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@twiecki
Created August 5, 2013 14:16
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{
"metadata": {
"name": "GLM-blog"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Bayesian Generalized Linear Models"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"John Cook recently drew the insightful connection that [Bayes : Python :: Frequentist : Perl](http://www.johndcook.com/blog/2013/07/13/bayes-python-frequentist-perl/). The idea is that Perl prides itself with offering many different choices while Python's mantra is \"There should be one \u2014 and preferably only one \u2014 obvious way to do it.\"\n",
"\n",
"This is the reason I'm such a big fan of both -- Python and Bayesian statistics. Frequentist stats have individual tests for all kind of different scenarios. In Bayesian land you define your model exactly as you think is appropriate at hit the *Inference Button(TM)*.\n",
"\n",
"One example of this generality becomes apparent in Bayesian General Linear Models (GLMs). I'm very excited about the upcoming [PyMC3](https://github.com/pymc-devs/pymc/tree/pymc3) which uses [Theano](deeplearning.net/software/theano/) as its computing backend. Since `Theano` allows automatic differentation of the resulting compute graph, implementing state of the art samplers like Hamiltonian Monte Carlo (that are also used by [Stan](http://mc-stan.org)) that use gradient information is pretty simple. The compute graph is then compiled to C so we can get good speed without getting our hands dirty (PyMC2 used Fortran for its likelihoods...).\n",
"\n",
"I recently contributed a GLM module to PyMC3 that makes specifying of various models very easy. \n",
"\n",
"In general, frequentists think about a GLM as follows:\n",
"$$ Y = f(X \\ast \\beta) + \\epsilon $$\n",
"where $Y$ is the data we want to predict (or *dependent* variable), $X$ is our design matrix containing the *independent* variables, $\\beta$ are the coefficients to be estimated and $\\epsilon$ is our error term. Finally, $f$ is a link-function that turns this linear model into a *general* linear model. If we set $f$ to be the identity function (and assume Normal error) we get a linear regression. If we set $f$ to be a logistic function we get logistic regression.\n",
"\n",
"Bayesians take a probabilistic view of the world and express this same idea in terms of probability distributions. A linear regression becomes:\n",
"$$ Y \\sim \\mathcal{N}(X \\ast \\beta, \\epsilon^2) $$\n",
"\n",
"With the new GLM module in PyMC3 it is very easy to build this and much more complex models.\n",
"\n",
"First, lets import the required modules."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import matplotlib.pyplot as plt\n",
"import numpy as np\n",
"from pymc import *\n",
"import pandas as pd\n",
"from statsmodels.formula.api import glm as glm_sm\n",
"import statsmodels.api as sm\n",
"from pandas.tools.plotting import scatter_matrix"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 1
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Create some toy data to play around with and scatter-plot it."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"size = 100\n",
"true_intercept = 1\n",
"true_slope = 2\n",
"\n",
"x = np.linspace(0, 1, size)\n",
"y = true_intercept + x*true_slope + np.random.normal(scale=.5, size=size)\n",
"\n",
"plt.plot(x, y, 'x')\n",
"plt.xlabel('x')\n",
"plt.ylabel('y')\n",
"\n",
"data = dict(x=x, y=y)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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fj7vNhg0bUFhYCLfbjc7OTj2KYSs+n8/sIkiDdTGKdTGKdZE6zRPC0NAQ1q1b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\nAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x19799d2c>"
]
}
],
"prompt_number": 40
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets fit a linear model to this data. The new `glm()` function takes a [Patsy](http://patsy.readthedocs.org/en/latest/quickstart.html) linear model specifier from which it creates a design matrix. `PyMC3` then adds random variables for each of the coefficients to be estimated (by default, 'PyMC3' uses wide Normal priors, but see below for how this can be specified). \n",
"\n",
"Also by default, this function assumes `y` to be normally distributed. \n",
"\n",
"Here we use `Slice` sampling to perform inference and draw 2000 samples. Note that `glm` already initializes the model to a good starting point by estimating a frequentist linear model using [statsmodels](http://statsmodels.sourceforge.net/devel/)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with Model() as model: # model specifications in PyMC3 are wrapped in a with-statement\n",
" glm.glm('y ~ x', data) # specify glm and pass in data. The resulting linear model and all its parameters are automatically added to our model.\n",
" trace = sample(2000, Slice(), progressbar=False) # draw 2000 posterior samples using Slice sampling"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 41
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Bayesian inference does not give us only one best fitting line (like maximum likelihood) but rather a whole posterior distribution of likely parameters, we can plot the posterior predictive that shows various plausible regression lines on top of the data."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"plt.figure(figsize=(5, 5))\n",
"plt.plot(x, y, 'x')\n",
"glm.plot_posterior_predictive(trace)\n",
"plt.xlabel('x')\n",
"plt.ylabel('y');"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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hTJhod4OvRBUVFWRnZ2Nra0tAQADm5ubGdklnZ2eys9uIjMwlOdmXSZN6KSsr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\nI4nAFARBMJIITEEQBCP9f3sMW/+u1uLTAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x19df59cc>"
]
}
],
"prompt_number": 42
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Lets look at the summary statistics of our posterior (`.describe()` is a `Pandas` method that runs commonly used summary stats)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"trace_to_dataframe(trace).describe()"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>Intercept</th>\n",
" <th>sigma</th>\n",
" <th>x</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>count</th>\n",
" <td> 2000.000000</td>\n",
" <td> 2000.000000</td>\n",
" <td> 2000.000000</td>\n",
" </tr>\n",
" <tr>\n",
" <th>mean</th>\n",
" <td> 0.996933</td>\n",
" <td> 0.491986</td>\n",
" <td> 2.097299</td>\n",
" </tr>\n",
" <tr>\n",
" <th>std</th>\n",
" <td> 0.104635</td>\n",
" <td> 0.037226</td>\n",
" <td> 0.175197</td>\n",
" </tr>\n",
" <tr>\n",
" <th>min</th>\n",
" <td> 0.611638</td>\n",
" <td> 0.396025</td>\n",
" <td> 1.603397</td>\n",
" </tr>\n",
" <tr>\n",
" <th>25%</th>\n",
" <td> 0.922888</td>\n",
" <td> 0.466618</td>\n",
" <td> 1.969252</td>\n",
" </tr>\n",
" <tr>\n",
" <th>50%</th>\n",
" <td> 0.998701</td>\n",
" <td> 0.488008</td>\n",
" <td> 2.092708</td>\n",
" </tr>\n",
" <tr>\n",
" <th>75%</th>\n",
" <td> 1.072940</td>\n",
" <td> 0.513759</td>\n",
" <td> 2.223524</td>\n",
" </tr>\n",
" <tr>\n",
" <th>max</th>\n",
" <td> 1.289055</td>\n",
" <td> 0.645372</td>\n",
" <td> 2.735541</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 43,
"text": [
" Intercept sigma x\n",
"count 2000.000000 2000.000000 2000.000000\n",
"mean 0.996933 0.491986 2.097299\n",
"std 0.104635 0.037226 0.175197\n",
"min 0.611638 0.396025 1.603397\n",
"25% 0.922888 0.466618 1.969252\n",
"50% 0.998701 0.488008 2.092708\n",
"75% 1.072940 0.513759 2.223524\n",
"max 1.289055 0.645372 2.735541"
]
}
],
"prompt_number": 43
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, the posterior mean of each variable is very close to the true parameters used to generate the data (`x` is the regression coefficient and `sigma` is the noise)."
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Robust GLM\n",
"==========\n",
"\n",
"Unfortunately, we do not live a Normal(ly distributed) world. Outliers violate the Normality assumption and can seriously skew our estimation, as we'll see next."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Add outliers\n",
"x_out = np.append(x, [.1, .15, .2])\n",
"y_out = np.append(y, [8, 6, 9])\n",
"data_outlier = dict(x=x_out, y=y_out)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 31
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with Model() as model:\n",
" glm.glm('y ~ x', data_outlier)\n",
" trace = sample(2000, Slice(model.vars), progressbar=False)\n",
"\n",
"plt.figure(figsize=(5, 5))\n",
"plt.plot(x_out, y_out, 'x')\n",
"glm.plot_posterior_predictive(trace)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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8vDx1dNZisVBWVoZer8disVBeXp6yo0dfXx///Oc/2b59O42NjQwMDKSU9Te/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\n3t4uFCe8fVuJ4uI8xMbadt1JSkpCZGQi7tzJwAs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"text": [
"<matplotlib.figure.Figure at 0x16f2552c>"
]
}
],
"prompt_number": 32
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Why is this? The reason is that the normal distribution does not have a lot of mass in the tails and consequently, an outlier will affect the fit strongly.\n",
"\n",
"A Frequentist would estimate a Robust GLM and use a non-quadratic distance measure to evaluate fit.\n",
"\n",
"What's a Bayesian to do? Since the problem is the light tails of the Normal distribution we can instead assume that our data is not normally distributed but instead distributed according to the [Student T distribution](http://en.wikipedia.org/wiki/Student%27s_t-distribution) which has heavier tails as shown next.\n"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"normal_dist = Normal.dist(mu=0, sd=1)\n",
"t_dist = T.dist(mu=0, lam=1, nu=1)\n",
"x_eval = np.linspace(-8, 8, 300)\n",
"plt.plot(x_eval, theano.tensor.exp(normal_dist.logp(x_eval)).eval(), label='Normal', lw=2.)\n",
"plt.plot(x_eval, theano.tensor.exp(t_dist.logp(x_eval)).eval(), label='Student T', lw=2.)\n",
"plt.xlabel('x')\n",
"plt.ylabel('Probability density')\n",
"plt.legend();"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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b8ZmIm8OUmoMMZxWWZDQ5DBw4kC1btnD8eh08ICAAexkqIW4BjemMNtdIJR3d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\nv9YLUrQ4U86dZmtWioyMJD09nYyMDCo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DlZCQEOWFF16wdjgGvfXWW4pGo1GuXLli7VDq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\nAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x198f1bec>"
]
}
],
"prompt_number": 44
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As you can see, the probability of extreme values of `x` are much more likely under the `T` distribution than under the Normal distribution.\n",
"\n",
"To define the usage of a T distribution in `PyMC3` we can pass a family object `T` that specifies that our data is T distributed (see `glm.families` for other methods). Note that this is the same syntax as `R` and `statsmodels`."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with Model() as model_robust:\n",
" family = glm.families.T()\n",
" glm.glm('y ~ x', data_outlier, family=family)\n",
" \n",
" trace = sample(2000, Slice(), progressbar=False)\n",
"\n",
"plt.figure(figsize=(5, 5))\n",
"plt.plot(x_out, y_out, 'x')\n",
"glm.plot_posterior_predictive(trace)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
"png": 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Xl0dERATNzc38+c9VLF2qITLSf4wxMTFYLJl8+KFm1ICXUBNBJRiGmYx1QPML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\nkkvGvv2Ryn+s58907XDw8S5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GnE4n9fX1xMfHk5ycTFJSEvPnz//coodT+UE/nrCcjA/m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\nAABJRU5ErkJggg==\n",
"text": [
"<matplotlib.figure.Figure at 0x170567ec>"
]
}
],
"prompt_number": 34
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There, much better! The outliers are barely influencing our estimation at all because our likelihood function assumes that outliers are much more probable than the Normal distribution."
]
},
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Logistic Regression"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Logistic Regression is commonly used when you have binary distributed data. It can also be used as a classifier.\n",
"\n",
"The idea is pretty simple, we still estimate a linear model as before but pass the output (that ranges from $-\\infty$ to $\\infty$) through a logistic function which brings it into the the range [0, 1]. These 0-to-1 values can then be interpreted as the probabilities of a Binomial distribution. In other words, as we before had a Normal and T distribution, we now use a Binomial as our likelihood after passing the predictors through a link-function (the logistic).\n",
"\n",
"Lets load some data about the height, weight and sex of individuals. One obvious hypothesis to test would be whether height or weight is a better predictor of sex (if you didn't know)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"htwt_data = pd.read_csv('data/HtWt.csv')\n",
"htwt_data.head(8)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"html": [
"<div style=\"max-height:1000px;max-width:1500px;overflow:auto;\">\n",
"<table border=\"1\" class=\"dataframe\">\n",
" <thead>\n",
" <tr style=\"text-align: right;\">\n",
" <th></th>\n",
" <th>male</th>\n",
" <th>height</th>\n",
" <th>weight</th>\n",
" </tr>\n",
" </thead>\n",
" <tbody>\n",
" <tr>\n",
" <th>0</th>\n",
" <td> 0</td>\n",
" <td> 63.2</td>\n",
" <td> 168.7</td>\n",
" </tr>\n",
" <tr>\n",
" <th>1</th>\n",
" <td> 0</td>\n",
" <td> 68.7</td>\n",
" <td> 169.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>2</th>\n",
" <td> 0</td>\n",
" <td> 64.8</td>\n",
" <td> 176.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>3</th>\n",
" <td> 0</td>\n",
" <td> 67.9</td>\n",
" <td> 246.8</td>\n",
" </tr>\n",
" <tr>\n",
" <th>4</th>\n",
" <td> 1</td>\n",
" <td> 68.9</td>\n",
" <td> 151.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>5</th>\n",
" <td> 1</td>\n",
" <td> 67.8</td>\n",
" <td> 158.0</td>\n",
" </tr>\n",
" <tr>\n",
" <th>6</th>\n",
" <td> 1</td>\n",
" <td> 68.2</td>\n",
" <td> 168.6</td>\n",
" </tr>\n",
" <tr>\n",
" <th>7</th>\n",
" <td> 0</td>\n",
" <td> 64.8</td>\n",
" <td> 137.2</td>\n",
" </tr>\n",
" </tbody>\n",
"</table>\n",
"</div>"
],
"metadata": {},
"output_type": "pyout",
"prompt_number": 16,
"text": [
" male height weight\n",
"0 0 63.2 168.7\n",
"1 0 68.7 169.8\n",
"2 0 64.8 176.6\n",
"3 0 67.9 246.8\n",
"4 1 68.9 151.6\n",
"5 1 67.8 158.0\n",
"6 1 68.2 168.6\n",
"7 0 64.8 137.2"
]
}
],
"prompt_number": 16
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"As before, we can pass a `family` object to the `glm` function that specifies the likelihood distribution of our data. By default, these `families` also have a `link-function` associated with them. While by default the logistic function is used for `Binomial` you can also specify others (see `glm.links` for other options)."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with Model() as model_htwt:\n",
" glm.glm('male ~ height + weight', htwt_data, family=glm.families.Binomial())\n",
" trace_htwt = sample(1000, Slice(), progressbar=False)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 12
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"In the models we estimated above we have been negligent about making sure that our estimation procedure (MCMC) actually worked (at least I didn't show this process but take my word that it worked well) and converged to the one-and-only true posterior. One way is to just plot the chains. Here we'll be looking at a scatter plot comparing pairwise all parameter combinations. Each dot is a sample generated from our MCMC algorithm while the diagonal contains the marginal of individual parameters."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"trace_df = trace_to_dataframe(trace_htwt)\n",
"scatter_matrix(trace_df, figsize=(8, 8));"
],
"language": "python",
"metadata": {},
"outputs": [
{
"metadata": {},
"output_type": "display_data",
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vKSwsx2xu4McfD5GX1w23uwvNzRu5fKva24AQYBXwOzw9jxAX501ZmY6IiN4k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\n3LcoKfGlSxdfFi6cyJYtx6i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B07M70dHlzJkzCbVajbe3NxaLhU8++YaTJ3VYLN+j1Vo5\nedJCYKAXzz47ln37LtGly58oK5tHUFAWU6bMxOVy8u67KZw5k063bhv48MMFREVFUVdXR0pKGl26\ndCImJuZn6+Lv78/cuQ/y6adfc+CAnpqaEmJjezBlitjW9npkNpvJzs6mW7cYRoz439Uia9Z8i1we\nhMtVj9nc+LOvLS4uJjMzlKamm/jzn79gyZKn2LJlMaWlJbz++h5On07CZovD4TjEqFG/4/77a3jz\nzd/z4IM5uFyuq7q3yoULF5gx4wWqq3WMGxfD22/PpaSkFJlsIAEBRnx9kykttTNq1CJqag7Rv38j\nhw5tZP9+D3788Us++sjEqVMFGAzT0WiW4+GxC7k8l4CAruzadRw/P1/WrUtGr7+HTz5ZQ79+va+7\nNfetUptx48bx7rvvMm3atCs2RrjeZyIKwn9DrVYTFRVFc3MzbrcbALdbiST5oNHU0NCgo3v3xwgJ\nab5i/a/NZkeSdDQ22vnkk+2Eh1/A37+ObdtSKS+3o1IZSUvzp2fPuP/H3pmHZ1Gd/f8z8+xP8mTf\nFxKSkLAkIYR9B9lBQVBxARUV3Kqg1qW1Vq1Wi/gqiorSVkUUZVVABNnDHggJEJKQhZB93548+zrz\n+yO+9OWnbbWlQtt8rivXBSczZ86cczL3zDn3fX+5884bKSoqYvXqbZhMkSQlRSIIhwgODuSGGx69\nrD11dXW8884WLl6MRa1uoqxsO76+4wkMTObs2aK/aeidTidOp5LQ0Axsth3ExsbyxRcb2bTpHH5+\nMgqFjbw8mbq6PERRhULxIEbjBhoaOujVy5eysj9z443DefDBO9i//zBHjhwnL6+Jzs4wwEtubgEJ\nCQm8++4XlJTEodVuYenSewgJCfleW/5X9XLOnEnk5CyjutqXLVsu0L//RRISEq7M4HVzRZBlmf/5\nn4+pqIgkIOAAS5c+cmmJ/oYbJuBy7cLHx5ehQ4f8oJqpTqfD7S7C7RZpbGxj9+4sjh+30tYWRERE\nKbW1HXi99UiSk4MHtzNgwHj69k2gX79+P5iwqb29naamJhITE8nJycNoNLFp0w7KysLwemeQm3uc\n+vp6MjL6M3r0ac6cOc2MGUNJTk7gs8/W4PW2kp1t49Ch43R2TkeWTbzwwh+Iisqgqekgkyf3ITRU\nw+efu6munsiBA/WMHFmNr68Lo/E4PXsGfC+PxLXAFTH069atQxAE3nvvvcvKKyoqrkT13XRzzXL2\n7DnefXcbwcE6fvnLO+nTJ4XIyKF4PO0YDFBZuZ+PPrJy4UIly5b9Co1Gw+jRIzAa95CTU0Z19fXU\n1TlYv/4rYAFudxYajT+7d1dgsZwmOzuX8+f9OH26kuuum4XZ3MTWrSt/8Ivh6NFT1NVF0N7egMFQ\nRVWVkqSkA2i1lUydevMPtr+4uJjOzk4GDBjATTf1Izf3ILfffhMrV67l/fcP0NIyGDhEfHwKFy/u\nRRDuwuP5GF/f9QQGBtCvXw/GjRtHa2srISEh7Ny5m1WrysnOPojZ3IAghNLS4mDnTompU8djs7lQ\nqwPweBS43W6gK9nO+fPniYiIYOPGPZw/X8c993Tlwe/Xry8uV0/c7osYjcZ/4Uh2848gyzKNjSb8\n/KZgNldit9svGXp/f39uumkKJSUlfPLJBo4fL2fKlAHMnXvDJSOdmZnJHXdk8umnWej1IXz11UHs\n9gE4HDLl5XtQKkOQpBjATVtbHps396Sg4Fsef9zC0KGDcbvdVFZWEhAQwJkzZ1iz5gCCkEhc3FYq\nKwOQpHAcDjM6nRWr9T10Ol9WrtzKvHkTeOWVxy+7l8rKGp5+OpvOzn7IcgKy3IQo2snPN9K37/1o\ntTtZsmQ2e/ZkExLioLr6EIIgs2jRtzQ3w6xZ7Tz11MvXZErmK2LoKysrr0Q13XTzb8fevbmo1XOo\nry+mvLycp5++jYMHTzN06EKio6MYN24Rsvxbduz4iLvvLiQzMxONRsPNN1/PiBGZPPTQy1RVVaDR\nhONy5aFWV6LVDsPj6cuhQ1kYjRoSEx8nOLiB9vaPuP/+W75n5Kurq1m1agu1tVX07duPHj18MZsr\nSU39DVVVaxg5MulSUpr/S2lpKX/4w7d4PMEMHZrPuXMduFw6KivrKC1tJCRkHI2NW1Ao7Pj6pgMH\ncLvNQABWayVpaSlUVdVhNBqJiIjgnXc+YceOc5w8mYvZnIgs+yCKF/H3H83Bg1peeukdFi++k/37\nT9K79xgiIyMBePvtTzl3zoDV+if0+nRiYu7jq6/WM2LEUObOnYws7yI8PIC0tLSfYUS7+SmIosgv\nfjGLTZt2MWxY7GVh1pIk8dprH1FREcLZs98yc+b77Nz5DjfcMPHSy4BCoeCdd5Zy4sQtVFTE4HYH\n4HAcRJanAQF4vV66RLkuAhINDQkIgkRrawcA77//Obm5Lurrj6FWp1FS0smoURlUVX0OBNLR0Ul8\nfMVsbOMAACAASURBVDhz53opK/PD4/FFrb6LtWs//V6GypycIrzeFCTJiiA0oVDUo1aHoNNFUln5\nCcnJWr78ch/R0UHcc08yshxPWVkZ+/e70GgeZO/e5390qt+fmysSA2e1Wnn55ZdZtGgRAGVlZWzf\nvv1KVN1NN9c0I0f2w27fSlBQGYmJiSQnJ7No0a2kp6cRHBxMUlIYDsdqDIYWIiIiLju3sbERg2EY\nQ4Y8Q3q6jsmTJVaufJBhw2xIUjkqVRwVFW6qqt5FqWzA6XSyY8dJTpw4dVk9X399mObmYTidgxg+\n3MTTTw/m9ttvprLyC6qrfdi82cz+/Ye/1/b6+nosFlCpoqmpacRu74laPZTS0joWLpzO0KFt3Hxz\nbxYvnkxQ0CH69OmNKG4E0hDFSHJyynn11aO88MIKGhsbyc6uIjPzZfR6EAQ9ktQDpdKOIDQQGjqW\nxsYup8DrrhtC795/2Z+vrW2jtFSgoMBLVdUhWlvXMXhwlydzREQES5bczW23zfrZcgh089OIjIyg\ntdXB7t2drFv3F2lyr9dLS4uVoKBB6PUS1dWr6NcvDK1We9n5giAwcmQSOp0ehaI/suwP+AI9kSQV\nsBuIQKNJIji4iri4C4wd2+ULUFRUS3DwNNrbZXx9+xIRIaLRbOOXv7yb0aOVmM1HqK9P4tgxI716\n/Zb6+hpaWraQmhp76frl5eX85jcr0GqV9OxZR0TESaKjE0lLewCl0g7okKRKgoL8KCzswzffNDFs\nWDoLFsyjb99+6HRVOJ3PM3hw1L+8r/9RrsgX/T333MPAgQM5duwYAFFRUdx8881cf/31V6L6brq5\nZhk2bDD9+vVGrVb/YB7u9957ngMHjpKe3oeoqMsfBIGBgajVrbjdEg8/fDu33joT6Mo0efvtT1FW\nFobVWkZlpYrQ0GBOnKikpSWJvXtfY82a5xgwoD8A4eG+nDixAkHwsGTJEoYPH87o0cNxuz/gyBE9\nSqXmkg8BwJkz+Xz9dRabNu2ntVVm2rQKHnnkCb78cj/t7SeYOXMWtbUNKJVqpk8fx803zyA39zTv\nvbcHPz8z+fk7sdvjkKRozOYEDh/ew403VtDR0UBW1nESE31obv4WQUjF6UxEr/fidn/I4MFT2bFj\nH199VYbB4ODFF+8lJCSEu++eSE7OSgYOvBGdLo9XXplLdHT0v3DUurmStLS0YLEE4+s7jNLSg5fK\nVSoVDz98A3v2HGfu3F+QnJxIaGjoZTlWCgoKeeWVP9LSosXPL5e2tvbvfrMfCKLra96KINSi0chE\nRITy0ktPIUkSHR0dLFgwmY0bN7Bw4VguXsymqqoBs9nFM88spbFRxmLxJSBAh15vp6lpGzNnDmHe\nvPEUFpazcOFLyLKFsrJmIiPvRq2uZdmy0SgUCh555M+0tJQjyxZUqsk0Nxei1SpwOqvRaCyXpHNv\nvnkmvr4+OBxW5sy58Wfr85/KFdGjHzhwILm5uQwYMOCSHn3//v05e/bsP93AH8O/o87zf5oevZ9f\nEGZzx086x2AIxGRq//sHXgV+rjlVWVmJ0WgkNTX10pK8w+Hg0083sH79ZrTauZSXZ2M0+uJ05uF2\nh+LjY2Xy5ETWrPkfAHbs2MUbb9Si0wVy660y8+fP4bnnlrF+/VnU6laeeuou5s2bi1qtxmq1smTJ\nCgoKIsnJ2YRSOYqkpL0UFu691CZZllm06GX8/RfS2rqOZcvmER4eTktLCytWfMbhw/lcvNiOydSO\nLFsICBiKWj2ZurpVeL1eXK5aYAKwH1G8DYPBRo8eWhyOEuLi9PTq9SQWyymefDKD9PR0ZFnm6693\nc+TIea6/fshlntv/Sfw7Pqd+DG63mzVrvqS8vIm77ppC794pP+o8SZJ46KFXOXnSidPZH6v1U2pq\nTMhybyAGWAPYgSEoFE569sxg2LDhTJ/eSVZWNR6PwOLF0+jfv2tLZ/z4e6itvYGqqj8jimaUyvFk\nZKgZNUrC41GQk1OCJGlIT4+jtdWJSjWXrKw/kJw8kJqaYmJiFDz77E2sWbOHo0erSU4eRmPjbtra\nhhERIbFs2Vh0Oh1hYWHXjFPoz6pHr9FosNvtl/5fXl5+xVWGurm26TLyP+0hZjZfe04rPzc/JL+5\nf/9hDhzQYDBMQ6fLZcAAAbc7kfb2DkpLPYjiJOrq9iFJEqIo0tzcQlXVUQCUyik4HA4OHCjDYHiV\nzs43CAryR61WA117ohoNNDeXI0nNeL0luFxd4ybLMtXV1RgMBvr2jebs2R2EhcmXYuAFQaC62suw\nYW8hyw8gy2mEhs5l9+5XcLnW4XI1AQMBB6AGwlEoijCbz1FYOAaVqhaHww+D4X3GjMkkOTn5Ur3X\nXz+Jjg4z69YdxO32MGHCmH9xz3dzpVCpVNx3361/97jW1lZWrPgCl8vD4sW3EhkZSXi4H5GRTior\n12I0XkSWA4AGoALwAglAGJLURkvL1zQ31yLLU7HbM5Flmdde+4jhwwcwfnwmwcE6ystLkCQrKtVM\nPJ5vSEkZxvz583n99X2oVKOpq1PT2emLv/9JDh58G4ejjZqaQoKC7ERE3MEnn2xDkqYRFNRMe/s2\nbrttEvn5QSgUJkJDQ0lNTf3Xdua/iCti6F988UWmTp1KbW0td9xxB0ePHmX16tVXoupuuvm35ezZ\nfMrLaxg9eshPSiCl0agRBDsKBaSlRTN16gRcLiceTx+WLfuM06d3AzEcPnyMsWNHoVL5kJIykNra\nbN56awMnTpQxcWIi69b9koQEPUOHDr5Ut1arZfbswRQUbMFiiUAUFdx7b1eM//bte9i0qQSt1kpi\nogGoYsiQofzxjxuJiwtlxoyJjB0by/79SwkKCqKuzsahQ79CoQhElssRhDuR5QOAFdgB+OB2tyEI\nfVCpSvF6B+DxRGGznaGysoVdu7KIiAimqKiS9PQE9u+vAYbx9tufMWbM8B+9J2+z2fB4PH8zKU83\nVw9Zlmlvb+f48RwqK1NQKHR8+eVO0tKSWLDgemJiDnD2bC8++KAA6KTLdawNyAAswAlk2YTdHkV2\ndg3x8acJDQ2ksLAUlWoyS5fmsXTpKtLTk8nMLCAuzo+OjmZSUgaxbNlT+Pv7k5mZQ3v7KWJjvURH\n92LWrFns3fsCen0QEREdJCQMwmRqxc9PRqM5idVaQmLiRNrarCxenHKZamRzczMnT54mPj6a6uoG\ndDoNY8aMvCbD6v6XK2LoJ0+eTGZmJtnZ2QC8/fbb3ZnxuvmvpqGhgbfe2oMk9efcuQ0sWTKPL7/c\njY+Pltmzp2K329m79zBhYUGMGjWcuro6Dh7MoXfveMaNG4VWq2LNmi0UFIyhrGwfr7xyB5GRkSxY\n0I5a3Y5arcNmcwAQHKyjoGAfra16fH0T6ezU8dhjAYwb1x+tVv29pb3evXuTnBxHaGgCgwcruP/+\nO8jPzycvrxS9fix1dbspL68jOXkBzzyzhKCgTNzuFtau/Zpbb53EvfdO4uOPGxg4cCDV1Y/gdM7B\n7V4JrAbCEYRIZLkVuBv4BpVqGArFBnx9czGZWjh0yIHDIdHQcAyFQotON56Cgv2IYgMHD1YTHBzF\n6tVrSUqKJzNzAE1NTRQWXmDo0Izv+TnU1tbyhz+sxeGQeeSRaZf8Frq5uuTnn6OiopaRIwezbds+\nDh6sJjDQikKhxeuVOHSog+zscOz217BYgqmpiUIUDUhSH8BE18viIGALMBc4ictlxe2eztatx7jj\nDhUKhZ3Cwm00NblRqeI5ejSPhITFOByHuPVWPQsWLCA4OBiAxYsX8NBD8xAEAYVCwerVG3C7J2Ey\nmSktPUxMTDMmUzUq1WDS0y0UF/vgdkdhsRSg1/tw9mwZer2enj17snz5WurqUqmv/wBZ7klnp5HH\nH69j3rzbgS4n26ysE6SkxF8z8/GKGPoJEyawb9++y5zv/rfsb9HQ0MCMGTM4f/48VqsVURR5/fXX\n2bZtG3FxcaxevRqlUsnatWtZuXIlQUFBfP755z+o5d1NN9cqTqeD5cv/SFFREmq1hZiYHM6cqSAr\nS8TtziU4OICPP97JuXM9KC9/nQULhvHMMw+zd+9pKip8kCTxuzAjGD16OFVVmwkLMzB+/CgANm7c\nj0IxGFm243TmoVY309Y2AEmajNFo5fTpc0RGRiLLMvn5+bhcLn7721sxm82kpKTw+9+//53sZg16\n/TY6OgpoaYHm5ldwuwdQXHwRl0uktNTM1q2/JT4+ltDQAHS6Q2i17bS3H6RrqV4BVKLTubDZMoDj\niGIlsvwpsqzH7fag18fh9bppackjIyMdk0nA6WzDz0/PlCnT6eiowGSSeP75PxMZOYLrrz9DY6MT\nl2sohw9/xhtvPHVZnHJZ2QVMpnT0+nBycoqvmQfrfzMNDQ3fqRGmkZ+/gYsXm4mJeZra2lU888wU\nOjs7efbZT2hqqqGl5QK+vorvFA29yHIsgpCHQuHA6dwCtABbASPgQRAOYbdLrFu3D5MpEIejFa9X\nxOsdg9N5mtLSXFQqgQ0bLiKK3/D8879AEAQEQbi0fQWQnByLj88u7HYjAQG3UVvrxuMpoGfPNHJz\nP8XfP4PW1gOMGDGIpUs3YTZn8NprTzNp0hBsNjtuN5hMFhobG9Bootiw4SCTJk2goqKC9esP0NEx\nnF279rB0acQ1oVf/Txl6u92OzWajpaWF9va/OFWZTCbq6ur+7vlBQUHs37//UmrL5uZmsrKyOHz4\nMMuWLWPLli3MmjWLVatWcfjwYTZt2sSqVat48skn/5lmd9PNv5ywsDDGjw+nri6f5mY7x4+7qK8/\nTmZmNL6+/bhwoZj9+4tQq/04cOA4arWS8vJKBCGevDwz9fX1PPjgzRw4kE1i4hhiYmJwuVy89tpH\n5Oc7UalyiY4OZ+zYkfj4aIAT6HTNpKbG8tJL9xAaGsarr66jvLySvLwBjB07koMHD/Lxx0Wo1cHM\nnt3ApEljAaipMRIYeAOdnXXcddc43nknBKXSzsWLX9DaWoLTqQVk3O4WIIXy8kgaG48jCKm43T2Q\n5fN0fb3no9EcQqEIRKHwQ5JKSU4Op7U1BJfrDiAHrXYHvr6hPPvsAm688UYaGxuprKwmOXkmDoeD\n22+38vLLK7Ba0ygr05GXd4bIyD5IEpSXV7J27RecOlVDaKgfixfPJzW1HxERn2CxnGb8+Fuu1nB3\n83+QZRmHw0ljYwM+Po3MnDmcrVtfZ8iQngQGBnLPPS9TUqLHZvsYtTqK+PhAUlNbWL58KWvWbCc/\nX6az8yFaWtS4XO8BHmAK0IQs52EyuTCZUoFgur78ReAAghCK270blysRk0lHRUUzkiR9b0nd6/US\nExPN/Pkp7N9/GpPpCPX1HrzeDszm5zAYwlAoKoiKCqS09AIHD+bgcon4+YXS3JzOoEFlbNmynsDA\nMGS5EEkSUCol5s79JR5PLG73RXr1ykCjkamtrcVoNJKcnHxVE+n8U4Z+1apVvP3229TX1zNw4F8S\n+RsMBh555JG/e75Go7nktCfLMqdOnWLcuHFAV4jR2rVr6devH2lpaYiiyMSJEy/F6nfTzbXMoUNH\n2bXLjST5Y7Gcp3fvR/H1/TPz5iWh1WqpqWlDqx2OQuFHU5OZJUvu4MCB+6itNVBXJ+Hv74+/vz+3\n3TYL6PJszsvLY8eOAhobJyMIJ1i2bAMdHS00NiowGJLRaifSs2c/jEYbY8f2YdSoJJzODAoL3Xzw\nwZ/Zs6eJ8vIWEhJ68f77J/n22/M8/vgN3H//NHbs2MmMGUPIyMggKmo3J08a0Wgm4HafQqlciCT9\nEVlOQJIGIEkmrFY/ZLk/otiGSnUaWI3H48LrvQ6L5SRqdRK9etm5444xrF69nfb2VURHa4mLW0xb\nWyOrVx+kX780MjLSCQsL44UXVtHcrMbpLMHhAJVKiUplJTk5hoaGNlpbV+HjM5rly4/Qo8dMWlut\nnDt3jhEjRvDaa08gy/I1vUf630RUVBQBARbq62sxGpUMHdqfG26YhEKhYNu2nXR2BiBJcYCEw3Ge\n8+fbsdkSmDtXwRdfvMemTVv5zW8+RBBsaDQqysvd39WsQJb9AD8gEJCAZEAPuFAoqnC7fTAYYnE4\nKrn55uE/OCdWr97Ehx8ep6iomMTE+9DptmEwBNLePpjW1gLi428mN/cVoD8bN0oIwjAMhlzCwwPx\n8TlLXFwKUVEhyHLkd6muRQoKmnE4RqLVakhIaOLGG51oNL15551DSJKGBQuauO66q+dg+k8Z+sce\ne4zHHnuMFStWsHjx4n+6MZ2dnZccavz8/DAajRiNxu+VddPNtY7d7gR8EEWYMWMoFksuU6dOYfv2\nAkymShQKBeHhF+noKCckZDZ+fn707j2Y1NQZ2O27kCSJkydzWbcui/T0HjQ3d3DqVDtmcxuwD5ut\nnby8njz77GdIkhZB0NDWdg6rtY6+fe8FoLa2hqNHL+J0NnP2rAVJuh2NRoEgHKehoQdut8Tp0+fp\n1y+RMWN6M3z4ENRqNUuW3EtHx2fk5Z1HrZbxev9MRIQNmy0Qk2kbXq8FlSoUt3szen0PwsJisNv7\n09BQjMczBEG4gMfzETExA9i6NZeBA58ADvDiiwt58cU/UljoZsiQ+1i37gBer4fCwvMUFDTS2RlC\nW1sjkye/T2np77jjjukcP16KTjeLysq3iIqqJjDQH5frIOHhAfToMRTgsrjsbq4NoqJisVqTUCjO\nAVwKHU1JSaB//wBE8TA1NfV4PDKSNBObLY53313Njh2HCQ31IzNzPA0NuSiVt1BdnYXXewBJUtBl\n1OOAowiCHVCjUITi9VrR6fzQansDPRgwoJPp06dc1iZJkli3bgvPPfc+HR1T8HrPUFq6g6ioVkym\nizidlahULWRlGfF4etDQoEUQ7ISG6ggN9SE+PpYePXwZNWoUe/YsZ/v2NQiCCUjBalUREFCFr6+T\nBx6YyY03ziIr6yAuVw/U6kBqa1t+xt7/Pldkj37x4sUcO3aMysrKy/Sn77rrrh9dhyAI+Pv7U1tb\nC3Qt/wcEBODv74/JZLqs7Id48cUXL/173Lhxl1YGuunmanDddaOx27t8VGbMmInT6eStt95l48Zi\nPJ4MBgxo58YbMzl3bgLZ2VaGDj3LAw9M55tvTjB69AgCAwP57LN9KBS3sX//Vuz2CuLjf0129m4M\nBgeC4Ics96K9vYHERANOpz+ZmfPp0eP0JVW49nYBf/9BuFwldHRUEB5eh0pVQlRUH0pL4ygtPYTR\naGD58nq83kiqqrZz771ziYyM5JlnbiI39zTbt1/E63UwZUpPPvmkmCNHZCRJi9frS2JiDcHBkJIy\ngvz8bCwWB1brO9/tmQ5h9+4mVKpompq+Zt68HiQnJ/P664/z8ssfY7efIjAQ3nrrOFarmosXq1Cr\n++BwNHLo0O+YNq0XZWVNnD9fQ3X1SwQE3IpCkce9944mMNCPM2cquXChkpiYGNxuNwqFotvgX0Ok\npcVQVPQV118/4ZIDpSRJJCUl8e67T7BmzXqWLv0Gm82Oy/U1DoeXgoI0SkpSsdtXMX36a1RXH6C+\n/jOgE6XSiyDIuN1aJMmAKIJCMRGvtwZZdqNSXYdGk01iYgBKZS2TJg3HarVe5s9VX1/PZ5+doLMz\nBperCFluJSAgFH//QXg8SjyeIARhO6IYRVBQKq2tf2Lw4DRmzfLD4biOsrIBFBWVc+HCBQQBlMpZ\nWK11qNVFDBp0D21t72O3q/n97z8hP7+GBx64hVGj9mC1Gpk2beZVGokuroihnz9//iW94f+7VPJT\nDL0sywwaNIiVK1fy1FNPsXfvXoYPH05ycjIFBQVIknSp7If4v4a+m26uNlqtlptumgF0rVTdd9+v\nOXJEorOzET+/ZurrjfTpk0JxsQlRtKLVaunfvz9Dhw7C4/Hw+edbKCkpoKPjefr1C+fOOyexevUL\nqFQu0tNnUFz8BbJcgd0eilLZQHt7M83NbmbNGofD4eDMmTNkZERw9OgWlEo14eFa4uN9CQtLwWTq\nBEqRZRvLl69HqYwkMrI/Fks0siyzdOkK1q8/Qf/+4bz00hI0Gg16vZ5VqzbgcrUB8UA8ra1nqKnR\nkpenw+Px4Os7CqUyC1n2R5JsCEI6KlUAUVEuiotruP32RwkKimLq1Ez69k1i3bptFBYWEhs7mJiY\nACIj/SksjGHkyN9x/vwqDIY4MjJ+hcfzPD17BiIIBnbvLiEnp5jU1FspKTmJw2Fj06aTRET48vTT\n9+Ln54ckSXg8nsucr7r5+WhpaeG11zbR3h5HefkGZs+eiclk4rXXVmM02rj99tGcONFBSMi9VFf/\niWHDXiQw8GuKixvxelsJCwvC5dqAw+EBBuDxtOHj05egoF00NytwOjWIoh63u/y7K9YhSR1YLA78\n/Nq5cAFWrSqjqur3REcnEhcXwuzZU9i4cQsnT+7H4dAhyyEoFEri4wXi423k5JSjUgUSHp6Ey3UR\npzMfl0tPS0s4587VMmfOOAoKjqLXOxDFeM6fL6W1tRJRVKJStWI0rqax0YvL9QQez2rOnlVQXV3N\nww/Pv5pDcYkrYuhzc3MpKir6yc4GHo+HqVOncvbsWaZOncorr7zCmDFjGD16NHFxcTzxxBMolUoW\nLVrE6NGjL3ndX2v8I1nhuvnvoaGhAZPJH1/fMEymKjSargxws2ZNITIyBx8fPenp6ZeOLykpYceO\nZmpqgrBao4CzdHRsZc+ek6jVaeTmruahh6ZTXKzBbq+jpUWLQjGaysoPiY6ewzvvfMSZMwEUF+/B\nZgvC5arjySfvpqmpjT//2YnF0orXW4HDEYnLFYrTGYPb3Yi/f8x3LxlHUKuf5ciRP9PS0sKgQYN4\n+ulXKCnpRKXqicdTgywX0dkZDvRAkmoRBH/sdoEePcZjt3vQaA4RHKyjd2/Qag3I8l0cOPAxI0bM\nYOvWrYSHB1JSEk5YWDxBQSf5wx8ep62tjZ07B1Nff4SkpCAEoRmjcTPPP38PBoOe4uLeHD0ah0YT\nQUPDCaKivCxZshtRvI20NLhw4QLJycm89tqH1NebWbhw8veES7r516NWq+nosKJWz8LpXElnZyfF\nxcVUV8dQWnqGgwffJDY2gORkXwIDfYmJOURCQiiS1IbdfoDf//5JQCY7uxyj0YootmMwuFCpRPT6\nniiVnVgsXkTxQWT5M0TRgCyLaLV96ehoxGgMwuFoZt2640ybtpSSknqysn7F+vVNWCxjge0olQEo\nlX2prGxk2LA01q79LfPmPUtzsx/Dh4dz/LiCzs6+WCwmmptPsmPHXnr1Cuf555ewffsRysrScbm+\nRhTDUKsfxWTajr8/tLZ+iFpdTVjYDwtJXS2uiKFPTU2loaHhezGuf/fiSiV79+69rGzIkCE8/fTT\nl5XNnz+f+fOvjTejH+IfyQrXlZq2m/8GEhISmDw5kUOHTvLQQ1OZMWMKycnJiKLIqFEjv3d8UFAQ\nGk0bNlsDdnsElZU2SkvjsNnGY7eb0evdPPro/Rw8eIhXXz1ESYkZQWgkNDSc55/fRmenkejo4RQW\n5uN0+iKK1/PHP2YxeHAEHk8yXq8/Op0VaMPp7BIOMZttbNuWy+zZs4mKUnH48LMolW28+SbMndvM\nN9/kERDwOBbLW/j4qPHxuZuWlp3fSXmeQxS1+Pk1AlFMnJjOm2/uIygoCEEQ2Lx5Kx9++Al+fk04\nnVn06RNCWFgYGs0xAgL0TJkygr59+wIwaNAgNm78kv37rWRmJnLnnTcSGBgIQGJiIufPf8bw4S6m\nTh3OJ59sw2weitmcRXQ0xMfPpLy8nOrqUAIDZ7Fr185uQ38V8Pf355ln5rB580dMnTqKoKAgvF6J\n3NxPaGwUCAiYS0NDFr/6VRg33fQZLpeL5cs/JyHhtxiNR/H19cHHx4eBAzOJiGjDaq1Go6miT590\nTp6spLKyE61WAr5BoWhEklyIohOd7iK33z6HpUu/we2+GUHYzqFDf8Jms6BUNuHxxNIlltMHjaYI\nQQglOHgl33zze2Jj/amr0+LxmNi16zyynIHXuwuPR0NjoxG4nYYGmQceeJ3ZswdisxWgUNyCSrUH\nl2sDKSmZzJoVSkhICH369CI2NvaaCgO/Ioa+paWFvn37MmTIkEte9IIgsG3btr9zZjfd/OejVqt5\n8smFPPnkwh91fGRkJC+/fDcjRoSxZk0ObndPzp3LRhS1CEIcQ4cm4evry8aN+6mri0atHoTJ9A5W\nqxp//5n4+dmoqXkPpzMKCEeSqvB4jNx332IqKt6lqqoWm00N+KDVVuJyFaDV+lFREcH69VsICIgn\nPHwqZvMRcnIklMqL9OoVTG5uHkFBBuLiVBiNeXg8EmZzHdATvd4NjMFm86WtrZDAwEBOneoSKVm9\neg8VFRFkZKh46aVp9OjRA6fTyaxZyaxevY/Dh42MHTuUyMhIdDodOTm1hIYuJjd3EzNndjnoer1e\noqKieOONp4Cu58uBA6c5c6YVtdrC4sV3ERQU9J2T415aWtYxc+b3X6K6+Xm45547WLDg9kurvNnZ\nZYwe/TK7d3+Kx7OZ0NB+xMb2QK/Xo9frGTQoic2btxEU5CE6OpoTJ/JwuUwkJCgYPvxOtm/vxGp1\n4uvbREDABFpaDqPRlDF9en86OlLJyclCpYJz54oQBBuyvAVR1GC3lxMa+hqdnVvQ6bbjcJQAkSiV\nBvz93bS1vcDUqb3QaHyQZQ1OZziy3I4o5gHJiOJIJCkLOIckBWE2h1Jf7+Sxx4ayZ081PXuOZOrU\nvoSFhTF69IhrVmHxiojaZGVl/WD5z+UQd7XFIq51gZqfQ9TmH+2Da1Xk42rPKeBSghujsZPDh4/z\n+efF6PUiy5bNo6XFxBNPrMRsFvF4Ohk16l48niKCg614PG4OHGims7ORrvCjAh5//HqMRj0xMQa0\nWg+ffFKAJAVhsxUgijfQ3r6ezMxfEB/fgV5fw8mTAvX1J3C5nCgUHmbNGobFYkOrvY2amn2024Uj\nfgAAIABJREFUth6hvl6B2axDocjA7W5FkqpQqfyJirLw1lsPsGFDPZ2dDg4f3g3cjyi+yY4dy7BY\nHKxdm01tbSmxsQ/idrewaJGBMWO6wo8+/XQze/fWEBUl8/DDN7NixXqKi8uRJDs6nYJevdJ4+OGb\n0Ov1PPvsUi5edDFsWAK/+c0DaLVaXC4XDofjmkuJey3MqavFnj0HWbv2FE1NF+jstOPjAwkJPQAn\nkZFBBASEMWpUGn369OHAgWP85jcfYjDMp2fPdhISmqmszKCxMZ/y8mNUV6vxeDrRakcTHr4XvT6a\noiILYESnqyMgYAY2mx2V6iS+vn60tspERemx26G2diqwAbU6DVGsJCTEy5dfvkJUVBT9+99Ga+tI\nYC+gRavticvVhiQ1fXcXrYSETGbevHiWL/81TU1NaLXav+og/nPws4radHu4d9PNlUcQBPr378r0\nNmLEcMaPz0Gn09KjRw8eeuhd/Px+gVr9Lb16OVCpzlBXpyI4eAgNDZuw2ZIAM9CMUtmfnTtP07fv\n8+za9RFgx2SyERIyBZcrG6czB7VagySVotfr+PWvH8BoNPLBB16++CIAq9XO7t1nufHGTCoq1pCT\nU4PLJZKUFE1ycgf5+dvweAxAE9Cf8PCxNDU1IctafHxCUCjasNk243IZefjhd0lJCSc8/FHa2zdg\nNq8nLi6C5OQ76ejoICAggHnzZjNxYhOBgYHk5eVRX59AdnYRHs8QPJ49yHIY3357jEWLbkWhCCIz\n80Gqqz+nqamJuLg41Gp1tyPeNcbEiWNIT+/Nm2+uxem8iaysP+P16igrMyPLVfTpk0Rz81FefXUQ\nO3fmkpa2kBMnPmbgwN7cd9/dfPTRJpqb8zAazXi9GmS5Cln2JSVlArW1O767ioDTGYvLdY6AgHB8\nfAJobPTgcgXS0VFBZ2cQgnAWWe7A6y1DkiZisXRy4cIFHA4HarUDOAjciiAcQ62uRa/voKNjAOBA\no4lEq5UYO7YvgiAQERFx9Tr0J/JPGXpfX9+/6oAnCMKlsLhuuunmn0OlUjFyZJd8q9PpJD7el7a2\nAkTRwZtvPklNTQ2ffNKCIOgQxVCSkyMpLt6FJMWhUiVSW9tOR8ebgB21egyiuBebbTthYf4EBY3i\n4sWdaLVnCA5O44svNgEChw+fw+l0IsvhOBxGUlN7IUlGHI5SPJ5wLlyoYMWKBbz11tfU1NyH3Z6F\nwXAatzufuLi7mDixCb1ejcuVwldfFQIJ5OefxmKJpkePpWRkxPGrX/0arVbLAw88x8WLDmbPTuO2\n227A398fjUZDUlISISGHUCgqEcVeyLIFWS7EYBjAuXPnuOGGIWzYsIKMjNif7CPUzc+HIAiEh4cz\nZ84Y/vSnNfTpY6Khoem7zHVuHI5aAgN9ABg3LpVvvjnFDTek8NRTC6mtrWfNmoOYTF6s1hIkKZgu\nrfoafH2D8XhEoCcwHp1uO7LcjkIh4PW6MJtHIIo27HYT4EQQLqJQmJFlN7AXl8vEunW1NDZKeL0L\nUShWIkk5CMIFdLp0JElDcPBgLJb9BAR0MGhQBn369L5q/fiPckWW7q82V3tJrHvpvnvp/uempKSE\n99//gurqJiIiYnjwwZmUl9fgdLoxmy28++7nFBY2I8sSkuSHWh1JQEA7/v4umppacbvt6PUTCAtr\nITBQwGhMoa3NhslUhp9fLyyW08TEvEBDw4v07h1Hz55K7rzzFo4cKeDtt/fgdA7HYPBn1KhCAgNV\n7N1bgdvdiZ9fJC5XC/7+gciyngEDQqmvb+TwYQlJGoUofsqCBZsoKfktWq0/wcEic+aM5Zln9qPT\n3YvR+GtiYlJRKo3cffdk7r//DlwuFyUlJXz77R6SkhIIDg7i44/z8Hp9ue22eKZOvQ5RFK9qitEf\nw7U+p34uvF4vFouFRx55leLiVtraqsjMTOJ3v3uUlJQUFAoFu3bt5YsvzqLVehHFdj75JOo7Y/0e\nMA1QodWeoFcvfyoqLNhsSkRRS+/eahSKVByOVKzWzxCEyXR07CcmRondLgEp1NbmIMvTkKRW4BAK\nxQAE4RyiOBSX6xv0+r44nRJKZSP+/io0Gj/694/jN795gH37jrJlSx5jx6awbNlziKKILMtXbe79\nrEv33XTzc/GPhDIaDIGYTO1//8B/I7ZtO8zp05CfbyIsrIpTp15l3rzJl+J233prA0rlL3G59iMI\nu5DlnshyACqVA4UiBpNJwOEoRZYH0Lu3C4ejAllO+652N4Jgw2bLISxMg7+/h5MndZw/v5F+/RSM\nGdODQ4c2IYo9OHFCx/jxC7jzzgKqqho4e9aK0RhKS4sVUexHdXUewcF9CQ7egSiuY8SIAbhcX2K1\nWmlvH015uYWAgOPYbCU0N/+SsLB4LJbx+PgUsWfPWUaPHkCfPn1IT0+/FIJ47Ngx3O5IVKpwGhqa\nu1Pf/puhUCiwWq0oFJHo9RHY7aOw2Sw89dT7REUZePzx+Vy82IJGMx6rtYa+fYtwuzchCCGIYhwq\n1VHc7kBE8QHKynaiVEaj1SahVu/AYnHR3HwEr7cZhUKiT59mUlNDcTrjMJnOo1T60tCgwOM5BjQC\nvsjydXi9p1EoTgKzsdtPIsuzkeXtSNIERo7MYMECHRaLg+XLd2Aw3MGXXx7i7rsLqapq5MsvjzFi\nRAr33jv3mk3adG22qpv/EpSXlKV+7M9fQhl//M9/Wo6Dzs5ODh06RX7+EdzuFOrrJQIDr+f0aRc1\nNTUolUoGDepJYOButNpzxMYOQK9PICgoHIPBgyx3olCEoVAYiIpKxmSyYbOZ8fE5QmpqKXPm+LBy\n5aOoVJtxuwdTVOREklKpqLBQXJxMY2MtopiK2Sxgs7kpLMxl69YsTp3yUl1dgMMBstyO212A223H\naMzluuteYO7cm1m3bhVvvnkPd901Bbv9LAEBXgwGA4MHP8B11z3BiBHBhIZuQavNp6KimZtueov7\n7nvqsm3AzMxMJk5U0K/fBQTBw6ZN23E4HFdxRLr5qURGRnLrrWn072+id+8iLJZTdHYmsnWrkUcf\nXUlKSjj19R9QUrKB2NgkRo2KxGAI/E7W+XpiYxMRxQu43V6s1jL0+nM4nbHU1iZhs0UjigJqdTA2\nm5GcnAaKinyornbgcp0nLS0DHx87BsNElEovkrQcUVQgCC5EsRWlErTa8wQEBBAcXIqPTzGxsdF8\n9tlhBGEWtbXrcbkuEhwczObNxwgPf4LDh+tpbW292t36V+n+ou/mKuKhO//AT6eyspKAgFGkpvam\nubmU0FAwGEoJD/cnPDwcQRB4//1XOXHiBDqdjrNnS6isbCI9fRwu1zA2bPiaixfL8fEJICPjAhUV\nWgRhEVrtYYYNC2DmzOHU1lYjCH3xevshinloNJtRKGKxWGRMJhswFY8nD7X6BJLUiko1BLN5NCpV\nCcHBGkwmJ1ZrHaGhiQQHN5GW1siNN96ASqUiJCSEJUseYsiQbCwWG0lJPVm+fCMOh8Rjj91P3759\n2LVrF889V4gkJXL+/HEKCgoYMaLLR0Gr1XLPPbewY8ce1q41AjZ8fI4wbdrEqzou3fx4BEFg2rQJ\nTJs2AafTyZEjx7jjjpfxeK6nstKIw+EkJCSBtLRfsG/fO6xZ8wanT58jMTGOoqIKzpwp4fz5PA4e\nlPD3X0Jz8xuIYhRerx8GQx8CAr5h4sR0du1qxeOZR3v7n1CpQvF6jURHj0AUK9BqDXg8XnS6OYhi\nIxqNCV/fAQQFmbj++mRUKn8mTx5Mz55dqnvR0b74+lYQGjqI3r1FtFotQ4Ykkp39IQkJ6kv5Hq5F\nuvfor9D1r+X99mt5j/5avp9r9U/DbDazdOmHNDSYmTQpmbFjRyOKIgEBAWi1WoxGI+vX70SnU3PL\nLdPR6XQAZGdns2JFCYLgz4AB9UyePIrk5GSee+4dsrPd2GzH6ds3ioICqKk5g9crolJFkJwMvXr1\n5fz5UCyWk/TtC1u3NuB2h6FU+hAebkejMWEyGdBoyomPHw5o6OhopkcPP+bNG8/8+XP+5j05nU4k\nSbrUVrPZzK9+tYxjxyoICFCRkZHE3XffQEbGXzIIbtnyNS+/vAOlUsHvfjeLqVMnXdX90r/HtTyn\nrhb19fWsXPkFRUVl1NQ0YrfHEBLSyVdfreD999dRUuKlTx8VTz+96HvL4jU1NcyZ8xStrQZ8fJqJ\nihpKefk3hIbG8eKLC8jPr2HVqtPU1LTjdpcBfYHjqFQhqNX98HqPEho6mra2CgIDHQwcOBQ/vxTi\n4loIDIykX78IQkJC6N+/PyqVCovFwooVf6KgoJ2RI3vx0EPzkWWZ5uZmgoODr0qkx4+dU92G/gpd\n/1o2ct2G/j/L0EOXQ5Pb7Uar1X7vd198sYUdOzR4vWYWLgzjuuvGfVe+jg8+yCY0tB+33x51WS7+\nrKwsNmwo49tvT9DRYQPcqFQm9PpxKJUFCEIFHR1h+PjomDEjjO3bL2AydQCJhIZaSEtLobxcRK+P\nYO5cX6ZPH4mPjw8BAQGcOpWPy+VhxowJ6PX6n3SfZ86cYdmybwkJuRlJ2si77/4ar9dLdnY227bt\n4/TpnoCVJ56IJz+/mgsXmli4cDpDhgz8u3X/3Fzrc+pq8MQTL/Hpp6W4XHYSE325774h3HLLLYSF\nheFwOCgtLSUlJeVSIrb/n/b2durr6/H19aWxsRGPR+LChXrGjx/MoUOHWbRoOU6nAFiABCAEOIoo\nxiLLBnQ6HXp9JyNHzmHevBDCw0P56KMTuN2p5OZuYODAcQwaZCUpKYHBgzMIDw/H4XCg1WqviRfK\nbme8brr5D0ahUPxVJ7TgYH9k+QJKpZPAwC4lu9raWnbtqkOvH4goHqO9Xc3u3bsZNWoU/v7+REVF\nIQiduN0qZHkU0Azswmr9FklKQBRBpZqEIKjIytqI1xsOqBCECLzeE9TVNdHe3khw8FgKC5tJTo6i\nocGG221k27Y62tvNnD9fwvPPP/mT7rMrvE7EaDxKWJiXd9/9jFOnctmxoxZJMhMb20F6ejxOp5OC\nAjVBQXexbdvXf9PQl5aW0t7ezoABA/6qAenmX09DQwO7dp3Cah2P07mHsrI2YChhYWHIsswf/7iO\n3NwWMjNzefTRu3/Q0S0oKAhRFFm5ch1tbUaKiuppbx/Etm1vkJYWhCz3ApxAMRAOpAB5SJKASnUT\nTudGvN5WamuzCAy8j/79++N2b6OqqhaHw0ljYyMbNpSRnJzC4cNree21Jy6tOv070W3ou+nmP4yJ\nE8cSFhaIWq2mT58+QJdEKCjw9w/k/PlWTpwoQ6PZw6JF1Tz11EIyMjKYMKGcnTuL0ema8HobCA31\npblZgywvQpL+B6/3I4xGEaMxmK4XAQMKRSSiGIzbPRqDIY/S0mO0t8dx9uwm4uOn0Ni4l8pKM6KY\nzM6dJ/jtb2Xa2trIzz9HUlLi3xX+8PX15cUXF3LhwgVWrqyipSWa3bs34HLdj9e7ET+/Wu6++wa0\nWi3BwSV0dGzmuuv6/dX6KioqePXV7bjdEUycWMM999xy5Tq+m5/E1q0HCA0dQXn5ZiATr/ciW7ce\nY9KkiVy4UM6xY2UkJT1PXt4b2Gw2fH19f7CeU6fy2LfPSH19Iw0NB9FqBS5cyKa+vgcqlR8uVzyg\nBY4BRXQlkpJwu9cB1ej1d1NYuJkPPjjO/v1HcTpDMJsLUaniaGlpJCRExG7vxOPx/kw9c+XpNvTd\ndPMfhiiKZGRkXFbWo0cPfvGL0eTnnycnx0x9fRtKZRM7duxDpVIzffowwsP9USgigQjAiUbzIKK4\nDFH8I9CJ1zuOrgfmQOANFAoVOt1uAgN9aW1tQBDKCQycDYTgcn1KcXEOHs8AHI4jqFSDsdl2AvD6\n659QX98XX98veP31X/zVB/j/EhQUREZGBn5+B2hrs9Czp4rKyvcwGDRMnTqGTz89i9WqIi0N5swZ\nzODBg/9qXRaLBa/XgFodTUfHxUvlnZ2d2Gw2IiIirokl2f8EJEmivr6eoKCgH9yyiY0NJSqqlYiI\nENrbg3C7y6iq6uS55z7Cbk/DbL6ISvUqEyak4uPj81evExERRnV1HqJ4K273SRyOVmAQNlsEGs1+\nJCkXp9MFTEQUg/B4dtK1hO8D6DCbz6JUqjh6VMWxYzuJivp/7N13eFRV/vjx95RM6kx6TyCNkpBE\nUigBpHdREMEGii52XBRs66oLimWVVcSKih1UFhSQIqChKU1CSAgJaYT0nsxkkkyfub8/st/s8gMV\nNBLKeT0Pz0My98z93Ds387n3nnvO51osFl9aWuzYbO0oFLWUla0iJWXYJXtsiEQvCFeIAQNS6NOn\nFx98kE5LyzCs1pO0tLhQUNCfoqJ1uLoqkMsnYrdn4epqQZLy6d8/gtZWH1pbFTQ15WOztQOngFYk\nqTdqtYy4uF74+s6gsdGAt3cbzc2lTJ58E5s2laHXh2M2O+PhUUliYiSSJNHebsHV1R+zuaNU9blQ\nqVT8/e9z/tNn+w5GoxGj0UhzczMZGQXs2nWKjRu38frr60hMjMTLy5spU4bxl7/MOu3LuV+/fsyc\nWU1NTTXXX9/xjEJNTQ3PPfcZJpOK2bNTGDNm+J+w9688n332Nbt31xIYaOUf/7j3jGQ9adIYoqLC\nKCqK5NlnP6Gysh8VFccoLt6Nk5MzYWES8+cPZPr0a351PXFxcUyfnkJmZi42WwBmc09ATn39bpKS\nbsTTU09oaC0bNuRhNjvR0NCGJIUADYARpdIVlWoYdXVf4Ooai0r1Lb16RRMenkRjYyWNjd6o1Xey\nYcMnLFhguSSnVxaJXhCuIGq1mvvvn8g773xLSEgEGk0QBQUb0OnyiI31xt1dhpeXml69+jFpUg9W\nrDhEUVE2Tk5aBg9OJj+/nrq6fOz2XiiVITgcx3nwwQc5cSKfsWMfJCoqEplMhkqlIiXlCPn5JRQX\nj6O93cTDD9+LXC5nwYIb2bXrCMnJE86rIEhQUNAZ84ubzWaCgjag1/+E3e5Dc3MTe/acQK0OJSen\niREjBhMTEwN0nFTs2LEbo9HMzJkTqKiowGw2U11dTVtbFB4efcnKOiISfRc5cqQEP7851NZ+Q0ND\nQ2eiLyws5Pjx44SGhvLuu2s4erQena4Cnc6KxdIDqMdszsLXtx9NTa2/uR65XM6zzz5EcXExu3b1\n4OjRXAYNikOj6c/27Xn06RNAQEAIX36Zi05nQpKcUSpP4uzcTkJCLBqNGzU1ZZSXj0Au98fPrwUv\nLw1lZQe59tpkvvvuZ0pL30GSzBQUFJKQEP8n77muJxK9IFwBLBYL6el7cTgcTJ06gbS0JMLCwtBq\ntdx774v07/8mBQWvExFRTEBAMC+9tIjS0lLy8iqw21OxWo9w7JiDyZPfZ9OmB7DZbsRm+4K5c8eR\nkBCHw2ElJCS48+G2zMwsSkurmTBhBLfdFnBaLNHR0URHR3fJdlmtVkpKypCkMGAK8BlyeSBGoxaV\nypf29vbOZY8cOcI77+RSVWXn88+/xstrBC4uTTz22HXExh6lrm4rHh6BzJ37LImJocybdwdKpfiK\n/D3sdjupqWG8997j9OkTgFqt5pVX3icjo4Dy8lrq60Pw8mqgttYCzKeu7kmUSmcgC5ksCKWyniFD\n+jN16mgkSaKmpga1Wn1Gjffy8nIOHMgiKakv8fHxxMefnoSnTzejUqlYsOAV2trasNkikMnuRJI+\nxNlZQWurghtvjCIxcRr/+tcX6HQnCAsLQ6/vQ48e/RkyJASl0si6dWbi4iby3Xc/i0QvCMLFKT19\nDy+88ANms4WIiA24uaXQo0cbixbN45pr0jh48AuqqnLw9x+PXl+CTCbj5ZfXYLd70fHUsg+NjTms\nW3cP3t5GbLbv8fHxQaPxZerUhzh50gW1egkbNryNn58fb7yRjiT1Jy9vLYsWzfvV2IqLi/nss+1E\nRvoze/b151XT+7nnlrJnjx5JagdeQaWSo1aH4OwM9947gH79/vtgnkqlorCwCIgnL6+GIUMiMZs7\nToL+/vf7sNvtzJ37HKWlo9m9+xOMRhNPPDHvku2X7S6SJPHOO6tYvfowVmsQJlM827dv5/hxFxyO\naVRXv4pSGYPDocLLK5eKipdwc1Mhk1kIC5PT0HAKhyOIrKwqjEYj27btZM2aHDw8LCxadCf+/v5A\nx8nE0qVf0N4+jPT0b3jttQdpb2/nww834ObmzNy5N3SeGJSUHMJsdgdqkaR3sNubaW6+j+bmH1m4\ncCUymZnY2N6EhWnIzMynrc2JwMBKVq2K56efdJhM1eh0+fj5xVFeXv6bD5FebMQUuIJwBTh1qoTK\nSlcaGqLIza3H3/8aKioMGI1G7rnnFv75zxvx8fGmpMSFkhIdWq2WvLxCIJiOmvY+gDsGg4Lq6ihM\nJldUqmg+/3wLhYWt6PXDqKgI5sknP8BsNiOXgyTZzylJfvbZNsrKUti5s5WCggKg46E5g8EAdCTi\ntrY23nvvC55++k1OnjzZ2TY7uwy5/HqUyqk4O7vh6dkxscqLL97KQw/NRavVUlJSgiRJ/xlZ4EFE\nRC1Dh/and+9cJk70Ij+/lFdf/ZiKigp69/ajrOwT7HYba9bsoqmpqes/jMvc/v0HWbnyOwwGH0pK\njqHVHiImJgYfnzpcXQ8ycmQPkpOzueuuGNavf5nnn5/A5MlXceutfQkJCcJiCcZmu5/c3DCys49x\n9GgJHh4T0evDqKysRK/X8+qrH/Hss2/T0qLFbrdit9swGo2sWbOZwsI+HD7sSUbGEQCamprYt68e\nSAQ8gFacnPrSUXc+FxiJJF1NXl49O3cmUlamRi4Pxd/fHas1AHf3Ubi5eeHq6oHJNIUPPtjYbfv2\n9xJX9IJwBRg2LI2NG9dgt5sYNCgZs/lLbrxxQOcVT3BwMMOHp3L4sDOentEEBgYyfnwiX3xRgMFg\npGPCERUwCknah8kk5+TJDDw8hmG3H8ZqfRe5PI7c3OM4HA4WLJjAqVMVDBly46/GZTabOXToEBkZ\nhwkMbMPHZxK5uXksW/YtTk4wc+ZA1qw5SGtrMxZLD/z8hrNmTTq9ep2gsLCaCRNSyMpahUxmxM1N\nwt3dgF5fy6pV28nKKqGkpB4Pj2hmzUpk8uSxLF36NCdOnODQoeMcPlyGSuUgN9cZlSqRr76aT3m5\nEaiktXUiLS0KPv30C66/fgo//niUlJS+xMf/8tC9K5VWq2Xbtj34+3szfHgaH330A4GBc9i7dzHu\n7jFUVBRiNlt49tl7ePnlZaxceRyr1Y6Xl5o777yRhx56gPnzJe66az779pUhSXqUyvcICHAlOfku\noqP1rFixgfh4X1xcXHj44WfJz++J0ViGQlGPTPYybW0KJkw4gL9/JBZLMRERfgQHdzzEJ0kScrkS\nmawdScpCqQxDofBHqTyC1arDZrPSMZpEjyTZkMnsBAa24+/vi8lUTEJCKXFxcRQUmDEYSvHx+fVR\nIhcjMTNeF63/Yp4VTsyMd/nNjHe+JEkiPz+ftrY2+vfvf9bb41qtloMHM+jRI5R+/eJoa2vj7rv/\nyvffn8LNrS96/UlaWgKBLBQKD5RKFTADZ+fDeHiYaGgIRyY7RkSElQUL5jJz5jX4+vr+alxVVVWM\nH/8IVus12Gx72LLlEQ4fPsG2bc4UF+8nIKCS4OB5aLXVGI1b8fNLZsAAJT//bMXdfSgWyxrM5l44\nO/fFzW0bx47lUlXlid0+AJNpFxBCSIgLs2b1ZuHCO4COuwXz5r1BePgjFBQ8h5ubK+3tnmzb9h2u\nrsvQamcgSZHIZD7Ex1dx1VUDUamuQ5J2sWzZvDP6ic/V5XZM/Z+3317FwYN+QBmPPz6Edet2k5en\nID19KxrNg2i1b9OrVwJyeQaFhU0YDInI5dcQFXWIr766rbMqoYdHKu3tDwCbGDiwnq1bvz3j+Hn+\n+ffIzNRw6NBaZDI1gwffQ3r6IlxcHkKrXcW0aXfg7X2Qp566m7CwMABqa2u5884Xyc4uob3dE40m\nDlfXKozGE9TUWLDbtXTctbLj4VHHqFGRjByZxldfmdDrNYwZU8lbb71AWVkZNTU1JCYm/upwvwtJ\nzIwn/AFK0S95mZHJZJ2T5/wSb29vJk0a1/lzXV0dkhRPaGgQdruWlBQ/Nm2qxG7vhatrCHK5CaNx\nL3Z7PSaTCZutGJnMlaqqcL76ykZGxr8YMCCR668fQ0BAwFnXmZOTj8mko7FxNykpznh6ejJsWH9W\nrPgH7e1DMZtlNDevJSTEj7vvfhBXV1c8PT3Jzf2E9vajxMYGc/JkAxaLjWHDkhk1aiDvvnuQoqKD\ngAlv7wSs1m1ce+2dnet0c3Ojf/8gsrLeZMiQaK6/fjR1dXWcOLGFsrJ/oFRasdmMyGQxFBcXYrEU\nExZWRHQ0oiTuWbi4OOFwtKNQdAw9e/zxv5Cfn09kpI6dO9fi7BxASYkNg8EdSXLC4TiIUllO7959\nTuvr9vNzwWA4gVzezpQpk7FYLOzfv5+4uLjO0RnBwZ4UF+/AyUlDZKQRV9cdBAU5qKjYhlLZTFXV\nKhYuXNiZ5Dve149Ro+IpL6/GxQWqqjYgl5uw2yXs9plACXAEd/ce3HrrKF5/fTG7d++msnIVbW1B\nbNuWz/Hjx0lISCAiIuLC7twuIhK9cBaiqpzQMVGNn5+duLhQkpLCcHWV8/PPpbS2uuPisgU/P2+c\nnPrT3OxEz55zyMn5DEnS4OLShNWqJSenBbs9GKNxKw8/fMdZ15GdXcq4cS9TXr6VefMSCQkJAeDe\ne6fy/fdGnJy8eeKJa4iMjDxtutpFi26nrq6O2NhYGhsb0Wq19O3bF0mSCA/3p6CggPff301z8yGu\nvTaJXr16dbaVy+VMmzaKkpJVtLeb8Pb2xtfXlxdfvJ+1a79l//5wGhr0KJV78Pbuh8OhpLn5S155\n5YXznqv/SnDLLdcSEXEIH59oevfujUwmIyUlhauuuoqqqiqeeeYVvv56JxaLFwqFkrAIYz1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eCBB7r8bFiSJFat+oZ7732BzZu/P+/2NpuNRx55lddfP0xjoxG5vASHowiQ0d7uYO9eIwsXvkZz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gr58apuVVUVEhISFNJ9kzXVyVdjY2P4+vpi9uzZMDMzA4/Hw9GjR2FsbCy3pqrWD1CXPH3T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\nMyPxAAAAAElFTkSuQmCC\n",
"text": [
"<matplotlib.figure.Figure at 0x13bc9a4c>"
]
}
],
"prompt_number": 13
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"Posteriors are like Oatmeal -- if it's clumpy, it's no good.\n",
"\n",
"This is a common problem with MCMC -- failure to converge. Fortunately, `PyMC3` supports not only Slice sampling but also *Hamiltonian Monte Carlo* (HMC) which is a new sampler that also takes the gradient of the posterior into account when choosing where to jump next and has much better convergence. NUTS is a recent extension that auto-tunes most parameters of HMC.\n",
"\n",
"So lets estimate the same model but with `NUTS` instead of `Slice` by simply passing in another object to the `sample()` function."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"with Model() as model_htwt:\n",
" glm.glm('male ~ height + weight', htwt_data, family=glm.families.Binomial())\n",
" trace_htwt = sample(1000, NUTS(), progressbar=False)"
],
"language": "python",
"metadata": {},
"outputs": [],
"prompt_number": 14
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"trace_df = trace_to_dataframe(trace_htwt)\n",
"scatter_matrix(trace_df, figsize=(8, 8));"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P(weight < 0) = 0.115\n",
"P(height < 0) = 0.0\n"
]
},
{
"metadata": {},
"output_type": "display_data",
"png": 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66ify84tRKFQYjaXIsjdGYw21taGAOwpFDt7e/ixYMJlz5zJ4550VKJW+DB0a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\n",
"text": [
"<matplotlib.figure.Figure at 0x162943cc>"
]
}
],
"prompt_number": 15
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"There, nice and creamy.\n",
"\n",
"We can now also see why Slice sampling failed. There is huge correlation between the `height` coefficient and the `Intercept` which any Gibbs sampler like Slice is notoriously bad at (because it only updates one random variable each step). `HMC` however updates all random variables and is guided by the gradient which helps greatly with the correlation. Kruschke in his book *Doing Bayesian Data Analysis* re-parameterizes the model to still work with Gibbs sampling but this can be quite cumbersome.\n",
"\n",
"Note that correlations are also a huge problem for frequentist GLMs that can cause the error to be underestimated and lead to wrong inference. Bayesian estimation on the other hand allows us to correctly model these correlations.\n",
"\n",
"Finally, we can also do hypothesis testing on the posterior by looking at the probability mass below zero."
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"print \"P(weight < 0) = \", np.mean(trace_htwt['weight'] < 0)\n",
"print \"P(height < 0) = \", np.mean(trace_htwt['height'] < 0)"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"P(weight < 0) = 0.115\n",
"P(height < 0) = 0.0\n"
]
}
],
"prompt_number": 37
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
"We can thus say that height is highly predicative of sex.\n",
"\n",
"Something I haven't talked about yet are *priors* which are another great benefit of the Bayesian framework. Specifically, we can easily build hierarchical GLMs in which individual coefficients share statistical power. I will leave this to a future blog post."
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Summary"
]
},
{
"cell_type": "markdown",
"metadata": {},
"source": [
" - `PyMC3` allows GLM specification with convenient syntax borrowed from R.\n",
" - Different models can be expressed by changing the likelihood distribution and link function.\n",
" - Advanced samplers like Hamiltonian Monte Carlo allow inference even when there are high correlations in the posterior.\n",
"\n",
"*Further reading*: Most of the theory and the Logistic Regression example including data is based off of the excellent book [Doing Bayesian Data Analysis by John Kruschke](http://www.indiana.edu/~kruschke/DoingBayesianDataAnalysis/)."
]
}
],
"metadata": {}
}
]
}
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