{ "metadata": { "name": "" }, "nbformat": 3, "nbformat_minor": 0, "worksheets": [ { "cells": [ { "cell_type": "heading", "level": 2, "metadata": {}, "source": [ "Lab6: Bayesianism, with MCMC." ] }, { "cell_type": "code", "collapsed": false, "input": [ "%matplotlib inline\n", "from collections import defaultdict\n", "import json\n", "\n", "import numpy as np\n", "import scipy as sp\n", "import matplotlib.pyplot as plt\n", "import pandas as pd\n", "\n", "from matplotlib import rcParams\n", "import matplotlib.cm as cm\n", "import matplotlib as mpl\n", "\n", "#colorbrewer2 Dark2 qualitative color table\n", "dark2_colors = [(0.10588235294117647, 0.6196078431372549, 0.4666666666666667),\n", " (0.8509803921568627, 0.37254901960784315, 0.00784313725490196),\n", " (0.4588235294117647, 0.4392156862745098, 0.7019607843137254),\n", " (0.9058823529411765, 0.1607843137254902, 0.5411764705882353),\n", " (0.4, 0.6509803921568628, 0.11764705882352941),\n", " (0.9019607843137255, 0.6705882352941176, 0.00784313725490196),\n", " (0.6509803921568628, 0.4627450980392157, 0.11372549019607843)]\n", "\n", "rcParams['figure.figsize'] = (10, 6)\n", "rcParams['figure.dpi'] = 150\n", "rcParams['axes.color_cycle'] = dark2_colors\n", "rcParams['lines.linewidth'] = 2\n", "rcParams['axes.facecolor'] = 'white'\n", "rcParams['font.size'] = 14\n", "rcParams['patch.edgecolor'] = 'white'\n", "rcParams['patch.facecolor'] = dark2_colors[0]\n", "rcParams['font.family'] = 'StixGeneral'\n", "\n", "\n", "def remove_border(axes=None, top=False, right=False, left=True, bottom=True):\n", " \"\"\"\n", " Minimize chartjunk by stripping out unnecesasry plot borders and axis ticks\n", " \n", " The top/right/left/bottom keywords toggle whether the corresponding plot border is drawn\n", " \"\"\"\n", " ax = axes or plt.gca()\n", " ax.spines['top'].set_visible(top)\n", " ax.spines['right'].set_visible(right)\n", " ax.spines['left'].set_visible(left)\n", " ax.spines['bottom'].set_visible(bottom)\n", " \n", " #turn off all ticks\n", " ax.yaxis.set_ticks_position('none')\n", " ax.xaxis.set_ticks_position('none')\n", " \n", " #now re-enable visibles\n", " if top:\n", " ax.xaxis.tick_top()\n", " if bottom:\n", " ax.xaxis.tick_bottom()\n", " if left:\n", " ax.yaxis.tick_left()\n", " if right:\n", " ax.yaxis.tick_right()\n", " \n", "pd.set_option('display.width', 500)\n", "pd.set_option('display.max_columns', 100)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 1 }, { "cell_type": "markdown", "metadata": {}, "source": [ "### The Bayesian formulation of regression and the posterior predictive distribution" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "(taken from Am207 class notes)\n", "\n", "In the linear regression model we have data $D$, of $n$ observations \n", "$D=\\left\\{ ({\\bf x}_1, y_1), ({\\bf x}_2,y_2), \\ldots, ({\\bf x}_n, y_n) \\right\\} $ where ${\\bf x}$ \n", "denotes an input vector of dimension $D$ and $y$ denotes a scalar output (dependent variable). \n", "All data points are combined into a $D \\times n$ matrix $X$. \n", "The model that determines the relationship between inputs and \n", "output is given by\n", "\n", "$$ y = \\bf x^{T} {\\bf w} + \\epsilon $$\n", "\n", "where ${\\bf w}$ is a vector of parameters of the linear model. Usually there is \n", "a bias or offset is included, but for now we ignore it. \n", "\n", "We assume that the additive noise $\\epsilon$ is iid Gaussian with\n", "zero mean and variance $\\sigma_n^2$ \n", "\\[ \\epsilon \\sim N(0, \\sigma^2_n) \\].\n", "\n", "The likelihood is, because we assume independency, the product \n", "\n", "\\begin{eqnarray} L &=& p(\\bf y|X,\\bf w) = \\prod_{i=1}^{n} p(y_i|\\bf X_i, \\bf w) = \\frac{1}{\\sqrt{2\\pi}\\sigma_n} \\prod_{i=1}^{n} \n", " \\exp{ \\left( -\\frac{(y_i-\\bf X_i^T \\bf w)^2}{2\\sigma_n^2} \\right)} \\nonumber \\\\ \n", " &=& \\frac{1}{\\sqrt{2\\pi}\\sigma_n} \\exp{\\left( -\\frac{| \\bf y-X^T \\bf w|^2 }{2\\sigma_n^2} \\right)} = N(X^T \\bf w, \\sigma_n^2 I)\n", " \\end{eqnarray}\n", " \n", "where $|x|$ denotes the Euclidean length of vector $\\bf x$. \n", "\n", "An alternative way of expressing the likelihood, which is convenient\n", "when sampling ${\\bf w}$'s:\n", "\n", "\\begin{eqnarray} \n", "p(\\bf y|\\bf X,\\bf w) &=& \\frac{1}{\\sqrt{2\\pi}\\sigma_n} \\exp{\\left( -\\frac{| X^{-1} \\bf y- \\bf w|^2 \\,\\, (X^{-1} (X^{-1})^{T}) }{2\\sigma_n^2} \\right)} = N(X^{-1} \\bf y, \\sigma_n^2 (X^{-1} (X^{-1})^{T}) )\n", " \\end{eqnarray}\n", "\n", "In the Bayesian framework inference we need to specify a prior\n", "over the parameters that expresses our belief about the parameters\n", "before we take any measurements. A wise choice is a zero mean \n", "Gaussian with covariance matrix $\\Sigma$ \n", "\n", "\\begin{equation}\n", " w \\sim N(0, \\Sigma) \n", "\\end{equation}\n", "\n", "We can now continue with the standard Bayesian formalism \n", "\n", "\\begin{eqnarray}\n", " p(\\bf w| \\bf y,X) &\\propto& p(\\bf y | X, \\bf w) \\, p(\\bf w) \\nonumber \\\\\n", " &\\propto& \\exp{ \\left(- \\frac{1}{2 \\sigma_n^2}(\\bf y-X^T \\bf w)^T(\\bf y - X^T \\bf w) \\right)}\n", " \\exp{\\left( -\\frac{1}{2} \\bf w^T \\Sigma^{-1} \\bf w \\right)} \\nonumber \\\\ \n", " \\end{eqnarray}\n", " \n", "In the next step we `complete the square' and obtain \n", "\n", "\\begin{equation}\n", "p(\\bf w| \\bf y,X) \\propto \\exp \\left( -\\frac{1}{2} (\\bf w - \\bar{\\bf w})^T (\\frac{1}{\\sigma_n^2} X X^T + \\Sigma^{-1})(\\bf w - \\bar{\\bf w} ) \\right)\n", "\\end{equation}\n", "\n", "where $\\bar{\\bf w} = \\sigma_n^{-2}( \\sigma_n^{-2}XX^T +\\Sigma^{-1})^{-1} X \\bf y $\n", "\n", "This looks like a Gaussian and therefore the posterior is\n", "\n", "$$ p(\\bf w| X, {\\bf y}) \\sim {\\cal N}( \\frac{1}{\\sigma_n^2} A^{-1}Xy , A^{-1} ) $$ \n", "\n", "where $A= \\sigma_n^{-2}XX^T +\\Sigma^{-1}$\n", "\n", "To make predictions for a test case we average over all possible parameter predictive distribution\n", "values, weighted by their posterior probability. This is in contrast to non Bayesian schemes, where a single parameter is typically chosen by some criterion. \n", "\n", "Thus the predictive distribution at some $x^{*}$ is given by averaging the output of all possible linear models w.r.t. the posterior\n", "\n", "\\begin{eqnarray} \n", "p(y^{*} | x^{*}, {\\bf x,y}) &=& \\int p({\\bf y}^{*}| {\\bf x}^{*}, {\\bf w} ) p(\\bf w| X, y)dw \\nonumber \\\\\n", " &=& {\\cal N} \\left(\\frac{1}{\\sigma_n^2} x^{*^{T}} A^{-1} X {\\bf y}, x^{*^T}A^{-1}x^{*} \\right),\n", "\\end{eqnarray}\n", "\n", "which is again Gaussian, with a mean given by the posterior mean multiplied by the test input\n", "and the variance is a quadratic\n", "form of the test input with the posterior covariance matrix, showing that the\n", "predictive uncertainties grow with the magnitude of the test input, as one would\n", "expect for a linear model. \n", "\n", "\n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### Bayesian as an updating of knowledge" ] }, { "cell_type": "code", "collapsed": false, "input": [ "a0=-0.3\n", "a1=0.5\n", "N=20\n", "noiseSD=0.2\n", "priorPrecision=2.0\n", "u=np.random.rand(20)\n", "x=2.*u -1.\n", "def randnms(mu, sigma, n):\n", " return sigma*np.random.randn(n) + mu\n", "y=a0+a1*x+randnms(0.,noiseSD,N)\n", "plt.scatter(x,y)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 2, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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06KHDhw+HbEtOTtYXX3xxzkUj/PgP1jwyN4/MzSNz88jcPZpswpKTk1VRUdHk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\nb5rgPG+Z/Px8FRUVyefzSZI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"text": [ "" ] } ], "prompt_number": 2 }, { "cell_type": "code", "collapsed": false, "input": [ "from scipy.stats import norm\n", "likelihoodSD = noiseSD # Assume the likelihood precision, beta, is known.\n", "likelihoodPrecision = 1./(likelihoodSD*likelihoodSD)" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 3 }, { "cell_type": "code", "collapsed": false, "input": [ "from _multivariate import multivariate_normal" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 4 }, { "cell_type": "code", "collapsed": false, "input": [ "def cplot(f):\n", " plt.figure()\n", " xx,yy=np.mgrid[-1:1:.01,-1:1:.01]\n", " pos = np.empty(xx.shape + (2,))\n", " pos[:, :, 0] = xx\n", " pos[:, :, 1] = yy\n", " ax=plt.contourf(xx, yy, f(pos))\n", " #data = [x, y]\n", " return ax" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 5 }, { "cell_type": "code", "collapsed": false, "input": [ "priorMean = np.zeros(2)\n", "priorSigma = np.eye(2)/priorPrecision #Covariance Matrix\n", "priorPDF = lambda w: multivariate_normal.pdf(w,priorMean,priorSigma)\n", "priorPDF([1,2])" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 6, "text": [ "0.0021447551423913074" ] } ], "prompt_number": 6 }, { "cell_type": "code", "collapsed": false, "input": [ "np.transpose(priorMean)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 7, "text": [ "array([ 0., 0.])" ] } ], "prompt_number": 7 }, { "cell_type": "code", "collapsed": false, "input": [ "cplot(priorPDF)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 8, "text": [ "" ] }, { "metadata": {}, "output_type": "display_data", "png": 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LoFXFpx9MJ0I5WUIqYEmEukkhPjGu5VBqVSj7h08IWm8jZPklTdGy/orDGDcl13jFYTFC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\nm5+wWjzTimEjzBI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"text": [ "" ] } ], "prompt_number": 8 }, { "cell_type": "code", "collapsed": false, "input": [ "def plotSampleLines(mu, sigma, numberOfLines, dataPoints=None):\n", " #Plot the specified number of lines of the form y = w0 + w1*x in [-1,1]x[-1,1] by\n", " # drawing w0, w1 from a bivariate normal distribution with specified values\n", " # for mu = mean and sigma = covariance Matrix. Also plot the data points as\n", " # blue circles. \n", " #print \"datap\",dataPoints\n", " fig=plt.figure()\n", "\n", " for i in range(numberOfLines):\n", " w = np.random.multivariate_normal(mu,sigma)\n", " func = lambda x: w[0] + w[1]*x\n", " xx=np.array([-1,1])\n", " plt.plot(xx,func(xx),'r')\n", " if dataPoints:\n", " plt.scatter(dataPoints[0],dataPoints[1])\n", " ax=plt.gca()\n", " ax.set_xlim([-1,1])\n", " ax.set_ylim([-1,1])\n", " plt.show()" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 9 }, { "cell_type": "code", "collapsed": false, "input": [ "plotSampleLines(priorMean,priorSigma,6)" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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sL1JqzZoBzz7LQeurVgE/+QmDgw0bgKefBpo0AYYMAT74wFrOlBtLSGCN5Zw5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\nw2MfB6nFWiFrsF5ICwxiRERERDphECOHxz4OUou1QtZgvZA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"text": [ "" ] } ], "prompt_number": 10 }, { "cell_type": "code", "collapsed": false, "input": [ "# Given the mean = priorMu and covarianceMatrix = priorSigma of a prior\n", "# Gaussian distribution over regression parameters; observed data, xtrain\n", "# and ytrain; and the likelihood precision, generate the posterior\n", "# distribution, postW via Bayesian updating and return the updated values\n", "# for mu and sigma. xtrain is a design matrix whose first column is the all\n", "# ones vector.\n", "def update(x,y,likelihoodPrecision,priorMu,priorSigma): \n", " postSigmaInv = np.linalg.inv(priorSigma) + likelihoodPrecision*np.outer(x.T,x)\n", " postSigma = np.linalg.inv(postSigmaInv)\n", " postMu = np.dot(np.dot(postSigma,np.linalg.inv(priorSigma)),priorMu) + likelihoodPrecision*np.dot(postSigma,np.outer(x.T,y)).flatten()\n", " postW = lambda w: multivariate_normal.pdf(w,postMu,postSigma)\n", " return postW,postMu,postSigma" ], "language": "python", "metadata": {}, "outputs": [], "prompt_number": 11 }, { "cell_type": "code", "collapsed": false, "input": [ "# For each iteration plot the\n", "# posterior over the first i data points and sample lines whose\n", "# parameters are drawn from the corresponding posterior. \n", "mu = priorMean\n", "sigma = priorSigma\n", "iterations=2\n", "muhash={}\n", "sigmahash={}\n", "for i in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]:\n", " postW,mu,sigma = update(np.array([1,x[i]]),y[i],likelihoodPrecision,mu,sigma)\n", " muhash[i]=mu\n", " sigmahash[i]=sigma\n", " if i in [1,4,7,10,19]:\n", " cplot(postW)\n", " #plotSampleLines(mu,sigma,6,(x[0:i],y[0:i])) \n", " #print \"=========\", i, x[0:i],y[0:i]\n" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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"text": [ "" ] } ], "prompt_number": 12 }, { "cell_type": "code", "collapsed": false, "input": [ "for i in [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19]:\n", " if i in [1,4,7,10,19]:\n", " plotSampleLines(muhash[i],sigmahash[i],6, (x[0:i],y[0:i]))" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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A7du3x9GjR9G5c2ecPHkSXuly0a+++ioGDRoEAPD29kZQUJDV/dlViD2M27cp\nyMzF2ZEj1n5jAL2lzBsC6tcHKlV6vICKj2eO3tQAsGMHcO+e5W2KFbMcaN6wIeDra7enKeQgSvF3\nazAAK1cCyck8X6oU0K8fvcmkIPbx3LvHSOOsWdrw9kqVWMvSr584fAvC47h4kX8rmzbxuF8/mi0X\nLKjvutwIm3SLsgPr169Xfn5+KiUl5cG5GjVqqB9++MHididOnFAtW7ZUP//8s0pOTn7o/W3cuNEe\ny8o6iYlK/fOPUgsWKPX660q1aKGUv79SvORafhUqpFSbNkq9+aZSixYptX+/UvfvP/r+U1KU2rtX\nqU8+Uap7d6XKlrW+X19fpVq1UmrcOKXWrVPq5s1ceerOzJ9//qn3EpS6cUOpOXOUqlPH8vfZvr1S\nK1Yo9Yj9LvxLcrJSCxcqVaOG9vqVLKnU1KlK3b5tl4dwiL0iOA0Ov1+MRqWWLOH1CFCqeHGlfvxR\n71W5JbboFrsIsYkTJ6rAwECLc88884x67bXXLM59++23qkGDBsrb21uVLFlSbdiwIcP7002IZURa\nmlLHjyv13XdKjR2rVMeOvDhkJM7y5FGqQQOlBgxQ6tNPldq2Tam4uIfft9Go1Nmz/EMaPFipwMCM\n77duXaWGDFFq6VKlzp3jzwkPcKg3S6NRqe3blXrlFaXy5tV+hyVKKDV6tFInTui9QscnNVWplSv5\nt2R6/QoWVGrMGKWuXLHprh1qrwgOj0Pvl+vXlXrxRe1vpEsXpWJi9F6V22KLbrFLanLIkCE4cOAA\nduzY8eBcnz59EBcXh7Vr11rd/tKlSxg8eDC2bt2KEydOoHQ6V99NmzZhyZIlqFSpEgCgcOHCCAkJ\neVA0GRERAQD6Ht+4gTA/P2DfPkSsXw+cPImwy5f5//8+jzAA8PBARNmyQPXqCOvYEQgJQURiIlCk\nSMb3f/MmIgwG4OBBhF24AERGIuLfwvCwf+83onhxoF49hD33HBAaioibNwFPT8d6feQYYcHBwLJl\niJg9Gzh7Vvv9hYQAXbogbMIEwNfXcdbraMdt2gAbNyJi9Ghg3z6+fr6+iOjYEejRA2G9ejnWeuVY\njnPrePduhM2ZA8TEIMLPDxg6FGEffMDrjSOszw2OTd+fO3cOAPDSSy/pWyM2dOhQHDx4EFu2bHlw\nrlevXoiPj89QiAFAYmIigoOD8dZbb2Hw4MEW/5crNWI5wd27tNAw79o8fFhr1TenTBmt3sz0b5Uq\n1h1jycnzVJbQAAAgAElEQVTsfjE3mzUVNpsoUIBdZ6YGgCZNZMafI6EUawUNBs54M1msFCsG9O3L\nAv+aNXVdosOzeze9yNas4bGXF9CjB60v6tXTd22CkFvcu8c5rvPm8bhVKxbkS8e27uherD916lSs\nWLEC+/bte3CuU6dOqFSpEj7//POH/tzQoUNRoUIFjBkzxuK80wqxjLh/n00A6bs24+Ksb1ugABAc\nbNkYEBhIR3ITRiM79cxtM0yzEk14ewMNGlg2AZQqlbPPU0ciIpyoxfzOHWD5cr6R7t+vnW/Thr5k\nzz0nbeaP4sgR4IMP+BqaGms6d6b1RcuWj/1xp9orgu441H7ZuZO2FKdP85oweTLw1ltizuog6F6s\nv2PHDlWgQAGLc1WqVFHff//9I39uyJAhas2aNVbnHapGLCdIS1Pq1CnWwUyYoFSnTkqVKZNxfZiP\nj1IhIUr17avUxx8rtWWLUnfuWN5fdDQLwt94Q6mGDZXy9LS+n+rVlerXj40Ix465VJ2ZQ9dxPAyj\nUanISKUGDrRsCClaVKkRI5Q6ckTvFTo2584pNWyYUn5+2mvXqpVSv/76yL3tlHtF0A2H2C/JybxO\nmN7Xg4LYHCY4FLoX6xuNRlW3bl21efNmpZRSR48eVaVLl1bx8fFqwoQJ6sCBA0oppWbNmqWOHj2q\nlFLqypUrqm3bthadliZcXog9jJgYpX7/Xalp05Tq0YPdYx4eGQu0qlWVev55pd5/n92V0dHaBeju\nXaU2bFBq4kSl2rXLuPOzRAmlunZVauZMpXbtkq4+PblzR6kvv1Sqfn3L31GrVkotXqxUQoLeK3Rc\nrl1T6p13lCpcWHvdgoOV+vZbFv0LgjNz6JD2vuDhwYaVpCS9VyVkgO7F+gBw5swZTJo0CU2aNEFk\nZCSGDRuGhg0bolGjRhg/fjy6deuGp59+Grt378aQIUNQqFAhhIeHo2gGQ7pdKjVpK/fuAQcOWKY2\nDx7UnN3NKVnSegh69epMZ+7fbzmeKSbG8mfz5uVIJlOdWfPmQKFCufMcBY09e1hLtny55jlXuDDn\nxQ0aRMNTwZq7d5nunT1b29tVq3LY8csvS7pXcC6MRvqAjR/POuHKlTkaLDRU75UJD0H3GjF7I0Ls\nMaSksE7MfAh6VBTrj9Lj78+6M/PGgMBA4MoVS2F29Kjlz3l4sAjafKh5hQq58/yyiEPVcdiLuDgW\n9hsMwD//aOdbtGAt2YsvZn4clzuRlMQL1owZrKUB2BgzYgQwZAgi9uxxvb0i5Bi6vLecP88mHlN3\n3oABwEcfsYZYcFhEiAlMypw/by3OLl2yvq23N1C7tmX0rEIFFkKbhNnff1t3e1aoYCnMAgMdolDU\nJYWYOVFRdJ5fulRr8ihUiIW7gwZxRqpgSWoqZ4JOn641RRQujIguXRA2axZQooS+6xOcglx9b1GK\nHyLeeIMR3pIlgQULgC5dcufxBZsQISY8nOvXLbs1o6I4rNxotL5tpUqaODPNCT1xQpufefu25e0L\nFbK2zZBxNDlHfDzw/feMku3erZ1v2pRRsh49xLYkPUoBv/8OTJsGbN3Kc35+HD/19ttAxYr6rk8Q\nACA2Fhg8GPjxRx5368ZUu3xgcBpEiAlZIyGBdWbm0bMDB5jWSU+xYhRmwcF8U0hIAE6eZCv1v0Z2\nD/Dx4axMk2VGy5byRpJT7N/PKNmSJfz0DHCuXO/eFGUhIfquzxHZvp0Rsl9+4bG3N9CrF4ck16mj\n79oE9+WXX/jB4OpVph8//ZR1jY+bZSw4FCLEBNtJTWWkLH30LL15LMCIQlAQGwHy5mVt2vHjwKFD\n1pG2mjW1iFnLlkC1anZ/g3H51OSjSEjgwHGDgUPlTTRuTEH23/8C+fPrtz4HIyIiAmHFitGL7Lvv\ngLQ0/kfXrjSHbdpU3wUKDkWOvrfExQEjRzL9CABhYcCiRUBAQM48npCjiBATcgalgIsXLScF7NvH\nWrT0eHoCNWoAZcvy+9hYirP0UbaSJS3rzEJCGEmzAbcWYuYcOsQo2eLFWho5f35GyQYNYrTSzbHY\nK2fOADNnAl99xc40AGjbluaw7dtLRELIufeWbduAV17hHvT1BaZOBd5803qyiuA0iBATcpebNynI\nzKNnR49q0QVzSpUCihfn/125Yt3ZmS+fpW1Gs2ZMsQnZJzGRheoGA9/wTTRowChZz57yGptz9Sqt\nAj7/XEvzNmzICFm3bg7RkCK4CMnJwMSJ7OpVih9ElywRWxoXQISYoD+JiYzImIuz/fuZOkuPvz+F\nQFIScOuW5f95ejLtaR41K1cud56DK3LkiBYlM6WZ/f0pxsLDgUaNJPJj4s4dirE5c4Br13iuRg3W\nkPXpYzlqTBCyysGD3EcHDvB9buxYijLZVy6BCDHBMUlLY2G/eWozKoqdnOnx8mK9WUICPymaU6mS\nNjczNJSF1WYhfElNZoKkJGD1akbJtmzRzoeEUJD16uUWBr6Z2iuJicDXXwMffqg1pJQrx7l+gwZJ\nzZ0bYZf3lrQ0+oBNmEAj7qpV+cGoRQu7rFFwDESICc6DUsDly9ZD0NMPLjfh6WndAFC4sNaVGRqK\niMREhHXokPNrdxWOHWOB8KJFwI0bPJcvHwv7w8NpQ+KiUbIsXVhTU2kXMn06o70AULQoMGwYv4oV\ny7F1Co6BzULs7Fmas/71F48HD2Zdooh5l0OEmOD83L7NVKZ59OzIEV4MH4ePD1NsrVoxYtaihVwk\nM0NyMn2LDAbgzz+18/XqUZD16UPR6+4YjcC6dfQi27mT5/z9+RqNHAmUL6/v+gTHQylGVYcP56iy\n0qWBhQuBTp30XpmQQ4gQE1yT5GTg8GFLcbZ/vzaD8VFUrgw88QTQujXFWeXKLhvlsQsnTjBK9vXX\nWurYzw/o3p2Co3lzef2UoinstGk0iQX4IeCllzjTsmZNfdcnOAbXrvFvZu1aHr/wAvDFF2xaElwW\nEWKC+2A0coagWWozYtcuhKV3/U9PgQLshHvqKVoTBAfT0FOwJDmZF5D584GNG7XzgYFalKxoUf3W\nZyN2qyfct48py5UruSc9PIDnnqP1hdiEuAxZ3i9r17KOMDaWNZdz59I+xt0/xLgBtugWMS0RnAtP\nTxrJdu9O753ffmN67coV4Ndfee75563TRXFxHKI7dizTmHnz0ly2d29gxYrMRdncAV9fvrYbNgCn\nTvH1KlmSkcnhw+kT99JLjAw53me43CMkhIawx4/zwuvjA6xaxb3VoQNTve78+rgbd+8C/fvTGDg2\nltF4U5ekiDDhMUhETHBd4uKYyty7l8Wyf//NIegZzdkEaKlRowZTmc8/z1ozMVhkp9fPP7OWbP16\n7XytWoySvfyy1ORdvszOuC+/1ER9kyaMkD37rOwjV+avv2jOeu4cP+BNn85mDvmduxWSmhSEzHL/\nPs1nt2yhqNi3D4iJydiM1sODszIDA/kJ96mnWMju65v763YUzp5lLdlXX/F1A+iD9MILFGWtW7t3\nBODWLeCzz4CPP9Zq7WrXphdZr142T5EQHIjkZOCdd4BZsxj9bNiQthQyt9QtESEmuDU21/0YjezQ\nXLUK2LyZ39+4kXFqycODHVAhIUC7dkxFhYS4hQeXBSkp7CQ0GFi4bnqtatSgIHvlFYcsTs41z7n4\neHbJzZzJMWEAULEi8PbbwIABtAsRHJ6H7pf9+5l2PHSIHojjxwPvvitC242RGjFBsAVPT44YmTiR\nkbLYWAqNTZuA116j07+fH2+rFOvRfvuNF9WwMFo8lCnDFNT771OgREe7do2Qjw/rYX79lVGyd99l\n/diJE3xdypWjL9nmzQ9PBbsy/v7AG2+wsWTRIkbFLlzguYAA7pP0UyUExyctjanHxo0pwqpXB7Zv\nByZNEhEmZBuJiAlCZlCKw843bQJ++QXYvZuC7FEUK8b5jvXr8yskhG/crjq7MDWVwsxgoFA1CbBq\n1VjQ3rcvC//dEaMR+OknWl9ERvJc/vzAkCH0IitTRt/1CY/nzBnWQ27fzuPXXuPMSH9/fdclOASS\nmhQEPbh1C9ixg8W6GzdyhtzjDGjz5aN1RkiIJtDq1mWRrytx4QLryBYuZIMEoEXRwsNZc+eOxcxK\nsaNy2jTNHiRPHorUUaMoWgXHQinWRY4YwZRzmTL02+vYUe+VCQ6ECDHBrXGYWZPJycCePcC2bfz6\n6y8Okn4cXl5MXZmLs5AQoEiRnF9zTpOWxhoyg4GRRFOUrEoVLUpWunSuLcdh9grALt4PPuAMUKUo\nTF98kZYhISF6r04AELF6NcK+/pp7FwB69OBgeCf20hNyBhFiglvjUBdXc4xG+kyZhNn27awZyiwB\nAZooMwm08uWdtyvx0iVGEhYsYMQMoKnus88ySvbkkzkeJXPIvXLsGFNcS5ZoEdWnn6Yga9XKeX/f\nzs7q1Yjo1w9hd++yDvTzz4GePfVeleCgiBATBGfhyhUKMpM427fP2jrD15cX5IwsNYoVozAzF2c1\najjXlIC0NFqHGAz0JzM9z0qVgIEDgX79WPjvbly8CMyezdclIYHnWrSgF1nnziLIcos7d9hUsXgx\nj598kml2mSkqPAIRYoLgrNy7x8J/kzDbuZN1KOb4+bGwOz5eu0CbkzcvOzvNo2f16jmHRcLly1qU\n7Nw5nvPyArp0YZSsQwfXbW54GNevA59+yi9TZ2XduoyQ9ejhXKLb2fjzT6bLL1zg392MGSzKd8d6\nRiFLiBAT3BqHTDdll9RUehSZR83Sd2f6+DBi5OvLT+9Xr1rfj6cnh1CnT206qgO+0cjidYOB8/pM\nKbqKFem71b+/XSISTrVX7t3j6zFrFgUrwKjhqFGMGposVQTbSUqiF9hHH/G4cWNgyRJEXLniPPtF\n0BURYoJb41QX16yiFH26TDVm27bRcDY9lSuzm8vTkxGVkyczTm2WL28tzgICHCvtFRND763582kZ\nAPB5de7MKNnTT2c7SuaUeyU5GVi6lIX9J0/yXKlSwJtvAq++6n5mwvYmKormrEeOcF+9+y5FmY+P\nc+4XQRdEiAmCO3HjBm0zTMLs7785usmc8uU5aqV4cUaXLl5kpC2j1GbhwpowM/1bq5b+BpVGIw1h\nDQZgzRqa7AJ8bgMG8KtCBX3XmJukpbHDcto0igeA81Ffe42irFQpfdfnbKSmUty+9x6/r1mTDRON\nG+u9MsEJESEmCO5MUhLwzz9a1Gz7dmvX9oIFgebNKbAKFWLa69AhXtBjY63v09eXdUnm4iwoiLVq\nenDtGvDNNxRlp07xnKcno2Ph4UCnTu5TO6UUsGEDBVlEBM/lzcv07ahRTF8Kj+bUKZqz7tzJ42HD\n6JjvDHWVgkMiQkxwayR9kA6jkYPNTTVm27ZphfAmvL05pLhlSw41z5uXKdCoKHZyZmSz4eHByQDm\nXmf16+euW77RyDFUBgNng5qiZGXLalGygICH/rjL7ZVduygg1q7lsZcXLRbGjKGQFixRCpg3D3jr\nLUaHy5Vjs8iTT2Z4c5fbL0KOIUJMcGvkzTITREdbNgDs3289A7JGDSA0lF9BQYya7d9PcRYVBRw+\nnPHkgLJlrVOblSvnfKdZbCwtBgwGzrgEKBY7dmSU7JlnrNKrLrtXDh9mmm35cq02sEsXWl80b67v\n2hyFK1co1H/7jce9egFz5z7SONll94tgd0SICYKQNe7etbTN2LXLun6sRAlNmIWGsubs5Ektamb6\n99496/svWJCjnMzFWZ06HOdjb5TiFAODAfjhB61ernRppusGDqQwdAfOnwdmzqQdSFISz7VuTUHW\nsaNjNWXkJitXcq7nzZsUXl9+CXTvrveqBBdChJggCLaRkkJRZR41S2+L4ecHNG2qCbPmzVkzduaM\npTiLimLnY3p8fJgGNU9tBgdTtNmLGzcYJZs/n+lZEx06MEr27LP6NyHkBteuAZ98woiPacxWSAi9\nyF54wX282W7fBoYOBZYt43HHjjRndUfDYCFHESEmuDWSPsgBlGKdmLltxrFjlrfx9KRxrHnUzOT1\nFRNjGTWLitKsF9JTrZp1arNMGdvXv307o2QrVtACAkBEkSIICw9nlMwdBmzfvcvoz0cfaeK4WjVg\n9GgWq/v66ru+nGTTJpqzXrrEIvyZMxkVy0JUUN5bhMwiQkxwa+TNMpeIjaVthilitmePVixvIiCA\ngqxlS/4bGKjVisXFAQcOWIqzQ4esrTcAWjGkH4JerVr26s5u3qQPl8GAiMOHEWY6364do2Rdu+ZM\nytSRSEpi1+mMGZo3W5kywMiRwODBQIEC+q7PniQmMvL3ySc8btqUthTVq2f5ruS9RcgsIsQEQch9\nEhPpYWYSZjt2aGkwE4ULc16iSZw1bmzpCJ+SwhSiKaW5bx+/0t8PwDRocLBl9Kxu3cxHdZSiXYHB\nAHz/vVZDVaIEIyeDBmXrYu1UpKayjm7aNIpigDVTQ4fSwqFECX3XZyv//AO89BKjt97ewMSJFGXu\nYm0i6IYIMUEQ9MdoZPeeuW3GhQuWt/HxARo10lKZLVrQdNYcpWi3YS7OoqLY+Zkeb282AZhHz4KD\nKQAfxe3brBuaNw84eFA737Yto2Tdurl22k4pdg9Om8bfE0CBPGgQrR0qVtR3fVklNRWYOhWYPJnf\n167NKFjDhnqvTHATRIgJbo2kDxyYixctGwAOHKAIMKdWLcs6sypVMq7jiY21rjs7ftz6/gB2SaZP\nbZYrh4gtWyz3ilJAZCSjZN99p3WOFisGvPIKhUmtWnZ7ORySbdvoRbZuHY+9vYHevelFVru2vmvL\nDCdOMAoWGcnjN9+kKLPDLE55bxEyiwgxwa2RN0sn4s4dpgdN4mz3bqY4zSlVylKYhYQ8PLUUH8+I\nlnn07OBBLe1oTvHiiAgIQNgTT2gCrXp1rYPwzh36cBkMvB8TrVszSvb88zS+dVUOHKAX2XffMbrp\n4cH6ubFjgSZN9F6dNUoBn3/OaQKJiRx3tWgR8MQTdnsIeW8RMosIMUEQnJP79ymgzLsz049c8ve3\ntM1o1uzRxeWpqYyUpU9tph/7BLCbLijIMnoWGMgB0AYDhVl8PG9btCg7DQcNYjrUVTlzBvjwQzrO\n/9ttiieeoBdZu3aO4UUWHU2PuPXrefzSSyzOf1xKWhDszdWrwNSp2PTssyLEBEFwAZSizYV5nVl6\n2wtPTwonU2dmaOjjfaGUYr1a+tRm+ho2gBGyWrX4GLVr05vszz8to2ShoYySvfCCXVJgDklMDDBn\nDqNOcXE816gRI2TduuX85ISH8d13HHR+6xZTyPPmMVopCLnJrVu0RJkzB0hIwKaNG0WICe6LpA9c\nnKtXLW0z9u61HrVUubImylq2pIDKQChY7ZUbNyzHOO3bxy7O9OOfADr1580LXL6sWW4ULqxFyVx1\ntuPt28AXX9CLzBStrFmTNWS9e+ee9cfNm8Drr1OIARz0vmCB7Z5zj0DeWwQr4uMZfZ0xg38bAPDs\ns9j0xhsixAT3Rd4s3YyEBBZmm9tmmCI2JooUsYyYNWwI5M2bub2SmMg6M/Po2f791rVs6alWjTYY\nw4bZd1qAo5CYSFf6Dz/kKCWABr5vvUUh6u+fc4+9fj3Qrx9FsL8/MHs2HzOH06Ty3iI8IDmZ5QpT\npmhTR9q2ZWNIs2ZSIyYIghuTlkZjWJMw27rV2uoiTx56mJnbZhQtmrXHOHHCcoxTVBQjahlRsiTQ\nqhVrqurXZx1avnzZf46OREoKfdimT6ddCcDX8o03KEKz8ro+joQETgH47DMet2jBEVZVq9rvMQTh\nUaSm0hD6vfe0DyBNmlCAmekUEWKCIAgmTPVg5g0Ahw5Z21zUqWPZnVmpUtYiLEpR8EVFMUL3668U\nJqYCd3M8PJjOMx/jVL++tYeaM2E0Ar/8Qi+yXbt4zt+fTv0jRwLlytl2/5GRLMI/cYL+c//7H0WZ\nu8zJFPTFaARWrwbefVcb7xYYyIjYs89avVeIEBPcGkkfCI/l1i1g505ELFuGsEuXaJuRXjCVKWMp\nzIKCsufIvn07MGsWDVMzstEwp1w5S6+z+vWzLgj1Ringr78oyP74g+d8fFg7N3o0UKNG1u4vJQV4\n/31e8NLSePFbupSvTy4j7y1uiFJMhY8fz3pUgN6G//sf0LPnQz8I2KJbZO6DIAiuT5EiLO7Olw8I\nC6MI27tXS2du3w5cuQKsXMkvgCOVmjfXas2aNuW5x9GyJb8SEnhfBgPr2EyULEn7jStXGFGLjmZk\nyUShQtZD0GvXprhxRDw8gDZt+BUVxZTlypXAwoWsKXv+eVpfNGjw+Ps6doxRsH/+4f2+9RZFmSv7\ntwmOw7ZtwIQJ/GAB8MPZ//0frVJysClFImKCIAhK0XvM3Dbj9GnL23h5URSZDzUvXTpz93/4MDB/\nPgdvmzqt8ucHOnfmSKa7d7W6s2vXrH8+Tx52ZZqLs+DgzAlDPTh5kl1l33yjDYbv0IGCrE0b64if\n0QjMnctOzKQkDo//5hveVhBymqgo4J13WF4AsM5x7Fh26WaytlNSk4IgCPYmJsZyPFNUFFNl5lSt\nammbUavWo9OKiYnAqlWMkm3dqp1v0IBdgL16sT3e3OssKspaFAJ8nGrVrFObpUrZ5/nbg+ho2l58\n+aVmjNu0KQVZly60GLl4kR2Rmzbx//v2BT7+2DU7TwXH4vhxRrxWrOBx/vysbxw5kpHpLCBCTHBr\npI5DyCw27ZV79yxtM3bu5DlzihWztM1o0ODhw8OPHtWiZDdv8ly+fKxDCQ9nl6dJ1N29SwsNc3F2\n+LAWbTKnTBnr1GaVKvoZsAJ8fnPn0n/J1Glapw47S7/9ls+veHEK1G7d9FtnOuS9xUW5cAGYNIkj\nsdLS+Df6+uuMgpUoka27FCEmuDXyZilkFrvuldRUzmc01Zht3cq6L3N8fdnqbhJmzZuzXs2cpCR2\nZxkMwJYt2vngYAqy3r0z/nR+/z5HMZlHz/bts/ZUA1iTFhxsGT0LDMw9M1YT8fE0YZ0xg55gJurW\nBX76ica8DoS8t7gY167RduKLL/j34+UFDBjAzsjy5W26axFigiAIeqMUcO6cZQOAyWfLhIcHBZB5\nd2bFilrk6/hxCpVFi4Dr13nOzw/4738pypo2fXTq02gEzp61Tm2mF4gAi/8DAy2jZyEhOZ8S/O03\nFj/HxPC5mC5BJUoAw4czMiEzIwV7cvs2O5k/+khLkffsyU7I6tXt8hAixARBEByRmzctxzP9/bc2\nHslE+fKW6cx69RhtW7OGUbLNm7Xb1qtHQdanT9bEytWr1nM2T5609lYDWPdm7nUWEsJ0p62WGvHx\nwNtvs14M4HP9+mtGFadNY6ckwOjdkCHAiBE5Or5IcAMSEoBPPwU++IAWNgDwzDPsxA0OtutDiRAT\n3BpJHwiZRfe9kpQE7NljGTUzXSBMFChAB3lTA0CxYsCyZRQtplmPefMC3btTlLVokT2RdO8eRZC5\nODt40FooArTcSC/OqlfPfN3Zzp30FTt1iunQyZNpTWHyZFKKgnPaNK1o39eXhfujRunmpK/7fhGy\nx/37rL98/31GXgF24E6dyr+XHECEmODWyJulkFkcbq8YjfTOMrfNOHvW8jbe3iz6b96c6cTISM3n\nCGDRe3g4/bdsHS+UksL1mA9Bj4oC7tyxvq2/P6MK5qnNunUtPb/u32dR9LRpfK716tGcNSjo4Wv4\n+296kf34IwWapydF59ixdo9iPA6H2y/Co0lL44eWiRNZJgAAjRpRgLVvn6NGySLEBEEQXIXoaEbK\nTNYZ+/ZRxJgTEMBarvPn2XEIMIL04osUZaGh9rvoKMXHSS/OLl2yvq23N81nTenM1asZBfPwYGRr\n0qSHd5Gm5+hRFvUvXcpULUBT3nHj+PwEwYRSFO7vvMN9A/ADyvvvA1275sqkChFigiAIrkpcHGc5\nmlKZO3ey9sUcHx9LK4uaNSnIXn455+ZZXr9uXXd2/Li1aAQoypo2tUxtli+fuQvkxYsstJ4/X3ve\nLVtSkHXq5FzjoAT7ohSwYQPd8E01hpUqsQi/d+9cnUsqQkxwayR9IGQWl9grKSn0FDNPZ169mvFt\nvbzo1fX227kjWo4f5wVwzx4elyhBIZnRzM1ixayHoNeo8fCL5/XrLLz+9FOtri4oiCnLF1/M3lzQ\nx+AS+8VV2bGD8yBNli+lS9OGYuDA3LdlgW26RUeHP0EQBCHL+Piw7uXNN4EffqA1xalTtLwYOJDu\n/ibS0oCICHaK+fmxUHnePEaZ7IlSwOLF9Ezbs4fF/WvX0rcpLg44dIgpxrfeAtq1Yy3bjRvAxo3A\nzJkUb3XqsFGhWTN2Tc6bx3q4xEQ+RvHijHScP8+fKVuWzQa9ejEC+OWXjx+yLjg/+/dzKkPLlhRh\nRYqwK/L0aeC113QRYbYiETFBEARX4/p1RgzWreP8vIzquUqWpChq1YoXtcDA7KVyrl8HBg9mPRjA\nmhyD4dEO5UpRDJp7ne3bR5GVHk9Pikvz6FlICMfRLFnCi/CpU7xtqVK0vXj1VRmR5GqcPMki/G+/\n5bG/P3/Xb73lEL5zkpoUBEEQHk5cHEcMLV7MrsiMKFRIs80IDeWIJT+/R9/vunV0Jr96ldGsTz4B\nXnkl+ynQmzcpyMxrz44etZ7xCQAVKmjDzxMTaRRrMtAtVIjGsMOHU3AKzsvFi7Q7+eor7oM8eRj5\nGjfOoX63IsQEt0bqOITMInsFvLAtXMhU3sNqywCmQBs21IRZixZalOvePQ5Gnj+fx23aMDVaqZL9\n15uYyNSmuTjbv9+6YQFglMzbm07qAC/aAwYAo0dna22yX3QkNpa2J59/DiQnM1rbrx/rwCpW1Ht1\nVtiiW+xf3SgIgiA4LhUqAO+9xwva778zjbhunRZ1KliQaZ8rV9ituWsXa7IA1mJVrw7s3s0LpY8P\nL5YjRuTcUHE/P0bnGjfWzqWlMVVlntqMitLGQpm4f59zBb/4AqhWjaOiOnVikb+/f86sV7CNO3e0\ncY4Cg1kAACAASURBVET37vFcjx6sD6xZU9+15RASERMEQXB3oqPp3D9/PnDhAs95e9NyomJFirLd\nu7XCeRNFiwJhYVrULCSE4kwPlOIgcXM7jcjIjOvjPDzYoZm+a/NRdW1CzpKQAHz2Gc18b97kuc6d\n6QUWEqLv2jKBpCYFQRAE20lLoy+TwQD89JMWJStblt9fvaqJmJs3tZFLJvLlY9ejaXZms2b6F83f\nvg388Qdr5HbuzLjezETZspZeZ/XrA5Uri1dZTnL/PlPlkydrw+lbt6YbfsuW+q4tC4gQE9waqeMQ\nMovslSxw5QovkLNnW87DbNWK3l0dOnAck7mf2YkTlvfh6clietPczNBQoFy53H0e5ly9yoaCuXO1\niQTFi9PTLDpaS4X9SwSAsIIFLbs169en1YZekT9XIS2NHZATJwJnzvBcgwYUYB06OJ34lRoxQRAE\nwb4kJzM6ZhJhlSuz0H/rVn5VqEDfsv79WUQN0Ddsxw5NmO3Zo9Vvffopb1OpkpbKbNmSoian6svS\nU6oUMGUKi/e//JJ1SFevsrasWjUOGa9Uid2XUVFMx966xdme5vM98+Sh3Yd59Cw4mJ2jwqNRih5z\n77yjdbnWqsUU5HPPOZ0AswcSERMEQRA0lGIH5PDhtL0oVYqRsc6dKVoWLWLq0hTF8PRkAXx4OPD0\n05YO9wkJrNMyzc3csUOLRJkoXFiLloWG0qzWfHB4TpKUxOczY4Y2bL1sWXaEhodTWMXEWNadRUVp\nvmXmeHhQzKWPnpUunTvPxRnYuJFu+H//zeOAADaO9OmTI5MRchNJTQqCIAi2c+0aBcjatTx+/nlG\njtLPqzQagT//pCD78UdtzmW5crSLGDAgY4uBtDRaUZjmZm7dal1MnycPxZi5bUaxYvZ/ruakpgIr\nV7JQ/MABnitSBBg6FHjjDevnHxdHCw1zgXbokOW8TxOlS1uLs6pVcy8K6Ajs2sV5kJs387hUKUbE\nBg3K/BB4B0eEmODWSN2PkFlkrzyCtWt5YYyNZYH93LmMVDwuVXTtGvDNNxRlpkiRhwejY+HhjKQ9\nKtpx4YJlndmhQ4zKmVO7tibMQkNzroBeKU4imDYN2L6dNWL58vF1eestpmMfxv37NJ81F2f79llH\nAAH6nQUHW6Y2AwNdRpQ84OBBCq6ffuJx4cLAmDHAsGEuZx8iQkxwa+TiKmQW2SsZcPcufcC++orH\nbdsyXZdV00ylOPvPYABWraIwAZjq69+fUbLMmKrevs3uRpMwi4y0niFZpoxlOjM42P6prW3bEPH2\n2wjbvZvH3t4UpmPGWM7zfBRGI3DunOUYp6go2mykx9ubYsw8ehYSwikBzsapU9o4IqXYTTtiBIfP\nO8A4opxAhJggCIKQdf76iyOJzp1jNGb6dKbibE2bXb/OcUoGA3D8OM95eAAdOzJK9swzme86vH8f\n2LvXMmp244blbfz9gebNtQaAZs0YdbIH+/dznuX331NYeXgA3bqxc9TcZDYrXLtmGTWLimLHaUaX\n4ypVLL3OQkIobh2xqD06mjYUCxcy3ZsnDwe4jx/PdKQLI0JMEARByDzJyUwZzZrFi3+DBhygXaeO\nfR9HKdaBGQzADz/wcQHWTfXrx67LKlWyfp/Hj2sNANu2WRfPe3lRsJh3Z5YpY9tzOX0a+PBDGt+a\non3t2nHm4RNP2C6M7t1jKs9cnB08qL1m5pQoYS3OqlfP3tB2e3D9OkX83Llcr6cnBf7EiSzIdwNE\niAlujaSbhMwiewWM8Lz0Ei/ynp6MVrz7LqMXOcmNGxR7BgNrqUw8+SSjZM8+m/01xMRQmJnE2d69\n1satVapY1pnVrPnYyF+G++XKFWDOHI5NiovjucaNGSHr2tW+RfgpKRSd6VObplma5uTLxxStuUCr\nWzdnO1Dv3qXP3OzZ2mvx4ovApEmZT9+6CCLEBLdGLq5CZnHrvZKWxpmR777LC3z16kwfNmuWu+tQ\nioJp/nxgxQqt/qtkSS1KVq2abY8RH08PMFN35o4dVmatKFrUss6sYUOrYvlH7pfbtzmQes4cbcJA\nzZqsIevdO+eErVLA+fPWqc2LF61v6+XFRof00bMiRWxbQ2Iin/u0aVqa+Omn6QXWoIFt9+2k6C7E\noqOjMWXKFAQFBWHnzp0YPXo0AgMDrW5nMBgQExMDpRRSU1MxefLkDO9PhJggCIIdOXMGePllihIA\neO01emfp3bl26xawdCmjZIcOaefbtWOnYteu9ukkTE1lBNC8zix9wbyvLyNb5rYZmREsCQlsdPjw\nQ21OZ4UK7LIcODD3XuPr1zVLDZNAO3aMdW3pCQiwnrNZvvzj06spKXyukyZpr19oKN3wW7Wy/3Ny\nImzSLcpGjEajatCggdqwYYNSSqkjR46oypUrq9TUVIvbrVmzRrVo0eLBcffu3dWCBQsyvM+NGzfa\nuixBEATBaFTKYFDK318pQKkyZZT67Te9V2WN0ajUjh1K9e2rlJ8f1wooVby4Um+/rdTx4/Z/vLNn\nlVqyRKnBg5UKDNQe0/yrbl3+/5IlvL3R+PD7vH9fqW++UapOHe3nixVT6n//U+rGDfuuP7PExyu1\na5dSX37J59G0qeXra/5VrJhS7dop9dZbSi1dqtThw0qlpPB+UlN5rmpV7fb16yv166+Pfk3cCFt0\ni81CbP369crPz0+lmH5hSqkaNWqoH374weJ2LVq0UJMnT35wvHz5clW3bt0M71OEmJAV/vzzT72X\nIDgJbrVXYmKUeuYZ7cLZvbtS16/rvarHc+uWUnPnKhUUZCkUwsKUWr5cqaSknHncGzeU+uUXpcaO\nVSo0VKk8edSf6cVKuXJK9eih1CefKLV3LwVKetLSlFqzhqLH9HP581PgXLqUM2vPCikpFFnLllHk\ntm9PEZaROMubV6kaNZQqUkQ7V726UitW8HkKD9BViE2cOFEFBgZanHvmmWfUa6+99uA4OTlZ5cmT\nR61cufLBub///lt5eHio2NhYq/sUISZkBbe6uAo24TZ7ZfVqRpMApQoX5kXX2SIXRqNSu3crNWCA\nUvnyWUZuRo5U6ujRnH38pCT156efKvXBB0p16aJU0aLWQqVAAaU6dFBq0iSlNm1S6t49y/X/+Sf/\n33T7PHmUGjhQqRMncnbtWcVoVOrCBaV++okRvK5dlSpdOmNx5umpVO3aSvXqpdSMGUpt2OAcAj+H\nsUW32OyAFxMTg4IFC1qcK1SoEC6Zja24efMmUlJSUMjMmK7wv6Zuly5dQvH04yMA9O3bF5X+Nf8r\nXLgwQkJCHhRNRkREAIAcyzFMmBfV6r0eOXbc47CwMIdaj92P79xBRI8ewB9/IAwAnnwSEYMGASVK\nIOzf+h+HWu/jjps0QURCAtCtG8IuXgTmzUPEvn3A7NkImz0baN0aEaGhQOvWCOvY0e6PHzZ0KI+b\nNEHYmjXAsWOIWLgQOHQIYadOAWfOIGL9emD9er7eXl6IqFYNqFcPYT17Ai1bImLcOOD55xG2YQOw\nahUiFiwAFixA2IsvAuPGIeLOHcd5vStUQMSlS8DFiwiLieH/588PhIQgLCAAOHAAEYcPA0ePIuzo\nUWD5cvCngbDy5YH69RFRuDBQvTrCXnoJCAhAxJYtjvP87Hhs+v7cuXMAgJdeegnZxeZi/aFDh+Lg\nwYPY8u+LDQC9evVCfHw81v47r+z69esoWbIkNm/e/ODJnDhxArVq1cKePXtQv359i/uUYn1BEIQs\nEhFB76YLF2hZMGMG8PrrrjXTUClgzx4W9y9fzu5IgEX1L7/MAv8MGsVyjMuXNcuM7dtZJJ++OL5a\nNa0BoFw5zrRcskSbS9mxI60v2rTR16T10CF21K5Zw+NChYDRo2nwa26Om5TE25oPQd+/n00L6Slc\n2HrOZq1amTfzdSJ0LdafMmWKCg4Otjj39NNPq1dfffXBsdFoVHny5FFr1qx5cG737t3Kw8NDXb16\n1eo+JTUpZAW3STcJNuOSeyUxkak6U+qoUaOcT9s5AnfvshGhUSPL1FnLliyaT0iw+SGyvF/u3mWq\nbuJEFr6bmiTMv4oXZ7qydWvWYJnON2um1Nq1uV97deqUUn36KOXhwXXky6fUuHFK3byZ+ftITVXq\n2DGlvvtOqTFj+PxKlMg4tenrq1TDhkzRzp2r1PbtSsXF5dzzyyV0TU22bdsW06dPtzh3/Phx9O3b\n98Gxh4cHwsLCcPLkyQfnjh07htq1a6NkyZK2LkEQBME9iYri/MMjR+gZ9e67NGh1wYiDFQUKMAI2\naBANXOfPB5Yt04xdhw+nce2gQUC9erm3pvbt+QXQNmP/fkvbjJgYYP167WdMMzJ37QL+8x9GjMaP\nB/7735z9PV6+zHFECxZwnT4+wODBwIQJnHyQFby86KFWsybQowfPKUXz2/RD0E+fZlRzzx7t5z08\n6Gtn7nVWvz695dwBW1Wg0WhUdevWVZs3b1ZKKXX06FFVunRpFR8fryZMmKAOHDiglFJqxYoVqnXr\n1g9+rkePHmrmzJkZ3qdExARBEB5BSopS77+vlLc3oww1ayoVGan3qvQnLk6pBQuUatLEMgrTvLlS\nX39NOwc9MRqVOn2aEbtBg1j0nlHUyNRp+cor9rfuuH5dqVGjtGicpydtQ86ete/jPIzbt5XaskWp\njz/m4wYHa/s4/VfZskp16qTUhAlKrVzJ6J2DdmvaolvsYuh65swZTJo0CU2aNEFkZCSGDRuGhg0b\nolGjRhg/fjyee+45AMDMmTNx+/Zt+Pn54e7du5g+fTo8MsiJS42YIAjCQzh1ivVQO3fyeOhQDqXO\nl0/fdTka+/YxSrZ0KUfxAEDBgowghodzHJAjcOMGnf+3beNczshI6/FMhQpxFFTbtpwGULdu1udK\nxsUBH33E+aKm1+P55xkVq13bPs8luyQnM6qbPnqWfhoCwN9hcLBl5KxOnZwf0fUYdHfWtzcixISs\nEGHWMSkIj8Kp94pSLFIfOZKF0eXKcQD1k0/qvTLHJj6eo5QMBqb/TDRpQkHWo4dlMboZuuyXxESO\nZ5o/H1i3Dvi3q9KCggXp/G9qAmjc+OFCPCmJczGnTqX7PsAGgfffBxo1yrnnYStGIydCmIuzqCim\ndtPj48MmDfPUZnAwX6dcQoSY4NY49cVVyFWcdq9cuQIMGAD89huPe/UC5s61fWagu3HwIAXO4sWa\nwClQgLMhBw2ympOo+35RCtiwgbV/kZEPv523N2dlmoRZy5bsWFy0iOOITHZSLVpQkLVpkyvLzxFi\nYqznbJrVn1tQrZp112aZMjmyLBFigiAIrsrKlcCQIcDNmxReX3yhFUQL2SMhAfjhB0bJTPM3AYqZ\n8HCgZ08KNEciMhKYPh348UcemwrcPT2BEyesbTN8fDSLjFq1OAuzc2d9LTJyirg44MABS3F26BBw\n/771bUuVsh6CXq2azTYvIsQEQRBcjdu3Wf+1bBmPO3YEFi5kSlKwH4cPa1GyW7d4zt+fUcfwcIoz\nRxIvR4+yJnDZMnY7AkCHDtwff/8N/Pyz5q9mTsmSjJSZomb167t2d21KCl8r8yHo+/ZlnOrNn5+p\nTPPoWd26WRo4L0JMcGt0Tx8IToPT7JVNm4C+fZlSypcPmDmTUTFHEgSuRmIisGoVRdlffwEAIgCE\n1a9PQdarV67WHD2WCxdYeD9/PtduTrly3D9FimiNANeuWd7Gzw9o1kxLZTZv7ljPLydQCjh3zlKc\nRUUB0dHWt/X2ZhOAefQsOJgp3wwQISa4NU5zcRV0x+H3SmIiMG4c8PHHPG7alC7s1avruy534+hR\nYMECRMyfj7C4OJ7Ll48py/BwFsc7gij++29g1CjAbLINAEZzxo8HXnyRgkIpdtuaJgBs2wYcP275\nM56eQFCQZZ1Z+fK591z0JDbWuu7s+HG+bumpXNk6tVmuHDZt3ixCTBAEwan55x8akB47xovnxIkc\nfeNts++2kF2SkliTZTBwhJSJoCAKst69HxohyVGOHGEB/+rVPC5YkKOIfH2Bzz9ncwcAVKnCMUWv\nvMKxV+bExlqOZ/rnHy3VaSIgwFKYBQa61sisRxEfz+YO8+jZwYPcE+kpXhybvvtOhJggCIJTkpoK\nTJvG7rbUVBZWL13K2iTBcTh+nC70ixZpNhB+fmycCA9nmi+no2RnzwLvvccoqVJ8/GHDgDFjgKJF\neZvkZNa7zZjBKBhAp/wRI5jeflj6MSGBETaTMNu+XfMbM1G4sLVtRnqB58qkpnIfpE9t3rqFTRs3\n6jdrMicQZ30hK7jk/EAhR3C4vXL8uKUL/Jtv2mVGomAfMtwvSUmcqdiunaULfN26Sn3ySdZmNGaW\ny5eVeu01pXx8+Fje3jyOjn74z6Smcp0hIdoaCxemS30GM54z/Pn9+5X67DOlevZUqmJFa+d7Hx9O\nLRg1inMyY2Pt95ydBaNRqXPnbNItIsQEp8fhLq6Crhw5otQff/Df9DjMXjEaOfDYz48XtAoVlNq0\nSe9VCel47H45eZJDrkuW1MRJ3rxKvfyyUtu28fdsCzdu8P5N+8TDg/d9+nTm78NoVOq33zhk3LRG\nPz+lhg5V6ty5rK3n/Hmlli+nCAwK0gaFm3/Vrs2B3osWcSSRra+Bk6D7iCN7I6lJQRCyw4EDQFgY\nXQiKFGFZT1CQ3qtKR3Q00L+/Nvi5Tx/g00/1qTUS7MP9+8BPP7GWbMMG7Xzt2kxbvvyyljrMDPfu\nAXPm0PvLlB587jmmrwMDs7/OHTvoRfbzzzz28mI36Jgx2bvf27c5rcA00Hz3busaqtKltRqz0FAW\nt7tg3aN0TQqCIAD49lteV0wsX85GN4fh+++BV1+lUixWDPjyS+CFF/RelWBPzpxhLdlXXwFXr/Kc\nry9/z+HhQKtWD68lS0oC5s0DpkxhMT3AEVZTprAey14cPMgasm+/1eZa/uc/bA5p1iz793v/PrB3\nr9YEsG2bVk9nwt/f0jajWTPHM8/NBjbpFjtF5eyKpCaFrOAw6SZBdyIiLLMkW7ZY/r9ue+XGDdbZ\nmBbWqRPrfgSHxqb9cv++UqtWKfXUU5YpvJo1lZo1y7KeKiVFqQULmKI23a5ZM6U2b7b5OTySM2eY\nZsybV3vcsDDm9u2RUjQalTp2jM+tXz+lqle3TmV6eirVoIFSb7yh1IoVj657c2AkNSm4NQ7vDSXk\nGomJwNat/GrVil9+ftr/67JX1q8H+vUDLl9mNGD2bM41dAQfKuGR2G2/nDvHqQgLF2rWEnnyAN26\nATVqAN99p81LDApiBCw3xxFdvUrvus8+01KhDRowQvbcc0xh2vOxzG0z9u61ts2oXPn/27v3+Bzr\n/w/gr5lhDs1pwoY1h5CFkUJpoqLIoZAcQ+hLKZnTz1lyqiUVQjn79i2JHFIoOUQyOZ/GDDNzGOY0\nm23X749XMyPa7L7v677u+/V8PDwerrvb7k/bZ9f9vj+f9+f9Tj+Z+eSTPEns5GUztDUpIuJsrl1j\nDafPP+d17dosK1CunLnjEvMkJwMrVjCX7McfMxYMLVIEeP99bl+aFXTEx7OX6ccfp1fir1CB87h9\n+yy1/Mm0q1fZRzNtK3PzZvaOvFWhQhnbM9WsaZ+xZIMCMRERZ7J1K4uzHjrEfn4jR7ICugsmKUsW\nrV/PqvdpzcZz5Ehv2O3lxVWy7t2B+vXNC8gSElgvbeJE1i4D2Dapb1+OLX9++712Sgpz2NICsw0b\nuJp8q9y5GYylBWZ16mTtMIQdZCduce61PpFMWHdrxWuRe7D7XLlxgxXx69RhEPbIIwzKBg1SEGZB\nNp0v4eFAo0bA008zCCtalNvU8fE8xdi0KYOQb74BGjbkStT48ekJ/47k7c1DJYcOsbl4UBBP+773\nHlC6NOd4XJx9XtvTkycre/fmlm10NIPB+fNZkLZKFRat3bSJ35+mTbmaWKUK//u8eXy+860x3Z1N\nstRsTMn6khVK1pfMsutc2b/fMGrWTK/39N57hpGQYL/XE7uzyXzZt88wXnklPTm9QAHDGDnSMOLj\n73zuiRP8b7cm7efMyX//88+GkZKS/fHcj9RUw1i2zDDq1EkfV968LEB8/Ljjx3P+vGEsX24YgwYZ\nxlNPGUbu3HceAihZ0jBat2aR3fBwHoiwIyXri4iYJTUV+Owz1mK6fp39+WbPZkEzcV9RUdySnjuX\ncyRPnvR2REWK3PvfpqQAP/3EXLLly9NLTDz0ENCtGw9/lChh9/+FOxgGtwrHjWOOG8Dt1Pbt+f/1\n8MOOHxPAFbLw8IxNzc+fz/ic/PmZp5m2nfn44zw8YyPKERMRMcOJEyzOumYNrzt35umzu/XzE9cX\nG8tTj198wa3qnDkZPA0dCpQsmfWvd/IkMGsWa5MdO8bHPD2Bl15ivtazz9r2VGNm7djBgOzbbxlo\nenjwhOXAgczfMlNqKntCpuWZbdzI+m638vQEqlfP2NS8ePH7fknVERO3pq1JySybzZXUVMOYP98w\nfHy4DVK0qGEsXmybry1OI0vz5fx5bpXlzZu+Pd2+Pdv82EJyMlsVtWxpGJ6e6VtwZcoYxujRhhEd\nbZvXyaqICMPo3t0wcuVKH1PDhmzZ5UztjWJiDOPbbw2jTx/DqFEj4/cw7U/ZsobRqZNhzJjBVIMs\njD87cYuS9UVEsiIuDmjThtsx8fFMFt6zh6fdxP1cuQJ88AG3DceOZdmS5s3Zb2vePKBsWdu8jqcn\nk/2/+44rsWmveewYV9vKlGF1/BUr0rcyHaFcOa7+HT3Kk8H583OFuEEDVs3//vv0U6FmKlGC3Q0m\nTQK2bWN7pjVrgBEjeDgiXz7gyBFgzhzW+atUCfD15fd04kSW1UhMtMvQtDUpIpJZq1ZxK/LUKb7h\nTJrEaxVndT+Jiczhev/99JpbDRpwW/Lxxx0zhtRUYO1ajmPJkvTCqKVKAV27cm6WKuWYsaS5cIG1\n8z75JL29UcWKzCFr1445Zc4oORnYuTNje6a04rtp8uQBatVKr2lWp87NHrHKERMRsaerV4F+/dgb\nEuBNeM4cIDDQ3HGJ4yUnc6VrxAjg+HE+9vjjDMDMfN86fZqHRGbM4MoOwDpkL7zAXLLGjR1bQuXa\nNXYS+PDD9O9TqVL8Pera1aaJ8nZhGFzlu/UAwL59GZ/j4cGyGU8+ibUvv6wcMXFfyhGTzLqvubJ5\ns2GUK8ccEi8vwxg/nvk64vIyzJeUFPZCfPjh9JyiKlUMY+lS58qFSklhflabNpyvaWP18zOMYcMM\n49gxx44nKckwZs82jEqV0sdStKhhjBrFvDorOXfOMH74wTD69zeMunUz5MUpR0xExNaSkoAhQ7gN\ncfgwi1r++SfbvZhxSk3MYRgs1VCzJtC6NU/jBQaywOiOHTy96Exb0zlyAM88w2KoJ08yv6l8ef59\n1CggIICrZEuW8FSnvXl5AZ06MY/y+++5tXfuHDBsGIvDhobeWTnfWRUpwpzQ8eO5QhYfz3IeY8dm\n68tqa1JE5Hb79rFF0fbtfJMNDeWbmJP1txM727iR7Yg2bOB1yZIMILp0cd5cp39iGMBvvzGX7Lvv\n+CEDYAJ7ly4srxEQ4LixrFvH4GX1aj6WKxeDtf79LduLVS2ORERsITWVDY+DgxmEBQTwDWz8eAVh\n7uSvv7hq9NRTDMIKF+bK0uHDQI8e1grCAH6YCAkBFi7kylhYGBPoT51ibltgIE9kLl5s/1UyDw/2\n0fz5Z64wv/IKX3PGDBaEbdOG3383okBMLE+9JiWz7jlXjh/nMfa+fXkirmtXliB46imHjU9MdvAg\ntx+Dg4Eff8Q6b2/2VTx6lEnm3t5mjzD7ihYF3n2Xq77r17MMS65crOT/8stMqB88+M4CqPZQsyYL\nwu7fz5U5T0/22gwO5uGC9eut1TPyPikQExH3ZhhsQxMUBPz6K1CsGLB0KSuZFyhg9ujEEY4dY+Bd\nuTIDg9y52eD6v//l6UhX7JTg4cEPGfPmMUdr0iT+/58+zW3DsmWB557j9yNtK9NeHn6YJywjIxkk\n5s3LUjFPP80TysuWOUctMjtRjpiIuK9z57jVtHgxr5s3Zx6Nr6+54xLHOH2ahVGnTWOw4enJfKkh\nQwB/f7NH53iGAfz+O38HvvmGvVMB/j68/jq/N+XL238ccXHAp5/yT1rPyCpV2D6pTRvHluHIJOWI\niYhk1YoVvLkvXsyVr1mz+HcFYa7v4kUGW2XLApMnM0fptdeAAwcYlLljEAZwlaxuXdbIi4nh96ZK\nFeDsWWDCBKBCBdZK+9//7FZlHgBPJ44YwZXKsDDAz4+nLtu3ZyA4ZQqQkGC/13cwBWJiecoRk8xa\nt24dW9J07w40acIVkXr1mAvWubNzlSEQ27t6lY2qH3qISepXr7L8xI4dwIIFd5zYc+t7S6FCwFtv\n8Xdj82auiHl7A7/8Arz6KoPV0FDg0CH7jSF/fm5VHjnCrcsKFYCoKKBXLx6kGTuWJSQsToGYiLiP\nPXuAqlV5QitXLlb9/vVXxx3dF3MkJQGffcYVsEGDuCIWEsJtuKVLgUcfNXuEzsvDgz0jv/qKpyw/\n/5zfr3Pn+Pvz8MPpJzLTtjJtLXduJvPv28ecteBgtpUaPJi1yAYN4ocqi1KOmIi4vqQknn6bMIFJ\nv1WrsiBnlSpmj0zsKSWFP+cRI7iSAgCPPca8sAYNtAJ6vwyDpSemT+eBhmvX+HjhwqwHltY0256v\nv2YNV8R+/ZWPpQVroaFc8XQw5YiJiNzNnj2s5j1uHK8HDQK2blUQ5soMg4VLg4K45RwVBTzyCCu7\n//EHy5QoCLt/Hh78nZo5k6tk06YB1aszsf7jj3n6sl49BsH2yOXy8ACefZbbpFu28JBNYiIwdSpz\nyNq3B3bvtv3r2okCMbE8t87jkLtLSeHWSY0awM6dQGAg1n3yCVdDcuUye3RiD4bBQqGPPcZCofv3\nc3Vk7lzOgebNsxSA6d6SCQ88wJPH27cD27Yx/zJ/fhbC7dCBifZ9+gB799rn9R9/nAH23r1AkZYv\n8gAAIABJREFUx478+S5YwO3Tpk25/ezkFIiJiOuJimK/vdBQbkt27843Yq2Cua5Nm1ix/fnngfBw\ntu+ZMoUnITt0UH9QR6hRA/jiC564nD6dBVsvXEg/fZl2IjNtK9OWKlfm1z58mIcMvL2B5cv5mvXq\nsV+o82ViAVCOmIi4EsMAZs/mJ/DLl4EHH+RpqxdfNHtkYi87drAUxYoVvC5cmPWmevViYVAx1/bt\nPByzYAF/JwHAx4fBcffu3D62h7NnGQB+9hkPZwDMDR04EGjVyuaBuXLERETOnAFatGDC7uXLbNey\nZ4+CMFd16BDLKFSvziAsXz5g6FBWZw8NVRDmLIKDmbsVE8MPRY8/zpITn33G7cPatVnD7+pV276u\nry8wejRrkU2YABQvzlXxtm150nP6dPud8swiBWJiecrjEPzwAz9ZL13KnJW5c3nMvWjRDE/TXHEB\nJ07wVF7lyiwsmjs3a01FRgKjRnG1xUY0X2wof35+SNqyhauYvXrxd3XLFj5esiQf27HDtq/7wAMM\nzI8e5bZp2bKsS9ajB5udT5yYvlJnEgViImJdly6xR2CzZlwRq1+fp6U6dNCpOFdz5gwDrnLleFoP\nYEAWEcHq68WKmTs+ybyqVbkiFhPD1bDatfm7PGUKVzjTTmReuWK718yTh1uhBw6w5EbVqjzx2b8/\na5ENHcrtTBMoR0xErGnDBp6Sioriqsi4ccDbbwM59PnSpcTHAx99xLIIaW/Mr74KjBzJSuviGnbv\nZi7ZvHnpOV358wPt2jGACg627esZBhuLjx3LewnABP9u3YB+/RicZYFyxETEfSQm8lPs008zCAsO\nZkLwO+8oCHMl164xt+ehh5jrc+UK21L99RdXNBSEuZagICbXx8QwteDJJ/kz/+ILnsasWZN5Xbba\nRvTwABo3BtavBzZu5NxKSGCj8bJlWZh23z7bvNa/0F1LLE95HG5k507WiJo4kTfSIUPYB69y5Uz9\nc80VC0hK4hZV2bLAgAEsf/D00yxPsWwZUK2aw4ai+WICb2+mFmzYwNpg77zDvpfh4czrKlGCW9J/\n/mm7chR163Ju7drF5u+pqQwGH3mEB4D++MM2r3MXCsRExPmlpADjxzMI272beUKbNnGlRMVZXUNK\nCrelKlZk0nZsLFdCfvqJbWzq1DF7hOJolStzSzomhlX669Xj6cqZM5lHlnYi01aNv4OCWGYjIgJ4\n802mPCxZwl6bzzwDrF5tl1pkyhETEecWGcltgo0bef3mm1wRy5fP3HGJbRgG3+yGDEnfCqpUCXj/\nfa5G6NCF3OrAAQZis2cDcXF8LG9e5g12784AzVZzJjYWmDSJK7RpW6I1arAWWYsWGWqRKUdMRFyP\nYfCGW7Uqg7ASJVgde8oUBWGuwDC4wvD440DLlgzCypThG+zu3XxMQZjcrmJFti47eZK5gvXrM5/w\nq6+4clWtGvD55+kJ/9lRvDgPAR0/ztZoxYpxi7RVK67WffUVt9KzSYGYWJ7yOFzQ6dMsSfHGG0zY\nbd2ab86NGmXry2quOInNm7nV89xzzPV58EGWMzh4kKufTtKOSPPFieXOzVWwX37hvAkNZd3AXbuA\n3r1Zl6xzZ/aazO7GX8GCwKBBPBz0+edAQAALCnftylpkH3+crS+vQExEnMv337Mv3bJlvAEuWAB8\n/TVQpIjZI5Ps2rULeOkl5nutW8ck7HHjWGCzVy++uYpkVYUKPGEbHc0ivw0a8ATknDlMxE87kXnh\nQvZex9sb+M9/GITNm8dk/pMngb59s/VllSMmIs4hPp49IufM4XXDhiz26O9v7rgk+yIigOHDGVAb\nBreW330XeO89Btsitnb4MFMbZs1iMWCARV1btWIuWd262d/6Tk1le62xY7F29GjliImIha1bx75z\nc+bwZjl5Mk/LKQiztuholhyoVIn5PF5eDLaPHOGJVwVhYi/lynG19cQJYNEiboNfv86VrKee4mrW\npEnpCf/3I0cOoGlTnuDOBgViYnnK47Cw69e5KvLMM0yIrVmTBTvfessuxVk1Vxzk7Fn+XMuVYxFO\nw2A/wYgIvvk9+KDZI8wUzRcXkCsX8PLL/GB35AgweDCT8Pfv56qsnx+r9//22/3nkmVzZU2BmIiY\n46+/GHiFhTHoGj6cibUVK5o9Mrlfly7x5xgYyJ9rYiIPWuzbB3z5ZZbbxojYVGAgMGYMP/QtXszD\nP0lJwMKFQEgIV24/+gg4d86hw1KOmIg4VnIyE2tHjABu3GCi7bx5rP8j1pSQwNNkY8cC58/zsRde\nYC2w6tXNHZvIvURF8UPCV1+xcCzAVbSWLZlLFhKSqRUv1RETEWs4fJjVsf/v/xiE9e7NlTEFYdZ0\n4wYwbRq3IENDGYQ99RTb06xYoSBMnF9AAPMVjx0Dli4FXnyR8/rrr5kykXYiMy3h3w4UiInlKY/D\nAgyDzXurVmUNKT8/4Oef2WA3b16HDUNzxUZSUlhWpGJFdjqIiWHQ9eOPzLV58kmzR2gTmi9uJGdO\nllZZvpyrZMOH87DQ4cPseervz232NWt4WtKGFIiJiH2dOgU0aQL07MkK2G3bsjjrs8+aPTLJKsPg\nqkG1akD79mw/9fDDwLffAtu2MedG1fDF6kqXZurE0aOsZ9i0KT98fPst71vly/NEZmysTV5OOWIi\nYj+LFjEAi4tj8c6pU4E2bcweldyPtWt54mzrVl6XLg2MHMmALGdOc8cmYm/R0axJNnMmk/0Bzvtm\nzYDu3bHW01M5YiLiRC5eBDp0YPHEuDjg+ee5CqYgzHr++IPFdRs2ZBBWrBjrvB06xBYyCsLEHfj7\nA0OHchV45UqgeXOuEH/3He9v2aBATCxPeRxOZu1athSZP58tQT7/nLlDfn5mj0xzJSt27+abzRNP\n8GdasCAbH0dGss6bG7Qj0nyRO3h6Ao0bsxXb8eM8GVymTLa+pAIxEbGNhATgnXe4chIdzZOQO3aw\nN5vyhqzjyBFuN1atynywvHm5JRkZycbH+fKZPUIR51CyJE+AR0Zm68toTVksLyQkxOwhSHg4tyL3\n7+dW1bBhfNN2sm0rzZV7OHmSn+5nzmStNy8v5velVSJ3Q5ovkinZ7ALiXHdJEbGW5GQW8Rw1in+v\nWJFbkjVqmD0yyaxz54Dx44HPPmPLqRw5gNdfZzAdEGD26ERcnrYmxfKUx2GSQ4dYL2rYMAZhffoA\n27c7dRCmuXKLy5d56jEwEPjwQwZhr7wC7N3LKuMKwjRfxCG0IiYiWWMYLEPRrx/zwvz9gdmzAZWc\nsYaEBP78xo5N76nXqBG3JZ04iBZxVQrExPKUx+FAJ08CXbsCP/3E6/btWR2/YEFzx5VJbj1Xbtxg\nHaRRo/hzBIC6dXkSsl49c8fmpNx6vojDKBATkcz53//YzubCBaBwYbYseuUVs0cl/yY1lX3zhg3j\niUiAlfHHjOExfJ1oFTGVcsTE8pTHYWcXLgCvvQa8+ir/3rgxsGePJYMwt5orhsH2LNWqAe3aMQir\nUIEBdXg48MILCsL+hVvNFzGNVsRE5O5Wr+YJupMnWU8qLAzo3l1v4M7u119ZdmLLFl6XKsXeeR07\nOl1JERF3p99IsTzlcdjBtWvAgAEsaQAAtWsDc+cC5cqZO65scvm58uefLDC5ejWvfX2BIUMYPOfJ\nY+7YLMjl54s4BQViIpLRn38yCf/QIa6ejBwJ9O+vlRRntncv++B9/z2vfXyA0FCWFMmf39yxicg9\nKUdMLE95HDZy4wa3r2rXZhBWuTKbPA8e7DJBmMvNlchIbjcGBTEI8/bmSmZkJFfGFIRli8vNF3FK\npt9dExIScO3aNRQpUsTsoYi4rwMH2KJo2zbmf/Xty1N12s5yTqdOAaNHAzNmpLcj6t6dwVeJEmaP\nTkSywGaB2JIlS7BlyxYULlwYJ06cQFhYGLy8vP7xue3bt8fChQsBAAULFkRMTIythiFuSHkc2ZCa\nyjywAQNYWb10aWDOHMBFv6eWnytxccCECazdlpDAdkSdOgHDhwMPPWT26FyO5eeLWIJNArHw8HD0\n69cPhw4dQo4cOTBgwACMGjUKo0ePvuO5p06dQpEiRbBt2zYAQLFixZBHn7pFHC86mici16zhdadO\nwCefML9InMvly8CkSWxFdOkSH3v5ZRZnrVzZ3LGJSLbYJEcsLCwMISEhyPF3B/LmzZtj2rRpSEpK\nuuO5U6ZMQe7cueHp6Yng4GD4+/vbYgjixpTHkUWGASxcyLyiNWuAokWBxYvZpsjFgzDLzZXr1xmA\nlS3LgqyXLgHPPccDFYsWKQizM8vNF7EkmwRiv//+OypWrHjzunz58oiLi8OuXbvueO7x48fxzTff\noHr16mjYsCEuXrxoiyGISGbExbEwa7t2wMWLQJMmwO7dQIsWZo9MbpWcDMycCZQvD7z7LnD2LA9R\n/Por20vVrGn2CEXERmyyNRkbGwufWz5JF/y771x0dDRq3nbDmDNnDgDgxx9/xOuvv4433ngD3377\n7R1fs3PnzggICLj59apVq3Zzvz7tU4qudZ1m3bp1TjMep72+fh3o0gXrTp0CvL0RMnky0LUr1v32\nG3DggPnjc8B1SEiIU43njuvUVKwbMQL46iuE/N0Pcl3ZskC3bggZMADw8HCu8br4tdPPF12bdp32\n96ioKABAhw4dcL88DMMw7vtf/61AgQL49NNP0blzZwBAUlIS8uTJg++++w4t7vFJe82aNXj++edx\n9erVDHlia9euRYMGDbI7LBEBgKtXWVNq6lRe163L4qyBgeaOS9IZBrByJU897tzJx8qV48nI1q2Z\nlC8iTis7ccu//nafOHECvr6+d/3TtWtXlChRIsMWY9rf/fz87vm1GzRogHz58uFSWvKpyH249ROK\n3GbLFqB6dQZhXl7AuHHAb7+5bRDmlHPlt9+AJ5/kNvHOnYC/P8tS7NvHbWQFYaZxyvkiLudftyZL\nlSqFs2fP3vM5PXr0wOHDh29eHzhwAD4+Pqhevfo9/11qaip8fHzg6+ubyeGKSKYkJXE15YMPWKIi\nKAiYNw+oWtXskUma8HAWy/35Z14XLcoVsZ49Vb9NxI3Y5KNW165dsWrVKqSmpgIAVq5cifbt28PL\nywvR0dHo1asXACAiIgKTJ0/G9evXAQAzZ85Enz594KEGwpINaXv38rd9+5jY/f773PIKDeUpOwVh\nzjFX9u0DXnmFCfc//ww88ADLUERGAu+8oyDMiTjFfBGXZ5Nk/Vq1amH48OF477334O/vj/j4eISF\nhQFgwv6qVauQmJiICxcuICwsDLNmzULr1q3h5+eHHj162GIIIpKaCkyeDAwcCCQmAgEBLM5ar57Z\nIxMAiIpiC6l58/izypMHePtt9vFUZxERt2WTZH1bU7K+ZMW6W05Muq3jx4HOnVneAAC6dgXCwrja\nIjeZMldiY7k6OX06+3nmzAm88QYwZAhQsqRjxyJZonuLZFZ24hbTe02KSDYYBldY3nqLxT59fVl/\n6qWXzB6ZnD8PTJzIbgUJCezh2aEDV8Xc9LCEiNxJgZhYntt+Yj13DujRg1XxAaBZM666FCtm7ric\nmEPmypUrDL4mTgTi4/lYixY8PPHII/Z/fbEZt723iEMpEBOxohUruP14+jRQoADf+Dt35qqLmCMx\nEfjiC2DMGODMGT7WsCGva9Uyd2wi4rRUoEYsz61q/Vy5wlWwJk0YhNWrB+zaxebdCsL+lV3mSnIy\n8NVXbEfUpw+DsCeeANauBVavVhBmYW51bxHTaEVMxCo2bQI6dmSZg1y5WCPs3XdV8NMsqalsvD10\nKHDoEB8LCuIKWJMmCoxFJFMUiInluXweR1ISE7zHj+ebf9WqTNAPCjJ7ZJZjk7liGMCqVSy++tdf\nfKxsWdYCUyV8l+Ly9xZxCgrERJzZnj08abdjB9/gBw0Chg8Hcuc2e2TuacMGVsPfuJHXfn7AsGHc\nGvbyMndsImJJ+ugmlueSeRwpKcBHHwE1ajAICwwE1q/ndqSCsPt233Nl+3agcWPm5G3cyAKsH34I\nREQA3bsrCHNRLnlvEaejFTERZxMVBXTqxMALYPHPsDAgf35Th+WWDhxgDtiiRbw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0OXtWC14VFcaC6ZQUqe9at07aQbS3S+B6/nng0UeNXe8B+Ynj30JCf0XkaDAw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\n/cpXvqJ4PB7F4/EoY8eOVbq6umw8U7KTz+dTFi1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xyJHAx82cKTVbK1fKjM3Jk/Ja/fCHcrajEh8vQUPNei1fPnQb0Pp8ga0k/M+0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\nIa2slNC1Y4ccpdPbodFKU1PvM1tjxkg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xfhPCFMUgRq43LSocFBauWyvqto5/k3xtrfRzmf0AjIvzzdzyD11JSfY+ByvO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\n8w1CVRSgq0v+HhUFLFsWWOXKypreVS6VogB1dfr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0zngdO2a8PznZGLwKCoCYGFk23bwZ+Pa3gffeA95/v+fXcTjkwzN4ud0yu+XZ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\n9w8ZIu9bLTcG006jn/A3VgoWxwqFguOFzMAgpmi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"text": [ "" ] } ], "prompt_number": 13 }, { "cell_type": "markdown", "metadata": {}, "source": [ "###MCMC sampling" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Monte Carlo sampling \n", "is design to estimate various characteristics of a distribution such as the mean, variance, kurtosis, or any other statistic. \n", "\n", "Markov chains involve a stochastic sequential process where we can\n", "sample states from some stationary distribution.\n", "The goal of MCMC is to design a Markov chain such that the stationary distribution of\n", "the chain is exactly the distribution that we are interesting in sampling from. \n", "This is called\n", "the **target distribution**. \n", "\n", "In other words, the states sampled from the Markov\n", "chain should follow the same statistics of samples drawn from the target distribution. The idea is to use some clever\n", "methods for setting up the proposal distribution such that no matter how we initialize each\n", "chain, we will convergence to the target distribution. \n" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### MCMC, MH Sampler" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The Metropolis-Hastings (MH) algorithm is the most popular of the MCMC \n", "methods (Metropolis et al 1953, Hastings 1970). As a matter of fact \n", "we will see that most MCMC algorithms can be interpreted as special cases\n", "of this algorithm. \n", "\n", "Suppose our goal is to sample from the target density $p(x)$, with $-\\infty< x < \\infty$ . The\n", "Metropolis-Hastings sampler creates a Markov chain that produces a sequence of values:\n", "\n", "$$ x^{(1)} \\rightarrow x^{(2)} \\rightarrow \\ldots \\rightarrow x^{(t)} \\ldots $$\n", "\n", "where $x^{(t)}$ \n", "represents the state of a Markov chain at iteration $t$. The samples from the\n", "chain, after burnin, reflect samples from the target distribution $p(x)$.\n", "\n", "The MH algorithm, initializes the first state, $x^{(1)}$ \n", "to some initial value, and then uses a proposal distribution $q(x_s|x_t)$ to sample a candidate\n", "value $x_s$ given the current value of $x_t$ according to $q(x_s|x_t)$. The Markov chain \n", "then moves towards $x_s$ with the acceptance probability \n", "\n", "$$\n", "A(x_t,x_s) = \\min\\left[1, \\frac{p(x_s) \\, q(x_t|x_s)}{p(x_t) q(x_s|x_t) } \\right] \n", "$$\n", "\n", "otherwise it remains at $x_t$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### M to be precise.\n", "\n", "Note that if the transition probability is symmetric $q(x_s|x^{(i)}) = q(x^{(i)}|x_s)$ then\n", "the acceptance probability becomes \n", "\n", "$$ A(x,x_s) = \\min\\left[1, \\frac{p(x_s)}{p(x) } \\right] $$\n", "\n", "which was the original algorithm proposed by Metropolis, thus the Metropolis algorithm.\n", "\n", "A major advantage of the MH sampler is that equation involves only a ratio of\n", "densities. Therefore, any terms independent of $x$ in the functional form of $p(x)$ will drop out.\n", "We do not need to know the normalizing constant of the density or probability. \n", "The fact that this procedure allows us to sample from unnormalized distributions is\n", "one of its major attractions. Sampling from unnormalized distributions frequently happens\n", "in Bayesian models, where calculating the normalization constant is difficult or impractical.\n", "\n", "\n", "The MH algorithm is very simple, but it requires careful design of the proposal distribution \n", "$q(x_s| x)$. \n", "\n", "Later we will see that many MCMC algorithms arise by\n", "considering specific choices of this distribution. \n", "A way to design these sampling mechanism is to ensure that detailed\n", "balance is satisfied. However, it is also important to design samplers that converge quickly\n", "or the burnin time is short. " ] }, { "cell_type": "code", "collapsed": false, "input": [ "Nmc=200000\n", "burnin=40000\n", "t1 = np.zeros(Nmc)\n", "i=0\n", "#Try 0.1, 1.0, 10.0, 100.0\n", "sig=1.\n", "t1_prev=np.random.randn()\n", "print \"Init\",t1_prev\n", "\n", "def randnms(mu, sigma):\n", " return sigma*np.random.randn() + mu\n", "\n", "posterior = lambda x: np.exp(-x*x/2.)\n", "\n", "proposal=randnms\n", "\n", "while i < Nmc:\n", " #proposal\n", " t1_star=proposal(t1_prev, sig)\n", " #New Posterior\n", " P_star=posterior(t1_star)\n", " #Old Posterior\n", " P_prev=posterior(t1_prev)\n", "\n", " A=np.min([P_star/P_prev, 1.0])\n", " U=np.random.rand()\n", " \n", " if U < A :#accept\n", " t1[i]=t1_star\n", " t1_prev=t1_star\n", " else:#reject\n", " t1[i]=t1_prev\n", " \n", " i=i+1\n", " " ], "language": "python", "metadata": {}, "outputs": [ { "output_type": "stream", "stream": "stdout", "text": [ "Init 0.929786392743\n" ] } ], "prompt_number": 14 }, { "cell_type": "code", "collapsed": false, "input": [ "t1clean=t1[burnin:Nmc:5]\n", "plt.plot(range(len(t1clean)),t1clean,'.')" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "pyout", "prompt_number": 15, "text": [ "[]" ] }, { "metadata": {}, "output_type": "display_data", "png": 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dJxlw0YcgiZWdrUtFq9WMJTvejbpqKpLEfTGQxOKJmSNQlJEtyX3NjomEVNgT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\nEDbPhjzSlY+6jpOaz6dlaqfs2U+3sYkw0pXPQMg8cJ5A/gSu1NpQyBbX1aJ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tdU7LtNa+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"text": [ "" ] } ], "prompt_number": 15 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.acorr(t1clean-np.mean(t1clean), maxlags=100, lw=1 , normed=True);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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IYwAAAB4KSRgrKSnRjBkztGjRIk2dOlXbtm1rdf+MjAyNHDkyFIcG6OuAbfSMwQlqC9wS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\nxclhrLW6cjo1p83+ofDWPkz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"text": [ "" ] } ], "prompt_number": 16 }, { "cell_type": "code", "collapsed": false, "input": [ "plt.hist(t1clean, bins=50);" ], "language": "python", "metadata": {}, "outputs": [ { "metadata": {}, "output_type": "display_data", "png": 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