hat, tau=tau_y, observed=log_radon)\n", " \n", " # St Louis county prediction\n", " yhat_stl = Normal('yhat_stl', mu=a[69] + b, tau=tau_y)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "with prediction:\n", " \n", " step = NUTS()\n", " \n", " prediction_sample = sample(2000, step)" ] }, { "cell_type": "code", "execution_count": null, "metadata": { "collapsed": false }, "outputs": [], "source": [ "summary(prediction_sample[-1000:], vars=['yhat_stl'])" ] }, { "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" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## References\n", "\n", "1. Gelman, A., & Hill, J. (2006). Data Analysis Using Regression and Multilevel/Hierarchical Models (1st ed.). Cambridge University Press.\n", "\n", "2. Gelman, A. (2006). Multilevel (Hierarchical) modeling: what it can and cannot do. Technometrics, 48(3), 432–435." ] } ], "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": "3.4.2" } }, "nbformat": 4, "nbformat_minor": 0 }