{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "Metropolis and Gibbs Sampling\n", "====" ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "collapsed": true }, "outputs": [], "source": [ "%matplotlib inline\n", "import matplotlib.pyplot as plt\n", "import numpy as np\n", "import seaborn as sns\n", "from functools import partial" ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "collapsed": true }, "outputs": [], "source": [ "sns.set_context('notebook', font_scale=1.5)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Introduction to MCMC" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In regular Markov chain models, we are usually interested in finding the equilibrium distribution $\\pi$ at whihc $\\pi^T T = \\pi^T$ for a given transition kernel $T$.\n", "\n", "MCMC inverts this thinking - we fix the equilibrium distribution to be the posterior distribution\n", "\n", "$$\n", "p(\\theta \\mid X) = \\frac{p(X \\mid \\theta) \\, p(\\theta)}{\\int{p(X \\mid \\theta) \\, p(\\theta) d\\theta}}\n", "$$\n", "\n", "and look for a transition kernel $T$ that will converge to this equilibrium distribution." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Island hopping\n", "\n", "We first provide an example to show the mechanics of the Metropolis algorithm concretely, then explore why it works." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "[Kruschke's book](https://sites.google.com/site/doingbayesiandataanalysis/) begins with a fun example of a politician visiting a chain of islands to canvas support - being callow, the politician uses a simple rule to determine which island to visit next. Each day, the politician chooses a neighboring island and compares the populations there with the population of the current island. If the neighboring island has a larger population, the politician goes over. If the neighboring island has a smaller population, then the politician visits with probability $p = N_\\text{neighbor} / N_\\text{current}$ where $N$ is the island population; otherwise the politician stays on the same island. After doing this for many days, the politician will end up spending time on each island proportional to the population of each island - in other words, estimating the distribution of island populations correctly. How a simple comparison of only two states at a time can lead to accurate estimation of a probability density is the topic of the next few lectures." ] }, { "cell_type": "code", "execution_count": 3, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def make_islands(n, low=10, high=101):\n", " islands = np.random.randint(low, high, n+2)\n", " islands[0] = 0\n", " islands[-1] = 0\n", " return islands" ] }, { "cell_type": "code", "execution_count": 4, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def hop(islands, start=1, niter=1000):\n", " pos = start\n", " pop = islands[pos]\n", " thetas = np.zeros(niter+1, dtype='int')\n", " thetas[0] = pos\n", " for i in range(niter):\n", " # generate sample from proposal distribution\n", " k = np.random.choice([-1, 1], 1)\n", " next_pos = pos + k\n", " # evaluate unnormalized target distribution at proposed position\n", " next_pop = islands[next_pos]\n", " # calculate acceptance probability\n", " p = min(1, next_pop/pop)\n", " # use uniform random to decide accept/reject proposal\n", " if np.random.random() < p:\n", " pos = next_pos\n", " pop = next_pop\n", " thetas[i+1] = pos\n", " return thetas" ] }, { "cell_type": "code", "execution_count": 5, "metadata": { "collapsed": true }, "outputs": [], "source": [ "islands = make_islands(10)\n", "thetas = hop(islands, start=1, niter=10000)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### True population proportions" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "image/png": 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1KXBgkj0a6pMkDaAlMJYB60YbquoBYGO/rLlf7+6RfvsBz5lmvbv72l7SUJ8kaQCpqs2v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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data = islands[1:-1]\n", "data = data/data.sum()\n", "sns.barplot(x=np.arange(len(data)), y=data)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Estimated population proportions" ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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FHJJkr4b6JEkDaAmMFcD60Yaqug/Y2C9r7te7a6TfAcDTZlnvrr625zXUJ0kaQKpqyysk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\nSU0MDElSEwNDktTEwJAkNTEwJElN/j+w+90WxTF9JQAAAABJRU5ErkJggg==\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "data = np.bincount(thetas)[1:]\n", "data = data/data.sum()\n", "sns.barplot(x=np.arange(len(data)), y=data)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Generic Metropolis scheme" ] }, { "cell_type": "code", "execution_count": 8, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def metroplis(start, target, proposal, niter, nburn=0):\n", " current = start\n", " post = [current]\n", " for i in range(niter):\n", " proposed = proposal(current)\n", " p = min(target(proposed)/target(current), 1)\n", " if np.random.random() < p:\n", " current = proposed\n", " post.append(current)\n", " return post[nburn:]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Apply to island hooper" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "image/png": 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R5JnAYXR7IqMuBQ5KskdDfZKkAbQExv7AutGGqroP2Ngva+7Xu3Ok337AM6ZZ786+thc2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\n", "text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "target = lambda x: islands[x]\n", "proposal = lambda x: x + np.random.choice([-1, 1])\n", "post = metroplis(1, target, proposal, 2000)\n", "data = np.bincount(post)[1:]\n", "data = data/data.sum()\n", "sns.barplot(x=np.arange(len(data)), y=data)\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Bayesian Data Analysis\n", "----\n", "\n", "The fundamental objective of Bayesian data analysis is to determine the posterior distribution\n", "\n", "$$\n", "p(\\theta \\ | \\ X) = \\frac{p(X \\ | \\ \\theta) p(\\theta)}{p(X)}\n", "$$\n", "\n", "where the denominator is\n", "\n", "$$\n", "p(X) = \\int d\\theta^* p(X \\ | \\ \\theta^*) p(\\theta^*) \n", "$$\n", "\n", "Here, \n", "\n", "- $p(X \\ | \\ \\theta)$ is the likelihood, \n", "- $p(\\theta)$ is the prior and \n", "- $p(X)$ is a normalizing constant also known as the evidence or marginal likelihood\n", "\n", "The computational issue is the difficulty of evaluating the integral in the denominator. There are many ways to address this difficulty, including:\n", "\n", "- In cases with conjugate priors (with conjugate priors, the posterior has the same distribution family as the prior), we can get closed form solutions\n", "- We can use numerical integration\n", "- We can approximate the functions used to calculate the posterior with simpler functions and show that the resulting approximate posterior is \"close\" to true posterior (variational Bayes)\n", "- We can use Monte Carlo methods, of which the most important is Markov Chain Monte Carlo (MCMC). In simple Monte Carlo integration, we want to estimate the integral $\\int f(x) \\, p(x) dx$. With Bayesian models, the distribution $p(x)$ in the integral is the posterior\n", "\n", "$$\n", "p(x) = p(\\theta \\ | \\ X) = \\frac{p(X \\ | \\ \\theta) p(\\theta)}{\\int d\\theta^* p(X \\ | \\ \\theta^*) p(\\theta^*) }\n", "$$\n", "- MCMC allows to sample from the posterior distribution - the samples will not be independent unlike simple Monte Carlo integration, but this is OK as we can compensate for the auto-correlation by drawing a larger number of samples." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Motivating example\n", "\n", "We will use the toy example of estimating the bias of a coin given a sample consisting of $n$ tosses to illustrate a few of the approaches." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Analytical solution\n", "\n", "If we use a beta distribution as the prior, then the posterior distribution has a closed form solution. This is shown in the example below. Some general points:\n", "\n", "- We need to choose a prior distribution family (i.e. the beta here) as well as its parameters (here a=10, b=10)\n", " - The prior distribution may be relatively uninformative (i.e. more flat) or informative (i.e. more peaked)\n", "- The posterior depends on both the prior and the data\n", " - As the amount of data becomes large, the posterior approximates the MLE\n", " - An informative prior takes more data to shift than an uninformative one\n", "- Of course, it is also important the model used (i.e. the likelihood) is appropriate for the fitting the data\n", "- The mode of the posterior distribution is known as the maximum a posteriori (MAP) estimate (cf MLE which is the mode of the likelihood)" ] }, { "cell_type": "code", "execution_count": 10, "metadata": { "collapsed": true }, "outputs": [], "source": [ "import scipy.stats as stats" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [ { "data": { "image/png": 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+21egBla5u5t4IA28GhDRMELHQDRl4lADIqW8iAqWnwOSgNnAauBOR+qh0dRq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\naAOiqRZr1kCvXmp20qOPwuLF0KCBs7VyMO+9p85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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "n = 100\n", "h = 61\n", "p = h/n\n", "rv = stats.binom(n, p)\n", "mu = rv.mean()\n", "\n", "a, b = 10, 10\n", "prior = stats.beta(a, b)\n", "post = stats.beta(h+a, n-h+b)\n", "ci = post.interval(0.95)\n", "\n", "thetas = np.linspace(0, 1, 200)\n", "plt.plot(thetas, prior.pdf(thetas), label='Prior', c='blue')\n", "plt.plot(thetas, post.pdf(thetas), label='Posterior', c='red')\n", "plt.plot(thetas, n*stats.binom(n, thetas).pmf(h), label='Likelihood', c='green')\n", "plt.axvline((h+a-1)/(n+a+b-2), c='red', linestyle='dashed', alpha=0.4, label='MAP')\n", "plt.axvline(mu/n, c='green', linestyle='dashed', alpha=0.4, label='MLE')\n", "plt.xlim([0, 1])\n", "plt.axhline(0.3, ci[0], ci[1], c='black', linewidth=2, label='95% CI');\n", "plt.xlabel(r'$\\theta$', fontsize=14)\n", "plt.ylabel('Density', fontsize=16)\n", "plt.legend(loc='upper left')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Numerical integration\n", "\n", "One simple way of numerical integration is to estimate the values on a grid of values for $\\theta$. To calculate the posterior, we find the prior and the likelihood for each value of $\\theta$, and for the marginal likelihood, we replace the integral with the equivalent sum\n", "\n", "$$\n", "p(X) = \\sum_{\\theta^*} p(X | \\theta^*) p(\\theta^*) \n", "$$\n", "\n", "One advantage of this is that the prior does not have to be conjugate (although the example below uses the same beta prior for ease of comparison), and so we are not restricted in our choice of an appropriate prior distribution. For example, the prior can be a mixture distribution or estimated empirically from data. The disadvantage, of course, is that this is computationally very expensive when we need to estimate multiple parameters, since the number of grid points grows as $\\mathcal{O}(n^d)$, where $n$ defines the grid resolution and $d$ is the size of $\\theta$." ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [ { "data": { "image/png": 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HlFIfKqWGOD8sIfzY/v0QHAxlBsvuytxFaGAorSNaO/+ejrrySk8sUYUaJRCt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\nGrNgnd947z3zPGECK1NXsiNzB7d0uYX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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "thetas = np.linspace(0, 1, 200)\n", "prior = stats.beta(a, b)\n", "\n", "post = prior.pdf(thetas) * stats.binom(n, thetas).pmf(h)\n", "# Normalzie so volume is 1\n", "post /= (post.sum() / len(thetas))\n", "\n", "plt.plot(thetas, prior.pdf(thetas), label='Prior', c='blue')\n", "plt.plot(thetas, n*stats.binom(n, thetas).pmf(h), label='Likelihood', c='green')\n", "plt.plot(thetas, post, label='Posterior', c='red')\n", "plt.xlim([0, 1])\n", "plt.xlabel(r'$\\theta$', fontsize=14)\n", "plt.ylabel('Density', fontsize=16)\n", "plt.legend()\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Markov Chain Monte Carlo (MCMC)\n", "\n", "This lecture will only cover the basic ideas of MCMC and the 3 common variants - Metroplis, Metropolis-Hastings and Gibbs sampling. All code will be built from the ground up to illustrate what is involved in fitting an MCMC model, but only toy examples will be shown since the goal is conceptual understanding. More realistic computational examples will be shown in coming lectures using the `pymc3` and `pystan` packages.\n", "\n", "In Bayesian statistics, we want to estimate the posterior distribution, but this is often intractable due to the high-dimensional integral in the denominator (marginal likelihood). A few other ideas we have encountered that are also relevant here are Monte Carlo integration with independent samples and the use of proposal distributions (e.g. rejection and importance sampling). As we have seen from the Monte Carlo integration lectures, we can approximate the posterior $p(\\theta | X)$ if we can somehow draw many samples that come from the posterior distribution. With vanilla Monte Carlo integration, we need the samples to be independent draws from the posterior distribution, which is a problem if we do not actually know what the posterior distribution is (because we cannot integrate the marginal likelihood). \n", "\n", "With MCMC, we draw samples from a (simple) proposal distribution so that each draw depends only on the state of the previous draw (i.e. the samples form a Markov chain). Under certain conditions, the Markov chain will have a unique stationary distribution. In addition, not all proposal draws are used - instead we set up acceptance criteria for each draw based on comparing successive states with respect to a target distribution that ensure that the stationary distribution is the posterior distribution of interest. The nice thing is that this target distribution only needs to be proportional to the posterior distribution, which means we don't need to evaluate the potentially intractable marginal likelihood, which is just a normalizing constant. We can find such a target distribution easily, since `posterior` $\\propto$ `likelihood` $\\times$ `prior`. After some time, the Markov chain of accepted draws will converge to the stationary distribution, and we can use those samples as (correlated) draws from the posterior distribution, and find functions of the posterior distribution in the same way as for vanilla Monte Carlo integration. \n", "\n", "There are several flavors of MCMC, but the simplest to understand is the Metropolis-Hastings random walk algorithm, and we will start there." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Metropolis-Hastings random walk algorithm for estimating the bias of a coin\n", "\n", "To carry out the Metropolis-Hastings algorithm, we need to draw random samples from the following distributions\n", "\n", "- the standard uniform distribution\n", "- a proposal distribution $p(x)$ that we choose to be $\\mathcal{N}(0, \\sigma)$\n", "- the target function $g(x)$ which is proportional to the posterior probability (the target function is essentially an unnormalized distribution)\n", "\n", "Given an initial guess for $\\theta$ with positive probability of being drawn, the Metropolis-Hastings algorithm proceeds as follows\n", "\n", "- Choose a new proposed value ($\\theta_p$) such that $\\theta_p = \\theta + \\Delta\\theta$ where $\\Delta \\theta \\sim \\mathcal{N}(0, \\sigma)$\n", "- Caluculate the ratio\n", "\n", "$$\n", "\\rho = \\frac{g(\\theta_p \\ | \\ X)}{g(\\theta \\ | \\ X)} \n", "$$\n", "\n", "where $g$ is the posterior probability. \n", "\n", "- If the proposal distribution is not symmetrical, we need to weight the acceptance probability to maintain detailed balance (reversibility) of the stationary distribution, and instead calculate\n", "\n", "$$\n", "\\rho = \\frac{g(\\theta_p \\ | \\ X) p(\\theta \\ | \\ \\theta_p)}{g(\\theta \\ | \\ X) p(\\theta_p \\ | \\ \\theta)} \n", "$$\n", "\n", "Note: The Metropolis algorithm refers to symmetrical proposals, and Metropolis-Hastings refers to this correction for asymmetrical proposals.\n", "\n", "Since we are taking ratios, the denominator cancels any distribution proportional to $g$ will also work - so we can use \n", "\n", "$$\n", "\\rho = \\frac{p(X | \\theta_p ) p(\\theta_p)}{p(X | \\theta ) p(\\theta)}\n", "$$\n", " \n", "- If $\\rho \\ge 1$, then set $\\theta = \\theta_p$\n", "- If $\\rho \\lt 1$, then set $\\theta = \\theta_p$ with probability $\\rho$, otherwise set $\\theta = \\theta$ (this is where we use the standard uniform distribution)\n", "- Repeat the earlier steps\n", "\n", "After some number of iterations $k$, the samples $\\theta_{k+1}, \\theta_{k+2}, \\dots$ will be samples from the posterior distributions. Here are initial concepts to help your intuition about why this is so:\n", "\n", "- We accept a proposed move to $\\theta_{k+1}$ whenever the density of the (unnormalized) target function at $\\theta_{k+1}$ is larger than the value of $\\theta_k$ - so $\\theta$ will more often be found in places where the target function is denser\n", "- If this was all we accepted, $\\theta$ would get stuck at a local mode of the target function, so we also accept occasional moves to lower density regions - it turns out that the correct probability of doing so is given by the ratio $\\rho$\n", "- The acceptance criteria only looks at ratios of the target function, so the denominator cancels out and does not matter - that is why we only need the target function to be proportional to the posterior distribution\n", "- So, $\\theta$ will be expected to bounce around in such a way that its spends its time in places proportional to the density of the posterior distribution - that is, $\\theta$ is a draw from the posterior distribution. \n", "\n", "Additional notes:\n", "\n", "Different proposal distributions can be used for Metropolis-Hastings:\n", "\n", "- The independence sampler uses a proposal distribution that is independent of the current value of $\\theta$. In this case the proposal distribution needs to be similar to the posterior distribution for efficiency, while ensuring that the acceptance ratio is bounded in the tail region of the posterior.\n", "- The random walk sampler (used in this example) takes a random step centered at the current value of $\\theta$ - efficiency is a trade-off between small step size with high probability of acceptance and large step sizes with low probability of acceptance. Note (picture will be sketched in class) that the random walk may take a long time to traverse narrow regions of the probability distribution. Changing the step size (e.g. scaling $\\Sigma$ for a multivariate normal proposal distribution) so that a target proportion of proposals are accepted is known as *tuning*.\n", "- Much research is being conducted on different proposal distributions for efficient sampling of the posterior distribution.\n", "\n", "We will first see a numerical example and then try to understand why it works." ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "Efficiency = 0.1861\n" ] } ], "source": [ "def target(lik, prior, n, h, theta):\n", " if theta < 0 or theta > 1:\n", " return 0\n", " else:\n", " return lik(n, theta).pmf(h)*prior.pdf(theta)\n", "\n", "n = 100\n", "h = 61\n", "a = 10\n", "b = 10\n", "lik = stats.binom\n", "prior = stats.beta(a, b)\n", "sigma = 0.3\n", "\n", "naccept = 0\n", "theta = 0.1\n", "niters = 10000\n", "samples = np.zeros(niters+1)\n", "samples[0] = theta\n", "for i in range(niters):\n", " theta_p = theta + stats.norm(0, sigma).rvs() \n", " rho = min(1, target(lik, prior, n, h, theta_p)/target(lik, prior, n, h, theta ))\n", " u = np.random.uniform()\n", " if u < rho:\n", " naccept += 1\n", " theta = theta_p\n", " samples[i+1] = theta\n", "nmcmc = len(samples)//2\n", "print(\"Efficiency = \", naccept/niters)" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "image/png": 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/YlQyHwNeA/4IfAhcbdYxhBCd5KhnkOIk0QmmDomhtf4OuMTMfQoRMurrGXlg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\nz+DssyEurulNd8VLjuVSxBR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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "post = stats.beta(h+a, n-h+b)\n", "\n", "plt.hist(samples[nmcmc:], 40, histtype='step', normed=True, linewidth=1, label='Prior');\n", "plt.hist(prior.rvs(nmcmc), 40, histtype='step', normed=True, linewidth=1, label='Posterior');\n", "plt.plot(thetas, post.pdf(thetas), c='red', linestyle='--', alpha=0.5, label='True posterior')\n", "plt.xlim([0,1]);\n", "plt.legend(loc='upper left')\n", "pass" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Assessing for convergence\n", "\n", "Trace plots are often used to informally assess for stochastic convergence. Rigorous demonstration of convergence is an unsolved problem, but simple ideas such as running multiple chains and checking that they are converging to similar distributions are often employed in practice." ] }, { "cell_type": "code", "execution_count": 15, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def mh_coin(niters, n, h, theta, lik, prior, sigma):\n", " samples = [theta]\n", " while len(samples) < niters:\n", " theta_p = theta + stats.norm(0, sigma).rvs() \n", " rho = min(1, target(lik, prior, n, h, theta_p)/target(lik, prior, n, h, theta ))\n", " u = np.random.uniform()\n", " if u < rho:\n", " theta = theta_p\n", " samples.append(theta)\n", " return samples" ] }, { "cell_type": "code", "execution_count": 16, "metadata": { "collapsed": true }, "outputs": [], "source": [ "n = 100\n", "h = 61\n", "lik = stats.binom\n", "prior = stats.beta(a, b)\n", "sigma = 0.05\n", "niters = 100\n", "\n", "sampless = [mh_coin(niters, n, h, theta, lik, prior, sigma) for theta in np.arange(0.1, 1, 0.2)]" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [ { "data": { "image/png": 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TeNM3wD6Tl8n56WHCIBBVbmvq43JhYFMy7DV6g+63v3pjT9wYjrZ8I4UtmooY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\nMzi7IXcqAx9/TFnDm5qbTd/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vUtKTDVQf6sITUkfH51MQGdrHM1k02ttzWP1DnfD9yvg4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\nUe6rAW1AV6ULUQVUDwNUFwNUFwOOLPUvrOqd+5xz84H5AGb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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Convergence of multiple chains\n", "\n", "for samples in sampless:\n", " plt.plot(samples, '-o')\n", "plt.xlim([0, niters])\n", "plt.ylim([0, 1]);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Why does Metropolis-Hastings work?\n", "\n", "There are two main ideas - first that the samples generated by MCMC constitute a Markov chain, and that this Markov chain has a unique stationary distribution that is always reached if we generate a very large number of samples. The second idea is to show that this stationary distribution is exactly the posterior distribution that we are looking for. We will only give the intuition here as a refresher.\n", "\n", "#### One: There is a unique stationary state\n", "\n", "Since possible transitions depend only on the current and the proposed values of $\\theta$, the successive values of $\\theta$ in a Metropolis-Hastings sample constitute a Markov chain. Recall that for a Markov chain with a transition matrix $A$\n", "\n", "$$\n", "\\pi^T = \\pi^T A\n", "$$\n", "\n", "means that $\\pi$ is a stationary distribution. If it is possible to go from any state to any other state, then the matrix is irreducible. If in addition, it is not possible to get stuck in an oscillation, then the matrix is also aperiodic or mixing. For finite state spaces, irreducibility and aperiodicity guarantee the existence of a unique stationary state. For continuous state space, we need an additional property of positive recurrence - starting from any state, the expected time to come back to the original state must be finite. If we have all 3 properties of irreducibility, aperiodicity and positive recurrence, then there is a unique stationary distribution. The term ergodic is a little confusing - most standard definitions take ergodicity to be equivalent to irreducibility, but often Bayesian texts take ergodicity to mean irreducibility, aperiodicity and positive recurrence, and we will follow the latter convention. For another intuitive perspective, the random walk Metropolis-Hasting algorithm is analogous to a diffusion process. Since all states are communicating (by design), eventually the system will settle into an equilibrium state. This is analogous to converging on the stationary state. \n", "\n", "#### Two: The stationary state is the posterior probability distribution\n", "\n", "We will consider the simplest possible scenario for an explicit calculation. Suppose we have a two-state system where the posterior probabilities are $\\theta$ and $1 - \\theta$. Suppose $\\theta \\lt 0.5$. So we have the following picture with the Metropolis-Hastings algorithm:\n", "\n", "![Markov chain](figs/mcmc.png)\n", "\n", "and we find the stationary distribution $\\pi = \\left( \\begin{array}{cc} p & 1-p \\end{array} \\right)$ by solving\n", "\n", "$$\n", "\\begin{align}\n", "\\left( \\begin{array}{cc} p & 1-p \\end{array} \\right) &=\n", "\\left( \\begin{array}{cc} p & 1-p \\end{array} \\right) \\left( \n", "\\begin{array}{cc}\n", "0 & 1 \\\\\n", "\\frac{\\theta}{1-\\theta} & 1-\\frac{\\theta}{1-\\theta} \n", "\\end{array} \n", "\\right)\n", "\\end{align}\n", "$$\n", "\n", "to be $\\pi = \\left( \\begin{array}{cc} \\theta & 1-\\theta \\end{array} \\right)$, which is the posterior distribution.\n", "\n", "The final point is that we can find a stationary distribution using the detailed balance (reversibility) criterion that says that the probability of being in state $x$ and moving to state $y$ must be the same as the probability of being in state $y$ and moving to state $x$. Note that detailed balance is a sufficient but not necessary condition ofr $\\pi$ to be a steady state distribution (assuming ergodicity). Or, more briefly,\n", "\n", "$$\n", "\\pi(x)T(x \\to y) = \\pi(y)T(y \\to x)\n", "$$\n", "\n", "and the need to make sure that this condition is true accounts for the strange looking acceptance criterion\n", "\n", "$$\n", "\\min \\left(1, \\frac{g(\\theta_p \\ | \\ X) p(\\theta \\ | \\ \\theta_p)}{g(\\theta \\ | \\ X) p(\\theta_p \\ | \\ \\theta)} \\right)\n", "$$\n", "\n", "### Intuition\n", "\n", "We want the stationary distribution $\\pi(x)$ to be the posterior distribution $P(x)$. So we set\n", "\n", "$$\n", "P(x)T(x \\to y) = P(y)T(y \\to x)\n", "$$\n", "\n", "Rearranging, we get\n", "\n", "$$\n", "\\frac{T(x \\to y)}{T(y \\to x)} = \\frac{P(y)}{P(x)}\n", "$$\n", "\n", "We split the transition probability into separate proposal $q$ and acceptance $A$ parts, and after a little algebraic rearrangement get\n", "\n", "$$\n", "\\frac{A(x \\to y)}{A(y \\to x)} = \\frac{P(y) \\, q(y \\to x)}{P(x) \\, q(x \\to y)}\n", "$$\n", "\n", "An acceptance probability that meets this condition is\n", "$$\n", "A(x \\to y) = \\min \\left(1, \\frac{P(y) \\, q(y \\to x)}{P(x) \\, q(x \\to y)} \\right)\n", "$$\n", "\n", "since $A$ in the numerator and denominator are both bounded above by 1.\n", "\n", "See [Chib and Greenberg](https://eml.berkeley.edu/reprints/misc/understanding.pdf) for algebraic details." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Gibbs sampler\n", "\n", "Suppose we have a vector of parameters $\\theta = (\\theta_1, \\theta_2, \\dots, \\theta_k)$, and we want to estimate the joint posterior distribution $p(\\theta | X)$. Suppose we can find and draw random samples from all the conditional distributions \n", "\n", "$$\n", "p(\\theta_1 | \\theta_2, \\dots \\theta_k, X) \\\\\n", "p(\\theta_2 | \\theta_1, \\dots \\theta_k, X) \\\\\n", "\\dots \\\\\n", "p(\\theta_k | \\theta_1, \\theta_2, \\dots, X) \n", "$$\n", "\n", "With Gibbs sampling, the Markov chain is constructed by sampling from the conditional distribution for each parameter $\\theta_i$ in turn, treating all other parameters as observed. When we have finished iterating over all parameters, we are said to have completed one cycle of the Gibbs sampler. Since hierarchical models are typically set up as products of conditional distributions, the Gibbs sampler is ubiquitous in Bayesian modeling. Where it is difficult to sample from a conditional distribution, we can sample using a Metropolis-Hastings algorithm instead - this is known as Metropolis within Gibbs. \n", "\n", "Gibbs sampling is a type of random walk through parameter space, and hence can be thought of as a Metropolis-Hastings algorithm with a special proposal distribution. At each iteration in the cycle, we are drawing a proposal for a new value of a particular parameter, where the proposal distribution *is* the conditional posterior probability of that parameter. This means that the proposal move is *always* accepted. Hence, if we can draw samples from the conditional distributions, Gibbs sampling can be much more efficient than regular Metropolis-Hastings. \n", "More formally, we want to show that \n", "\n", "$$\n", "\\frac{P(y) \\, q(y \\to x)}{P(x) \\, q(x \\to y)} = 1\n", "$$\n", "\n", "We start by noting that $P(x_{-i})$ is the same as $P(y_{-i})$ since apart from the component $i$, the old state and the proposed new state are identical in Gibbs sampling. We also recall that \n", "\n", "$$P(x_i \\mid x_{-i}) \\, P(x_{-i}) = P(x_i, x_{-i}) = P(x)$$ \n", "\n", "by definition of conditional probability. So we have\n", "\n", "$$\n", "\\begin{align}\n", "\\frac{P(y) \\, q(y \\to x)}{P(x) \\, q(x \\to y)} &= \\frac{P(y_i \\mid y_{-i}) \\, P(y_{-i})\\, P(x_i \\mid x_{-i}) }{P(x_i \\mid x_{-i}) \\, P(x_{-i})\\, P(y_i \\mid y_{-1})} &= 1\n", "\\end{align}\n", "$$\n", "\n", "\n", "**Advantages of Gibbs sampling**\n", "\n", "- No need to tune proposal distribution\n", "- Proposals are always accepted\n", "\n", "**Disadvantages of Gibbs sampling**\n", "\n", "- Need to be able to derive conditional probability distributions \n", "- Need to be able to (cheaply) draw random samples from conditional probability distributions\n", "- Can be very slow if parameters are correlated because you cannot take \"diagonal\" steps \n", "\n", "![img](https://theclevermachine.files.wordpress.com/2012/11/gibbssampler-2dnormal1.png)\n", "\n", "Source: https://theclevermachine.files.wordpress.com/2012/11/gibbssampler-2dnormal1.png" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Motivating example\n", " \n", "We will use the toy example of estimating the bias of two coins given sample pairs $(z_1, n_1)$ and $(z_2, n_2)$ where $z_i$ is the number of heads in $n_i$ tosses for coin $i$." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Setup" ] }, { "cell_type": "code", "execution_count": 18, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def bern(theta, z, N):\n", " \"\"\"Bernoulli likelihood with N trials and z successes.\"\"\"\n", " return np.clip(theta**z * (1-theta)**(N-z), 0, 1)" ] }, { "cell_type": "code", "execution_count": 19, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def bern2(theta1, theta2, z1, z2, N1, N2):\n", " \"\"\"Bernoulli likelihood with N trials and z successes.\"\"\"\n", " return bern(theta1, z1, N1) * bern(theta2, z2, N2)" ] }, { "cell_type": "code", "execution_count": 20, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def make_thetas(xmin, xmax, n):\n", " xs = np.linspace(xmin, xmax, n)\n", " widths =(xs[1:] - xs[:-1])/2.0\n", " thetas = xs[:-1]+ widths\n", " return thetas" ] }, { "cell_type": "code", "execution_count": 21, "metadata": { "collapsed": true }, "outputs": [], "source": [ "from mpl_toolkits.mplot3d import Axes3D\n", "\n", "def make_plots(X, Y, prior, likelihood, posterior, projection=None):\n", " fig, ax = plt.subplots(1,3, subplot_kw=dict(projection=projection, aspect='equal'), figsize=(12,3))\n", " if projection == '3d':\n", " ax[0].plot_surface(X, Y, prior, alpha=0.3, cmap=plt.cm.jet)\n", " ax[1].plot_surface(X, Y, likelihood, alpha=0.3, cmap=plt.cm.jet)\n", " ax[2].plot_surface(X, Y, posterior, alpha=0.3, cmap=plt.cm.jet)\n", " for ax_ in ax: ax_._axis3don = False\n", " else:\n", " ax[0].contour(X, Y, prior, cmap=plt.cm.jet)\n", " ax[1].contour(X, Y, likelihood, cmap=plt.cm.jet)\n", " ax[2].contour(X, Y, posterior, cmap=plt.cm.jet)\n", " ax[0].set_title('Prior')\n", " ax[1].set_title('Likelihood')\n", " ax[2].set_title('Posteior') \n", " plt.tight_layout()" ] }, { "cell_type": "code", "execution_count": 22, "metadata": { "collapsed": true }, "outputs": [], "source": [ "thetas1 = make_thetas(0, 1, 101)\n", "thetas2 = make_thetas(0, 1, 101)\n", "X, Y = np.meshgrid(thetas1, thetas2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Analytic solution" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [ { "data": { "image/png": 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3Nf9Ogq3JcDAVQjPMNLiOmGlvK1ugqSt08oD2HmBRF4/9/nd46n2wOMHiidDR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CNZBFyFFRERTHhIpaE5lMkpZQdXQ4fO/JKCIZ2hadDjjJJf9blUoyufalTneo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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "a = 2\n", "b = 3\n", "\n", "z1 = 11\n", "N1 = 14\n", "z2 = 7\n", "N2 = 14\n", "\n", "prior = stats.beta(a, b).pdf(X) * stats.beta(a, b).pdf(Y)\n", "likelihood = bern2(X, Y, z1, z2, N1, N2)\n", "posterior = stats.beta(a + z1, b + N1 - z1).pdf(X) * stats.beta(a + z2, b + N2 - z2).pdf(Y)\n", "make_plots(X, Y, prior, likelihood, posterior)\n", "make_plots(X, Y, prior, likelihood, posterior, projection='3d')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Grid approximation" ] }, { "cell_type": "code", "execution_count": 24, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def c2d(thetas1, thetas2, pdf):\n", " width1 = thetas1[1] - thetas1[0]\n", " width2 = thetas2[1] - thetas2[0]\n", " area = width1 * width2\n", " pmf = pdf * area\n", " pmf /= pmf.sum()\n", " return pmf" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [ { "data": { "image/png": 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nUwknDWsCyOQaGSoKanWEuMtwcT+mFha0/fBDMlNSWDViBJqhcFPxJl65wvwu\nXUhPSKDLjBnYVqhwc+HGbyAlDlqPyB7Qmk4ECezChrpY4Jm96mb0uqY59rn2v82Yir1FLQq0b18E\nAPXqFX00uBDF6KGsU0TJy8w0EBGRwLFj19i/P4IDB65w6lQ00dHJkqGifCsXdUpWloHffjuEq6s1\nffsGPejD5+LqasOsWT0wGDReeWWlvP6KWWG6wTgDsfmUxxiXFVZ/YJ+maafzlO8HdqH3NXMH3kL/\nCqulpmm777RTpdQk4H2ASpVuJh93cNAD87i4NCo5w9EL4JFuCRYQRhqdqUs8m0hiP04NnoY982H3\nPPBuwCNDhnBo7lxOLlvGyhEj6PLNN5iYFXyrLu3Zw18DBhBz9izNxoyh7jPP3FwYEw5rPtZb79u+\nnl18jQWAATeezi5LxcB64vDAnNrY5DrG6r36c4d6Bd+LnTsvYWlpSt26Fe9w14QoUQ9lnSIerLCw\nWLZtu8CePZc4cuQap09Hc+lSAgZD/kGBra05/v6u1K/vQevWvnTtWgNXV5t81xVlTrmoU3buDCcy\nMolhwxpgaVny0+S0bVuV/v1rs3DhEf755yS9eskY/uLyQP7aSqlK6F9Fjcu7TNO0/8uz7irgKDAB\nfaDHbWmaNgmYBNCwYcPsWtzZWc/4Ehubipcx2YpZlCVmnnCKFOxoDEACO3AKGg927rB9FnR9HxNr\nB/r++Sdz2rZl7/ffE75jBx0+/5xq7dtnp0bSNI2rBw+yZ+ZM9s+ahWYw0GriRNp88MHN9EmGLJgz\nBNIS4amvwFqf1SiDaKKYhxluOHNzptRVxJBAFv1xyzVzaVYW/L1D76/eNCD/+xAbm8qBA1do3rxK\nqXgRC1GcSqJOEcXLYNDYtu0CS5eeYPnyU5w5cz3Xci8vB5o188LT0x4XF2usrPR6LjExnWvXkgkL\ni+X48Sj277/CrFkHMDVVdOvmz+uvN6FtW99iSWsnyo6HoU65MUNply417nUX993Eia1YuPAIX3+9\nS4L1YlSYqC4GyG++WmfjssLoiz470aI7rahpWrLxhdC9kPvOl4uLnuM8KiqZqsZeIRevmODnac0J\nUrCgDqY4EMcmvMwnoh5/E/6ZAP9Ohd6fYO3iwpBNm1g1YgTH//6buR07YuPmhmtAAEoprp85Q+IV\nfeZRt5o16TJjBlXbtct9En+PhZMboG4PaDE0u/gyX2EgBU/ewiQ7jaTGr0RiCvTLk8px7QGIjIPh\nncCsgC5cx+bZAAAgAElEQVRqwcFnMRg02rd/cCPDhbhHD2WdIorH5csJ/PjjXmbN2s/Fi3o3QDs7\nC3r2DKB1ax+aNvWibt2K2NreOSVtVpaBw4cjWbv2bHZr3z//nKRtW1++/bYLgYHuxXw1ooSUizpl\n5059HF3Llt53WDO3mBT4aiesPAMX4sDSFJp6wZC60M1fn7PxXgUGutOqlQ8bN4Zx+XICnp72d95I\n3LXCBOsnyNPnSylVBbAhTx+x2+gPbNM07WIh19e4MZvRPXJ31wdoXruWRG1jBsVTl+GRBjacJIUT\npONIO66zlET2Yt9uFGz9HjZ8BQ37Q5V6WDs702f+fC7t3s2emTO5sHUrF//7DwBHHx+C+vUjqG9f\nAnr0yN1NRtNg+f9g/VfgUQuGzMl+NcSznev8jTUBuNE3e5M1xHKGVLrjjCe535R+MCaWer59wde7\nZIn+p+jevYCmdyFKj4eyThH314kTUUydupUFC46QmWnA3t6CoUPr8/TTgbRp43tP3xCamppQr54H\n9ep5MHZsc3btusTkyVtYteo09ev/wOefd2DkyMbSyl72lIs65ciRSDw97XFzK3z3riOR0HWBHqSb\nm4CfC8Slwl/H9Uf/IJjTC4oyVvXJJ2uyZct5Vq8+zdChDe68gbhrhakNVwNjlVL2mqYlGMv6ASnA\n5jttrJTyBZoCrxbmhJRS1kBXYG9h1i+Ih4eea/zKlUT6Gj+EHr0APbDnD6LZTSL9eZLrLCWKedhb\nTIcB38OMLvBDb3h7p569BajcuDGVG+vdZm4Moiiwsk9PgUWv6V1q3KrByDVg4wRABtc4zzuAGd5M\nzp65NBUD07mMGYpXyd2f7dQlWLYbGvtDowK++UpKSmfZspP4+TlTv74MLhWl3kNZp4j74/LlBN57\nbwNz5hzEYNAIDHTnjTeaMGhQnUK1nheWUoqmTb1YuXIgy5ad5KWXlvPGG/9y7Ng1Zs7sKrmhy5Yy\nX6ekpWUSHh5Pq1Y+hd4mMR26zIeL8TCpNYxpBrYWenvi4Uh4ZSUsPKrPiv5773s/tzZtfAHYsSNc\ngvViUphg/XvgdeBvpdSnQDX0vldf5kyTpJQ6A2zWNG1onu37A5nA4rw7Vko5AiuAucAZwA14E/CE\nHCMv78GNr2IuXUqgppfefeRgKEzFDgVsIo6hPIo1gcQSTCqhWNXuDN0/1FvFp7WC11aBu1/ecy74\noKG74PehEHEUvB+FV5eDox58G0gllDfI5BqejMGG2tmb/cAVLpLOc1TAx5ix5oapi/UX1tjeBX9V\ntWTJCZKSMhg4sI60GImHwUNZp4iiycoy8M03u5k4cSOJiekEBbkzeXJbevasWajAOSsLLl6B85fh\n2nVITgUTBfa24OEGAVXBqYApJnr0CKBBg0p0776AH37Yi4mJYsaMLlJflh1lvk65di0ZTYPKlQs/\nj8r0nXqg/k4LeD9H7hqloG5FWDcY2syBuYdhaH0wxtx3LSioAmZmJhw/HnVvOxB3dMdgXdO0GKXU\n48C3wHL0EddfYRwskWdf+X2R0h9Yr2lafn/FNOAa+gxjFYBUYAfQWtO0kEJeQ77s7CxwcrLi4sV4\nLM2htjccCAW7DHMamNuyjySukYkHLxPKG1xmGtX4Fjq/B2lJsPZT+KgedJ8Mj70MFtb5H0jT4HwI\nBH8O+4yv89Yj4MnPs7cxkE4ob5LEAZzpSoUck6AdIomfuYoH5owgd6v4kfPw+yYI8oYnm1Gg77/X\nb9WQIY/c8/0S4kF5WOsUce/Onr3OM88sYefOcFxdrfnyy2688EJ9TE0Lzh6clQU7DsC/22DzHth3\nHJJTbn+c6t7Qvhn06wytG+Vu4PDycmDDhmdp23YO330Xgr+/K6NGNb1PVyhKUnmoU2JjUwFwcrK8\nw5o3LToGNubwTsv8l1ubwxcdoNUc+OPYvQfrZmYmVK5sz4ULcfe2A3FHheoUqGnaMaDdHdbxLaC8\nwGSDmqalAk8W5hzuha+vEydPRqFpGk0CFAdC9YC9i78ze0liOdd5gfbY0ZA4NhDDvzirTtD7E/AM\ngj/egD/fhCVvQ6OBULUpOFXWdx4Xoc96eiIYIo1ZnnwaQp9puSY+yiKJUEaRwH/Y0xJvPkIZM73E\nkskYwjAAU/HBNkcdomkw6mcwGOCz58CkgPe0PXsu8d9/F+ncuTp+fi7FcBeFuP8e1jpF3L0lS44z\nZMhSEhLS6dcviG++6Zw9pig/x8/CD3/AglUQGa2XmZpCoB/UqQFVvaCCC9ja6PVjfCJcioRjZ/Xg\n/vtF+qNWNXhvOAzoejNod3a2ZtWqQTRo8ANjxwbTpo2vzEtRRpT1OiU1NRMgOwtSYZy5DoHuYH+b\n+L6Jlz6q9khk0c7PwcGS8+clWC8uZTrHn5+fMwcOXCEiIpHWQfb88C9sOgwv+TvzGZdYTDTPUYEq\nfMgJnuQik7CmBlb4QZPBENhJHyS6bzHsnKM/8rKwgQZPQ8thULN9rqacNM5zjjdI5RQOtKEqX2Ji\nHDyajoG3CCOcdF7Bg6Z5JkFasAXWH4QuDaHzowVf42efbQdg9OjbNL0LIcQDpmkaU6du5b33NmJj\nY85vv/Vi8OCCv/3bcQAmfwert+q/uznDS09D97Z6K7l9wfF9tsxM2BICs5fAwtUw6G34cTH8/glU\nMQ4H8vS0Z86cXnTqNI8XX1zG7t3DpP+6KPVuhBZ3M/eQuQlk3WFeR4Omj5K9H5OhSq+y4lOmg3V/\nf1cATp6Mol09PRheewDe7mNGd1z4k2jWEktnfPFmEucZzxleogazscQb7N2h11ToMQUuHYTLR/UW\nddAHn1YMgCr1wSz3oCgNA9dZQjgfYyAZNwbixfjsAaUGNCZygR0k0BZHXs3T/SXiOoz8EWws4ZuX\nCn4BHD58lb/+Osajj1bi8cclZaMQonQwGDRGjlzFzJkh+Pg4smzZgAInawu7BKM/hSXr9N9bNoBR\nz0KPtmBufnfHNTODdk31x4cj4c1P4J8NUO9JWPoNPNZQX++JJ6ozcGAd5s8/zPz5h3nmmbpFuFoh\nip+1tf5iSEnJKPQ2AW5w8ApcTwGXAnrybtRTt1OnQv7LCysuLi17Mkpx/xXcYbAMqFlTz1d+/HgU\nFZ2hgR9sOQpxSfAiFTEFviGCDDRc6EEl3iSDCE7Sn3i239yRiYkelDd5BjqO1R9Nn4WqTW4J1JM4\nwGme5QITARN8+JQqvJcdqGeh8T8usJwY6mLDF/himmcCpEHT4HqC3v2l2m2+oZ0wYQOaBh980EYG\nSgkhSgWDQWP48BXMnBlC3boV2bFjaL6BusEA03+DoB56oN68Pmz5DbbOhT4dbwbqmgan0uCHGBh2\nGR4LhWqnwf0keJyEgDPQ8TyMvwrBiZBhbHms6gVLvoHv34f4JHjiJdiw8+bxP/qoHebmJkyevIWs\nOzU/ClHCnJz0OVliYlILvc2AIMgwwAcF5MNJzoAxxg/J/YLu/dwyMw1EREiO9eJUpoP1oCB9Aoyj\nR/XOWL2aQEYm/LMLvLHkKdwII4056Ms9GEYVPiCLRM7yImGMJYUzdzyOgRRiWM1phnCKgSSxDyc6\nUot/cMkxZ0KasevL31ynNjb8gB/Wef4E782FjYehZxN4tUvBx1y//hwrVpzisce8S9VsZkKI8m38\n+HX89NM+6tf3YOPGIVSqdOsbeFQMdH5Zb/m2sYLfPoFtc2+2fANEZMCUaxB4FgLOwvAI+DkWtqdA\nmgZupuBoCtezIDgJPo2Gjheg8in4XyTEZOnfSr7cD5Z8rTeEPPkGnA7T9+/r68Szzz7CqVPRrF59\n53peiJLk7m6DUhARkVjobUY0An9X+GY3TNoEmTk+k56Ohg6/w7FrMLKxPknSvTpz5joZGYbsBlJx\n/5XpbjCBge6YmioOHLgKwIBW8L/58NtGeLYdvEEl1hPLN0TwGA4EYI0bT2NDIBf4HzGsJIaVWFIN\nR1pjRXXM0AdxZhJLGudJ5giJhKChf9q1pwUeDMeO3B3Nr5DOKEI5RDKNsOMbquKQ5/bP3Qif/AXV\nK8HsNwru/pKWlslrr61GKZg+vZO0qgshSoXvvw/h88+3ExDgSnDw4OyZpHM6fha6DNe7v3RpBbM/\nggquN5dfzIDJ1+DXWMgArBU8aQ8d7aC5NdS0BPM8VV5cFuxKgRWJMDcWJkfBdzHwrQf0c4RubeDn\nyfDseD1gD1kMlhbw2muN+eWX/fz44166dfMv1nsjRFGYm5tSubID584VdkJWsDSDxU9Bj4XwwRaY\nGQLutnqGmH0Ren/1fkHw+W0mXCyM7dv1eaQaNfIs2o5Egcp0sG5tbU5QUAUOHLhCZqaB6p4mPBao\nD9w8fRlqeJoxGW9e4RwjOMcC/HHHHBuCCGAxcWwgij9IYj+RzC7wOFb44Uh7XOiOFdVuWb6eWCZy\ngViy6IEzH+KNRZ4W9bX74fmvwdEW/nkXnO0Kvq5PPtnGiRNRjBjRiAYNKhW8ohBCPCDbt19k5MjV\nuLnZsHr1IFxdb51lcfchvUX9ehy8/yr879Wbma4yNPg0CqZGQYoGNSxgtAsMcgT7Owx+czTVg/mO\ndvBJBfj6ut4q3/8S7EiBLyvC4B7w3z4908wnP8H7I8ie7fTff88QE5OCs3MBHXuFKAVq1nRj3bpz\nxMcXvn943Ypw4GV4byMEn4OwWEjLhKaVYXQz6FOr6Oe1Zs1Z4ObkSOL+K9PBOkCTJpU5dOgqhw5d\npUGDSozoCluPwVf/wMxXoDWOjKQS3xDBUM7wE35UxAKFCU60x4n2ZJFEMsdI5wKZ6J9qTXHEgspY\nE4A5rvke+yrpfMIl1hCLBYqJeNEft+zUjTesPwi9PgJTEz1QD/Qu+Hr27YtgypStVK5sz9Spj9+3\n+ySEEPcqLi6VQYP+xmDQWLToKapWdb5lnX3HoOMwSEiCWVPg+RzJ8E6l6YH1/lTwMIMZFeBZRzA1\nVpVZZBFKKKGc5TKXiSWGVFJRKGywwQ13fPGlJoE4mTgx3g1620OfcPi/65BsgO8rwWdjYPkm+ORn\nGNoHvDygb99AJky4wooVp26brUaIklavXkXWrTvHvn0RdxUYO1nBt531n9Oz9MnEzO5TJ+ikpHRW\nrjxF1apOBAa635+diluU6T7rAC1b6pHv5s1hgD65UDUP+CUYQq/o6wynIoNx5wyp9OcUu0jItQ9T\nbLGnEa70oSIvUpEXceNpHGieb6AeQyZfcZnOHGMNsdTDlj8JYADutwTqy3ZBt8l6eqW/34HWtW/Z\nXbaEhDQGDPiLzEwDs2f3lJHXQohSYdy4dYSFxTJhQkvatbs1M1XYJej0kp4T/fdPcgfqaxKhUage\nqD/vBMf99GdTBbHE8C+r+IyP+Y3ZbGULZzlDKqlYY40llsQRxzGOsoqVfMUXLGQ+UUQRYAlbfKG+\nFfwUq/dpd7DTs8SkpsFnv+jH79EjAICVK08/gDslxL1r1qwKAFu3nr/nfViY3r9AHWDRoqMkJWUw\neHBd6ZJbjMp8y3rbtr4ArFsXyptvNsPcDCYP0jOuvPM7LBwLCsV4KlMRc77iMs9zhh44MxwPfLEq\n1HE0NA6SzN9Es4LrpKLhjhnv4klvXDDJE6RrGsxcBa//BFbmsORd6HSbfOqapjFs2HJOnYrmrbea\n0aGD3z3eESGEuH927Qrnhx/2EhTkzsSJrW9ZnpwCPUbAtevw7XswsNvNZfPj4NlLYKbgd094xkkv\nTyONDaxnNzvJIgtbbGlKM2oQQBWqYJWjXtbQiCOW05xmLyEc4ygnOE5HOtHMtDlrvBUNzsF7kdDK\nBp7tAZNmwKy/YfLr+tgmT0971q8PRdM0CThEqdW6tQ9Kwdq15/J9rT1oWVkGpk3bgZmZCcOG3SaA\nEUVW5oP1KlUcqVXLjY0bQ0lNzcTKyoz+j8H/LYdFW2HAY9CzqR6wv0BFGmHH/7jIMmJYRgyNsKMZ\n9jyKLVWwxME4y2giBiJI5xQp7CeJ7SQQiZ7/1AsLBuPOU7jdku0FICVNz6P+SzC4O8Ly96BJwO2v\n47PP/mPRoqO0aFGFjz+W7i9CiJKnaRqjRq0BYObMrljkM7PKm5/A4VMwvB+MGHiz/M94GHwJ7E1g\npTe0MHZxP08Yf7KYOGJxxpk2tKMOdTEr4O1KoXDCmUY0piGNOM4xVrCMf1nFNSLpbtaTBV4mtAqD\nlyPgQDV4tT9MmA4LV8HL/RStW/uwYMERTp++nj0/hxCljaurDc2aVWH79otERiZRoUIhZgorRgsW\nHOHYsWs891w9vLwcSvRcyroy3w0GoFs3f1JSMgkO1gdBmJjArNfB0hyGfgMXrt1ctw62/EUA0/Cl\nMXbsIZGviWAIZ2jHURpyiIYcog1HGMAp3uciS7lOBho9ceFH/PiXQAZTId9A/XAYNB2rB+r1q0HI\nl3cO1BcvPsr48eupXNmeP//si7n5fZhqTAghimjVqtPs3BlOnz61aNXK55blwdv1GUTrBsBX42+W\n70yGQZfA1gTW+twM1Pewi9n8QgLxtKINr/EG9WmgB+pZEZA0A2L6wrVAuFoBrnrCtQYQOwxSV6K0\nLAIJYjgj8MSTvYQQzBpa2sBQJziaBnPj4Nmeerat+Sv14zY15q3bs+dScd8yIYrk6acDMRg05s8/\nXKLnER+fxrhx67C0NOX990u+lb+sKxfBeh/jcOdFi45mlwV5w1dDIToBOk2C6Pib65ug6Iwzv1KD\nzdRmOlV5kQp0xZnHcKAl9nTBiSG48wFV+JsAtlKbj/GhJQ63dHkBSE2HDxbAo6PhUBgM7wTbPwPv\nO4zHWL/+HM88swQ7OwtWrBiIh8dt0sQIIcQD9NFHWwHyfbNOT4dXPwRTUz09o5VxiE1Upj7wM1OD\nxV7Q2JiAZStbWM4yrLFmCC/Qng6YYw6ZZyB2MER6Q/xrkLoYsi6DcgFlC5nHIeVniOkG12pD6koc\ncGAwz+GGO/+xjeMc4313sFB6lphKFfRJmLbu1XO+16unzz538ODVB3LfhLhXgwbVwcLClO++C8Fg\n0ErsPN56aw2XLycwfnxLfH2dSuw8yosy3w0GoHHjyvj5ObNkyQni4lJxdNT7Ow7vDKcj9Mwwbd+F\nVe+DV56c/u6Y0xEnOnJv/4wGA/y5HcbPgdCr4OkCP46Aro3uvO3mzWH06LEQgCVL+mW/oQghREnb\ntSucHTvC6d7dnzp1bp2hdOZCOHMBXn8GGgTeLB8eAZczYWoFeMLY9hDCboJZgyOOPMdQXHEFzQBJ\nn0LCJCAdzALBZjhYdgNT35sTUWiZkBECyb9Aymw9aLcdg639J/RXA/meGSxjKa+bV2WQozWzY/VJ\nlLq20lM5Bm+HJ5rpc60fPhxZrPdMiKJyd7dl0KA6zJ59gKVLT/Dkk/ch9+JdWrDgMD//vJ969Tx4\n552WD/z45VG5aFlXSvHiiw1ITs7g118P5CiHL56H17rC4fPQcDSsCrk/x8zIhPmbof4o6PcZhEfD\n6J5wYmbhAvU1a87QufM8MjKy+PPPp2nf/tb87UIIUVJ+/nkfACNHNr5lWUqqnsvc3lbPpX7DygT4\nKwFaWMPbxq7hYYSxguXYYMPz2YF6MsT0gIQJYOIGTgvB7QjYjgSzqrlnjFNmYNEUnH4CtwNgGgBJ\nX0D861TQ3GlNW5JIYhtbGWZsc5kbB4831X/euhdcXKzx8LDjxImo4rhVQtxXb7/dAhMTxbvvbiA9\nPeuBHnvnznCef/4fHBwsWbCgD5aW5aLNt8SVi2AdYOjQ+lhZmTF9+i4yMm7+c5uYwNcvwf8Ng5hE\n6Poh9JwC+87e/TE0DQ6F6q3oPi/qGWeOXIBn2sCxb2HaULC/dZ6QW/z66wG6dVuAwaCxdGl/une/\nQ6d2IYR4gNLSMvnzz+N4eTnw+OO3NiTMWwFXo+HVAeBqDJAzNRh7FUzRc56bKj3ry9/8iYZGfwbi\ngisYkuB6V0hbCRYdwf0gWPe7GaCnJELIGlj9MwTPgSPbICtTX2ZeG9x2gFldSJ4JKT/RnBbYYcce\ndlHfOg0fc1ieALVr6l1zdhjbb/z9XTl/Ppa0tMziv4FCFEHNmm4MH/4oJ05E8emn2x7YcffvjzA2\nIhpYuLAPNWu63XkjcV+Um2Dd3d2WF1+sT1hYLLNnH8i1TCl4vTvsngYtA2HZbnj0TWg0Gj76A7Yc\ngah4PRjPKT4Z9p+FX9fDS99CtWHwyBvw6V+QnKbv8/T38PtoqF6IWXizsgyMGxfM88//g729BcHB\ng+nSpcZ9vAtCCFF069adIzY2lb59AzExuXWMzncL9b7qr+XI/rI4Ho6n6znUaxszL25kPbHE8Bit\n8KWqXsnGDYX0TWD1JLis0FvWAS4ch08GQl9XeK+T3sIy7TkY8xgMrASLP4P0VDBxBpflep/2+NGY\nZ0XRiCakksphdZBudhBngJAMqOsPR87o/eurVnVC0+Dixfi8lyNEqTN16uN4etrz4YdbipR3vbA2\nbAilbds5xMWl8vvvvencWWKTB6lcfX8xYcJjzJp1gIkTN9KvX1B23/UbHqkKWz6Gtfvh6xWwZh+E\nnLm5XCmo4Kj/nJCiB+Q5OdpC35bwVHPo1gis72LOoqtXExk06G/Wrw/F39+VZcv6ExAgn1qFEKXP\njQmEevWqecuyE+f02Uq7ttZnCL1hejQoYLyxWoslhl3sxAlnWtNWL0z+AVIXgXlzcFoAylwP4JdM\nh1/e1lvQvWtB895Q2V///cxe2LQQfhkHW/6AKf+CozfYT4X44ZA4iQaOn7GJDRziIO1sGzMjBrYk\nwyM1YfdhOBkGVaroqefCw+OpXt2lGO+eEEXn6GjF/PlP8vjjv/HUU4v5778XiuX/VtM0vv12N2+9\ntRaAefOeZMCAOvf9OOL2ylWwXqmSPRMmtOS99zYyZsxafvqpxy3rKAVPNNAf1xNg/UHYdQrOR0JY\nJMQl6+t5uemBu28FqO0DTfz1YN/sHrIqrlhxiqFDlxEZmUSPHgH89luvWz5ICCFEabFpUxi2tubZ\nKQ9zWrpef+7b6WbZkVTYnQpd7MDPQi/bzn9kkUU7HtezvmRdhYRxoJzA+Q9QFnqg/v0o+OdrcPaA\n12ZC8165+6wzFIZ8BD+MgnW/wbh2MH0H2LwISV9C8mwc7SZT2dSLi1zgcetUwIqQVGhlnGz1VJj+\n/gBw5Urifb9fQhSH1q19+frrzowYsYrWrX9l7dpnCAqqcN/2Hx4ez6uvrmT58lO4u9vwxx9P06aN\n733bvyi8chWsA4wZ05zFi4/x88/7adPGl0GD6ha4ros9PN1SfxSHyMgkRo9ew7x5h7GwMOXLLzsy\natT/s3fe4VFUXRx+Zze9kUJIoSUEAoReQhEIHanSpSiCgKKIIHZRARULCDaafCpNlI4UAem9hCKh\nQxpJSCGk92Szu/P9cSekQ4CAlHmfZ58h994pO+zcOffec36nlZpBT0VF5ZElOTmby5fj6dzZs8Sc\nD9sPCVu6VwE1x7WKZ8lLyspkLrkEcAZbbGmA0gdnzAI5FezmgrayKNv0k/h41Icvd4KTW8kXZesA\nby8BUwvY/j9Y9imM+w6sX4fUyZC9Di9rbyK5To5pGC7aOpzNhlHKWCP0Ong4i4CiuLiM+71FKioP\njfHjfdHpDEyevIOWLX9lwYJejBjR8L7siNTUHH788TjffHOEzMxcOnXy5Pff++PubluOV65yNzw1\nPut5mJubsHbtYGxtzRg7dgsHDoQ99GvQ6Qz89JM/tWvP448/zuPr686pU68weXJr1VBXUVF5pDl/\nXmiRN2lSXEpWp4PjZ6FR7fzAUoB/0sEU6KFINQYRSDbZNKYJWrRgTBcuMJoqYPWKaBQdIlxfHFzh\ni+2lG+p5aDTw2g9QuRZs+hEiA8FisKjL3kg1qgEQSSR1zSE8Fyoph4yMFYowAImJWfd0X1RU/ive\neqsVa9cORqORGDlyI507L+fw4Yi7Pk5QUAIffLALD48fmDp1PzY2Zvz6ax927RqhGur/MWUy1iVJ\n8pEkaY8kSZmSJEVLkvS5JEm3dfiQJMlDkiS5hM+qEtr2lSTpvCRJ2ZIkXZIkaci9fqGyUKuWE2vW\nDMZgMNKnz0r27Al9kKe7hcFgZMWKc/j4zGfSpH+QZZmffurOsWNjStQpVlF5UnnS+pSniUuXRMrn\n+vWLL7dfDAZdLrQo4NKaYYTT2eBrCXbK/3AQgQDURRFgz/4L5AywGgOSEuyz7BPI1QkD3Lm4u02J\nmFsKlxijEbYuFDP0Jg1AdxhXWWhFxnKDGmYgA3oHsVtsArdcD1NScko5uMqjzNPepwwa5ENAwGv0\n6lWLffvCaNduCT4+8/n88wMcPBhebBBqNMpERKSwdWsgH3+8h6ZNF+HtPY9Zs46i0Uh88UVHgoLe\nZMyYpiUGkas8XO7oBiNJkgOwG7gE9AW8gDkIQ/+TMpzjXeBIgb8LCdlKktQWWA8sACYCPYGVkiQl\nybK8swzHvye6d6/JypUDGT58A927/8G333Zl4sSWD+RHmZaWw7JlZ/nuu2Ncu5aMqamGCRN8+fTT\n9lSqZF3u51NReZR5UvuUp4WQkCRATHoU5co1sa1fQCjiQjYYgGaW+WURhGOGGe4o7i4528XWYpDY\nJt6AQ2vBsyH4PX93F/hMP7CuAEf+gle/A7PWoD+Pjf465qbmJJJIZeXNl6VI6SamgI2NcKbPyNDd\n3flU/nPUPkVQo4YDf/89nMOHI1i48BTr1l1i2rT9t+otLEywsTHDaJRJScnGYMiXuDM11dC9e01e\neKEBgwb5YGHx1HlJP9KU5X/jNcASGCDLciqwS5IkO2C6JEmzlLLbcVWW5eO3qf8UOCjL8kTl732S\nJNUDpgIP9CEYONCH3butGThwDZMn72D9+svMnt2Vli3LOItzGwwGIwcPhvPHH+dZvfoi6ek6zM21\njBvXjI8+akv16mp6XpWnlie2T3kaiI5OA6BKFbtideHRYlujan5ZkGL71lUCS/XoiSeeqlRDk7e4\nmw073UsAACAASURBVHtMSDSa1BN/n/oHjAboOqpIMKlyjOxszi5fjo2rK959+hR2HzQxhcad4cgG\niLsO1vUBkPRXqGBagVRScFbefKkaMDOF1HSwtBSFmZmqzvpjiNqnFKBt22q0bVuNefN6sG9fGEeP\nXufq1QRu3EgnI0OHRiNRp05FqlWrQN26FfH1dadt22rY2t6FhJ3KQ6UsxnoPYEeRH/sqYCbQHthy\nryeXJMkc6IgYqRZkFbBEkqQKsiyn3Ovxy0K7dtU5f/51Xn99K3/9dYVWrX6jQwcPRo9uTO/e3jg4\nWN75IApRUakcOhTB7t2h/P13ILGxIlCpalU7PvigDa++2kydSVdRecL7lCedhASxnF6xYvEMb7EJ\nYutSYNI9UrF9q5mKbQopyMg4osjMyVlgCAOzjvmG+eVjYtuoY7FzZCUm8kfPnkT5+wNQd8AABq9d\ni6Qp4NVZq5kw1q+dg0bKyMEQjRV23OQmlTUGQEuKAawsISOLW5kYH3ZGSJVyQe1TSsDBwZIBA+oy\nYEDd//pSVO6TshjrdYC9BQtkWY6QJClTqbvTQ7BEkiRH4CawEvhYluU85ykvRNzRlSL7XEYsX3kD\nJ8twjfeFi4sNGzYM4eDBcL744iC7d4eyf38YkgR16zrTqlVlvLwccXGxxtraDEmCzMxc4uMziYxM\nJTAwkXPnYm/NOAE4O1sxdmwThg1rQIcOHk+lz5fRKBMZmUpoaBIxMWmkpOSQk6NHkiRsbc1wdbXB\ny8sRLy8HtNqnLtb5aeaJ71OeZDIydEhS/kx0QdIUIRU7m/yyZMX2dVC8hzMR+rfWKBMXhptiqymQ\nOS42TGwrF0+8cvyHH4jy98e7Tx/SoqO5vGED4QcP4tGhQ36jioqBnhANkrf4t5yMGULk3VyTC2jJ\nlsXMeq4etFrRRxsMxjvdApVHD7VPUXmiKYux7gAkl1CepNSVRg4wH7FElAp0AD5A/PD7Fjg2JRw/\nqUh9qUiSNB2YBuDmdge1gDvg51edXbtGEBiYwLp1l9ixI4SAgBssXhx3x32rVLGjb9/atG5dhU6d\nPGna1O2pM0DT03UcOBDGgQPhHD8eSUDADdLS7uz/aW1tStu21ejVqxaDBvnc0jtWeWJ5avqUJxGD\nQUar1ZSoXGVQDHPTAm8WveIWa6Y0NyIaaW+9fpQ+QiqwiqnLErPsFsVXItNiYgDoOmsW1/buJeb0\n6Vtlt7BQZv1zc4ReO4CsR6u43WgQF2WUQasR8ah5EypFM1WrPBaofYrKE80DiyCQZTkGmFCgaL8k\nSbHAAkmSGsmyfLaczjMdmA7QvHnzculmvb2dmDKlHVOmtCM310BQUCJhYcnEx2eSni5eLFZWpjg6\nWuLubkvNmo7Y2z+dSYzS03Vs3HiFVasusGtX6K0lZI1Gom7ditSvX4maNR1xd7fFwcECc3MTjEaZ\ntLQcoqLSCAxM4OTJaHbsCGHHjhDefnsngwf7MHVqe+rUUTO4quTzOPcpTxJarYTBYESW5WIGu4ny\nRskt4PZtojTRKXdSg5hiN5DXKM+YLqBWYWYprObsjGIGu627mIHf8MIL6LOzC5XdIluZ4jezADlv\nMGCCATFrbpDFRWkkMBiF6qPRKC5QVc99elD7FJXHhbIY60lAhRLKHcgfWZaVdYho6mbA2QL7Fz1+\n3kj1bo9f7piaavHxccbHx/m/vpRHivPnY/npJ39WrrxARkYuAA0aVKJ3b286d/akZcsqt9QVykJU\nVCobN15h0aLTrFx5gTVrLjJxYku+/LITlpamD+prqPw3PNV9yuOOtbUZsixcAa2tCz/jtopdnVog\nCWie+0uSMutujZj1zkAxqLWKBKQxKn8nVyW1aGQg1GxS6BytJ0/m2p49XD8ixDvqDRlCdT+/whd5\nU9GYdnQHWfkvl+zRKbP4Oln0KZaSkJo0NeGWMsbTtiL6hKD2KSrFyMrK5eTJaE6diubixZuEhCQR\nFZVGYmIWGRk6ZFko5Dg4WFC5sh21azvRtKkbfn7VadCg0iOV96YsxvoVhM/XLSRJqgpYUdyH607I\nRbYhQK5y/AMF2tUBjKCI8ao8Mhw6FM6MGYfYuTMEAA8Pe959txHDhtWndu17nwmvXNmON95owfjx\nvmzadJX339/F998fZ/fuUDZvHoaHh6qe8wSh9imPMU5Owl0lPj6zmLFeSYkZvVFA+K6KMtaOEGN6\n7KiAhEQiiaJAsgStJ+SeF7PpkgR1W8O2RXB2bzFj3cLenpf27CHu4kUy4+Op0bVr8Zdq8L9i69kA\nDJvEv7WVyeQGFliQahQjCDstZGaBtSXk5IiZfnPz20pzqzyaqH2KCgBXr8azYcNltm0Lxt8/ktzc\n/BgUSRIxim5uNrfiD7Oz9SQkZOHvH8nRo9dZsiQAEMIgQ4bU45VXmuHtXVym9mFTFmN9O/CeJEm2\nsiznRVAOAbIo/MMtC4qILqcBZFnOkSRpHzAYWFSg3RDg2KMaYf00EhBwgw8/3M2OHcJIb9++Ou+8\n05qePWuV60yUJEn061eHbt28eOedHfz882latvyV3btHqImjnhzUPuUxpnJlEVMSGZlaTILWQ5FN\nD72eX1ZLsecvK94oJphQEWduEIMRo5BvNH0Gsv8A/QUwbQC+PUBrAruWQv/Jwk+lACbm5rg1bVry\nBebqIGAPuHiAc1VIOQ+AbFKHFK5ijz03FA+cCkYxs17BFrKyRGFJgbMqjzxqn/IUk5KSzYoV51iy\nJIDTp0X8ikYj0bSpG23bVqVVqyo0aOCCl5fDLdWnouS5PPv7R7J79zW2bQti9uxjzJlzjMGD6zFj\nRscSc0s8LMrSK/2MkCzaIEnSTKAGwvfqu4IySZIkBQMHZFkeo/w9HbBFJBpIBfyA94ANsiyfK3D8\nLxB+Yj8AGxHJBnoC3e/rm6mUC8nJ2UyZsoeffz6FLEPnzp588UVHWreueued7wMrK1MWLuxNvXqV\nePPN7XTt+juHD4+mZk3HB3pelYeC2qc8xnh5iWcwKCiRNm2qFaqro3ivXAzOL6tvLl40Jwu4pFej\nGqe5SRSRVKUaWPQQxnr2WmGs21cSyZD2/QkHVkHH4WW/wCMbIDMVnh0jptJyjwKWpJtUIYccHHHk\ntGKsmyueOI4VuBWPVHS1QOWxQO1TnkIiI1OZM+cov/56hvR0HVqtRM+etRg6tB49e9bCyam4vGxp\nFHR5fvnlJuTk6Nm06SqzZh1hzZqLbNhwmY8/bsfHH7fD1PThr77dcUpUluUkoDOgRcgffQZ8jxLZ\nXAATpU0eVxD6pkuAbcBw4FtlW/D4hxEj2S7ADuA5YPijlBXsaWXDhsvUqTOPhQtPUadORf755wV2\n737pgRvqBZkwoQVz5/YgNjaDvn1XqdkFnwDUPuXxpm5d4e528eLNYnU+XmBuBv4FzBwrjcheeioL\nUhS/dW9qA3CZS6LAvB9INpD5G8giaJSRM8DUHBZNzvdBvxPZmbDsY9Booc94MESC/iKYtSNGEr45\nLrgSqgMJMFG8jV2cxOwcQIUKamKYxw21T3m6iI/PZNKk7Xh5/cQPP/hjb2/BV191IjLybbZuHc6I\nEY3uylAvCXNzE55/vh4nT77CunWDcXOz4bPPDtCx4zJiY9PvfIBypkzrfbIsXwI63aGNR5G/VyGS\nBpTl+BsRo1WVR4D0dB1vvLGN5cvPYmFhwldfdeKdd57BzOy/8eWcMKEFgYEJzJ17gjff3M7ixX3v\nvJPKI43apzy+NGwo3NH+/fdGsTozM2jdGA6chPgkqKiE4PWwAf8s2JYOwypATWphgQVnCaATXTDR\nWIPV65DxLWQuAutJIsj0lTmwYAJ80h2+3AnOt8kubTSKtjGhMOg9cK8J6d+JOot+RCAM/ipU5XIO\neJhCXLioruKSn+zJ0bHsifBUHh3UPuXJx2AwsnDhKT79dB/Jydl4eNjz6ad+vPhiwwdmn0iSxMCB\nPnTpUoNx4/5m9eqLtGz5K3v3jqRGjTuqdpYbati7SiEuXrxJ8+b/Y/nyszRv7k5AwDg++qjdXT8I\nqZmw41/4ag2M+A78PgSfN8BzLHi9Cs0mQ/+vYMpy2HICMrJvf7zZs7vRtKkbS5YEsGdP6H18QxUV\nlfuhQgULfHycleCt4tk+u7cVcaJ/788vG2wntssVpWpTTGlCU9JI4zzKNLz1eyDZQ9o0MChO733G\nw8B3IOIyTGgKB9cIo7woKfEw60XYuQS8GsOL00HWQ+ZCwAwsBhFCMBo0mOVW56YBGllAiHKaGlXF\nbB2As7OaZVpF5VEjMDCBtm2X8Oab2wH4/vtnuXp1AqNHN3koE4kVKliwcuVAPvusA+HhKXTosJTw\n8JKk/R8MaiSNyi02bbrCiy/+RXq6jrffbsXXX3e5q4fgRhKsOQzrj8KRy0K/OA+NBhxtwNIMcg1w\n+Tr8G5I/TWFpBoPawOTnoIlX8WObmWn55Zc+NG/+PyZP3sGZM+NUiTUVlf+Ijh09mD//JEePXqd9\ne49Cdf27wIffwZp/YFR/UeZjDq0sYUcGBOVALXNoTRtO4M9e9lCfBphqncFuFqS8CkmDwekASOYw\n9ltw8YT/TYavhoispq36QsXKwk0m8BQcXif81Ou0hC+2iaRIGQvAEAxWr5GiNSWKSDzw5HSWyInh\nawFXronr8/aAMwdFXKKbmw0qKiqPBrIss2RJABMmbCMrS8+QIfX48cfuuLjc33OqN4pJBRNN2XMr\nSJLE1KntMTfX8uGHe+jdeyVHjozGzu7Bu86pxroKAD/95M9bb/2DpaUpa9YMYvDgemXaT5bh4EX4\nfhP8fVIY6JIELb2hU0OxrV8dqlYsnNVQliEuBc6Fwb7zsPYI/L5PfIa2g+/HgmuRFaamTd0YObIx\nS5cGsGrVBV54oWH53QAVFZUy06tXLebPP8nGjVeKGeveHuDbAHYehYhoqKbkK3rLEYZGwdcJsNgd\n7LGnFc9whEPsYy/deBYsx0LOARFsmvQ8OKwVGUifewOadYNVX8HB1bB+duELcnCFEZ9B7/Fgagb6\na5D2MUi2YDOd00LYg4Y0YrESVOpnDRuvin7JuzpERIg4xCpV7B7gnVNRUSkrOp2BN97Yyq+/nsHe\n3oKlS/vx/PNls03ySMiEfWFwLBLOxUJoMsSkgSL+hIkGKlpBDXto6gYdPKBbDbC9jf39wQdtiYxM\nZd68k7zyyhZWrRr4wDXZJfkJyq3cvHlz+dSpU//1ZTxWyLLM1Kn7mDHjEK6uNmzdOpymTcuWDnl3\nAEz9E44pKrZNvWBUZxjcprihfSeMRth5Bj79A04Fg5MtrHgbujcr3C40NAlv77n4+Dhz9uxrt31A\nJEk6Lcty87u7EhWVfNQ+pWR0OgOurrOxtDQlIuKtYqtcSzbA6E/gvdEw611RZpChUShczoEzNaCh\nBeSQwwLmkUwSI3mZGniJTKaJz4FuN5h1Avs/QVtAtjUnCy4fg/QkyM0Rvum1mufLOxrjIaGDCCyt\n8Cs6qxF8z2wMGHhb/gDvIDPSjBDlCY4tRVDsv+vBz28Jhw9HkJ39SakrimqfonK/qH1K2UhJyaZf\nv9Xs3x9GkyaurF//PJ6eZTMsErPgj/Ow+iIcvZ4vmA/gZgPutmBnLjIYZ+ZCbAaEJ4s+CsDCBPrX\ngXdaQTP3Ek+BXm+kQ4elHDlynT//HMCwYQ3u6XuWtU9R/QieYmRZZsqUPcyYcQgvLweOHRtTJkM9\nOBp6fQ5dpwpDvW9LODITTn8Pb/a+e0MdxHu2ezPwnw0/vQoZOdD7C/itSKx9jRoODBrkw/nzNzl4\nMPzuT6SionLfmJlpGTzYh+joNHbvLh5DMqwXuDnDgpUi0BRAK8FsF5FFZlyMeDGaY85ABqFBw2pW\nEk+8SJLkuBnM+4JuL8Q3gswVICt+deaW0LgTtB0oJB1rt8g31HPPQHxrYahbTQKrMRzlCBlk0JJW\nnM4y47oenrOF81cgRycCYkH4xHp42P9ngfQqKiqCuLgM2rdfyv79YQwYUJfDh0eXyVC/Gg9jt4D7\ndzDxHzGb3qYqzOgIB0dCygcQ/TacegX2vgS7R8DR0RDyJqR/BEdfhml+UK0CrLwAzX+FgWsgogQl\nfRMTDcuW9cPS0oRJk/4hOfkOgXf3iWqsP8XMmHGQb745gre3EwcPvnzHLKF6A3yzDuq/CdtOQccG\nwkDf+DE8U7d8rkmjEQb/vhlgbw1j58HKIiktxo/3BeDXX8+Uz0lVVFTumrFjRVKiuXNPFKuzMIcP\nx0JGFkybl1/e3QaG2MHxLPhKyXJajer04TmyyGIJvxJPnDDYHf4C29lgTIaUERBXV6i75F7MN9wB\n5BzQHYLkkRDfTPipW08Bu++I5QYH2IcNNrShHb8oA4cXK8Ce4+Lffs0hISGT2NgM6tS59yzMKioq\n9098fCadOy/n7NlYXnutGWvWDMLKyvS2+0SnwejN4LMQfjsDVSvA7K4QNRkOvQwft4N21cVsemlY\nmEDrqjC9A1wZD7tehGeqwIYrUG8hrLpQfB8vL0c++cSPuLhMZs48fH9f/A6objBPKYsXn2HMmM14\neNhz6NDLd/TTjIiD4bNF4KirA/z0iggIvZ2bViYGzpHJRTKJIId4csnCiAYJe7RUxZx6WNECG+xK\nCJ84dw38pkBmDhz8ClopyaRlWaZmzbnExqZz8+Z7pT7I6pK1yv2i9im3p1074ToSEDCORo1cC9Xp\ndNCwPwSFg/8qaF5flCcaoFEIROthc1XoJRKicoTD7GA7VlgxmCF4UVNU6MMg/XPI+gNQ8ixI1qCp\nBBjAEIPIBg+Y1AO778C8G+mk8xv/I4EEXmAElrl1qBUM1U3hihe0fUHowccegovnwujQYRnvv/8M\nM2d2LfX7qn2Kyv2i9imlk5Gho2PHZZw8Gc2ECb789FOP27q6GmWYewI+2QfpOqjnDJ91gH61oTz0\nJ2QZlp4Vs/TpOvi0nTh+wUvKysqlVq25JCZmERb2FpUq3Z2alOoGo1Iq+/eHMW7c3zg5WbJjx4t3\nNNT3noWmbwlD/fm2cHEeDG5bsqGegYH1JPAKwbTmPKMJZg7RrCWBfaRynHSOksY2kllELBO5RlvO\n8yahnCSt0LEaesL6D8WM/vA5kCaU1ZAkieef9yEjI5edO0PK67aoqKjcJVOmtAVg+vTiGd3NzGDh\nVBGPMmoKZCmrxI5a2FAVzCQYEgnHlOe6DW3pS39yyGE5S9nBP+jQgYkH2C+GSpFQYTFYjgRtTZB1\ngASmTYVGu+NOqHgWzLuRQjLLWUICCbTDj9rUYXoc6GT4pCJE3YBjAdCumdCCDwgQmvFFBxwqKioP\nB6NRZtiw9Zw8Gc3IkY3uaKhHpUKn5fDWDjDTwqJecHYcDKx7e0NdRiabbJJJIolEMsjASAlysAgb\n5+XGcGos1HCALw7BB7sLt7G0NOWjj9qSlaVn7lz/e/nqZUJVg3nKiIhIYfDgtUgS/PXXELy9nW7b\nftE/8MbPwj1l4eswrnvJRvoNdCzlJutJIEP54dfBktbY0ghramBOJUyxRIsRmUT0XCObf8lgDym3\nPn7YMY2quCFSfnduBB8OhK/XwccrhD87QL9+dfjmmyP8/Xcg/frVKdd7pKKiUja6d69JmzZV2bjx\nCvv2XaNjR89C9R1bwvhhwnd94lfwv89E/+FrCSsrw6BI6B4hZtjbW0MzmlOJSqxjDUc4xAXO0Z6O\nNKKxkHa0ell8SkFG5gLn2MoWMsnElxZ0oRsHMmBpMjQwhxcqwNdKGpwXeovt8eNRAPj6lhJNpqKi\n8kCZPn0/W7YE0qVLDX75pc9tDfWD4TBoLcRlikDQn3tBaRPaBgyEE04wgUQQQRw3ySKrUBsTTKhI\nRarjSR3q4EkNNAXmsmtXhMOjoNPv8O0x4WbzZov8/V9+uQlTp+5n0aLTfPKJH+bm5W9aq24wTxG5\nuQb8/JZy/HgkCxb05PXXfUttK8vwxWqY9idUtIONU6CNT/F26RhYxA1+Jw4dMi6YMhgn+uJIZcqu\nPXqWDH4gGn/SsUHDt3jQngoA5ORCgzch9IaY1a9dRWQyc3HJV6Mo6cFWl6xV7he1T7kzp05F06LF\nL9SuXZGAgHHFXlRZ2fDMcAi4Aj98BJNG5NetSYEXooQqw89u8LISNqNDx372cZyj6NFjhRU+1KMW\n3lSjOtbkv5mNGEkikWCCOM0pbnADLVp60BNfWnJTL9EkFG7q4bAHNDUBz26Qmg5R+8HWWqZy5e/Q\n643Exr6rKkypPFDUPqU4u3eH0q3b73h42HPq1Ku3zSK84pzwT5eB77rBBN+SJxCTScKf4wRwhgyE\nXquEhBNOOOCIFVZISOjQkUwycdwkV3Gns8eedvjRlOZoyQ84D0+Glr9BfCYcGiV83PN4992dzJlz\njHXrBjNwYAnGUimUtU9RZ9afIj7//ADHj0cyfHgDXnvt9r+NaX8KY92jEuz8HGqVMOG0m2RmEMlN\ncnHFlDdwow8OmN2Dd1UjrFlMTTaQyAyu8wahfEk1+uKEuSl88xIM/AamrYRV74FWq6FjR0/WrbtE\nSEgSNWs63vU5VVRU7p/mzd15/fXmLFhwiunT9/P1110K1VtawOb50GIITP4G7G1hZD9R93wFcNKK\nGfbR0bA3A350BUetGd14lla0wp/j/MtpTnGSU5wEwAILLLFERiaDjFsvWQ0a6tOALnTFESfi9dA1\nHGL0MKsStLKCX9ZC9E146yWws4ELF+KIiUln2LD6D1wrWUVFpTDJydmMGrURrVbD6tWDbmuo/3wK\nXt8G9hawYTAUWcgDII1U9rGXfzmNESNWWNGCltSmLtWohnkpk4h69FwngnOc5SwBbGEzJzlBfwbi\nhjCAqtvD6oHQcTmM3CTcbiyVkLmRIxsxZ84xVqw4f1fGellRjfWnhFOnovnqq8NUr16BhQt73fal\nNGu9MNS9XGH/V1CliEBCNka+IpJ1JGCKxBu4MgYXLEow0mVkcggji0ByicVIBqDBlIpY4IUlddEo\nD4+ExECcqIkF4wjhYyKwx4T2VKB/a2hSQ2RI/XoEeLqCn1811q27xOHDEaqxrqLyH/LNN134558Q\nZs48QqdOnnTtWjgNcVU32PELdBgp9Nd1ufDKYFHX2QZO1YBhkbAiBXakw4xKMNoe7KQKdOVZOtGF\nSK4TQjAxxJBEItlkI6GhIhWpiDMeeFCbutghYnAuZsPASLiqg/EO8K4TJKfC1LlgZSk04EFkbgaR\n6ElFReXh8sEHu4iKSuOzzzrg61u51HbLzgpD3dlKSC42dClcLyNzkhPsYgc55FCRirSjPQ1oiEkZ\nTF0TTPCkBp7UoBNd2MMu/uU0v7CIvvSnEULjtb0HvNUSvveHmUeEegxAgwYu1KvnzPbtQaSn67Cx\nMbvHO1La9ak88ej1Rl55ZQtGo8zixX1vmxr3zwPwwTJhoO/9srihHoOOCYRymSzqYMksqlOTwiNh\nGSNpHCeJv0nlEHoSSj2fBkvs6EAlRmCtPAyNsGYRXowiiHcJYwN1qCqZM7kvvPQ9LNoB34yEZ54R\na1D+/pGMGtX4Hu+OiorK/WJra87KlQNp124JQ4eu58SJsXh5FR5AN6wNuxfDs6/Aq9MgLAo+fxO0\nWvAyg6OeMCcBvogTOuzfxIuspy/Zg71WS3U8qI7HHa8lzQA/JMLX8ZAlCyN9ZiWxVP7ut3AjHmZM\nBPdKov2aNZcwM9PSq5f3A7gzKioqpXH8eCT/+9+/1K9fiQ8/bFtqu10hMGYzOFgIffT6lQrXZ5LJ\netYSRCAWWNCH54q5sNwNttjSjwH4UI91rGE9a8kll+YI1+HPO8KfF2D2MXi9ObjYiP369avDl18e\nYteuEPr3Lyc9awVVDeYpYOHCkwQE3GDUqMZ06lTCupHCqSAY/RPYWcE/06Gac+H6QLIYTiCXyWIQ\nTqzEu5ChLqMngY1cpg8hjCWRjYCEA71w5z08+REvfsWLRVTjC5x5AVMqkcx2AhlOCG+gIwYQBvt0\nqpKBkU+IwIjM4DbgYAPL9gqFmAYNXDAz0/LvvzcewF1TUVG5G1q0qMz8+T1JTMyie/c/iIvLKNam\nqQ8c+QO8qsJX/4Me4yAmTtSZSPBBRQiqKWbCo/UwKRZcAqF3BPyQACezIKsE4YZ4PWxNg9djoEoQ\nTI0DOw2sqwLfugif+CUb4Lf10Kh2/qz66dPRnDsXS48eNbG3t3iAd0dFRaUgsizz7rsi6+GCBT1L\nTUZ2LQmGbhAKL1uGFjfUE4jnF34miEC8qMmbTMKXlsUNdV0ahP4FR9+Hrc/Bulaw1hc2doZ9r8Cl\nxZB5s9Au3tRmDK9ihRVb2MQVLgNgYwZT/SAjF747nt++Z0+xOrdrV/FEcfeLOrP+hJOUlMXUqfux\nt7dg1qwupbdLh0EzQaeHDR9BvWqF66+QycsEk4KB93DnZQqvQaVzmut8QTaBSJjgSF+cGIQ1TZBu\nMyYUPqeniWEuqezjCv/iyU/Y4stzOLKHFHaTwmYS6WfmxJC28PM/cOACdG6kxcfHmfPnYzEYjMVS\nnquoqDxcxo5tSmhoEl9/fZguXX5nz56XqFjRqlAbbw84sRpe+gi2HoD6z8G378Ko/kJ1ys0U5rvB\nNGdYkgx/psDWdPHJw1kLthqRDTXJACkFDHhXE3jPCSY6gp3yvt64G8ZNB3s7WP+jkJUEmDdP+MC/\n+mqzB3ZPVFRUirN9ezBHjlynX786tGtXvcQ2eiMM2wCJWfBLb2hTxC65SSxLWUw66bTDj850LaTi\nAkDsCTj7I4SuB0NOfrnGFDQmoM+CqL1w6VeQtFCjP/hOAyeRGMIFF15iFL/xCxtYx3jexB57RjcR\nUo6LTsO09mBlKtSkrK1N2b8/rBzvlHK55X5ElUeKb745THJyNlOmtMXZuWRtI1mGcfMh/CZMHQI9\ni8SehpHNaIJJxcAMqhUy1I3oiGI2QbxENoE4MgAfdlCdr7Gh2W0NdRB+6jY0pyZLqcJUDGQQe8qG\nsAAAIABJREFUwhhSOYyExIdUwQyJucSgw8jgNmK/jcpotl49Z7Ky9ISFJd/zPVJRUSk/vvyyE+PH\nN+fcuVg6dFjK9evFc3U72sOWBTBP8V8f8ym0GgZ7j4v+CKCSiZhpP+sFoTVhubuYce9oBQ5ayJbB\nIENVU+hlA59WhP3V4Xot+MRZGOqyDHNXwKDJYGYKG+eCl/LCDw1NYsWKc9Su7UT37jUf4h1SUVGZ\nMeMgAJ9/3qHUNrOOgH8UDK8PSsLkWySReMtQ70UfuvJsYUM9LQK29Yd1LSHoT7DzhOafQr99MCYe\nXsuBcZni8/wZaPMdODWAkHWwuhH4TwWjHgB3KtOT3mSTzUY2ICNjYQJjm0BKDqy9JE5paqqlVasq\nXL4cT1JSYXnI+0WdWX+CuXkzg3nzTuLubsuECS1Kbbf2iPi0qQufDilcl0gurxJCMgY+oyoDyNdl\nzyWBa0wig38xpzrV+AobmhQ/QUYihJ2AuBDIShajWYcqUK05uHiDJCEh4cxQLKhOCOO5xiRq8Tvu\n+DCUiiwnji0k8Vw9J2wtYftpcei6dYVT/ZUr8cV8ZFVUVB4+kiQxb15PTE21/PijP888s5hNm4bS\ntKlbkXbwxnB4riO8NxtWb4fOo6FlQyHvOKArmCsz4J5m4jPCvuzXERwutN23HxKJjzbNg2cKdE9T\npuxBrzcybVp7NBpVBUZF5WHh7x/JsWOR9O7tTYMGLiW2uZYkZq5dbWB+z8J12WSzguWkk05PetGS\nVoUbBP4J+8dBbjq4tYEWn0PljiVrPJpYgnNj8Wn0FoRvhYMT4NQXEHcauq8DE0ua0oyLXCCYIK5y\nhTrUZVQjmHEI/jwPIxuJw7VqVYU9e65x4kQUzz5bfpMA6sz6E8y8eSfIzMzlww/bYJmnL1SE1EyY\n9AtYmMGSSSLYKw89Mu8QRiQ6xuPKYPKjTXOIIpDhZPAv9vSgNusKG+q6LDj8C8xuB+9VhHk9YPUE\n2PwJbPwQlrwIn9WBad6w53vRHrClNR58i5FswngHI1mMohJa4A/iMDGR6dQQQm6IlYDatcU1BQaW\nHsSqoqLycJEkie+/f5aZM7sQGZlKmzaLWbz4DCXl9ajqBqvmCNeYvp3A/xwMfw/c/GD0x7BuByQV\nn5wvkdxc2HEYhr4DdXoLQ71zKzj7V2FDfdu2IFavvoivrztDhtQvp2+toqJSFhYuFDrzkya1LLXN\nlL2QrYc5XYVUY0H+ZjNxxNGKZ2jFM/kVsgzHPoRdL4CkgU6Lof8hqNKpZEO9KJIEHr1hyFmo1h3C\nt8H2gWDUIyHRg55ISOxhNzIyXo7g6w57wyBZydDcvLmQeTxzpnxj6dSZ9SeUrKxcFiw4iaOjJaNH\nlzDbrfDlGriRBJ8PL66lvogb+JNOZyrwBvlpuHXEEMRL5BKDC6/hxptIKA+C0QBHl8CWTyH1hvjx\ne7UF7w7g6gPWjmDIhYRrEHQQzm+BdW/Dgfnw0lKo2RZ7uuDMS8SxjBjmU5l36UAF9pDCFbLoUN+K\nTf5w8CLU93IAIDg4sZzvoIqKyv0gSRLvv98GHx9nXnxxA2PGbGbr1iDmz++Jq6tNsfa+DWDjPAgK\ng/+thT+3wpK/xEeShK97g1rgWQUqOQr5RVmGtAyIjIVLIXDiHGQoq88Na8Onr8HAboXf05GRqYwa\ntRFTUw2//facOquuovIQSU/XsWbNRWrUcChV8OLiTVh1EZq5wdAiY+lLXOQcZ6lCVZ6le36FLMOR\nt+HsD2DvDb22iO29YF4Bem6Ebf0gYjuc/AxafoEzlWhAQ85xllBC8KImfbzhZDTsDoVBPtBQ0ZQ8\nf/7mHU5yd6jG+hPKmjUXSUjI4sMP22BtXbLeZ2Q8/LhFqL68279w3SUy+ZkbuGLKDKrdMsYNpBHC\nK+QSgxuTcGVc/k4J4bDsJWGEm1lBtw+g45tgX4p2aocJkJ4A/3wJe3+EHzrByGXgOwx3JpLCHm6y\nnIoMo68SbLqNJNrVFQFrx69Cn6HCWA8PL+PUm4qKykOld29vzp59jREj/mLDhsvs3XuNGTM6Mm5c\nc0xMii/u1vKAb9+Dme/Av5dg20E4cBJOXYSr125/Lh8vMZM+pIeYSS86mZaQkEmPHn8QF5fJ3Lk9\nSl2CV1FReTBs2xZEVpae4cPrlzpQnqPEpH3qJ5Sc8sgll21sxQQTBjCwsOLLuZ+Eoe7gI/zSrYrI\nxgDXjx3jwsqVhB84QGJwMEa9HhtXV9x9fak/dCh1+vVDY6KYxVpz6LYS1jSFU1+CZz+o1IwWtOQc\nZ/mX03hRky6eMHU/7AsTxnr16hWwsDDh6tX48rlhCmVyg5EkyUeSpD2SJGVKkhQtSdLnkiTdVsBS\nkiRfSZKWSJIUrOx3VZKkaZIkWRRpN12SJLmET/fSjq1yZ5YsCQBur3IwawPk5MK0oWBZQHrdiMxn\nXMcAzKAaFZQxnYxMGB+QTSjOvFTYUA85Al83E4Z64wHwWRD0/6Z0Qz0PGycY9B1M2i0M/CUvwoVt\naLDEjQmAnpssoR12WKJhDyk08gQTLZwOBnt7C2xtzbh+PfUe75TKf4HapzxdVK9uz/79o5g/vyey\nLDNhwnbq11/A6tUXMBhK0GJEKMM0rw9Tx8OeJZDsD1H74eifwv985WxYPQe2LoTT6yDtJFzcAj99\nDG2aFjfUw8OT6dhxGRcu3GTixBa88Ybvg//iKg8NtU95PPj770CAUnXIk7Nh5QXwcoA+RSbG/TlO\nKim05hkqUkBbOvYkHH0XLCvBczuKGerxV6+ytEMHFj/zDCfmziUxOBgnb29cmzTBkJvL5fXrWTt4\nMD83bkzUyZP5O5rbQ8dfAVlIPgJVqYYTTlzhMjp0NHMHcy0cjRS7aLUaPD3tCQ1Nuq/7VJQ7zqxL\nkuQA7AYuAX0BL2AOwtD/5Da7DlHazgSCgIbAF8p2YJG2KUDRH/3lO1++Sklcv57CwYPh+PlVx9PT\nocQ2Canw604xqz6iY+G6v0niPJn0xJ5nlGyAAPH8QSr7saU1lXkvf4fLu2FhHzDoYdhCaDeuRP8w\nWZYx5uYiaTT5o9c8aneEiTvhu/aweDhMOYNDxZ7E8BOJ/IUbE2mFLftIIcFUR50qZlyIAKMR3N1t\niYlJu+f7pfJwUfuUpxONRmL8eF8GDqzL1Kn7+O23Mwwduh5v7/1MnNiCESMa3TZhmySJREbuxSfM\n7sj69Zd47bWtxMdnMmGCL99/3/22WZxVHi/UPuXxQJZldu4MwdXVhiZNXEts89cV4as+unHhWXUD\nBo5xBDPMaItffoXRIIJJjXro+ifYVCl0vItr17Lp5ZfJzcigZo8etJw0Cc9OndCa5sfx3bxwgeM/\n/MCZxYtZ2r49z69bR62eSlRrlU5Q7VmI2AE3jiO5tqIu9TjMQa4RSm1tHRq7wukY0BnATCsmJy5f\njictLQdb29L7tLuhLDPrrwGWwABZlnfJsvwz8BnwtiRJdrfZ7xtZlv1kWf5FluX9siz/BLwHDJAk\nqaiopl6W5eNFPqpfwz2yYcNlZBmGDq1XapuleyBLB5P6gGkBu1mPzHxiMEViMvmz4jqiieZ7THCg\nOt8g5S0/RfwLi/oJf7HXN4Pfa4UM9ezkZPznzmVZp07MdHBghrk5M8zNmVenDv+89RZxlwv0dR4t\nYOgCyEqBtW8hYYITz2Mki2R20Arh53qKdOpVg4xsuB4Prq42xMVlkptrKJ8bqPKgUfuUpxgXFxsW\nLerDlSsTGD26MWFhyUyYsB03tzmMGPEXW7ZcJSsr977PI8syhw6F07Xr7wwatJb0dB0LFvRk7tye\nqp/6k4fapzwGhIQkERubQfv21UsdLG+6KraDfQqXB3KVNNJoQjMsC2ZND1oF8Weg9gio2rnQPlc3\nb2b90KFIGg0DV63ihW3bqPnss4UMdYBK9evz3K+/MmzLFgDWDBxI3KVL+Q0aK5OTl38DwAuh8hJG\nGCASNemNkBc6V7myLQDR0eU3iVgWY70HsEOW5YJ+BqsQD0b70naSZbkkh50zyta9hDqVcmLLFrHM\n1K9fnVLbLNkDZiYwslPh8p0kcx0dA3GiMvm+7lHMxkgW7ryPad7yU2YyLOoPukwYsxLq97jVXjYa\n8Z87lx89Pfln4kTC9u/H1s2NGl26UKV1a9JjYvD/8UcWNmjA3k8/xagXeqa0HgW1/ODcZri6Dwd6\nAZDMLhohdOLPkoG38gsKioZKlUR5QkL56pqqPDDUPkWFmjUd+e23vly/PpkZMzri4mLNihXneO65\nVTg5zaJnzz+YNesIBw+Gk5wntXAHcnMNnDgRxYwZB2nY8Gf8/Jaye3co3bp5ERAwjtdfV11fnlDU\nPuUx4PTpaEBkOy4JgxH2XoOajlDLqXDdRS4A0KSoPHTAHJHMqMXnhYqTw8NZP2wYJhYWjNi5k/pD\niuhSl4B3r14M+OMP9NnZbB4zJl+9qnIHsHKF0I0gG6lCFSQkohC+L96KanSesZ5nk8TFZd7xnGWl\nLAGmdYC9BQtkWY6QJClTqdtyF+drjUg6F1Kk3F6SpHigAnAB+EKW5Q13cVwVhexsPYcPR9C4sStu\nbrYltrkYIT79W4FTkTmHPxG5v18q4A+WxVWS+QcrGuDIc/mNV78JiRHQaxo0zo9Q1WVksHbwYIK3\nb8fCwYHOX39No5EjsXXL11k25OZyddMmdr77LodmzCDh6lUGrlyJRquFAbNhZgvYORPz2v9ggTfp\nnKA2EiaI4NduSlxY2E1wdBSj7KSkrBJVJlQeOdQ+ReUWlSpZ8/HHfkyZ0g5//yj++usyf/8dxPbt\nwWzfHnyrnYuLNdWr2+PiYo2zsxUWFibIMmRk5BIXl0FYWDLBwYnk5gofeDMzLYMG+TBpUkvatq1W\n2ulVngzUPuUx4MoVMTaqX79kX7Yr8ZCmg0FFHlcZmRCCscUWt4JjqMTLYlbdow/YeRTaZ/f775Ob\nmUnfpUup0qqIDvttqNu/P3UHDODyhg0EbduGd69eoNFC1W5wdTkkXsTcqQEOOBCHUHypVkHsG6Gs\ns+TZJGWdZCgLZTHWHYCS0kMmKXVlQpIkV4Tv2O+yLBfUtAkG3keMZm2BccB6SZIGqg/C3XP6dDQ5\nOQbaty85fS/AZn+xHdSmcPl1cviXDFpjiwf58TU3WQaAK+PzJRpDj8GJFVCtGfTIdwnUZWTwZ8+e\nhB88iNezz9Jv2TJsXIorLmhNTfEZNAivbt1Y2acPl9auxd7Tk64zZ4KHL3i2gss7ISUG2wqtySYQ\nPRfwwJZgshnjLAMSkfHg4CCuNSmp/B4MlQeK2qeoFEOSJFq1qkKrVlWYObMrUVGpHD4cwalT0Zw/\nf5OgoETOnInBaJQxGIrrtdvbW9C0qRtNmrjSvr0H3bvXxL6oQLPKk4rapzwG5Km2eXqWnN3skrLO\n0bCILZ9CChlkUI/6+TYIwPVdYltjQKH2qZGRXFq3DremTWn00kt3fZ1tP/qIyxs2cHH1amGsA7i2\nFsZ63BlwaoADjoQQjA4drjbCC+FmhmiaF3uTkvJwjfX7RpIkM2ANkA5MLlgny/KKIm23AEeBqcAd\nHwJJkqYD0wDc3Nxu3/gpwN8/ChBZtEpjlxCK4dkiq0m7lb6uZ4G+zUA6SWzHnOrY0S6/8d/TxHbw\nD6DN/xltnziR8IMH8Rk8mAF//FHMN6wo5nZ2DN28mV98fTk2ezaNRoygUv360OIFuHYcAv7Cpn1T\n4lhGBgF40oVgsrF00gOmRCdCjQrihVyeD4bKo43apzz5VK5sx5Ah9QslLTIaZZKSskhKyiY7W49G\nI2FlZYqTk2W5BXKpPJ2ofcqD56Zizbq4lLwCnjcz7VHElk9AWPHOFLHi45RU5q6tCxUHbt2KbDTS\nZOzYewokd2vWDCtnZ8IPHswvtK8ttilBANgiPBfSScPBQvjs5M0XWlkJuycj4/5jb/Ioi896EmLZ\npygOSt1tkcSdWg7UA3rKsnzbfWThJLQBaHgn2SWl/XRZliVZliV3d9XF7OzZWIBSI60NBvAPhHrV\nirvAHEMEQ/gVUIBJ4QAyOTjQBynv5xJzGS7vAu+OULPtrbYhO3cSsHgxrk2aMGDFijsa6nlYVKhA\n9x9+QDYa2fuJMkvfoI/YXtqBJULiKYtAKiNeyHoHHQBxqWBtLc6Tnq4r0/lU/nPUPkXlntBoJJyc\nrKhZ05H69Svh4+OMh4e9aqirqH3KY0BamnhH29iUnPslSQk7c7QsXJ6BMPJtKGLkpyt6iUVcYPKC\nQyv73luMiiRJONetS0pEBIZcxeC2VAYKWWLgYK54H+SQg2Kbk6WE3pmbi5+ETld+ohdlMdavIHy+\nbiFJUlXASqm7Ez8gpJT6yrJclvYAsvJRuUsCAxMwMdHg5eVYYn1wDGTmQDOvwuVGZALIwBNznMk3\nstM4AkAFOuQ3Pr1GbNuMLXSMvR9/DJJE38WL0ZqV/DCWRs0ePXD39SVwyxbSY2PBqTo4eUDoUcxk\nNyRM0RFBJeXasi3EA5SckT+Kzcp7UlQeddQ+RUVFpTxR+5THAFmWkSRKVWPK824rmivNiIhDKZQE\nCcCoGNKawvaGIScHAFNr63u+VhMLC5BlZINicGsUDwJZ/K1R3HFk5FsSk3nxqA9CFrYsxvp24FlJ\nkgpGKw4BsoADt9tRkqSPgAnAi7IsHy7LBSkj3IHAWVmWVS2+uyQ8PJmqVe1KzAwIEBQjtnWKeMnE\nkEs6RupSeEibyXk0WGNZsB+8ugckDTTofaso7tIlok+dwrt3b1wbN77r65YkiXrPP49sNHJtrxIn\nVLkhpMcjZSRjiis6YnFUPLdStXqszCE1EywsRFl2tmqsPyaofYqKikp5ovYpjwF5QeGlvavzZqiL\nLpKbKcp02RRxdTVX/GVyEgsVWytxcslhYfd8rWkxMZhaW+dPPOYqMoymYgCQixgomGBK3gS6qTKW\n0OuVwYW2/Iz2shjrPwM5wAZJkrpIkvQqMB34rqBMkpIB7LcCfw8HvkIsLUVJktSqwMe5QLsDkiRN\nlCSpmyRJ/YGtQEvlHCp3gSzLxMVlluoPBhCVILZVKxYpR4xEq5G/nCxjJJtwLKiR7wIjy3D9DLjW\nBct8d5mQnTsB8Bk06J6vv0pr4XcWfeqUKHBUgmSTIjDBET1J2Cgj63QMWJmLVQIzs/JfclJ5oKh9\nioqKSnmi9imPAU5OVgDEx5csaZgn5hZVRJ7cHmGUJ5FYpELxI48LKFRcrY1Qz7i0bt09XWdmfDxx\nly7h2qgRkkaxfVLDxNamqmiD+A5WWJEqzCdsFbs+L09E3kRieXBHY13x3eoMaBHyR58B36MESxTA\nRGmTRzdlOwo4VuTTq0C7YOAtYBOwAhFp3UuW5c1391VUcnIM6PVGbG1Ld0FJVqKVHYrY88kIQ9eh\nQMyxgVRAj2nBoI6sFMhJh4qehfbPS27k1rTpPV+/Q40aAKRGRIgCa0VoNSMJLVaAHgvEiDwHGTMT\nyNWL9L5AqWnLVR4t1D5FRUWlPFH7lMeD6tVFWEFoaMkhAXWVScTzsYXLnamEFi0RRBSuqKIkQbq2\nqVCxZ+fOONWuzbnly4k5c4a75cT8+cgGA3UGFFCZiVVk9JwaAZBEEiaYYI01sYpd5SzGIqQq1vvt\nMjLfLWUy+2VZvgR0ukMbjyJ/j0I8AHc69piyXIPKnTEahcNUaS4wIAJMoXDWUgCD4npnWkAWSVaW\neaQCyZHQK+tTpoXdZQzZYnnKzObedc5NLcUxDTrlHFplTcyoJ69/1Si+a0ZkNBrhMJjn/yar3oOP\nDWqfoqKiUp6ofcqjT56+ekDADfz8istLN3UDMy3sDy9cboopHngSQjCJJOKIEpNXpRNYu8OVpdBi\nGiiqLBqtlme//54/e/Zkdf/+jNi5Eydv7zJdY9SJExz68kts3d1pOkb5b5dlCNsCJpbg2ho9em4S\niwuuSEiEKaKh1RWvnMREESmbt5JQHpTFDUblMcHUVPx35uSU7g5inhe1nFO43Ewx0rPIn53WIH5o\nRiUSGwALxRjPKixpa+EoHp70Gzfu+rrzyEoSo20zW8XtUKcslZla3Bo46BWjXYuEwQgaKX+Q8gBi\nOlRUVFRUVFTKgdatRbDc/v1h/2/vvsOjqtbFj3/XlFTSEwgQWkJLkBqagIIIKBakGMWOBzzc49Fz\nUbFi4WcvFz3wOyKoXAUVkCIoUkSaFCmGEmpCDSUJaYSE9GRm3z/WhEwaghMlwPt5nv3kYc3ee9YM\nM++8s2atd1d7u5cV+jWDnafhUGbF2zqi18Jt4dfyRrMbdBqv55NvrFBtk1aDB9P/rbfIPn6cz7p3\nZ8eMGeWVXaphGAZ7585lZv/+GDYbQ2bMwMPfkX0nrYOzCfriS1YvTnICGzaaoK/etE9fS5I2jskA\nycl6Hk+DBn98gWtlkqxfRaxWM97e1vPf6qoT4ihulVrp8hHBjiorqZS/mE14YaIeRY5L6gLg5gV+\nDSF5b4Wh7LLpL0dXr/7D/U/dvRuAwFatdEOOI/GvF4KNHEx4ku94yXphorBYf/koKdFfTqzW362g\nJYQQQojLICIikNatg/jppyOcO1dU7T4P61kmTI2t2N6eDvjhz29sI8NxpXUAOjwJIdGQ8BXETalw\nzA0vvcTQWbMwbDaWjBnDv5s1Y8W4cRxYtIiUHTtIP3CAY2vWsOHtt5nWoQML77sPDIOYBQtoeeut\n+iS2kvIvAh2fBmAfewFojR6t35oE7maIcqxySEzUBeObNq2umugfI8n6VSYszJcTJ7IxapgTEu4o\nv15WFaZMhKNmaALlib5C4UUURRyj1PnicK36QnYKnIo739RmyBAsnp5snz6d4tzcP9T3g0v0FaFb\n9Hf8knl6v646ExxOCalYCSHbMWfd17CQWwg+nuW/JJTVNhVCCCFE3XP//deRn1/Ct9/uq/b2mCgI\n84Xp28svkgS6bONgbsOGje9YeL4aCyYL3DofvEJh43/D9ncqDCR2fOghHt+/n+5PPklJfj5bJ09m\n3vDhfBodzdSoKGbdfDNrJkwg/cAB2j/wAH/fsYPIYcP0wYYBm56BzDiIHA2hPcgnnzh24Ysv4USQ\nlgdxqXB9mJ7CAxAfn0Hjxj54e19aCesLkWT9KhMZGcKZMwWkpFSfMHdorqeLbE2o2F4PM23wYCd5\nFabC+NAbMMjGacS860j9d91/zjd5+PnRc9w4ck6eZNkTT9T4ZaEmGQkJxM2aRUB4OE169YKCHEj8\nDZpGU2otoJQzuNOc0443qG+RlZJSCPSB/HzdVptvDCGEEELUrtGju2CxmJg0afP5EofO3Mzw5k36\nAkP/WAp2p1Qikig60olTnGQRC7E5CmPg2wKGrIJ6YbDlJfjxdsg+cv44vyZNGDxlCuNTU3l4zRoG\nvPce148fT/TYsdwwYQIj5szh2bQ0hn/9NcFtHBVmbEWw4UnY8/8hIAp6TwJgA79QRBE96YUZMwt1\nbQ2GlBWmSc/j1KkcOnas/sKUf5Qk61eZbt301dE2bTpR7e2+XvqCSJsT4GylfL4ffhRjsMppFD2Q\n2wATaXyFUZbEt78DQtvC5v/VCbVD39deo2F0NHEzZ/L9o49SUlDzdBxnBWfOMD8mBntJCQPefx+T\n2Qw75uuFpR3uJA89gu9JJImOOqvWs3qVdQM/yM7WbReqgiOEEEKIyysszJdRozoSH5/Bp59ur3af\nhzvAgBaw7DC841T5XqEYwlCa0oy97OFb5lDkKDtNUDuI2Q5hA+DEcpgdCev+AZl7zx9vcXenxU03\n0fu55xj0wQfcMW0a/d98k+tGjsTTse5Ol6f+GeZ3gz0f60T9rtXg7kcix/iVTfgTQA96YhgwbTuY\nFdwTpQ9fv16vju3Zs3GtPm+SrF9lbr5Zl1RcvvxwjfsMvx5KbTBnfcX2oQShgC9Jw+6oDuNGYwK4\njUIOksl3ekeTGe77RL+oP78HsvXccou7Ow8sX06jbt2ImzmTjyMjifvqK0qLqp+bZhgGh5YvZ3qX\nLqTt2UPXxx8nasQIsJXCqv/R99NzFDmOa1r40JP9FOCDmbwUPce+Wf3yldcBAZ7V3o8QQggh6oY3\n3uiPr687L7ywqtoyjkrBN8P1dJiX18InTvPXrVh5iEcIJ4J4DjCNjzlZVtLRqz4MWQmDvtX10PdN\ng7ntYc51sOlZOLpYj7jbnHISww55KXByFWx5WSf5PwyCzD3QbizcvRW8Q0khmbnMRqG4mxisWFl4\nAHan6qk7jR2XnSnLvQYMCK/V50xd6nSFuqxr165GbGzs7+94FbPbDcLCPqSwsJSkpKfx9LRW2ed0\nFjQdDc3rw77/VCzj+CyJLCWLt2jKMPTS5mJOc4A7AWjNbDxxLABd9iYseQUatIF/LoWQCABK8vNZ\nN3EiWydPxlZcjMlqJWLQIELatcMrOBhbcTFZR46QuG4dZ48dA6XoN3EiN0yYoEfVl7wKy96APo9h\nf2Aye+mPwkIDVtKPePrgQ7sfWjLuc5j9DKz88nu+/HIXhw49ScuWgecfi1Jqu2EYXf+kp1pcAySm\nCGcSU4SrJKZoX3+9m4ceWkSnTqGsXz8KH5+qNcn3p8NNsyAtD169EV7rqyvAAZRSymp+5lc2Abpa\nzE30J6CsrKO9VNdfT/gKTvwEtkpXP7V4AiYozQec8mCzB4QPg07PQP1oAPayhx9YTBFF3MUwuhBN\nVgF0+hRSzsH+x6FlIBQVldKo0Ye4uZlJSnr6fFnpC7nYmFJ7l1cSdYLJpHj00U68/fZGZs2KY+zY\nqq+B0AD42wCYvkJvT9xRfts4GrGWbN4lia7UownuuBFKU14nkWc4wn/Rii9wpykMngCFOfDzB/BO\nV4j5CHo8jNXLi4Hvv0+3xx9n28cfc+Snnzi0dCmHli6t0A93Pz+uu+8++rz4Ig3at9eNGz/TiXpQ\nc7jrHTKYh41sGvBfrHGUkLwBX352TEfrFA4zTupVKI0b+yCEEEKIuu3BBzuwYcNxPv24cHINAAAT\nzklEQVR0B8OHz2Px4nurrDuLCoG1D8Mdc+D19bAtCT67U4+4W7BwC4NpQ1uW8iO72Mlu4ogkii5E\nE26KwBwxAiJGQGkBpGyC1G26BGNBOhSm61F1i7cekfdrDQ17QaO+4KZzidOksIbVxHMAK1ZGEEMH\nOlJqh4cX6wWwr96oE3WA+fP3c+ZMAc8+2+uiEvVLISPrV6Hk5HNEREwhONiLgwefqHF0PfJxKLHB\njo+gtdP0qkVkMoETNMedr2lFoKOs42k+I4WPsBBICyZTD/2tk80zYe7jui56ky5w64vQYQhYyt94\nuampnDl8mMKsLEwWC75NmhDcpg0mi+P7Yk4afP8S/DoDvANh3FqKwgKIZygKK5Es5UEy2Es+Pxvt\nuH6MG+cKIONriIiYTGFhKSkpz1R4jDIKJlwlMUU4k5giXCUxpVxpqZ0RI+bxww8J9OwZxg8/jCQk\npGpt8ox8eGgRrDgC3lZ4+QZ4sjuU5fZ27OxlDxtYTyp6Wq4nnrSkFc1pThOaEkwIlt8Zn7ZhI41U\njnKUfezlFCcBaEozhjKcYIIpLNV9WXAABobD8vvBbNKP5brrpnLkSBYJCU8QHh5wUc+BjKxfwxo1\n8mHcuB68++4mXn55DZMm3VJln9AA+OQfcN//wJ1vwqb3INgx52oYQRylkBmk8SCHmE4ETXAnlMcw\n48Mp3uQQj1Cfhwnln5ivfwTa9IfFL0DsHPgsBrwCoP2dEDkQmnWlXnA49Rr0Lu+AYUBOKhzbArsW\n6QWlJQUQ1hH+/h0lIX4cZRR2CmjGa/yKhT3k0x8/Mo+7cSId7u4F+fnFHD9+lr59m/81T64QQggh\nXGaxmFiwIIZHH/2eb77ZQ6dO05k9e3iVz/NgL1h2P3yxC55fDS+ugY+2wpPd4O/RUN/bRAc60p4O\nnOIku9nNAfaxh93sQV+/xYQJP/zxxRcvvHDDDYWilFIKKCCHHM6Qeb7CjELRitb0oCetaI1CEXca\nHvlel2q8sSksjNGJOsB7720kISGTsWOjLzpRvxQysn6VyssrpnPn6Rw+fIbFi0cypKyuUCUvzIT3\nFuqSjismQsOyBdEYfEQyn5OGL2Zeowm34o9Ckct2jvMSxZzEQiAhPEIw92DBD07H66kssXMhO7n8\njpRJj5i7eYNhg9xMnZyXCYmA/k9Bn8fIs+wnkecp5iQhPII/47mbBE5RxCLa8skMTz76HuY9B/Vt\nifTrN5Onn+5Z5UuJjIIJV0lMEc4kpghXSUypym43+OCDTUyYsAa73WDs2GjeeKM/wcFeVfbNKoCP\ntsDkbZBTBBYTDG6pq7Hc1goCHXUmDAzSSecEiSSRRBppZHGGPPIwqJr3euBBEEGE0pCmNKMlrfBB\nT4fZmwaTNsOs3bqU5GNdYMqt4OEY7l6//jgDBswiJMSbvXv/cUnFLi42pkiyfhXbsSOFG274AoCV\nKx+kd++mVfax2+GJ6fDJcl1Z5dtnoYdTXr+QTN7mFAXY6YcvT9GIVnhip5BUZpDGTOzkovDAn5vx\nZyA+XI/Z7g2ndsGh9ZCyD1ITIDddT5VRJj3yHtQcGneEqEEYLXpQoA6QztecYQlg0ICxBPFP/ptE\n1pPDaOozKqcxzR/TF0M69hm8+/Y6Jk78he++u4dhwyIrPDb5YBWukpginElMEa6SmFKzzZtPMmbM\nEvbvT8fPz52nnurJv/7Vo9rk91wRzIyDz3fqkW7Qi0+jG+pR7+6NoXMohAeUj36DnupSSCElFGOg\n57574IGV8unCBSWw8zSsTYTFCRDrGHdsFwKTBsItLcvPt3HjCW6/fTYFBSWsWPEg/fu3uKTHLMm6\nAOD77+MZMWIe7u4WFiyIYfDgVlX2MQx4ez688o1+sb9wN7wUA16OxdnHKeJVTvAbuShgEP48SAhd\n8MZOLhnMJ4NvKXbM7wITnrTBi/Z4EI47TbESjBkfFG6AHRv5lJJBESfJZz/n2Hz+eA9a0oRXKaAj\n40nkN3Lpgw9TiWDsFMX/roKPRsO4uyA6+lN2704lPf1Z/P09Kjwu+WAVrpKYIpxJTBGukphyYcXF\nNqZNi+X1138hM7MALy8rDzzQnjFjutCtWyOUqrpwMz4DvjsAyw/DliRwvtaSmxla+EMTXwitB0Fe\net67p0WXiCyxQW4xnCmE5HNwNEtvNkdqbFZ6bvrYaLizdXniX1pqZ/LkLbzwwmoMw2DOnBHExLS7\n5Mcrybo4b8mSBGJi5lNcbOOVV27klVf6YrFULbG/djeMmgwn0qFRILw2EkbdDG5W/ZPSOnKYSgr7\n0NNXmuHObQTQHz/a4kERB8hmHefYTD57MMouB3wRTHjhyw0EMhRFL+aSyWekkoedQfjzDs34aoWJ\nsVOhUwvYNgn27ztNp07TGTy4JcuWPVDlnPLBKlwlMUU4k5giXCUx5eLk5hYzfXos//nPbyQm6gs1\ntmwZyPDhbbnjjtb07BmG1WquclxeMfyWrEfDd6fpRP5IFpy5uGs0EuQJbYOhS0O4oSnc3KJ8ag3o\nKTtLliTw2mvriItLpX59b+bOHcFNN13aiHoZSdZFBbGxycTEzCcx8SydO4cyZcpg+vSpOi3mXD68\nuxA+/B4Ki/VC1DED4dEBEB6qk/Zt5LKATFZzlkLH3C8/zHTBm/Z4E4kn4ZgI4CQlHKeIU5SSiY1c\nDIoBE2a8sBCIG42w0pJUmhNHMRs5x3qyKcTAHzP/ohEx9iA+XKx4fiYE1tOJengo3HvvAubN28eP\nP97H7be3rvJY5INVuEpiinAmMUW4SmLKpbHZ7KxceYSZM+NYsuQg+fl6ENDHx40+fZrSq1cTundv\nTMeODWjQoF6N58kv0fXaswr0SHphqa6ubjWBl1Un5KH1oJpy75SU2IiNTebHHw/yzTd7OH5cl4se\nNaoT77578wXv9/dIsi6qyMoq4KmnfmLmzDgA7rijNS+91IeePcOq/LSUnAmTFsOMVZCty5vTozUM\n7Qm3dtELUgtMNjaSwy/ksI1ckimucA4LUB83AjATgAVPTJhRGEAxdrKxkUEpKRRT4rTgoxnujCCI\newhiX7yFF2fBL3uhcRD8+Iqurf7jjwe58845dO/emM2bR1db01Q+WIWrJKYIZxJThKskpvxx+fkl\nrF17jGXLDrFq1TEOHsyscHtgoCeRkcG0aRNEixYBNG3qR8OG9ahf35ugIC98fd3x9rZiNlecWWAY\nBvn5JWRnF5Genkdy8jmOHs0iPj6DXbtS2b49mYKCUgDq1XNj5Mh2PPXU9URFhbj8mCRZFzXasuUU\nzz77Mxs36kv0du3aiDFjOhMT047AwIoLOfIKYf4m+HodrNsDNsdcsEAf6B0J3VpC11ZwXVOwBhez\nXxWQQAFHKSSJYk5TTBalFFWz+loBAVhojBsReNABL6LtPhSdcmflDsXcDfDbIb3vXT1g2uN6pH/b\ntiQGDvyKoqJStm4dQ8eOodU+TvlgFa6SmCKcSUwRrpKYUntOn85l69ZTxMYms3t3GvHxGRw+fAa7\n/cJ5rcViwmrVCbvNZlBSYqOmVNhkUrRrF0Lv3k245ZaWDBwYXuXiTa6QZF1ckGEYrF9/nH//eys/\n/JCA3W5gsZjo1685t9/eikGDIoiMDK4w4p6RAyt36m3tHj233ZmXO0SE6qoyjYOggT8E+YCft4G7\nl4Fys4PZAAOMEhO2fBPZeYq0s3AyAw4mw57j5SP5JhPcFg3jh0Hf6/TPYdOmxTJ+/M8UF9uYPXs4\n9957XY2PUT5YhaskpghnElOEqySm/LmKiko5duwsx45lcfJkDqdP55KWlkdWViHZ2YXk55dQUFBK\nqWMVqtmscHMz4+3thr+/B8HBnjRs6EOzZn60bh1EVFRIrSbnlclFkcQFKaXo27c5ffs259SpHGbP\n3sO8eftYteooq1YdBaB+fW9699bzwTp3DqV9+wbcd2M97u+rE/jkTIg9DLuOwd7jOtk+clon3JXu\nzbFVXdTqzGSCVg3hzm7Qv4NO1BsEQHp6HlOn7mfKlK0kJGTi7+/BggUx1c5TF0IIIcS1yd3dQtu2\nwbRtG3y5u1KrJFkXhIX58txzvXnuud4kJeWwYsVhVq8+xoYNJ1i0KJ5Fi+LP7+vn506rVkG0aRNE\neHgAzZr50b2xL0OjfKhf35vAQE/yi80knYG0s5B5To+U5xVBUYmeRqMUWM3g7QF+XhDiB2FB0Ky+\nwbnsfBITzxIfn8F7b5xm48YTbN+egt1uYLWa+NvfOvHWWzcTGvrHF3QIIYQQQlwpJFkXFTRu7Mvo\n0V0YPboLhmGQlHSO335LYufO0+zbl87+/ens3p1KbGxyjefw8XHDz88DHx83vLyseHpacXc3Yzab\nzi8EtdnsFBfbKCgoJTe3mKysAjIy8ikpsVc4l8ViolevJgwd2ob7729Pw4Y+f+rjF0IIIYSoSyRZ\nFzVSShEW5ktYmG+Fq4OWlto5cSKbxMSzHD9+lqSkc6SknCM9PZ+MjPzzc8PS0/PJyyumsLC0xsUb\n7u5m6tXTc8W6dGlYYa5Yhw4N6Nw59E+dLyaEEEIIUZdJsi4umcViIjw8gPDwgIva3zAMSkvt2GzG\n+VXaZrPCajVXW3JRCCGEEEJokqyLP51SOjG3Wi93T4QQQgghriwXLs8hhBBCCCGEuGyuqjrrSql0\noErhwL9YI6Dm1ZfSh79SM8MwXL/EmLhmSUyRPlQiMUW4RGKK9KGSi4opV1WyXhcopQzDMC7rRGzp\ngxBXj7rwXpI+CHH1qAvvJenDpZFpMEIIIYQQQtRRkqwLIYQQQghRR0myXvv+3+XuANIHIa4mdeG9\nJH0Q4upRF95L0odLIHPWhRBCCCGEqKNkZF0IIYQQQog6SpJ1IYQQQggh6ihJ1oUQQgghhKijJFkX\nQ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aQFIhqWcyWSCmnHrSMOtK+dAiyhIgz35rTlIJhw/TLjkaCdRSsOGq/MtSBOkJ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "_prior = bern2(X, Y, 2, 8, 10, 10) + bern2(X, Y, 8, 2, 10, 10)\n", "prior_grid = c2d(thetas1, thetas2, _prior)\n", "_likelihood = bern2(X, Y, 1, 1, 2, 3)\n", "posterior_grid = _likelihood * prior_grid\n", "posterior_grid /= posterior_grid.sum()\n", "make_plots(X, Y, prior_grid, likelihood, posterior_grid)\n", "make_plots(X, Y, prior_grid, likelihood, posterior_grid, projection='3d')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Metropolis" ] }, { "cell_type": "code", "execution_count": 26, "metadata": { "collapsed": true }, "outputs": [], "source": [ "a = 2\n", "b = 3\n", "\n", "z1 = 11\n", "N1 = 14\n", "z2 = 7\n", "N2 = 14\n", "\n", "prior = lambda theta1, theta2: stats.beta(a, b).pdf(theta1) * stats.beta(a, b).pdf(theta2)\n", "lik = partial(bern2, z1=z1, z2=z2, N1=N1, N2=N2)\n", "target = lambda theta1, theta2: prior(theta1, theta2) * lik(theta1, theta2)\n", "\n", "theta = np.array([0.5, 0.5])\n", "niters = 10000\n", "burnin = 500\n", "sigma = np.diag([0.2,0.2])\n", "\n", "thetas = np.zeros((niters-burnin, 2), np.float)\n", "for i in range(niters):\n", " new_theta = stats.multivariate_normal(theta, sigma).rvs()\n", " p = min(target(*new_theta)/target(*theta), 1)\n", " if np.random.rand() < p:\n", " theta = new_theta\n", " if i >= burnin:\n", " thetas[i-burnin] = theta" ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "image/png": 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hFw2j9K5dOXcM7N0bpnv1+kPb2b2jYdRVS6lSn+oNG07dyMvPla1tSrFNg7lw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jAyZFyYSSiKMtCiauRtXjNBNrT6r6jAHZe9pQkTRwjJvnfMSMMZtRZj9aKShk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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kde = stats.gaussian_kde(thetas.T)\n", "XY = np.vstack([X.ravel(), Y.ravel()])\n", "posterior_metroplis = kde(XY).reshape(X.shape)\n", "make_plots(X, Y, prior(X, Y), lik(X, Y), posterior_metroplis)\n", "make_plots(X, Y, prior(X, Y), lik(X, Y), posterior_metroplis, projection='3d')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Gibbs" ] }, { "cell_type": "code", "execution_count": 28, "metadata": { "collapsed": true }, "outputs": [], "source": [ "a = 2\n", "b = 3\n", "\n", "z1 = 11\n", "N1 = 14\n", "z2 = 7\n", "N2 = 14\n", "\n", "prior = lambda theta1, theta2: stats.beta(a, b).pdf(theta1) * stats.beta(a, b).pdf(theta2)\n", "lik = partial(bern2, z1=z1, z2=z2, N1=N1, N2=N2)\n", "target = lambda theta1, theta2: prior(theta1, theta2) * lik(theta1, theta2)\n", "\n", "theta = np.array([0.5, 0.5])\n", "niters = 10000\n", "burnin = 500\n", "sigma = np.diag([0.2,0.2])\n", "\n", "thetas = np.zeros((niters-burnin,2), np.float)\n", "for i in range(niters):\n", " theta = [stats.beta(a + z1, b + N1 - z1).rvs(), theta[1]]\n", " theta = [theta[0], stats.beta(a + z2, b + N2 - z2).rvs()]\n", " \n", " if i >= burnin:\n", " thetas[i-burnin] = theta" ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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bX5hc9BaN4cMRcE+OX6zWcCgV/kuErUkQnAKn0s0wuPaYYW/9HaGJC7Rzh9bu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\nS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mIdBRM6vHdDIfgCkVfiRlYh31pKxkarRq6TjEVO9d7IEyxmxZGldRTqJVBbWQ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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "kde = stats.gaussian_kde(thetas.T)\n", "XY = np.vstack([X.ravel(), Y.ravel()])\n", "posterior_gibbs = kde(XY).reshape(X.shape)\n", "make_plots(X, Y, prior(X, Y), lik(X, Y), posterior_gibbs)\n", "make_plots(X, Y, prior(X, Y), lik(X, Y), posterior_gibbs, projection='3d')" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hierarchical models\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Hierarchical models have the following structure - first we specify that the data come from a distribution with parameters $\\theta$\n", "\n", "$$\n", "X \\sim f(X\\ | \\ \\theta)\n", "$$\n", "\n", "and that the parameters themselves come from another distribution with hyperparameters $\\lambda$\n", "\n", "$$\n", "\\theta \\sim g(\\theta \\ | \\ \\lambda)\n", "$$\n", "\n", "and finally that $\\lambda$ comes from a prior distribution\n", "\n", "$$ \n", "\\lambda \\sim h(\\lambda)\n", "$$\n", "\n", "More levels of hierarchy are possible - i.e you can specify hyper-hyperparameters for the distribution of $\\lambda$ and so on.\n", "\n", "The essential idea of the hierarchical model is because the $\\theta$s are not independent but rather are drawn from a common distribution with parameter $\\lambda$, we can share information across the $\\theta$s by also estimating $\\lambda$ at the same time. \n", "\n", "As an example, suppose we have data about the proportion of heads after some number of tosses from several coins, and we want to estimate the bias of each coin. We also know that the coins come from the same mint and so might share some common manufacturing defect. There are two extreme approaches - we could estimate the bias of each coin from its coin toss data independently of all the others, or we could pool the results together and estimate the same bias for all coins. Hierarchical models provide a compromise where we shrink individual estimates towards a common estimate.\n", "\n", "Note that because of the conditionally independent structure of hierarchical models, Gibbs sampling is often a natural choice for the MCMC sampling strategy." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Gibbs sampler example from [Robert and Casella, 10.17](http://www.springer.com/statistics/statistical+theory+and+methods/book/978-0-387-21239-5)\n", "\n", "Suppose we have data of the number of failures ($y_i$) for each of 10 pumps in a nuclear plant. We also have the times ($_i$) at which each pump was observed. We want to model the number of failures with a Poisson likelihood, where the expected number of failure $\\lambda_i$ differs for each pump. Since the time which we observed each pump is different, we need to scale each $\\lambda_i$ by its observed time $t_i$.\n", "\n", "We now specify the hierarchical model - note change of notation from the overview above - that $\\theta$ is $\\lambda$ (parameter) and $\\lambda$ is $\\beta$ (hyperparameter) simply because $\\lambda$ is traditional for the Poisson distribution parameter. \n", "\n", "The likelihood $f$ is \n", "$$\n", "\\prod_{i=1}^{10} \\text{Poisson}(\\lambda_i t_i)\n", "$$\n", "\n", "We let the prior $g$ for $\\lambda$ be \n", "\n", "$$\n", "\\lambda \\sim \\text{Gamma}(\\alpha, \\beta)\n", "$$\n", "with $\\alpha = 1$ \n", "\n", "and let $\\beta$ to be a random variable to be estimated from the data\n", "\n", "$$\n", "\\beta \\sim \\text{Gamma}(\\gamma, \\delta)\n", "$$\n", "\n", "with $\\gamma = 0.01$ and $\\delta = 1$.\n", "\n", "There are 11 unknown parameters (10 $\\lambda$s and $\\beta$) in this hierarchical model.\n", "\n", "The posterior is \n", "$$\n", "p(\\lambda, \\beta \\ | \\ y, t) = \\prod_{i=1}^{10} \\text{Poisson}(\\lambda_i t_i) \\times \\text{Gamma}(\\alpha, \\beta) \\times \\text{Gamma}(\\gamma, \\delta)\n", "$$\n", "\n", "with the conditional distributions needed for Gibbs sampling given by\n", "\n", "$$\n", "p(\\lambda_i \\ | \\ \\lambda_{-i}, \\beta, y, t) = \\text{Gamma}(y_i + \\alpha, t_i + \\beta)\n", "$$\n", "\n", "and \n", "\n", "$$\n", "p(\\beta \\ | \\ \\lambda, y, t) = \\text{Gamma}(10\\alpha + \\gamma, \\delta + \\sum_{i=1}^10 \\lambda_i)\n", "$$" ] }, { "cell_type": "code", "execution_count": 1, "metadata": {}, "outputs": [], "source": [ "from numpy.random import gamma as rgamma # rename so we can use gamma for parameter name" ] }, { "cell_type": "code", "execution_count": 31, "metadata": { "collapsed": true }, "outputs": [], "source": [ "def lambda_update(alpha, beta, y, t):\n", " return rgamma(size=len(y), shape=y+alpha, scale=1.0/(t+beta))\n", "\n", "def beta_update(alpha, gamma, delta, lambd, y):\n", " return rgamma(size=1, shape=len(y) * alpha + gamma, scale=1.0/(delta + lambd.sum()))\n", "\n", "def gibbs(niter, y, t, alpha, gamma, delta):\n", " lambdas_ = np.zeros((niter, len(y)), np.float)\n", " betas_ = np.zeros(niter, np.float)\n", " \n", " lambda_ = y/t\n", "\n", " for i in range(niter):\n", " beta_ = beta_update(alpha, gamma, delta, lambda_, y)\n", " lambda_ = lambda_update(alpha, beta_, y, t)\n", "\n", " betas_[i] = beta_\n", " lambdas_[i,:] = lambda_\n", " \n", " return betas_, lambdas_" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Setup" ] }, { "cell_type": "code", "execution_count": 32, "metadata": { "collapsed": true }, "outputs": [], "source": [ "alpha = 1.8\n", "gamma = 0.01\n", "delta = 1.0\n", "beta0 = 1\n", "y = np.array([5, 1, 5, 14, 3, 19, 1, 1, 4, 22], np.int)\n", "t = np.array([94.32, 15.72, 62.88, 125.76, 5.24, 31.44, 1.05, 1.05, 2.10, 10.48], np.float)\n", "niter = 1000" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [ { "name": "stdout", "output_type": "stream", "text": [ "2.450\n", "0.701\n", "[0.06905699 0.15597648 0.10703469 0.12354692 0.61892855 0.61668945\n", " 0.8360853 0.86031655 1.28183177 1.83725868]\n", "[0.02517981 0.09228058 0.04070685 0.03129867 0.29249547 0.13439944\n", " 0.54271836 0.5482083 0.55513921 0.38773635]\n" ] } ], "source": [ "betas, lambdas = gibbs(niter, y, t, alpha, gamma, delta)\n", "print('%.3f' % betas.mean())\n", "print('%.3f' % betas.std(ddof=1))\n", "print(lambdas.mean(axis=0))\n", "print(lambdas.std(ddof=1, axis=0))" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [ { "data": { "image/png": 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AfgvAm4UQP+7ws3QE9gXk+2SI9TyhPCG9Bi+S5Qg5KWYlOan30XPCpC7uvP3H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6UggiYrugBm7RSy/p4XUcyJgC7oNMYrd6yHlRI42KBhmMn9x2b03wohMJy1ddBjCVM5Ue/l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GcKUeTSulI4wTAEMA/s7+eR2AfcrvQxWeVzfpXAERy4BpMNdNRBczAPTYF7nXc0JpnhHL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\nsU+16bQ0Gs0aRs8rG4+NEta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"text/plain": [ "" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plt.figure(figsize=(8, 16))\n", "for i in range(len(lambdas.T)):\n", " plt.subplot(5,2,i+1)\n", " plt.plot(lambdas[::10, i]);\n", " plt.title('Trace for $\\lambda$%d' % i)\n", "plt.tight_layout()" ] } ], "metadata": { "kernelspec": { "display_name": "Python 3", "language": "python", "name": "python3" }, "language_info": { "codemirror_mode": { "name": "ipython", "version": 3 }, "file_extension": ".py", "mimetype": "text/x-python", "name": "python", "nbconvert_exporter": "python", "pygments_lexer": "ipython3", "version": "3.6.10" } }, "nbformat": 4, "nbformat_minor": 1 }