{ "cells": [ { "cell_type": "markdown", "metadata": {}, "source": [ "# Probabilistic Programming 1: Bayesian inference in conjugate models\n", "\n", "#### Goal \n", " - Practice forming factor graphs out of probabilistic models.\n", " - Familiarize yourself with message passing on factor graphs.\n", " - Practice specifying models and inference procedures in a probabilistic programming language.\n", "\n", "#### Materials \n", " - Mandatory\n", " - This notebook\n", " - Lecture notes on factor graphs\n", " - Lecture notes on continuous data\n", " - Lecture notes on discrete data\n", " - Optional\n", " - Chapters 2 and 3 of [Model-Based Machine Learning](http://www.mbmlbook.com/LearningSkills.html).\n", " - [Differences between Julia and Matlab / Python](https://docs.julialang.org/en/v1/manual/noteworthy-differences/index.html)." ] }, { "cell_type": "code", "execution_count": null, "metadata": {}, "outputs": [], "source": [ "using Pkg\n", "Pkg.activate(\"../../../lessons/\")\n", "Pkg.instantiate();" ] }, { "cell_type": "code", "execution_count": 2, "metadata": {}, "outputs": [], "source": [ "using CSV\n", "using Random\n", "using DataFrames\n", "using LinearAlgebra\n", "using SpecialFunctions\n", "using Distributions\n", "using ReactiveMP\n", "using RxInfer\n", "using Plots\n", "default(label=\"\", linewidth=4, margin=10Plots.pt)\n", "\n", "import CairoMakie: tricontourf\n", "import ReactiveMP: @call_rule, prod, ClosedProd" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Problem: A Job Interview\n", "\n", "Suppose you have graduated and applied for a job at a tech company. The company wants a talented and skilled employee, but measuring a person's skill is tricky; even a highly-skilled person makes mistakes and - vice versa - people with few skills can get lucky. They decide to approach this objectively and construct a statistical model of responses. \n", "\n", "In this session, we will look at estimating parameters in various distributions under the guise of assessing skills based on different types of interview questions. We will practice message passing on factor graphs using a probabilistic programming language developed at the TU/e: [RxInfer.jl](https://biaslab.github.io/rxinfer-website/)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 1: Right or wrong\n", "\n", "To start, the company wants to test the applicants' programming skills and created a set of bug detection questions. We will first look at a single question, which we treat as an outcome variable $X_1$. Your answer is either right or wrong, which can be modelled with a Bernoulli likelihood function. The company assumes you have a skill level, denoted $\\theta$, and the higher the skill, the more likely you are to get the question right. Since the company doesn't know anything about you, they chose an uninformative prior distribution: the Beta(1,1). We can write the generative model for answering this question as follows:\n", "\n", "$$\\begin{aligned} p(X_1, \\theta) =&\\ p(X_1 \\mid \\theta) \\cdot p(\\theta) \\\\ =&\\ \\text{Bernoulli}(X_1 \\mid \\theta) \\cdot \\text{Beta}(\\theta \\mid \\alpha = 1, \\beta=1) \\, . \\end{aligned}$$\n", "\n", "The factor graph for this model is:\n", "\n", "\n", "\n", "We are now going to construct this factor graph / probabilistic model in RxInfer." ] }, { "cell_type": "code", "execution_count": 3, "metadata": {}, "outputs": [], "source": [ "@model function beta_bernoulli()\n", " \"Beta-Bernoulli model with single observation\"\n", " \n", " # Allocate data variable\n", " X = datavar(Int64)\n", " \n", " # Prior distribution\n", " θ ~ Beta(1.0, 1.0)\n", " \n", " # Likelihood of data point\n", " X ~ Bernoulli(θ)\n", " \n", " return X,θ\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Note that we may define random variables using a tilde symbol, which should be read as \"[random variable] is distributed according to [probability distribution function]\". For example, $\\theta \\sim \\text{Beta}(1,1)$ should be read as \"$\\theta$ is distributed according to a Beta($\\theta$ | $a$=1, $b$=1) probability distribution\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Having defined the model, we can now call an inference procedure which will automatically compute the posterior distribution for the random variable:" ] }, { "cell_type": "code", "execution_count": 4, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = inference(\n", " model = beta_bernoulli(),\n", " data = (X = 1,),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Under the hood, RxInfer is performing message passing. Each variable definition actually creates a factor node and each node will send a message. The collision of messages will automatically update the marginal distributions. \n", "\n", "We may inspect some of the message and marginal computations with the following commands:" ] }, { "cell_type": "code", "execution_count": 5, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=1.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message1 = @call_rule Beta(:out, Marginalisation) (m_a = PointMass(1.0), m_b = PointMass(1.0))" ] }, { "cell_type": "code", "execution_count": 6, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message2 = @call_rule Bernoulli(:p, Marginalisation) (m_out = PointMass(1),)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Alright. So, they are both Beta distributions. Do they actually make sense? Where do these parameters come from?\n", "\n", "Recall from the lecture notes that the formula for messages sent by factor nodes is:\n", "\n", "$$\\underbrace{\\overrightarrow{\\mu}_{Y}(y)}_{\\text{outgoing message}} = \\sum_{x_1,\\ldots,x_n} \\underbrace{\\overrightarrow{\\mu}_{X_1}(x_1)\\cdots \\overrightarrow{\\mu}_{X_n}(x_n)}_{\\text{incoming messages}} \\cdot \\underbrace{f(y,x_1,\\ldots,x_n)}_{\\text{node function}} \\, ,$$\n", "\n", "visually represented by\n", "\n", "
\n", "\n", "The prior node is not connected to any other unknown variables and so does not receive incoming messages. Its outgoing message is\n", "\n", "$$\\begin{aligned} \\mu_1(\\theta) =&\\ f(\\theta) \\\\ =&\\ \\text{Beta}(\\theta \\mid \\alpha=1, \\beta=1) \\, . \\end{aligned}$$\n", "\n", "We can also derive the message from the likelihood node by hand. For this, we need to know that the message coming from the observation $\\overleftarrow{\\mu}(x)$ is a delta function, which, if you gave the right answer ($X_1 = 1$), has the form $\\delta(X_1 - 1)$. The \"node function\" is the Bernoulli likelihood $\\text{Bernoulli}(X_1 \\mid \\theta)$. Another thing to note is that this is essentially a convolution with respect to a delta function and that its [sifting property](https://en.wikipedia.org/wiki/Dirac_delta_function#Translation) holds: \n", "\n", "$$\\int_{X} \\delta(X - x) \\ f(X, \\theta) \\mathrm{d}X = f(x, \\theta) \\, .$$ \n", "\n", "The fact that $X_1$ is a discrete variable instead of a continuous one, does not negate this. Using these facts, we can perform the message computation by hand:\n", "\n", "$$\\begin{aligned} \\mu_2(\\theta) =&\\ \\sum_{X_1} \\mu(X_1) \\ f(X_1, \\theta) \\\\ =&\\ \\sum_{X_1} \\delta(X_1 - 1) \\ \\text{Bernoulli}(X_1 \\mid \\theta) \\\\ =&\\ \\sum_{X_1} \\delta(X_1 - 1) \\ \\theta^{X_1} (1 - \\theta)^{1-X_1} \\\\ =&\\ \\theta^{1} (1 - \\theta)^{1-1} \\, . \\end{aligned}$$\n", "\n", "Remember that the pdf of a Beta distribution is proportional to $\\theta^{\\alpha-1} (1 - \\theta)^{\\beta-1}$. So, if you read the second-to-last line above as $\\theta^{2-1} (1 - \\theta)^{1-1}$, then the outgoing message $\\overleftarrow{\\mu}(\\theta)$ is proportional to a Beta distribution with $\\alpha=2$ and $\\beta=1$. So, our manual derivation matches RxInfer's message 2.\n", "\n", "Let's now look at these messages visually." ] }, { "cell_type": "code", "execution_count": 7, "metadata": {}, "outputs": [ { "data": { "image/png": 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vXr2WLFny9ttvt2jRIicnJycn59y5cxYWFuvXrx80aFCrVq3y8/Pd3d0r8UZcXFw2bNjg4eHRqFEjuVz+9OnT2NjYvLy8IUOGNG/eXEdHJyUlZc+ePXl5eZ07d27UqJGpqWliYuKqVasASCQSHx+fDRs2PHv2rPRDxq5du/73v//t0aOHWCyeMmVKgwYN6tWrB2DdunU+Pj7Nmzd3cHC4e/fupEmTli5dWomGiYi0xK1bCA3Fl1+ioEC1pKuLMWMgleIF54bUKSJFDTzNqMLGjBnj5eXl6elZiccWFRXJ5XLlVQNcXFy+++4755q8ptEbKykpKf2gTS6X37t3z9raun79+hV8+N27d83MzJQHfpSePXuWnp7evHnzsp/lpaSkpKenN2rUqOwzFxcX37t3z8jIqOwHbc+fP3/w4IEyDFX6TSkUirt37+rp6dnb25deu+HevXs6OjpNmjRRPrNCoXj48GF+fr6Dg4O+vr7ygdnZ2UlJSc2aNVP+D6AiISGhQ4cOGRkZun8fts7MzHzy5Enjxo2NNXcJ4S1btpw6dWrz5s2aaqC2K7vLk1bJzs42MTHRdBda4eJFRERgxw6Bk2uMjTFhAhYsgIuLmpopLCxUKBQa3OV5BEtblM0xYrHY0dHxtR5e/nMxKysr5WWiymrYsGHDcgtE6erqNm/eXGWjkZFRixYtXquH8kQikcobKf9aIpFI+QFlWSYmJi1btlTZOG3aNBcXF7lcvmnTpiVLluiWOSnAzMzMzMzsDbslIqqTFAocOoSQEJw+LVC1tsacOZg5E5aWau9MoxiwiP4yffr0c+fOASg9MYuIiF6isBC7diEkBNeuCVQdHREQgA8+qGvjgRXEgFU3yeXykpKS8lOEL6FQKIqLi5UPKSwsLP00TXt06dKFuYqIqCKys7F5M0JDhccDO3TA/PkYP75ujgdWENcirAsCAgLOnz9fdktsbGzv3r0B5OTkiESiwsLCVz7J999/X3q+ubGx8dOnTwEMGDAgJiamqvpcu3btuHHjym+3sbG5efNmVb1Kedu3b/fw8Ki+5yci0h5JSVi4EE2aYN481XQlEmHgQBw/jkuXMHmyVqcrMGDVDYcPH1Ze6rOUm5vbsmXLKv2Eu3fv5ilHRERU1o0bmDoVjo4ICUFm5j9KenqYOBF//IHvvkOfPhrqr4bR7nj5Umlp+PlnFBVpuo8y6tdH376oyGd3WVlZCQkJPXv2LLsxIyNj+fLlEyZMaNmy5YULF77++uusrKyhQ4cOGTJE5eFXrlwZMGCA8lPCwsJCmUx27dq19957z9vbW3nF0cePH69duzYpKcnNzW3atGnKM+iVSzhfuXKlWbNms2fPLh053Lp1688//9ymTZuXfGT55MmTLVu2ZGZmjh8/Xtl2WlpadHT0lStXjI2NR40apTwgB2D37t3Hjh0rKSlp1arV/PnzlQsvfvnll2fOnGnQoIGfn1/pae87duw4fvy4s7OztbV1+Vf8/fff//zzTysrq927dzs4OCxcuPDWrVvr1683NjaWSqXKNbABHDx48OjRowYGBpMnT1ZedD41NXX16tXx8fHm5ubKxvLz86Oioi5evGhkZPTee++NHTu2uLg4Ojr6/PnzJSUlPXv2nDBhgvL7lpeXt2LFivj4+AEDBujp6dnY2CgvcvHgwYMNGzYkJSV17dp16tSpZQcziYg07iXjgfXrw9cXQUH4e8kP+gsDlrDkZHTsiMePNd1HOe7u+PlnvPL3761btzZv3uzr61u6JSkpycPDY9y4cS1btjx8+PDs2bM//vhjU1PTf//738nJyWXvCWDp0qX+/v7KC0F99tln/v7+Hh4eEolET09vwoQJ6enpnTt3njJlyrBhw1asWHHmzJno6GgAw4cPNzQ0nDZt2nfffde1a9crV64YGhouXbp0//79H3300c2bN8PDw1WuYloqICBg0aJFBQUFnp6ee/bs6dmz5507d54/f+7p6Zmamurt7b1p06b+/fvv37//k08+WbZsmb6+/m+//VZSUqKrqzt16tSUlBR/f//ExETlqs92dnYrVqzYsGHD559/fu/evU8//bR0GZxSf/7556JFizw8PEaOHBkREXHx4kVdXV1vb+9Dhw55eXn9+OOPAD799NMjR45IpdKMjIwhQ4bExsZ26NBhwoQJLVq0mDJlSlpa2sOHDwEsWbIkISFh1qxZz58/T0xMBJCbm3v9+vXBgweXlJR88cUXDx8+XLRoEYARI0ZYWlpOnjz5yJEju3btWrhwYY8ePRITE3v27BkYGNitW7e1a9deunRpzZo1r/V/BRFRdZDLcfAgZDL88otA1cYGc+bA3x8WFmrvrFbQ0BqIVaP6FnuuyWs9X7um+l6cnZ337dtXdsvBgwfd3d0VCoVyyZeLFy86OzvHxMQoq506dTp48KDy619++aVt27YKheLo0aNubm7Kjbq6uikpKQqFon///h999JFyY1hYmLe3t0KhkMlkAwcOVG5MSUkxMDC4d+/ehQsXLCwscnNzlds7duwYHR1dUlJiamp6+fJl5caJEyeOHTu2/M+iYcOGW7ZsUX4dGho6fPjw0lJubm5iYuLHH388depUhULxxRdfeHp6ll2/88aNG1ZWVs+fP1fenDt37ueff65QKOzt7U+fPq3c6O/vP2TIEJUX3bp1a4sWLZTLRZ88eVJXV1e5SnRGRoZYLM7Pz8/MzDQyMkpOTlbef/ny5dOmTVMoFI6OjocOHSr7VEOHDg0ODi5debpUfn7+vXv39u7d2759e4VCceXKFUtLy9Lm27VrFxYWplAopk+f/uGHHyo35uTkGBkZKZcnUsHFnt8QF3vWWlzsuRIKChTbtilatxb+NeTkpFixQvH3v/c1FBd7rqFcXSEWQy7XdB/lWFpW5jBsv379goOD33//fQAKheLatWuzZs2aN28egJKSEuX57C/y1ltvKb+wsrJKS0sDEB8f36lTJ+VGa2vrJk2axMXFPX36tFWrVvX+HsZ9++234+LikpOTc3Nz27Ztq9zYsWNH5cn4S5YsOXPmDIA5c+aMGjUKgHLFG+V9Nm3aBCAhIWHs2LGFhYU2NjZPnjxRXstq8uTJhw4dsrW17devn6+v76BBg65evZqdnd2mTRvlwzMzM0eMGJGTk5OUlFT2Oe/fv1/+rbm4uCg/ubO0tLS2tlZ+pmlmZqajo5ORkfHw4cPCwsJu3bop75ybm6t8lWXLlvn4+FhZWQ0ZMmT+/Pn29vaLFy+eNGnSqlWrBg4cOHfu3LZt2+bk5IwfP/7atWuOjo7Pnz9PSkoCkJiY6OzsXHrVu9Jvy9WrV/fv3799+3blzaKiort375a+IyIidVKOB8pk+OeZvX/p2BHz5mHCBLzBJaK1BQOWsE6d8O232LUL+fmabqUMc3PMno0KX339f7Zs2eLv7+/q6tq1a1eRSGRmZnbw4MEOFVuqQBlB/tmGeebf5zcqFIrMzExzc/OioqKMMitOpaent2zZ0szMTC6X5+TkKJeULn2Uj4+Pcmnqpn+nxaysLOUXGRkZyvPrP/7449GjRy9evBjAypUrDx8+DMDOzu7UqVOPHj365ptvxo0bd/ToUXNzcycnp+vXr5ftsKSkRF9fPzMzU3lB+QzBpbD+uZ50+dOezM3NjYyM4uLiVK41P3bs2DFjxpw9e3bNmjVDhw69ePFit27dEhIS/vzzz+3bt/fo0ePRo0ebNm3S09O7ffs2gF9//VW52KKlpWXZLJuSklL6Qp9//vm0adMEmyQiUo+HD7FiBaKikJ2tWhKJMHgwJBL06qWJzmonBqwXGjwYgwdruokKUygU8r8PuJWPRIMGDdq5c6enp2dMTEz37t1HjRr1f//3f9HR0QYGBnK5PC4urvQwVUUMHDhw/PjxS5YssbW13bVrl6GhYdu2bZXHaU6cONGnT5+EhISjR49++OGH9erVe/fdd9etW6c8jWnnzp2dO3cGUP7C7uvXr+/Zs2dJScnGjRsHDhwIIDc3V3kt9aysrE2bNtnZ2QG4fft2kyZNGjVqNHv27K1btz5+/Lhv375ZWVkxMTFeXl7KO2dnZzdq1Khfv37r1q1bunRpTk7O9u3by1/M/ZUcHR1btGgRGhq6cOFCAPn5+UlJSU5OTjdu3GjVqpW7u7uOjs7IkSMBKLe0a9du8eLF4eHheXl5pc2XlJSsXLlS+YRubm7FxcXbtm3z9vY+efLkqVOnBg8eDGDUqFGRkZEjR460tLQEcP369datW79ut0RElRYfj1WrEBUlcExBTw9jx0Iqxd/H3KmiOKxUF+jr63t5eRn+7eOPPxaLxSoje7169dq1a5enp+cPP/wQHBxsYGDg5OTUpUuXpk2bRkVFASj7EH19/fIprVTv3r1nz57t6uravn37//znPzt27DA0NGzQoMH27duVo3bu7u7BwcHt2rUDsH79+g0bNrRv397d3b179+4vek4rK6u2bds6OzuLRKKgoCAAEokkNDS0S5cu77zzTunndPv27XNwcOjWrZuzs3OLFi0GDx5sYmKyf//+ZcuWvfXWWx06dHB1db1x4waAlStX7t27t127dm5ubqUrOr8WsVgcExNz+PBhJyenTp06tWjR4vTp0wA8PT1dXFy6d+/u5eUVHh4O4MMPP2zatGn37t1dXV0//vhjKysrHx+fy5cvu7q6tmnTpnHjxsonNDAw2Ldv35o1a+zs7NatWzdo0CDlATZfX98RI0a0adPm7bffdnJymjNnTiW6JSKqhNOnMXQoWrZEZKRquqpfH3Pn4vZtREczXVUGF3vWlsWeyyssLExOTm7YsGHl1sIsKipKTU21tbVV2f748eOGDRuqfKz28OFDGxubl19ZPjs7u6CgoOz6hkVFRY8fP7a3ty+7LGBBQUFycrKFhYXKStXp6ekFBQU2NjZlo+GjR4+sra3f8Kr0OTk5WVlZNjY2pW8qIyMjJyfH1ta2tLHc3Nxnz57Z2tqWfjPlcnlSUpKlpaWRkVH55ywuLm7VqtXGjRt7/X3AXS6XP3r0yNLSst4LFpXgYs9viIs9ay0u9lyeXI79+xESgnPnBKq2tpg7F/7+MDdXe2dVh4s9k8bo6+tX4oOzUnp6euXTFQDlZ3kqSo/ivISJiYnKP4J6enpNy53Sb2BgUH4jgNLLbpXVqFGjV77uK9WvX18lzJmbm5v/8x8eY2NjY2PjslvEYnH5dx0SEvLkyRMLC4sjR464uLiUvVCZWCx+kx8HEVFFKFcP/OIL3LghUG3eHHPmYPp0CP1hSK+HAYtIfSZOnPjjjz9mZ2d//PHHffr0ecnnsEREVSs9HWvXIjISyckC1W7dIJFg+PBXX2eRKogBi0h97O3tx48fr+kuiEi73L+P8HBs3IicHNWSSAQPD0ilePddTXRWpzFgERER1U1XriA0FLt2CSz7pq+PCROwYAE4tVxNGLCIiIjqmpMnIZPhyBGUn2QzNYWfHwICUBUnqdILMWARERHVESUl2LsXMhnOnxeo2tsjIAB+fjAzU3tn2ocBi4iIqNZ7/hzbtiEsDAkJAtVWrbBgASZOxJtdtYZeAwMWABgYGPTp0+flV2miOkOhUNTG8b3s7OzRo0drugsiqnHS0rBmDVauxN/rb/2DuzukUnh4cDxQ3RiwAODnn39+0XJ1VPfk5uaqXLOqtqjI5cSISHvcu4fwcGzaJDAeKBZj2DBIJHjxChpUvRiwAMDCwsLCwkLTXZCa8LLORFTbXb4MmQwxMSguVi0ZGGDSJAQF4XXWmKWqx4BFRERUa5w4gZAQHDsmMB5oZoYZMxAQAKEFNUjdGLCIiIhqOrkcsbH4/HPh1QNtbDBjBubNq92rB9YxDFhEREQ1V14etm5FWBgSEwWqrVtDIsH48RwPrHEYsIiIiGqizExs3YrgYDx+LFB1d0dAAEaP5nhgDcWARUREVLPcuYPwcGzejNxc1ZJYjOHDIZXinXc00RlVGAMWERFRTXH5MsLCsHOnwHigvj68vNJrdeIAACAASURBVLB4MVq10kRn9JoYsIiIiDTv++8hk+H77wVK5ubw98fcubC1VXtbVFkMWERERBqjHA/87DP89ptA1dYWfn4cD6yVGLCIiIg0IDcXmzdj+XLcvStQbdsWEgnGjQNXcaulGLCIiIjU6ulTrFqF1auRmipQfe89SCQYNAi1cNFU+h8GLCIiIjW5cwcrVmDjRuTlqZbEYgwejH//G926aaIzqmoMWERERNXuwgXIZPjmG5SUqJaMjODtjaAgODtrojOqHgxYRERE1ej0aQQH49AhgZKpKaZMwcKFsLdXe1tUzRiwiIiIqp5yPHDpUpw/L1B1cIC/P2bMgJmZ2jsjtWDAIiIiqko5Odi0CeHhuHdPoNq+PSQSeHlBl7+B6zT+eImIiKrG06dYvRqrVgmPB7q7Y+FCeHhwPFArMGARERG9qfh4hIVh2zbk56uWdHQwejSkUnTurInOSEMYsIiIiCrvt98QEoJ9+yCXq5aMjODjg8BANG+uic5IoxiwiIiIKuMl44FmZvD2xqJFsLNTe1tUMzBgERERvYaiIuzcCZkMV68KVB0dMX8+fH1hbKz2zqgmYcAiIiKqkOxsbNiAFSvw4IFAtWNHSCQYM4bjgQQwYBEREb1SSgrWrMHKlUhLE6hyPJDKY8AiIiJ6oVu3EBaG6GgUFKiWdHUxZgwkEnTsqInOqGZjwCIiIhLw66+QyXDggMB4oLExfH0xfz4cHTXRGdUGDFhERET/o1Dg0CHIZDh1SqBqbY3ZszFrFiwt1d4Z1SoMWERERABQWIivvkJoKK5fF6g2b47AQEyZgnr11N4Z1UIMWEREpO2ys7F5M8LChMcDO3TA/PkYP57jgfQa+D8LERFpr6QkRERg/XpkZqqWRCIMGACpFH36aKIzquUYsIiISBslJGDlSkRFCaweKBZj8GB8+CHc3DTRGdUJDFhERKRdzpxBSAgOHRIYD6xfH1OnYv58ODhoojOqQ9QXsK5du/bjjz9ev369d+/enp6e5e9w6tSp7du3l95csmRJkyZN1NYeERHVbXI5YmMRHIwzZwSq1taYORNz5nA8kKqG+gLWxo0bU1JSbt68aWRkJBiwbty4ceHCBT8/P+VNIyMjtfVGRER1WEEBtm9HaChu3hSoOjsjKAhTpsDQUO2dUd2lvoAVHh4OYPr06S+5j5OT08vvQEREVHGZmYiI0F+3Do8fC1S7dIFEglGjIBarvTOq62rWOVh//vnnpEmTbG1tJ02a5Orqqul2iIiotnr4EBERiIpCVpaBSkkkwqBBkEjw3nua6Iy0Qw0KWI6Ojr6+vk2aNPn999+7dev23Xff9ezZ8+UPuXXrlkQi+fzzz5U3zc3N9+/fL67YXyJFRUVyubywsPBN+6baJicnR9MtkAZwl9ceN26IIyP1d+/WK//T1tODp2fR3LmFbdrIAWRna6A9Uo/CwkKFQlHpXd7Q0FBPT+9NGqhBAat///79+/cHMG7cOJFItHz58lcGLAcHhx49evTt21d509DQ0MzMrIIvp/zX1sBA9S8b0gYmJiaaboHUjbu8Njh9GsHBiI2FQqFaql8fvr4ICkLTpnrAG/3ipFpBGbA0uMvXoIBVlrOz8+nTp195N0NDQycnp86dO6uhJSIiqpnkcuzfj5AQnDsnULWxUQQEiPz9YW6u9s5Ii2n4vL7U1NSVK1cWFxcDSEhIUG7MzMzcunVr9+7dNdoaERHVdPn5iIpCq1YYPVogXbVogagoXL2as3gx0xWpm/oC1ueff25hYREdHb169WoLC4vIyEgASUlJc+fOLSgoABAQEGBvb9+pU6emTZs2bNjwo48+UltvRERUu2RlISICzs7w80NcnGq1Uyds24br1/HBB+DHwqQR6vuIMDAwcObMmaU3lZe5atu2bU5OjrGxMYDY2NgHDx6kpqY2bdrUwsJCbY0REVEt8uABVqzAhg0Cp6iLRBgyBFIpevTQRGdEZagvYBkZGZW/dqhIJFKmK6UmTZrw6u1ERCTo6lXIZNi5E0VFqiV9fYwfjwUL0KaNJjojKqeGnuRORERU6pXjgQsWgH+eU43CgEVERDWUXI59+xASgt9+E6ja2WHuXMyYwRPYqSZiwCIiohqnoAAxMfi//xNePbB5c8yZg+nTwUVrqcZiwCIiohokLQ1r1yIyEikpAtXu3SGRYNgwrh5INR0DFhER1Qj37yM8HBs3ovxyVmIxPDwgkeDddzXRGdHrY8AiIiINu3IFoaHYtUt4PNDLC4sWoXVrTXRGVFkMWEREpDEvGQ80MYGPDyQSNG6sic6I3gwDFhERqVtJCb75BjIZLlwQqDZqhIAA+PnB1FTtnRFVEQYsIiJSH+V44LJluHVLoOrsjNmz4ecHQ0O1d0ZUpRiwiIhIHVJTsXo1Vq3C06cC1XffhVQKDw+IRGrvjKgaMGAREVH1unsXy5dj82bk5qqWxGIMGwapFN26aaIzomrDgEVERNXl0iXIZNi9G8XFqiUDA0yahAUL0LKlJjojqmYMWEREVPV++AEhIfj+e4GSuTlmzEBAAGxt1d4WkbowYBERUZUpLsaePZDJ8PvvAtUmTRAQgOnTYWKi9s6I1IsBi4iIqkBuLrZswfLluHNHoNq2LSQSjBsHPT21d0akCQxYRET0Rp4+xerVWL0az54JVHv1glSKQYM4HkjahQGLiIgqKTERYWHYuhV5eaolsRgjR0IqRZcumuiMSNMYsIiI6LVdvAiZDHv2oKREtWRoCG9vBAXBxUUTnRHVDAxYRERUUQoFjh1DSAhOnBCoWljA3x9z5sDGRu2dEdUwDFhERPRqcjliY7F0Kc6fF6ja2WH6dMyfDzMztXdGVCMxYBER0cvk5GDTJoSH4949gaqrKyQSeHlxPJDoHxiwiIhImHI8cNUqpKYKVN3dsXAhVw8kEsaARUREqhISEBaGbdvw/LlqSUcHo0dDIsHbb2uiM6JaggGLiIj+59IlhIdj507h1QPffx//+Q9XDyR6NQYsIiKCQoEjRxASgh9/FKhaWmLWLMyeDWtrdTdGVEsxYBERabWiIuzfj5AQXLggUG3WDPPmYdo0GBurvTOi2owBi4hIS2VnY8MGrFiBBw8Eqh06QCrFmDHQ5S8KotfH/YaISOs8eYLISKxbh/R0gWq/fpBK0b+/2tsiqkMYsIiItEhiIiIisGGDwHigWIzBg7FkCbp21URnRHULAxYRkVY4exYyGfbvh1yuWqpXD76+CAyEo6MmOiOqixiwiIjqMoUCx48jIgKHDglUraz+Gg+0slJ7Z0R1GgMWEVHdVFSEnTsREoJr1wSqjo4ICMAHH6BePbV3RqQFGLCIiOqarCxERSEiAg8fClQ7d4ZEAk9P6OiovTMircGARURUd6SkYM0aREYKjwdy9UAitWHAIiKqC27eRGgotm9HQYFqSVcXXl5YsAAdOmiiMyKtxIBFRFS7nTkDmQzffiswHmhsjKlTERgIBwdNdEakxRiwiIhqJYUChw4hOBhnzghUra0xcybmzIGlpdo7IyIGLCKiWqegANu3IzQUN28KVJ2dERQEb28YGam9MyL6GwMWEVGtkZmJdesQGYmkJIGqmxukUowaBbFY7Z0R0T8xYBER1QLJyVi79hXjgUOHqr0tInoBBiwiohrt+nWEhuKrr1BYqFrS08PYsZBI0K6dJjojohdjwCIiqqFOn0ZICA4dgkKhWjIxwbRpmD8fTZpoojMiehUGLCKimkUux8GDkMnwyy8CVRsbzJ0Lf380aKD2zoiowhiwiIhqioICfPklQkNx65ZA1cXlr/FAQ0O1d0ZEr4kBi4hI8zIysG4dIiLw5IlAtUsXSKUYOZLjgUS1BgMWEZEmPXyIFSsQFYXsbNWSSITBgyGRoFcvTXRGRG+AAYuISDOuXkVoKHbuFBgP1NfHuHFYsABt22qiMyJ6YwxYRETq9tNPkMlw+LDweOD06Zg3D40ba6IzIqoiDFhERGoil2PfPshkOHdOoGpri4AAzJgBc3O1d0ZEVY0Bi4io2uXnY9s2hIUhPl6g2rIlFizApEkwMFB7Z0RUPRiwiIiqUXo61qzBypVIThaodusGqRTDhnE8kKiuYcAiIqoW9+8jPBwbNyInR7UkEsHDA1Ip3n1XE50RUfVjwCIiqmJXrkAmQ0wMiopUS/r6mDABCxagdWtNdEZE6sKARURUZU6fRnAwYmOFxwN9fCCRcDyQSCswYBERvamSEuzdi5AQXLggULW3x7x58PODqanaOyMiDWHAIiKqvIICxMRg2TLh1QOdnTF7Nvz8uHogkdZ5RcC6efPmiRMn/vzzz5SUFAMDA2tr665du/bt29fGxkY9/RER1UxZWdiyBSEhSEoSqHbujLlzMWECdHTU3hkR1QDCAUsul3/11VerVq367bffAJiZmVlYWBQVFaWlpUVGRurq6np4eAQGBvbo0UO93RIRad7duwgPx6ZNyM1VLYnFGDYMEgm6d9dEZ0RUYwhceuXatWudOnWaOXNmy5Yt9+7d+/jx44yMjMTExAcPHuTm5t66dWv9+vV5eXm9e/ceNWpUTvn5YyKiOuqPPzBhAlxcEBmpmq4MDDBtGq5fx759TFdEJHQE6+bNm6NGjZo3b56p0AmZLVq0aNGiha+vb2Ji4tKlS1NTU+vXr1/9fRIRaRLHA4notQgErNGjR48ePfqVj3RyctqyZUs1tEREVFMUF2PPHshk+P13gWrjxpg3Dx98wPFAIlLFKUIiIgHK8cDPP0dcnEDVxQWzZnE8kIhe6IUBKzc3NyYm5sSJEwkJCenp6fr6+tbW1q6urqNGjerZs6c6WyQiUqdnz7BqFVavxrNnAtWePSGVYvBgiERq74yIag/h9UV/+uknFxeXqVOnxsbGFhcXx8XFAUhJSdmwYUOvXr0GDRqUnp6u3j6JiKpdYiJmz4aDAz75RDVdicUYPRpnz+KnnzBkCNMVEb2CQMBKSkoaNmxYu3btLl26lJ6e/uuvvwL48MMPr169mpqa+s0339y4cWPatGlqb5WIqLpcvozJk9GyJVavRl7eP0r6+pg0CdeuYc8edO2qof6IqLYR+Ijwm2++adSoUWxsrK6uatXQ0HDUqFH29vbu7u7p6ekNGjRQS5NERNXlJeOBpqaYMgVSKRo10kRnRFSbCQSsjIwMBweH8umqlKOjo1wuz8zMrI6AlZaWZmRkZGRkVOXPTERUqrgYX38NmQx//CFQbdr0r/FAXoWGiCpH4CPCrl27njx58pdffhF8QElJyZIlS+zt7Zs0afJarzRz5kxXV1cLC4sjR44I3iEtLa13796tWrWys7NbsmTJaz05EVEF5eYiKgqtW2PCBIF01a4dtm1DQgLmz2e6IqLKEzhM1b9//9GjR/fq1WvAgAF9+/Z1cHAAcOXKlfz8/Fu3bu3bty8hIWH37t06r7nClqur69ixY729vYuKigTv8Mknn1haWj558iQ5Obljx479+/fv1atXJd4SEZGgp09FUVFYvRppaQLV3r0hkWDgQJ7ATkRVQCBgiUSiL7/8smfPnpGRkUFBQcqNn332GQB9ff1//etf0dHRnTt3ft1XmjFjBgA9Pb0X3WH79u379+8XiUS2trZjx47dvn17NQas9HSd0FBxcjIXYtVChkVFePH/h1QnJWQ1DL3cLzqu2/MS1ZKOSD7K8ZKk/TE367vYD+zXRH9UnbjLaydduVzRoAGCgmBjo5kGBLeKxWI/Pz8/P7/Hjx/HxcVlZmbq6+tbWVm1bt26Xr161dFHRkZGWlpaixYtlDdbtmy5Z8+eVz6quLg4OTk5MTFRedPQ0NDe3r5Crzdxovjw4co2S7Ub/6HVKufhJoNkL0aVQPWvKSM8n4KtgYrlzokJSNRId6QO3OW101+nQJ05gzNnNNLAK67kbmdnZ2dnp4Y+srKyAJSmN2Nj44yMjFc+Ki4u7pdffgkNDVXeNDExOX36tFgsfHGvsowvXOCHAER1mAKiIxgog+QkepevWiJ1JtbMxqqGSFF/b0SkPhcu5GRnV+KDfwMDg5d85lYRAgErPj7ewsLC0tLylQ++fv16o0aNzMzM3qQDJWtrawCZmZkmJiYAMjIyGjZs+MpHtW7d2svLy9PT87Vfz9sbMtnrt0lENV0R9HZhbCgWXIFr+Woz3J2P8KnYZIxc9fdGROo2eXJ9ExONvLJAwLpw4YKfn5+/v/+UKVNatWpV/g5yufynn36Kiorau3fv7du3qyRgGRkZNW/e/MKFC40bNwZw/vz5du3avfnTvlBwcPG//oW4OF2eg6V98vPzDbmAXF2UU6C34dRbK463u58mMP7XvvGzoH6XxnW9pytuAyxXf3ukKdzltVNxcbHC0VHvX//SVAMCAWvcuHEmJiYLFy4MCQlp3bp1165dXVxcLCwsiouL09LS/vjjj19//fXJkyeDBg36/ffflXmoIi5cuJCRkZGXl3f58mUjI6MuXbqYmpru3r37u+++27x5MwB/f/+PPvrI2dk5ISHhwIEDFy5cqMo3qkIkUvTsKX/3XV0Dg2p8FaqRirKzDTX0Bw1Vk+RkREZi7VoILuLVty+kUvTubSaX9+Qur4W4y2sneWGhQqFABc4aqibC52B5eHgMGTLk+PHjX3755Q8//LBlyxbldrFY3KZNm3Hjxk2bNk3w4NZLHDx48ObNm927d79y5cqVK1eaNWtmampqbGxc+lnkvHnzcnNzJ06c2KBBg127drm4uLzJGyMibRAXh7AwREcjP1+1pKMDT09IpejUCQBecH0YIqJqIVKUXx6inIyMjOTkZENDQ2tr62qaIqycMWPGVPIcLKCoqEgulxvwz1ntk52dbcI/Z2u/c+cQEoL9+yGXq5bq1YOPDwID4eT0v43c5bUWd3ntVFhYqFAoNLjLv2KKUMnc3Nzc3Ly6WyEieiWFArGxkMnw888CVSsrzJqF2bNhZaX2zoiIyqhQwPrtt98uX76clJRka2vbrl27bt26iXipYyJSr8JC7NwJmQzXrglUnZwQGAgfH9Skg+xEpL1eEbBSU1O9vLyOHz9edmO3bt327NlT0Ut6EhG9mawsREUhIgIPHwpUO3WCVApPT67LQEQ1yCvOrp80adJvv/0WGRn58OHDoqKipKSkDRs2xMfHV+60JyKi1/L4MRYvhoMDJBKBdDVgAH74ARcvwsuL6YqIapaXHcFKTU09cuRIdHT0xIkTlVvs7OymTZtmZ2fn4eGRmJjoVPYMUiKiqnP7NiIjsWEDnj9XLYnFGDwYH34INzdNdEZEVAEvC1gFBQUKhaJbt24q27t37w4gLy+vGvsiIm3166+QyXDggMB4oLExpk7F/Plo1kwDjRERVdzLApadnZ2zs/PPP//cvHnzstt/+umnhg0btmzZspp7IyItolDg0CHIZDh1SqBqbY3ZszFrFiqwiBcRkea9LGCJRKLo6OixY8empKSMGDHC1tY2JSXl8OHD4eHh27dvf8NFEImIlAoLsWsXQkKExwMdHREQgA8+4HggEdUmr7jQqKWlZVpa2sufYuvWrd7e3lXaVUXxQqNUCbzqYM2RlYX16xERgUePBKqdO0MiqbLxQO7yWou7vHaq6Rca/fDDD/PLr0DxT507d666fohIKyQlISIC69cjM1O1JBJhwABIpejTRxOdERFVhVcErICAAPX0QURaIiEBK1ciKkpg9UCOBxJRnVGhK7kTEb2506chk+HQIYHxwPr1MW0a5s2Dg4MmOiMiqmoMWERUveRyxMYiOBhnzghUra0xcybmzOF4IBHVKQxYRFRdlOOBwcG4fl2g6uSEuXM5HkhEdRMDFhFVvcxMrFuHiAg8fixQ7dIFUilGjoT4FYt1ERHVVgxYRFSVnjz5K1plZAhU3d2xcCGGDlV7W0RE6sWARURV49o1hIZixw4UFqqW9PQwbhwkErRtq4nOiIjUjgGLiN7Uzz9DJkNsLMpft9jEBB98gHnz0KSJJjojItIQBiwiqiTleOAXX+CXXwSqDRvC3x9z58LCQu2dERFpGgMWEb22/HxERyMsDHFxAtUWLbBgASZPBpelISKtxYBFRK8hPR1r1yIyEsnJAtVu3SCRYPhwjgcSkbZjwCKiCnnJeKBIhL59MXcuxwOJiP7CgEVEr/Dnn1i1Ctu2oaBAtaSvDy8vLFyINm000RkRUU3FgEVEL/TjjwgJwZEjAuOBpqbw80NAABo10kRnREQ1GwMWEalSjgcuW4azZwWqNjaYMQMBAWjQQO2dERHVEgxYRPQ/z59j2zaEhSEhQaD61ltYsAATJ3I8kIjoFRiwiAgA0tKwejVWrUJKikDV3R1SKTw8OB5IRFQhDFhE2u7ePSxfjk2bkJurWhKLMXQoJBK4u2uiMyKiWosBi0h7/fEHZDJ8/TWKi1VLBgaYOBELFuCttzTRGRFRLceARaSNjh9HSAiOHRMomZn9dQ67nZ3a2yIiqisYsIi0SEkJ9uyBTIaLFwWqjRsjIADTp8PUVO2dERHVLQxYRFohLw9btmD5ciQmClTbtMGCBRg/Hvr6au+MiKguYsAiquOePftrPPDZM4Fqz56QSDBkCEQitXdGRFR3MWAR1Vl37mD5cmzejLw81ZJYjBEjIJHgnXc00RkRUV3HgEVUB/3+O2Qy7NkjMB5oaIjJkxEUhBYtNNEZEZF2YMAiqlNOn0ZwMGJjhVcPnDIFUilXDyQiqnYMWER1QXExdu9GSAj++EOg2rQp5s3DtGkwMVF7Z0REWokBi6h2KyhATAw++wzx8QLVdu0weza8vbl6IBGRWjFgEdVWT5/+NR6YmipQdXfHwoXw8OB4IBGRBjBgEdU+t28jLAxbt+L5c9WSWIxRoyCVws1NE50REREABiyi2uXCBYSEYO9elJSoloyM4O2NoCA4O2uiMyIiKoMBi6h2UI4HHjokUFKOBy5cCHt7tbdFRERCGLCIarSiIsTEQCbDlSsCVQcHzJ+PqVNRv77aOyMiohdjwCKqoXJysGkTli/H/fsCVVdXBAVh3Djo6am9MyIiehUGLKIaJzkZK1dizRqkpwtU+/aFRIIBAzgeSERUczFgEdUg8fEIDUV0NPLzVUs6OvD0hESCzp010RkREb0OBiyiGuHSJYSHY8cOgfFAAwO8/z7+8x+0bKmJzoiI6PUxYBFpkkKB775DSAh++kmgamWFWbMwaxasrdXeGRERvQEGLCLNKCrCzp2QyXD1qkDV0RGBgfD1Rb16au+MiIjeGAMWkbq9fDywfXsEBmL8eOhy7yQiqrX4TziR+jx5gshIrFsnPB7Yrx+kUvTvr/a2iIioqjFgEalDXNxf44EFBaolXd2/xgM7ddJEZ0REVA0YsIiq19mzCAnBgQOQy1VL9erB1xeBgXB01ERnRERUbRiwiKqFQoHYWISE4NQpgaq19V/jgVZWau+MiIiqHwMWURUrLMSOHZDJcP26QNXJCYGB8PHheCARUV3GgEVUZbKyEBWFFSvw6JFAtXNnSCTw9ISOjto7IyIi9WLAIqoCjx8jIgLr1iEzU7UkEmHAAEgk6NtXE50REZEmMGARvZGbNxEaiu3bhccDvbwgkaB9e010RkREmsOARVRJZ85AJsO33wqMB9avj6lTMX8+HBw00RkREWkaAxbR65HL8e23kMlw5oxAtWFDzJmDmTNhYaH2zoiIqMZgwCKqqMJC7NqF4OAXjgfOnYsPPuB4IBERMWARVUBmJtatQ0QEHj8WqLq5QSrFqFEQi9XeGRER1UgMWEQvk5yMtWsREYGMDIGquzsWLsTQoWpvi4iIajYGLCJhCQlYuRJRUcjPVy3p6WHECEilePttTXRGREQ1HgMWkarTpxEZiW++ER4P9PVFUBCaNtVEZ0REVEswYBH9RS7HgQMICcHZswJVW1vMnYsZM9Cggdo7IyKi2oYBi+iv8cAvvsCNGwJV5Xjg9OkwMlJ7Z0REVDupNWDdvHnz6NGjDRs2HDFihFG5X1aJiYkXL14svdm/f39zc3N1tkdaKD0d69YhMhJPnghU33kHEglGjOB4IBERvR71Baxjx46NHTvWx8cnNjY2PDz8zJkzenp6Ze/www8/LF26tFu3bsqbb7/9NgMWVZ8HD7BiBTZsQHa2akkkwpAhkEjQs6cmOiMiotpPfQHrk08+WbZs2YwZM4qLizt06LB///4xY8ao3Oedd975+uuv1dYSaadr18RbtmDbNoHVA/X0MHYsFi5Emzaa6IyIiOoKNX3ykZWV9csvvwwbNgyArq7u4MGDjxw5Uv5uT58+3bVr14kTJwoLC9XTGGmVH3/EkCHo3t04Kko1XZmaYsEC3LmD6GimKyIielNqOoKVlJQkFottbGyUN+3s7P7880/VVnR1xWLx4cOHL126VFRUdPz48UaNGr38aVNSUvbu3Xvr1i3lTSMjo5kzZ4pEooq0VFRUJC8/hU91kVyO774Th4TonDsn8BdFw4aK6dPls2YVK8cDyx/WorqBu7zWKigo0NfX13QXpG6FhYUKhaLSD9fV1dXR0XmTBmrQFKGvr6+vry8AuVw+evTojz76aOPGjS9/iFwuz8nJyfj7Gttv8q2kOqmgAHv26ISE6Ny6JRC7nZwUM2eWTJ1awvFAIiKqWmoKWHZ2dnK5/OnTp7a2tgCSk5Pt7OxedGexWDxkyJBXpisAtra2Xl5enp6elWhJLBbL5XIDA4NKPJZqvrQ0rFmDlSuRkiJQdXeHRIKhQ0VisW6N+jODqg93ea1VWFjIn7sWEolECoVCgz96NZ2DZWZm1qVLl0OHDgGQy+Xfffdd//79ARQWFt6+fVt55Kns8adffvnFyclJPb1RHXPvHhYtgpMT/vtf1XQlEsHDAwcO5J0+jeHDefEFIiKqLur72/3DDz+cPHny3bt3r1y5IhaLR40aBeDWrVuurq45OTnGxsaenp4NGjSwtbW9ePHihQsXTp06pbbeRE48dQAAGW1JREFUqG64fBkyGWJiUFysWjIwwMSJCApCq1bIzi7RRHdERKRF1Pcn/JAhQ06ePGlubj5ixIjTp08rj9o5ODh8/fXXhoaGAD799FM3NzcTE5OJEycmJCS89dZbauuNarsTJzBwIDp2xFdfqaYrMzNIpUhMxMaNaNVKQ/0REZGWUevZJ66urq6urmW3mJqall4Nq02bNm04H0+vQy5HbCw+/xznzglUbWwwYwYCArh6IBERqRtP76VaKS8PW7ciLAyJiQLV1q2xYAEmTABHs4mISCMYsKiWyczE1q0IDsbjxwJVd3cEBGDUKLzZ5UuIiIjeCAMW1Rp37iA8HJs3IzdXtSQWY/hwSKV45x1NdEZERPRPDFhUC1y+jLAw7NwpMB6orw8vLyxezBPYiYioBmHAohrt++8hk+H77wVK5ubw98fcubC1VXtbREREL8WARTWRcjzws8/w228CVVtb+Plh3jyYm6u9MyIiogpgwKKaJTcXmzcjPBx37ghU27aFRIJx46Cnp/bOiIiIKowBi2qKp0+xahVWr0ZqqkC1Vy9IpRg0CCKBVZuJiIhqFgYs0rzbt7F8ObZswfPnqiWxGCNHQipFly6a6IyIiKhSGLBIky5eREgIvvkGJeWWBzQ0xJQpCAqCs7MmOiMiInoDDFikAQoFjh1DSAhOnBCoWlhg5kzMmYOGDdXeGRERUVVgwCK1Ki5GTAxkMly+LFB1cMD8+Zg6FfXrq70zIiKiqsOARWqSk4NNmxAejnv3BKrt20MigZcXdPm/JBER1X78bUbVLiUFK1dizRqkpQlU+/SBVIoBAzgeSEREdQcDFlWjhASEhWHbNoHxQB0djB4NqRSdO2uiMyIiourEgEXV4vx5hIRg717I5aolIyP4+CAwEM2ba6IzIiKi6seARVXs9GkEB+PQIYGSmRm8vbFoEezs1N4WERGRGjFgUdUoKsKuXZDJ8OefAtVmzf4aDzQ2VntnREREaseARW9KOR64fDnu3xeouroiKAjjx3M8kIiItAh/6VHlpaRgzRqsXCk8HujujoUL4eHB8UAiItI6DFhUGXFxCAtDdDTy81VLurrw9IREgk6dNNEZERFRDcCARa/n3DmEhGD/foHxwHr14OuLwEA4OmqiMyIiohqDAYsqRKHA8eOIiBAeD7SywtSpCAjgeCARERHAgEWvVFiIHTsQGopr1wSqTk4IDISPD+rVU3tnRERENRUDFr2QcjwwLAwPHghU27dHYCDHA4mIiATwdyMJePwYERFYtw6ZmQLVAQMglaJvX7W3RUREVEswYNE/3LyJsDB8+SUKClRLurp4/31IJOjQQROdERER1R4MWPSXixcREYEdO1BSoloyNsaECViwAC4umuiMiIiotmHA0nYKBQ4dQmQkfvhBoGptjZkzMWcOLC3V3hkREVGtxYClvQoLsX07QkNx44ZA1dkZgYGYMgVGRmrvjIiIqJZjwNJG2dnYvBmhoXj4UKDasSPmzeN4IBERUeXxV6h2efQIERFYvx5ZWaolkQgDB0IiQe/emuiMiIioDmHA0hbXryM0FF99hcJC1ZKeHsaOxYIFcHXVRGdERER1DgNW3XfqFGQyHDoEhUK1VL8+PvgA8+ahaVNNdEZERFRHMWDVWXI5DhyATIZffxWo2thg7lz4+6NBA7V3RkREVNcxYNVBBQWIjkZYGG7dEqi6uGDBAkyeDENDtXdGRESkHRiw6pSMDKxdi8hIPHkiUO3aFVIpRoyAWKz2zoiIiLQJA1Yd8eABVqzAhg3IzlYtiUQYPBhSKXr21ERnRERE2ocBq9a7ehUyGXbuRFGRaklfH+PG4f/bu/uoqOr8D+CfkYEBBATlUQoRC4UUQRACSUo8CD6BKEKebTlaLiZqWTuu2npyayXDx0pFT0o+dRat1rajx0Ox7KaDOBqiVkj4BAoM8iAOMDAMM/f+/rjt/KZxtIKZe2F4v/669/v9XOYD1y/34+X7vVcqpWeeESIzAACAwQoF1gD27beUm0unT5tYHuji8vPywCeeECIzAACAwQ0F1sDDMHTiBOXm0oULJnp9fGjVKlq2jFxdec8MAAAAiAgF1sDS3U3HjtF771FlpYneMWNo5Ur605/w9kAAAACBocAaGO7fp7w8+ugjunfPRG9MDK1ZQ3PmYHkgAABAv4ACq79TKGjfPtq5k5RK4y6RiGbNotdeo+nThcgMAAAAHgEFVv/1/fe0ZQsVFJheHpieTmvXUnCwEJkBAADAY6HA6o9kMnr/fTp1ysTyQGdnWryYpFIsDwQAAOi/UGD1IzodffEFbdlC331notfXl157jbKyyMWF98wAAADg90CB1S9wywNzcky/PfCpp2jFCsrKwtsDAQAABgYUWAJraaHdu2nXLmpqMtEbG0tr1tDs2SQS8Z4ZAAAA9BYKLMFUV9P27ZSfTyqVcdeQITR3Lq1ZQ9HRQmQGAAAAfYMCSwBXrtC2bfSPf5BWa9zFLQ9ct46CgoTIDAAAAMwBBRavvvmGtmyhb74x0eXqSq++SqtWkbc372kBAACAWaHA4gPD0KlT9Pe/m357oLc3ZWXR66/j7YEAAABWAgWWZXV2Un4+bd9Ot2+b6B0/nqRSevFFsrXlPTMAAACwGBRYltLc/PPywOZmE71xcSSV0syZWB4IAABghVBgmV91Ne3YQQcOmF4eOHMmrV+P5YEAAADWDAWWOV26RLm59MUXJpYH2tvTH/9Ib75JgYFCZAYAAAA8QoFlHl9/TVu2UFGRiS43N1q2DMsDAQAABhEUWH2C5YEAAADwMBRYvaRS0YEDtGMHVVeb6J0wgaRSysjA8kAAAIDBCAXW79bU9PPywJYWE71TptBf/oK3BwIAAAxqKLB+h5s3ads2OniQurqMu2xsKDWVpFKaPFmIzAAAAKA/QYH1m1y+TNu3m357oERCCxfS+vU0bpwQmQEAAED/gwLrcViWCgtpyxYqLjbRO3w4LV9OK1eSpyfvmQEAAEA/hgLLNG554Lvv0sWLJnpHjaJXX6Vly2jYMN4zAwAAgH4PBZaxjg7av5927KA7d0z0hobSn/9M6ekkxk8OAAAAHgFlwv+7d48+/JDy8qi11URvfDytWUMJCbynBQAAAAPNEN4+qampaenSpREREZmZmXV1dQ8HMAyTm5sbExMzY8aMYpOTnizm+nVatoz8/Sknx7i6srGh9HT67jsqKkJ1BQAAAL8JfwXWokWLtFrtJ5984uLikpKS8nDA7t27Dx48uHPnzszMzHnz5t26dYuHrORyWrCAxo2jfftIrf5Fl6MjZWdTVRUVFFB4OA+5AAAAgJXg6U+E165dk8lkTU1NTk5O27dv9/LyksvlUVFRhjG7du3KycmJjIyMjIw8derU/v37c3JyLJdSYaEoN9f27FkTXe7ulJ1NK1aQu7vlPh8AAACsFk93sK5evRoUFOTk5EREtra2kyZNunLlimGAWq2uqqqKjIzkdqOioowCzGv9epozR3z2rPG3P3o0ffQR1dTQxo2orgAAAKCXeLqD1djY6Obmpt91c3O7d++eUQARuf7vrcgPB5hUUVGRnZ0tlUr1R/3nP/8ZMuTXq8YDB5yIfvEum4kTda+9pklJ0YrFpNNRe/uvfg0YqDo6OoROAQTQ09PDMIxGoxE6EeAbhvzgpNFoWJbt9ZC3t7e37dvrhHkqsFxcXDo7O/W7KpVq2C8fIeXi4kJEnZ2dzs7ORNTR0aEvth7j6aefXr58eVJSErcrkUiG/bYnU4WFUWHhz9sJCSSV0vTpNkQOv+mbgYGP+2cGgwpXYEkkEqETAQFgyA9CXIEl4JDnqcDy9/e/desWwzDc7aUbN274+/sbBri6urq6ut64ccPLy4sLGDVq1K9+WVtbWy8vr4CAgN+bz9Gj9P77TGcnu3SpTWjo7z0aAAAA4HF4moMVGxvr4OBw/PhxIiosLGxtbU1ISCCiixcvHjhwgItZtGjR7t27iai5ufnYsWOLFi2yXD7u7pSTo9u+XYvqCgAAAMyOpwLLxsYmPz//jTfeGDt27EsvvfTJJ5/Y29vTLwusjRs33r59e9SoUYGBgRkZGfHx8RZNqa2t7f79+xb9COifampqhE4BBKBUKjHkBycM+cHpwYMHwg55EcuyvH2YVqutr6/38fF5zMQxhUIxdOhQbkrWr0pLS0tPT1+wYEEvktm6dWtDQ8PWrVt7cSwMaM7Ozk1NTVyJD4PH5s2bHzx4sHnzZqETAb45Ojoqlco+TliGAWfTpk2dnZ2bNm0SKgFeX5UjFov9/PweH+Pj48NPMjqdjmEYfj4L+hWc+sEJ533Q0ul0fN5KgH5C8CHP35PcAQAAAAYJFFgAAAAAZsbrHCyzi42N9fDwGDt2bC+OlcvlKpVq2rRpZs8K+rlt27atWrUKEzIGm9LS0u7u7ueff17oRIBvW7duXb16tY2NjdCJAK9KSkq0Wm1cXFzvDo+IiOjdDG89Xudgmd38+fNbWlp69wS58PBwjUZj+Hx5GCTS0tI8PT2FzgL4FhERodVqMeQHoYULF7rj3WeDT2RkpE6n6/WQHzp0aB8TGNh3sAAAAAD6IczBAgAAADAzFFgAAAAAZoYCCwAAAMDMUGABAAAAmBkKLAAAAAAzQ4EFAAAAYGYD+zlYj8EwzOHDh8+fP+/v75+dnW3yWVmlpaUFBQV2dnZLliwJCgriGtVq9d69e69duxYaGrp06VKx2Gp/RNZKoVDs2bOnpaUlKSlpzpw5Rr3d3d2FhYUymUytVkdHRy9cuJB7/ODly5cLCwv1YYsXL8azsgYWhmEOHTokl8tHjx6dnZ3t5ORkFFBUVFRWVqbflUqlQ4YMIaKurq68vLyffvopLCzslVdewZAfcOrr6/fs2dPa2pqUlDR79myj3pqamoKCAsOWBQsWjBkzpry8/Ouvv9Y3LlmyxMPDg490wRwYhvnhhx/KysoaGxtNjnciYln2yJEj586d8/PzW7FihYuLC9d+586dvXv3KpXK5OTkhIQEyyVptXew3nrrrR07dkRFRcnl8pkzZz4cIJPJEhMTR48e7eTkFBMTU11dzbUvWrTo5MmT0dHRR48ezcrK4jVp6LPOzs6YmJjGxsawsLDly5fn5+cbBRQVFW3evHn48OGBgYHvvPPOyy+/zLXL5fKDBw+2/o9Wq+U9d+iTtWvXfvjhh1FRUefOnXv4KktEX3311cmTJ/WnWN+ekZFx+vTp6OjoQ4cOZWdn85gymIFKpYqOjm5ubg4NDc3Kyjp8+LBRQE9Pj/6kV1RUrF+/nquhS0tLDx06pO/S6XRCpA+9VF1dPWvWrM8//3zt2rVtbW0mY95+++3c3NzIyMhLly4lJCRwT/1sbW199tlnOzs7Q0JCXnrppc8//9yCWbLWqK2tzdnZ+cqVKyzLajQaDw+Ps2fPGsUkJye/++673HZmZqZUKmVZtrKy0sHB4cGDByzLKhQKiURSV1fHb+7QJ/n5+REREdz2P//5z8DAQIZhDAM0Go1++9KlS2KxuKuri2XZvXv3pqWl8ZkqmJFSqXRycvrxxx9Zlu3u7h4xYsS5c+eMYlauXLlx40ajxh9//NHR0bGtrY1l2draWolE0tDQwE/OYBYff/xxVFQUt/3ZZ58FBQU9Jvhvf/sbd6FlWXb37t0ZGRkWzw8sSalUEpHJy7RKpXJ1dS0rK2NZtqenx8fHp7i4mGXZnTt3xsfHczEHDx7UXy8swTrvYF29etXe3j4kJISIbG1tp06dKpPJjGJKSkri4+O57fj4eC6gpKQkPDx82LBhROTt7R0YGCiXy/nNHfqkpKRE/37JadOmVVVVNTY2GgYYvoJQqVQ6Ojra2dlxuzdv3tywYcOePXsaGhp4SxjMory83NnZOTg4mIjs7Oyee+65kpKSh8PkcvmGDRvy8/NVKhXXUlJSEhkZyU0h8PX1DQgIuHDhAp+ZQx/JZDL9b/Jp06Zdu3atpaXFZCTLsocPH16yZIm+5caNGxs2bMjLyzP6LQFW4IcffhCJRJMmTSIisVgcFxfHXeVlMpnhNaKsrEytVlsoB+sssBoaGgzfPOXh4aFQKAwDNBpNS0uLPkYf8PCB9fX1vKQM5qFQKPQTKYYNGyaRSIxOvZ5arV69evW6deu4iTju7u6TJ092dHQsLi4OCgr6/vvv+Usa+uxXhzwR+fv7BwUFSSSSI0eOTJgwgbsMKxQKDPkBzXDIu7m5icXiRw354uLi1tbW5ORkbtfDwyMiIsLBwaGoqGjcuHEVFRU8ZQy8eNTvBMMh7+npybLso/7B9J11Tue0s7Pr6enR72o0Gv3sNo5YLLaxsdHPs9FoNPb29iYP5NphoDA8gwzDaLVak2dQo9GkpaWNGzdOKpVyLfPnz58/fz63nZWVtWnTJqOJsdCf/ZaR+8Ybb3Abb7311nPPPZeXl/fXv/4VQ36gMxryDMM86gweOHDgD3/4g743LS0tLS2N23755ZdzcnKOHj3KQ8LAj4eHtqOjI9dueOknIssNeeu8g+Xr69vQ0KD/IdbW1o4cOdIwYMiQIT4+Pnfv3jUK8PX1ra2t1YfV1tb6+vrylTWYgeEZrK+vZxjGx8fHKEar1b744otisfjw4cPcEkIjkydPrqmpsXiuYD6+vr4KhUI/T/nhIW9IJBJFRERwp/iJJ57AkB/QDIc8t/HwkCcipVL55ZdfLl682OQXwZC3Pr6+vo2NjVwJRY+4yt+9e9fW1tZyC8ats8AKDQ11d3c/efIkEdXV1clksrlz5xKRQqH497//zcUkJydztygYhjl+/HhKSgoRzZgx4/r169y94vPnzyuVyri4OMG+Dfj9UlJSTp482dHRQUQFBQUvvPACN6PuwoULVVVVRKTT6TIzMzs7OwsKCgznY7W3t3MbWq32yy+/nDhxohDpQy+Fh4e7uLicPn2aiGpra0tLS7kndNTX1xcXF3Mx+lPc0dFRWFjIneLExMSKiorKykoikslkXV1dsbGxwnwP0CspKSlfffUVN6muoKBg+vTpQ4cOJSK5XH79+nV92NGjR4ODg0NDQ/UtGPJW6cqVK9wEj/Hjx48cOfJf//oXETU0NHz77bfcX4dTUlJOnDjR3d1NRAUFBbNnzzb532zzsNz8eWF99tln7u7u6enpfn5+a9as4RqPHTv25JNPctt37tzx8/NLTEyMiYmJiIhob2/n2nNzc318fDIyMjw9Pfft2ydM9tBbDMPMmzcvODh4/vz5Hh4e58+f59pnzJjx9ttvsyx7/PhxbuyF/09tbS3LslOnTo2Ojk5NTR0zZkxoaCiWkg04x44d44b8k08+uW7dOq7x008/9ff357a9vb2nTZuWnJzs5eU1a9as7u5urv29997TD/n9+/cLkz30lk6nmzt37jPPPJOamurh4XHhwgWuPT4+/p133tGHhYWF7dmzx/DAKVOmxMTEpKamBgQETJo0qbGxkde8oc9iYmK4ijkkJCQ8PFyn07Esm5mZmZWVxQWcOHFixIgR6enp/v7+q1ev5hp7enoSEhImTpw4b948Ly+vq1evWi5DEcuylqrdhHb37t2ysrIxY8ZMmDCBa2lra2toaAgMDOR2VSrV2bNnJRJJbGys4c2Mn3766dq1ayEhIQEBAQLkDX3DsqxcLm9sbJwyZcqIESO4xpqaGgcHB09Pz/v379++fdswfvz48RKJpKOjo7y8vLm52c/PLywsjJv5DgPLnTt3Ll269NRTT40fP55rUSqV9+7d44Z8c3Pz5cuXVSpVYGCg/sHCnMrKysrKSgz5AUo/5GNjY4cPH841VldXDx06lJv/zjBMeXl5cHCwg4OD/qj29vby8vKWlpZRo0aFhoZiyA845eXlDMPodydNmiQSierq6kQikX6GQF1d3cWLFwMCArinCnAYhiktLW1tbY2NjXV1dbVchtZcYAEAAAAIAjU7AAAAgJmhwAIAAAAwMxRYAAAAAGaGAgsAAADAzFBgAQAAAJgZCiwAAAAAM0OBBQAAAGBm1vmyZwAAQ11dXaWlpQzDREdHc69SAQCwKBRYAGDl/vvf/y5cuFCtVotEIhsbm08//TQpKUnopADAyuFPhABgzRobG1NTUxMTE5uampqamhITE9PS0qqrq4XOCwCsHAosALBmu3btUqlUH3zwgUQisbOz+/jjj4lo586dQucFAFYO7yIEAGsWERHh4uJSXFysb5k5c+aNGzeqqqoEzAoArB7uYAGA1WJZtqKi4umnnzZsHDt27M2bN9VqtVBZAcBggDtYAGC1urq6HB0dfXx8Ro4cqW9saGioq6tTKBTe3t4C5gYA1g2rCAHAyvn7+0+dOlW/K5fL6+rq8H9LALAoFFgAYLXs7e3t7e1DQkI2b96sb5RKpWfOnHF1dRUwMQCwepiDBQBWSyQSBQUF3b5927Dx1q1bo0ePdnBwECorABgMUGABgDVLSko6c+ZMe3s7t6tWq4uKivCgUQCwNBRYAGDNVqxYYWtr++abb2q1Wp1Ot3btWo1G8/rrrwudFwBYOawiBAArV1hYmJ6eLhaLbWxsVCrVkSNH5s2bJ3RSAGDlUGABgPVTKpVnzpzR6XRxcXFubm5CpwMA1g8FFgAAAICZYQ4WAAAAgJmhwAIAAAAwMxRYAAAAAGaGAgsAAADAzFBgAQAAAJgZCiwAAAAAM0OBBQAAAGBmKLAAAAAAzOz/ANMzIw+Jus89AAAAAElFTkSuQmCC", "image/svg+xml": [ "\n", "\n" ], "text/html": [ "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Sample space of random variable\n", "θ_range = range(0, step=0.01, stop=1.0)\n", "\n", "# Plot messages\n", "plot( θ_range, x -> pdf.(message1, x), color=\"red\", label=\"Prior-based message\", xlabel=\"θ\", ylabel=\"p(θ)\")\n", "plot!(θ_range, x -> pdf.(message2, x), color=\"blue\", label=\"Likelihood-based message\", legend=:topleft, size=(800,400))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The marginal distribution for $\\theta$, representing the posterior $p(\\theta \\mid X_1)$, is obtained by taking the product (followed by normalization) of the two messages: $\\mu_1(\\theta) \\cdot \\mu_2(\\theta)$. Multiplying two Beta distributions produces another Beta distribution with parameter:\n", "\n", "$$\\begin{aligned} \\alpha \\leftarrow&\\ \\alpha_1 + \\alpha_2 - 1 \\\\ \\beta \\leftarrow&\\ \\beta_1 + \\beta_2 - 1 \\, , \\end{aligned}$$\n", "\n", "In our case, the new parameters would be $\\alpha = 1 + 2 - 1 = 2$ and $\\beta = 1 + 1 - 1 = 1$. \n", "\n", "Let's check with RxInfer. The product of the two Beta's can be computed with:" ] }, { "cell_type": "code", "execution_count": 8, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "prod(ClosedProd(), message1, message2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "Extra information:\n", "\n", "The `ClosedProd()` input indicates that julia should not use the generic `prod` function (e.g., for products of `Float64`'s or `Int64`'s), but that it should use the product operations defined by the RxInfer ecosystem for parametric probability distributions. It is an example of Julia's \"multiple dispatch\" feature, which is making waves in the programming languages world ([youtube](https://www.youtube.com/watch?v=HAEgGFqbVkA), [blog](https://medium.com/swlh/how-julia-uses-multiple-dispatch-to-beat-python-8fab888bb4d8)). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That matches our manual derivations as well as the posterior reported by the `inference` procedure:" ] }, { "cell_type": "code", "execution_count": 9, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "posterior = results.posteriors[:θ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Let's visualize the messages as well as the marginal posterior." ] }, { "cell_type": "code", "execution_count": 10, "metadata": {}, "outputs": [ { "data": { "image/png": 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Tp09funQpN9I7JyfHzMzM398/MzMzOjra398/JSXl6tWrY8eOfdZvZPjw4R9//HF8fHyfPn0AlJSUMAzDsiyPxzM3N589e3ZGRkZKSopMJissLLS3t+eywHXr1gEoKyvjLlCVlpYePXqUu4I1duzYsWPHLl++3MXFZfPmzVzKKBAIRo4cuXHjxq1bt/J4PJZl79+/33D3kBBCyONU5lZGbo+M+TamtlRDeWDXIV3FK8VdB3fVfmBaQwlWxyIQCA4fPjxr1qzt27ffv39/xowZ48aN++eXODo6hoWFff3116mpqfPnzw8JCQGwZs2afv36eXh4VFdXNyRkCxYsyMnJcXJySklJWb9+fadOnfr3779mzRo/P78ePXpUVlZWVlZGRkaam5t/9913I0aMcHNzq62tFYvFz/GNuLq67t69e/To0Q4ODiqVqqCg4Pz589XV1aNGjerWrRufz8/Pzz958mR1dbWvr6+Dg4OxsXF6evqOHTsArFixYv78+bt37y4sLGy4yRgYGPjRRx/169ePx+PNmzfPzMzMwMAAwLfffjt//vxu3bo5OztnZGTMmTOH26dFCCGEU1eH3Fzw+bCzA5+PortF0s3S+MPxyrqmt4B4Ojz3Ke7ilWJbb9sWCVWbmJadNf2CpkyZMm3atMmTJz/Ha+VyuUql4roGuLq6/vLLL927d2/uAFsRpVLZcKNNpVLdv3/fysqqU6en3UuYkZFhYmLCXfjhFBYWlpSUdOvWrfG9vPz8/JKSEgcHh8ZnVigU9+/fFwqFjW+01dTUPHjwgEuGnvubYlk2IyNDIBDY29s39G64f/8+n893cnLizsyy7MOHD2tra52dnXV1dbkXVlRUZGdnd+nShfsD0ERqaqq3t3dpaamOTv2/QMrKynJzcx0dHQ0NDZ872he0f//+q1ev7tu3r6UCaOsaf+RJh1JRUWFkZNTSUbRPxcUID8eNG5DLAcCwLMf6XsT9n2+qTw8UGAq8ZnmJ3heZu5prJzaZTMaybAt+5OkKVkfROI/h8XguLi7P9HL1+2KWlpZcm6jGrK2tra2tmzypo6PTrVvTNnFCobBHjx7PFIM6hmGafCPq78UwDHeDsjEjI6PGdYWcRYsWubq6qlSqvXv3rlmzpiG7AmBiYmJiYvKC0RJCSLuRnQ2JBHfuQKUCy7K8lBRIJNWZmRlqKw2sDALfDvR/019oIdR+nC2IEixC6r3++uuRkZEAGjZmEUIIaYxlkZYGiQT1E9SUSiQmMhIJCgrUF5u6mAYtDer7Wt92Vh74lCjBap9UKpVSqVSvIvwHLMsqFAruJTKZrOFuWscREBBAeRUhhGikUiExEVIpcnMBgJHJEBcHqRTlGsoDbb1tg94L6j2zd7ssD3xKHfc7b0+WLl0aHR3d+Jnz588PGDAAQGVlJcMwMpnsiSe5fPlyw35zQ0PDgoICAEOHDg0LC2uuOL/55psZM2aoP29jY5OUlNRc76LuyJEjjdufEkIIeXoyGSIi8NVXOHUKublARQXz22/sli24eLFJdsUC6N7dYtmri+MW93m1T0fOrkBXsNqHCxcuDBgwoKEgDoC/v/+GDRue+4QnTpygLUeEENLBVVYiKgrR0aipAQCmsBBSKRISoFQ2mdfG8niMpydEItbGxm94S8Ta+lCCpZlcjitXkJoKRdMZlNrA58PBAUOG4KmL/JoqLy9PTU0NDQ1t/GRpaemWLVtmzZrVs2fPmJiY48ePl5eXjxkzZtSoUU1enpCQMHToUO4uoUwm++KLL27duvXKK6/MnTuX6ziak5PzzTffZGdn+/v7L1q0iNtBz41wTkhI6NKly5IlSxpKDg8cOPD33397eHj8wy3L3Nzc/fv3l5WVzZw5kwu7uLj40KFDCQkJhoaGEydO5C7IAThx4sSlS5eUSqWbm9t7773HDV48fPiwRCIxMzNbvHhxw7b3o0eP/v777927d7eyslJ/x9jY2Js3b1paWp44ccLZ2fmDDz64e/fud999Z2houHLlSm4GNoCzZ8/++uuvenp6r776Ktd0vqioaOfOnSkpKaamplxgtbW1u3btun79ulAofOWVV6ZPn65QKA4dOhQdHa1UKkNDQ2fNmsX9ulVXV2/bti0lJWXo0KECgcDGxoZrcvHgwYPdu3dnZ2cHBgYuXLiwcWEmIYRoX1FRfXkg95cgk5PDRkSwN28y6p0HdHXh44PgYNbEBECvXmj0j/0OjX6Oa/brrwgPR0EBSkpa4L/CQsTHQ61L+TO4e/duk3r+7OzsgQMHctVzFy5cmDp1qqen5/Dhwz/88EP1yv/169dXVVVxX3/66acCgWD06NHr1q07evQogJKSEl9fX4VCMXbs2LCwsPnz53Mrx40b98cff0yYMCE3NzcwMLC2tpY71ddffz1+/HilUrlp06bHBbx06VJvb++goKDJkyf//fffAO7du1dTUzN58uSAgIC5c+devnwZwJkzZ9atWzdmzJipU6fW1NQolUoACxcuPH78+NixYx0cHMRicU5ODoBt27Z99tlnY8aMMTAw+OSTT9Tf8ebNm6tWrTpz5syECROuXr06derUdevWDRs2rLS0dNq0adyaTz755PPPPx8yZIiXl9eoUaNu3LgBYNasWYWFhfPmzQsNDX348CGANWvWXLlyZfbs2SNHjszNzQVQVVV1+/btkSNHjhw5cseOHRs3buROOH78+Js3b06dOjUiIuKtt97ibuymp6cHBwebmppOmjTp3LlzXIt5QghpEVlZOH4cO3YgJgYKOYukJGbfPuzaxSQkNMmuWENDDBzIvvsuO3w4TEysrDBxIqZNwwv03mlX6AqWZikpLR0BkJEBmQzNstc8MTFx2rRpn3322dSpUwF89NFH27dvHzNmDAAbG5vXX399wYIFj3vtjBkz3n33XQCZmZmXL1+eNWvW3r17+/Tpw92CDA4OdnJy+vTTTwsKCqKjox88eGBgYDB69Oi+ffueOHFi1qxZmzdvvnr1qpeX19ixY2/evKl4zCXB9957j9ueVVRUtGXLltDQUF9fX19f3+rq6ry8vIULF4aFhQ0ZMuTu3btubm7Dhg3T09MbPnw4gKSkpHPnzj148EBfXx9Aamrq/v37P/zwwy+++OL48ePcrrK7d+9mahrdbWxsvGvXLoZhTExMhgwZkp+fb2ZmNnDgQHNz87q6urq6us8//zwjI4NrPFFSUrJz587du3cnJye//fbbXPN6TnJyckhIyODBg7nLVABMTEw2b95cV1eXl5f3wQcfrFu3btWqVTdv3oyNjc3KytLT0xsxYsQff/zBLd64cePChQuXLVsGIDQ01MrK6osvvmjBhluEkI4pMxPXriGZG8T8j+WBMDNDYCD69mUFAgCdOyMwEG5uoIvvjVGCpZm5OcrKWjgGY2M8SxXgPxk8ePDGjRu57Ipl2Vu3br311ltc2qRUKgs0fn4e6dWrF/eFpaVlcXExgJSUlL59+3JPWllZOTk5JScnFxQUuLm5cd3PAfj5+SUnJ+fl5VVVVXl6enJP+vj4cNds1qxZI5FIALz99tsTJ04EwE284dbs3bsXQGpq6vTp02UymY2NTW5uLtfL6tVXX/35559tbW0HDx68YMGCESNGJCYmVlRUeHh4cC8vKysbP358ZWVldnZ243NqTLBcXV25lMjCwsLKyoq7p2liYsLn80tLSx8+fCiTyYKDg7nFVVVV3Lts2LBh/vz5lpaWo0aNeu+99+zt7VevXj1nzpwdO3YMHz78nXfe8fT0rKysnDlz5q1bt1xcXGpqarKzswGkp6d37969oetdwy9LYmLimTNnjhw5wj2Uy+UZGRkN3xEhhLxUSiUSEyGRID8feFQeyEokjKZBsaytLYKCGC8vlmEYBj17QiyGWqtBAlCC9TgjR+KHH1Bc3GIBGBhg/HgwzJNXPo39+/e/8cYbXl5egYGB3AWbs2fPcjuKnohRC8LU1LTsUfrJsmxZWZmpqalcLi8tLW1YU1JS0rNnTxMTE5VKVVlZyY2UbnjV/PnzudHUnTt35p4pf1SKUlpayu2vX7t27aRJk1avXg3g66+/vnDhAgA7O7urV69mZWX9+OOPM2bM+PXXX01NTbt27Xr79u3GESqVSl1d3bKyMq6hfOPAGmu81Ul925OpqalQKExOTm7Sa3769OlTpkyJiIj4z3/+M2bMmOvXrwcHB6empt68efPIkSP9+vXLysrau3evQCBIS0sDEB4ezg1btLCwaJzL5ufnN7zRZ599tmjRIo1BEkLISyKTITYW4eGPLiiUlyMigr1+nZHJmu5hB+DqyojFcHYGwOPD0xMhIdC0wZXUowRLMysrLFmC8nK01CQhY+Nnu43Nsiw3nxiaUqIRI0b88MMPkydPDgsLE4lEEydO/N///d9Dhw7p6empVKrk5OSGy1RPY/jw4TNnzlyzZo2tre2xY8f09fU9PT256zRXrlwZOHBgamrqr7/++u9//9vAwCAkJOTbb79duXJlaWnpDz/84OvrC0C9sft3330XGhqqVCr37NnD3furqqrieqmXl5fv3bvXzs4OQFpampOTk4ODw5IlSw4cOJCTkzNo0KDy8vKwsDBu41R5eXlFRYWDg8PgwYO//fbb9evXV1ZWHjlyRL2Z+xO5uLj06NFj8+bNH3zwAYDa2trs7OyuXbveuXPHzc1NLBbz+fwJEyYA4J7p3bv36tWrt27dWl1d3RC8Uqn8+uuvuRP6+/srFIqDBw/OnTv3jz/+uHr16siRIwFMnDjxq6++mjBhgoWFBYDbt2+7u7s/a7SEEPL0KisRGYnoaNTWAgBTXIyoKFy/rl7YxfJ48PSEWAxraxbQ14e/PwIDn78Gq+OgBOuxeDyYmrZ0EE9HV1e3YV82gNWrVwcEBDQp2evfv/+xY8cmT5586NChjRs3LlmypGvXrg4ODtnZ2VOnTt2yZQuPx2t4ia6urnqW1mDAgAFLlizx8vKys7OrqKg4evSovr6+vr7+kSNHXn31VUtLy5ycnI0bN/bu3RvAd999N3bs2O+//16hUIhEorq6Oo3ntLS09PT05G7DLV++HMCKFSsmTJhw4sSJysrK/v37Z2RkADh9+vSXX37ZpUuXvLy8gICAkSNH6urqnjlzZuHChR9//LG+vn5paemePXscHBy+/vrrMWPGnDlzRqFQiMVibu/5M+HxeGFhYQsXLvzuu+9MTU0LCws//fTTrl27Tp48WSaTWVlZZWVlbd26FcC///3vyMhIR0fHhw8frl271tLScv78+QMGDPDy8pLJZNzlKwB6enqnT59+4403Vq1aFRoaOmLECO4C24IFCzIzMz08PBwdHYuLi11cXH7//fdnjZYQQp5GURGkUsTHP0qlMjMZiYRNTtbwE19XFz4+jEjEGhsDMDZGcDD69gXN83xKNOy5owx7VieTyfLy8qytrZ9vFqZcLi8qKrK1bToRPScnx9rauslttYcPH9rY2PxzZ/mKioq6urrG8w3lcnlOTo69vX3jsYDcznFzc/Mmk6pLSkrq6upsbGwap4ZZWVlWVlYv2JW+srKyvLzcxsam4ZsqLS2trKy0tbVtCKyqqqqwsNDW1rbhF1OlUmVnZ1tYWAiFGsZvKRQKNze3PXv29O/fv2F9VlaWhYVFwz62JmjY8wuiYc8dFg175uTkICICN29CpQJYFklJkEiYrCwNSzt1QmAg6+cHfX0AFhbw94efH3Ta1DUZGvZMWoyuru5z3DhrIBAI1LMrANy9vCYcHR2feEIjI6MmPwQFAkHDJq0Genp66k8CaGi71ZiDg8MT3/eJOnXq1CSZMzU1Nf3vy5uGhoZN6v54PJ76d71p06bc3Fxzc/OLFy+6uro2blTG4/Fe5LeDEEI0YlkkJ0Mqxf37AB7tab92jSks1LDYzIwJDISvL6ujA6BLF4hEcHVttg3BHQolWIRoz+zZs//888+Kioq1a9cOHDjwH+7DEkLIC1IqkZAAqbS+0wJTW8tGRyMyknnU5rAx1nkw+rgAACAASURBVNGREYvRsydXHujuBpEIT/FPY/JYlGCRx1IqlVVVVVwB4NNTqVQVFRUtPmlHLpfX1dV1amX7MO3t7WfOnNnSURBC2rm6OsTFNSoPLCtjIiIQG8uozaVlAfToAbEYnTuzAJ8PT0/064dGmzXIc6IEqz2YN29efn7+qVOnuGabABYvXpyenn727FmNG4CeUmRk5MKFC+/cufNMr7p79+6AAQOeY1P5PygpKTl//vzs2bOf/iWnTp3au3fvpUuXmjEMQghp5SoqEBGB69frywORlwepFImJeFRm/v/4fLZ3b4hEXK8FoRB+flQe2JwowWoPpFJpSUnJ2bNnuVaiycnJp0+fLigo4CbJPDd3d/fdu3c3U4wvJDs7e+XKlc+UYPXv31+9GQQhhLRXDYOY66cHZmSwEglSUzVsRNDTY319maAgGBkBMDGpLw9slsEhpAElWI9VlVeVdilNXiNv6UD+n9Bc2GNUDx2hht+1mTNnHjx4kEuwDhw4MHPmzO3bt3OHoqOjjx079uDBA0dHR647A4C///47Pz+/qqrql19+Wbp0qZ+f35YtW+Li4nx9ffv06VNTUzNu3LiysrKIiIiQkBAAa9asmTFjxn/+85+KioqZM2dyraqysrL27Nlz9+7dTp06zZgxo2EeszpuQPLQoUO/+eYbQ0PDJUuWNLR6OnPmzLlz53R0dGbPns1NPq6urt6+fXtCQoKOjs7gwYPnzp3Lve+qVasA/Otf/zIyMoqJiTl06FBpaemQIUPmzJkDIC0t7eeff+7du/eBAweGDh3au3fvGzdu+Pn5ASguLt66dWtaWho3H5q7b7hly5b+/fuHhYXl5uYeOnSoGX+bCCFEm7KzERlZXx7IsCxz5w4rkSA7W0NqZWTEBgYyfn7Q02MBGxuIRPD0pOmBLwUlWJpVZFd86/1tdUF1SwfSlL2f/aKIRQy/6Qdn2LBhp0+fzs7OtrW1PXr06MmTJxsSrFu3bvn7+0+YMCEqKqpfv3537twxNjaOiorauHHjrFmz5s2bZ2tru3jx4ry8vBUrVsTGxs6ZM2fq1Knjxo3jOpK///77ADZv3iyRSJYuXVpaWjplypS4uLju3bvfu3fP0tJy0KBBDx8+nD179smTJxsGyzRRUlKyYcOG8PDwFStWxMfHh4aGJiYm2tra7tq1a+PGjdu2bauoqJg0adKRI0eGDh26evXq3NzcpUuX1tTUpKamAvD39z927NjgwYMB6OrqXrlyZcGCBRs2bLC1tV27du3Dhw9Xr16dmZnJ7RxfsGCBg4NDUlLS8ePHFy1aJJPJRCLRsGHDXnvttYMHDw4aNCg8PJzH4+3du3fPnj0rVqxoXMpHCCFtBcvi7l1IpeAmgTEKBW7cQHg4iovVUyvW0hIiEby8wOezgIsLxGJ060blgS8RJViapf2a1gqzKwDZMdmFdwut3JuOJ+Dz+TNmzDhy5EifPn169erVuOB/3rx5crk8NzfX3t7+1KlT165d4xqIOzs7b9u2DUBZWdmRI0e4llGvvPLKtWvXNL712rVruaZNP/30019//dW9e/eQkBCxWJyXl2dvbz9jxowff/zxcQkWgLq6uh07dnTr1m3gwIGRkZH79u378MMPN23atG3bNm7sdF5e3pdffjl06NCMjAx/f//AwEA+n8/NVPb399fT0+MSLADr1q37/PPPp0+fDsDR0XHAgAHcRB2uTzp3geru3bvc4rNnzwoEgm3btjEMExIS0qVLlz///HPgwIEAlixZMn/+/Of5bSCEkJajUNSXB9Z3WqipQXQ0oqI0lwc6OUEsRo8eYBgeD25uEIthb6/lkDsiSrA0s/O1Y/gMq2x1XVgNrQ1NnTU3mF+wYMHEiRN79+49d+7cxs/v379/7dq1rq6u5ubm9+/fz8nJ4Z5vuEmXmZlpampq9WimlLu7e5mmSdeurq7cF5aWliUlJQBiYmLmzJljYWFhbW2dkZHxzwNeDAwMGjZFeXl5paamKpXKjIyMhpHM3t7e3FSZjz76aP78+V999dXQoUOXLVvWMFi6wZ07d9avX79582YALMvW1tbKZDIAzs7O6mWDqampXl5eXEMEgUDQu3fv1NRULsGiiTSEkLaFKw+USsGNb2XKytjwcCYuDmrlgWAY9OzJikTcKGYdHXh4UHmgVlGCpZmNl82cS3Pu/HhHpVCrvGg5AgOB3//4CQw190Pv2bOnkZHRb7/9tn///obZyQqFYsmSJYmJiS4uLgBCQ0Mbevc39FW3srIqLS2tra3lihBzcnI0NhNXb9q0Zs2aFStWLFiwAMDHH3/M3c57nNra2pqaGq6qsbi42MzMjM/nGxsbFxcXc41Di4qKzM3NAfj5+d28eTM9Pf3w4cMDBgzIzs5u8tbm5uZff/01lyQ1pqOpzbC5uXlxo6ndhYWF3Ls8bj0hhLRClZWIiUFkJGpqAIDJy2MlEty6xaiVB7J8PtOnDxsczCVT+vro0wchIaBu9lpGf8E8lstAF5eBLi0dxbM5fPhwRUWFUChsSLBUKpVCoeAu8Fy9elUqlb766qtNXmVraxscHLx27dpPPvkkLi7uzJkzT9mrqa6ujjtzTk7OwYMHxWLxPyxWqVRff/31ypUr8/Lyjh07dvjwYQCjR4/eunXrgQMH6urqdu7cOXr0aABxcXF9+vTp2rXrm2+++dlnn9XV1VlZWZWUlJSUlHDt2qdNm7ZhwwY/Pz9jY2OVShUfH+/j4/O49x0yZMjy5ctv3Ljh7e39xx9/pKSkNEynIYSQ1q+4GJGRjQYx37sHiYRNS9Ow0UpPD35+TFAQ26kTAFNTBAVReWCLoQSrPTA2NuYuRzXcxePxeGZmZgzD6OrqbtiwISgoyMHBwdHRcdy4cdxgJn19/caXqb7//vs333yza9euvr6+U6ZM4W606ejoNHQZNTMz4/F43NcGBgbcta6PP/542rRpO3fu5PF448aNq6mpAcDn8zV2GTU3N3/w4IGbm1thYeEbb7zBlRxu3rx57ty5Xbp0kcvlQ4YMWblyJYAtW7ZcvnzZzs4uPz9/06ZN3AUn7l4hj8cLDw//8MMPV69e3bNnTwsLi+Li4okTJ+7YsUMgEDTuiaqrq8t9Fy4uLrt37x49erShoaFMJjt69Ch3M9TY2JiuYBFCWrP79yGVIjkZLAuwLJOSwv79t8bpgayhIfz8EBQEfX0WsLWFWAwPDzz6sU1aAA177hDDnmUyWU1NzVN2V+/fv/+iRYu43gdPpFKpSkpKzM3N/3nqS2pqamBgYFFRUWVlpa6ubpPpyzU1NTo6Oo1HQcvl8vLy8n8+Lcuy3DWtpxw4U15e/qxd6VsVGvb8gmjYc4fV5oY9c+WBEgkePAAAyOW4cYMJD0dJiYbVVlasSITevbleC1271pcHEhr2TLRBPadpYv/+/X/++aezs/O1a9fq6uqmTZv2lGfm8XgWFhZPH4nG2TXq7eYFAsETT8swTMNuqqfRprMrQkgHUVuL48eRng4ATF0dbtxgr11jKivVV7JOTkxQEOvmxpUHurtDLIadnbYDJo9DCRYBgClTptja2ubl5b3yyiuhoaHNfu/M2tp6y5YtzXtOQghpf37+GenpYEpL2fBwNi6OkcubXqJnGLZnT4jFcHRkAYEAPj4IDoaZWYvESx6LEiwCAJ06dRoxYsTLO7+xsXGT5hGEEEKaqKrCrd/rpweqlweCz2c9PJhHvRYMDBAQgIAAaCr7Ji2PEixCCCGk5aVfTr/yqQR/p2vYVaqvzz4axcwCZmYIDoaPDwSam/aQVoESLEIIIaTFsCo25XzK35/+nRWloTwQnTqxvr5ceSAAOzuIxXB3p/LANoASLEIIIaQFyKvkcfviwreEl2aUajhsbc2KREzv3lwy1a0bxGJ07artIMlzowSLEEII0arqguqoHVFRO6NqimrUj+r36lLTV8R2784wDMODpwdEIioPbHsowQIAoVDo5+fHo0uupBWTyWRUKEBIW1d6rzRiW0Tsnlh5tbzJIYbHuI507fdhP4cgx3v3kJMDPT24uuLpOhiSVocSLACIjIysra1t6SiIllRWVmpsx9X6tdGwCSEAsmOypV9Ib/94m1U27e+tI9TxnusdvDzYvHt9b7+uXeluYJtHCRYACIVC9V6XpL3S0dFpW22dCSFtWua1TMlGSfLPyeqH9Iz1vOd5iz8QG9nTD6X2hhIsQgghpPlx5YF/rf8rOzpb/aiJs4n/G/5+/+OnZ0Ljm9onSrAIIYSQ5iSrlMXtjQvfGl52v0z9qE0fG/EKscc0D54ObfxtzyjBIoQQQppHdUF11M6oqB2aywOdxE4hH4S4jnZ9yhH1pE2jBIsQQgh5UcUpxdIvpfEH4xW1iiaHGD7jPsldvFJs50u9FjoQSrAIIYSQ55cVlSXZJEk6ncSqNJQH+sz3CV4WbNaNRjF3OJRgEUIIIc/jn8oDTfS853qHrArpZEfdVTooSrAIIYSQJ0hPR0ICysthYYG+fVT5V25Kv5DmJ+arrzR1MQ1+L9hngY/AkEYxd2iUYBFCCCGaqVS4fRsSCXJyAICRydKvX4+JjEBZufpiWx9b8Qqx+xR3Kg8koASLEEIIUSeT4cYNhIejpAQAUFWF6GhERTE1VB5IngolWIQQQsj/q6pCVBSio1FdDQBMURErlSI+nlEqm6zk6fDcp7iLV4htfWxbIFDSulGCRQghhABASQmkUty4AbkcAJiHD1mJBHfvMmzT8kBWIHCZ6DPuf4NNXUxbIFDSFlCCRQghpKPLzoZEgjt3oFKBZVleSgorkSAzU/2GH2tggIAAJiBg8DtCU4cWCJW0FZRgEUII6aBYFmlpkEhw7x4AQKlkbt5kpFIUFGhIrczMEBwMb28IBK494EDZFflHlGARQgjpcFQqJCZCKkVuLgAwMhni4lipFOUaygNha8sGBaF3b/B4DANvbwwfruV4SdtDCRYhhJAORCbDzZuQSlFUBACoqGAiI9mYGKaurslVKxZAt24Qi+HiAoDPh6cnxGJYW2s9aNIGUYJFCCGkQ3jUaaG+PBDFxUxUFK5fh0LR9IYgw8DVlenfn7W3B6CnB29viMUwNtZ60KTNogSLEEJIO1dcDKkU8fGPygMfPIBEguRkqJUHQleX9fFhgoNZExMARkYICoKfH/T0tB40aeO0l2DdunXrzz//vH379oABAyZPnqy+4OrVq0eOHGl4uGbNGicnJ62FRwghpP3JycEff+ikpkKlAliWSUlhr13DgwfqK1kDA/j7M4GBEApZwNwcAQHw84MOXYggz0V7f3D27NmTn5+flJQkFAo1Jlh37tyJiYlZvHgx91AoFGotNkIIIe0JyyI1FRIJMjIgk/H1+EomIQFSKQoLNbRaNzdnufJAHR0W6NwZYjF69AB1ZScvQnsJ1tatWwG8/vrr/7Cma9eu/7yAEEII+QdKJZKSIJEgOxsAmLo6nchINjqaqazUsNrBgRWJ4OYGhmEYuLoiJASdO2s5ZNI+ta5Lnzdv3pwzZ46tre2cOXO8vLxaOhxCCCFthkyG2FiEh6OsDABQXs5ERuL6dX5dXZOVLMC4urIiEbp0waPywJAQWFlpO2bSjrWiBMvFxWXBggVOTk6xsbHBwcG//PJLaGjoP7/k7t27K1as+Oyzz7iHpqamZ86c4fGeaoy5XC5XqVQymexF4yZtTaXGf8iS9o4+8u1YVRUTHc2Li+PX1jIAeIWF/MhI3q1bUJseyPJ4rIeHMjBQZWUFQI+p8/FR+vurOnViAVRUaD928rLIZDKWZZ/7I6+vry8QCF4kgFaUYA0ZMmTIkCEAZsyYwTDMli1bnphgOTs79+vXb9CgQdxDfX19ExOTp3w77qetHlWGdEhGRkYtHQLRNvrIt0tFRfXlgQoFAOjmZjISCZucrGH3lK4ufHwQHMyYmOgAxsYICoKvL5UHtltcgtWCH/lWlGA11r1792vXrj1xmb6+fteuXX19fbUQEiGEkNYjJwcREbh5s748kNt4xWRlAWjaL9TQkAkKYv38oK8PwMIC/v5UHkheuhb+81VUVHT06NE33nhDR0cnNTW1e/fuAMrKyg4cOCASiVo2NkIIIa0NyyIlBVIpMjIAAAoF4uOZ8PBHfdn/m4UFRCK5m5tAKATQpQtEIri6Unkg0QbtJVifffbZl19+WV1dzTDMvn371q5d+84772RnZ7/zzjsLFizQ0dFZunRpXFycra1tWlragAEDPv74Y63FRgghpJVTKutH3OTnAwDq6pgbN1iJhNG4c8rOjg0MZLy8WIZhZXVubhCL4eio3YhJx6a9BGvZsmVvvvlmw0OuzZWnp2dlZaWhoSGA8+fPP3jwoKioqHPnzubm5loLjBBCSGvWpDyQKS9HRAR7/TpkMvXpgUyPHhCL2c6dAfD48PSEt7fcxYV2WhFt016CJRQK1XuHMgzDZVccJycn6t5OCCGEU1GByEjExKC2FgCQn89IpezNm4xK1fQuH5+P3r0ZkYi1sgIgFMLPD4GB6NQJFRVq83AIeflojx8hhJBWp7AQUikSEurLA5FZXx4ItT3s9eWBIhFrbAzAxKS+PFBXV9sxE9IYJViEEEJakexsREb+f3kgw/Vl11ge2KkTAgPxqDzQxgYBAejTh8oDSatAfwwJIYS0PJZFcjIiI5GeDgCMUonERObaNRQWalhsZsYEBjK+vqyODmh6IGmVKMEihBDSkpRKcIOYCwoAADU1TEwMIiOZqioNq52cWJEIPXuyDMMwcHeDWAwHB+1GTMhToASLEEJIy6irQ1wcpFKUlwMAysqYiAjExkJ9vAnDoEcPViTiRjHr6MDDA/36wdJS2zET8pQowSKEEKJtSiWuXkV4OOoHMeflQSpFYiJUqqZL+XzWw6NhFLNQCH9/BAaiUQE6Ia0RJViEEEK0imXx/ff1e60aygPVd0+xurqMjw8rEsHYGICpKYKC0LcvlQeStoESLEIIIVqVmIh7aSxu32akUmRnQ7080MiICQqCry+rpwfA1hYiETw9weO1RLiEPBdKsAghhGiPsk4ZvSeR/f4qo3F6oLk5AgLwqDzQxQViMbp1o/JA0vZQgkUIIUQbaopqonZGRe2Iqi6o1pAvde4MsVjl6sowDI8Hbnqgvb32wySkeVCCRQgh5OUqzSgN3xIety9OXiVveoxh0LMnxGLW0RGArgDe3hCJYGbWAnES0owowSKEEPKy5MblSr6Q3D5xW6VoWh7I8vlMnz4QiVgLCwAGBvD3R0AAlQeSdoISLEIIIc0v/bd0ySZJ+uV09UP6pvo+r/nV+QQmPexUXQ0ba/TtCx8fKg8k7QolWIQQQpqNSqG6ffK29AtpTmyO+lFjJ+OgpUG+r/vqGukCGKP18AjRGkqwCCGENAN5lTxuf1z4lvDSe6XqR609rUUrRL1n9OYJqNcC6RAowSKEEPJCqguqo3ZGRe+Mri6sVj/q3N9ZvFLcfUR3hnotkI6EEixCCCHPqSS9JPzL8BsHbsirm5YHMjym14Re4pVihwAaxUw6IkqwCCGEPLOc6zmSLyS3T95mlWyTQzr6On3m9hEtF5m7mrdIbIS0BpRgEUIIeVosy6ZfSpdskty7ck/9qNBc6PeGX+DbgYY21GuBdHSUYBFCCHkyVsWmnE/5a/1f2dHZ6kc72XXyfd03+L1gPRM97cdGSCtECRYhhJB/IquUxe2NC98aXna/TP2ojZeNaIXIc5onlQcS0hglWIQQQuqpVCgsBABLS/B49eWBUTuiaopq1Bc7iZ1CPghxHe1K5YGEqKMEixBCCGpqEB2NqChUVgJAJ1mx3b3wjJ9uKGoUTVYyfMZ9krtohcjej0YxE/JYlGARQkiHVlqK8HDExUEmAwAmN5cND69KTExVNZ0eyNfje0z1CP1XqEVPixYIlJA2hRIsQgjpoHJzIZHg1i2oVGBZlpeWBokEGRnqN/yEFsKAtwIClgQYWBm0QKCEtEGUYBFCSIeTng6JBGlpAMCoVExSEiORIFtDeaBpF9Ogd4P6LuorMBRoO0pC2jJKsAghpKNQqXD7NiQS5OQAACOTsdevsxERTHm5htW2tsLB4rf3u/N0qDyQkGdGCRYhhLR/cjni4hAejpISAEBlJSIj2ZgYprZWw+quXSEWs127egWBR39LEPJc6KNDCCHtWXU1oqIQFYVqbhBzSQkTGclev84ompYHgmHg6orQUNbBAYC9PV55RcvBEtJ+UIJFCCHtU0lJfXmgnBvE/PAhI5UiKQks23Qbu0AAHx8EB7OmpgA6dUJwMIKCwOdrPWhC2gtKsAghpL3JyYFEgtu368sDmXv3mMhIJCdrWGpgwPr7IyAABgYALCwgEqFPH+jQXw6EvBj6DBFCSPvBdVpITwcARqXCzZuMRMIUFKivZE1NmaAgtm9fCAQAHB0hFqNXL1BXdkKaBSVYhBDS5rEskpPx99/IygIA1NXh+nVERmosD2Tt7BixmHF3ZxmGYeDigsBA9Oyp5ZAJaecowSKEkDZMJqsvDywtBQBUVSE6GpGRGssDWScnJiSEdXUFw/D56N0bYjGsrLQcMiEdAiVYhBDSJlVV1ZcH1nCDmAsLIZUiIYFRKpsu5fFYDw+IRLC1ZQF9Pfj5ITAQxsZaD5qQDoMSLEIIaWNKShARgdjY+vJA5sEDViJhkpPBsk1WsgIB07cvgoNhYgKgU6f61Eoo1H7UhHQslGARQkibkZUFqRR37jyaHpiSwl67hgcP1DemswYG8PdnAgNZoRCApSVEInh5UXkgIVpCHzVCCGntWLa+PPDePQBglEomIYGRSlFYqKHmz9ycDQ5mvL1ZHR0W6NwZIhF69qTyQEK0ihIsQghpvZqUBzJ1dYiJQWQkKio0LLa3h1gMNzcwDBj0cEVICDp31nbMhBBQgkUIIa2TTIbYWISHo6wMAJiqKjY6mv3H8kD06AFARwdeXhCJYGmp5ZAJIf+PEixCCGldqqoQGYno6EflgQUFkEpx86Z6eSDL48HTkxGLYW3NAvr69XvYjYy0HzUh5L9QgkUIIa1Fk/JAZGZCIkFysoY97Lq66NuXCQ5mjY3ZR+WBQUHQ19d2zIQQjSjBIoSQlpeVBYkEd+6AZQGWxd27jFSKBw/UV7KGhggMZPz9WX19FrC2hkiE3r1pMDMhrQslWIQQ0mJYFikpkEqRkQEAjFKJ+HhIpUxRkYbF5ubMo1HMLODsDLEYrq5UHkhIa0QJFiGEtAClEomJkEiQnw8AqK3lygOZykoNqx0cuFHM3PRAV1f06wcnJ+1GTAh5FpRgEUKIVjUpD0R5OSIicP06I5M1WckCcHVlxGLW2RkAnw9PT4SE0PRAQtoASrAIIURLKivrywPrOy3k50MqZRIToT49kM9nPT0hEjUuDwwKQqdOWg+aEPJcKMEihJCXrqgIUini46FQAABz/z4rkSAlRXN5oK8vgoK4UcwmJggKQt++0NPTdsyEkBdBCRYhhLxEDx9CIkFSUn15IJOUxEokyMrSsDG9Uyc2MBB+flyvBWtriMXw9KTyQELaJEqwCCHkpVAq8fPPiIsDACgUTHw8K5WiuFjDVSsLC4hETJ8+XDLVpQvEYnTvTuWBhLRhlGARQshL8ccfiIsDU1uL6Gg2MhJVVRpSK0dHiMX1o5gZuLtBLIaDQwtESwhpXpRgEUJI81MqEXW5jPk7ArGxkMmapFYsgB49IBZzo5h1dODtjeBgWFi0RKyEkJeAEixCCGlmeQl5f22Qyk4kMipV02N8Ptu7N0QirteCUAh/fwQEUHkgIe0NJViEENJsMq9lSjZKks8ng0XTq1a6uoyPDysSNZQHBgejb1/o6rZIpISQl4sSLEIIeVGskr1z6o5kkyQ7JlvDYSMjBAXB15fV0wNgYwOxGB4eVB5ISHtGCRYhhDw/ZZ0yMSzx6oarRXc1TA8U2JjLfQJYX1/o6ABwcYFYjG7dqDyQkPbvCQlWUlLSlStXbt68mZ+fr6enZ2VlFRgYOGjQIBsbG+3ERwghrVNded2N/TckmyQV2RXqR+187QLfCew90yvtHvPgAQQCdO8OOzvth0kIaRmaEyyVSvX999/v2LEjKioKgImJibm5uVwuLy4u/uqrr3R0dEaPHr1s2bJ+/fppN1pCCGl5pRmlEVsjYvfGyqvkTQ4xPKbn2J6iFSInUf0oZldXuLpqPURCSEvTkGDdunVr1qxZaWlpEyZMWLVqVXBwsK2tbcPR5OTka9euhYWFDRgwYOzYsYcOHepE1S+EkI4h90au9AvpreO3VIqm5YF8PX6fOX1E74sselKvBUKIpgQrKSlp4sSJ7777rrGxsfrRHj169OjRY8GCBenp6evXry8qKqIEixDS7jUuD2xC10jXZ76PaIXI2FHDz0xCSMekIcGaNGnSpEmTnvjKrl277t+//yWERAghrYVKobp98rb0C2lObI76UWNH46B3g/q+1lfPmEYxE0L+C1UREkKIBvXlgZ9dLUrWUB5o7moe8FaA72JfHX36KUoI0eCxPxqqqqrCwsKuXLmSmppaUlKiq6trZWXl5eU1ceLE0NBQbYZICCHaVF1YHbUjKnpndHVhtfpR51Bn8Upx95HdGeq1QAh5PM0J1l9//TVjxoycnBxTU9Nu3bolJyd7enrm5+fv3r17+/btw4cPP3r0qJmZmZZjJYSQl6okvSR8S/iN/Tfk1RrKA3tN6CVeIXYIpFHMhJAn05BgZWdnjx07Nigo6MKFC97e3nK5XFdX99///veUKVNqa2svXLiwbNmyRYsW/fjjj9oPlxBCXoa8+Dzpl9LEHxI1lAfq8j2mefT7sJ9lL8sWiY0Q0hZpSLB+/PFHBweH8+fP6+g0Paqvrz9x4kR7e3uxWFxSUkIXsQghbU5eHuLjUVYGIyP4+KAu5bHlgXrGet7zvMUrxUYORi0RKSGkDdOQYJWWljo7O6tnVw1clModtgAAIABJREFUXFxUKlVZWdnLSLCKi4uFQqFQKGz2MxNCOrj795noaKSmgmUBlQq3bkVKpcjNVV9p0tmEKw/U7USjmAkhz4On/lRgYOAff/whlUo1vkCpVK5Zs8be3t7JyemZ3unNN9/08vIyNze/ePGixgXFxcUDBgxwc3Ozs7Nbs2bNM52cEEIeR6XCrVvYu5d3+DA/JQWQyXH9OnbuZE6dUs+urHtbjz84/p3Ud4LeC6LsihDy3DRcphoyZMikSZP69+8/dOjQQYMGOTs7A0hISKitrb179+7p06dTU1NPnDjBf8ZB8F5eXtOnT587d65c3nT3KGfdunUWFha5ubl5eXk+Pj5Dhgzp37//c3xLhBDCkcsRHw+pFMXFUKkYVFXi+nVERzM1NeqLuwzoIl4h7ja8G5UHEkJenIYEi2GYw4cPh4aGfvXVV8uXL+ee/PTTTwHo6uoOGzbs0KFDvr6+z/pO//M//wNAIBA8bsGRI0fOnDnDMIytre306dOPHDnyEhOskhL+5s28vDw8Y5pI2gF9uRyP/3NI2ocahSCqwCUqv0uVQg8A6up4uXkoLmRUTXdasQysbHUmBOXaW2XjjBRnWiBa8lLRR75j0lGpWDMzLF8OG5uWCUDjszweb/HixYsXL87JyUlOTi4rK9PV1bW0tHR3dzcwMHgZcZSWlhYXF/fo0YN72LNnz5MnTz7xVQqFIi8vLz09nXuor69vb2//VO83ezbvwoXnDZa0bfSDtn0rhWk4guPgI0MlkMigfvO6+lUp9tH/BuZ8b3/6jjaDJNpEH/mOqX4LlEQCiaRFAnhCD2I7Ozs7OzstxFFeXg6gIXszNDQsLS194quSk5OlUunmzZu5h0ZGRteuXePxNGwsa8IwJobuARDSzuTCVgpRIjxV4LFgeU9MrQAAtsjtibtaCpEQomUxMZUVFXj2+/56enr/cM/taWhIsFJSUszNzS0snjwQ/vbt2w4ODiYmJi8SAcfKygpAWVmZkZERgNLSUmtr6ye+yt3dfdq0aZMnT37m95s7F1988exhEkJao3R0lUKUhm4sGAZgAAYMNKVWAFig4bJWN6SNxxkemva+IoS0E6++2smoZdqsaEiwYmJiFi9e/MYbb8ybN8/NzU19gUql+uuvv3bt2nXq1Km0tLRmSbCEQmG3bt1iYmIcHR0BREdH9+7d+8VP+1gbNyqGDUNysg7twep4amtr9fX1WzoK0gxULHM7x0yaZpNdagAACgWT+QD30qFpDzuMjVVduzIODmAYMHC1KhN3z+tiYQeEaDlsomX0ke+YFAoF6+IiGDaspQLQkGDNmDHDyMjogw8+2LRpk7u7e2BgoKurq7m5uUKhKC4uvnHjRnh4eG5u7ogRI2JjY7l86GnExMSUlpZWV1fHx8cLhcKAgABjY+MTJ0788ssv+/btA/DGG298/PHH3bt3T01N/emnn2JiYprzG22CYdjQUFVIiI6e3kt8F9IqySsq9FvoHzSkucjliItDeDhKAHQDU1WFyEg2Ohq1teqLWRcXiMUqFxeWZXV1+Z6eEIlaatsraQH0ke+YVDIZy7J4il1DL4nmPVijR48eNWrU77//fvjw4d9++23//v3c8zwez8PDY8aMGYsWLdJ4cesfnD17NikpSSQSJSQkJCQkdOnSxdjY2NDQsOFe5LvvvltVVTV79mwzM7Njx465urq+yDdGCGmXqqsRG4vISFRUAACKipjwcMTHQ6FockOQZRi4u0Mshp0dAAFf2aePqn9/fnNccyeEkCdgWFZtPISa0tLSvLw8fX19Kyurl1RF+HymTJnynHuwALlcrlKp9OgKVsdTUVFhRP+cbYNKSxEejrg4yGQAwGRlQSJBUhLUf4gJBP/X3p2HR1ndfQP/nskkk32BbENYgwlZSMg+mZkgrbRu2IogQn21vlJb+2pba1t8tH2srb3k8bK2Wh+3VquI9noRfVrbF2vxQqqQeyaTHQgJJKwhGwkhC1knmTnvHxNinBlZk5ks389fM/d9gr8wnsyXyfmdIzMyoNcjIgJAUBByc5GVNaTRcMrPRJzyM5PVapVSenHKX6SL0CE8PDw8PHyiSyEicqu5GYqC6mrY7ZBSiro6YTLh5Ek3QwMDZW4u8vIQGAhg9mwYDFi2DGo1hoZg51p2IvKUSwpYxcXF+/bta2pqio2NTUtL0+v13OmYiDzg6FEoCka2urPZRFUVFEW0tbkZGhEBvV5mZDi2lJw7F0YjkpKuoDubiGgcXCRgtbe3r1+//pNPPhl7Ua/Xv//++5e6pScR0WWSErW12LMHjY0AgMFBlJUJiwXd3W7yklYLoxEpKVIIIbBoEXQ6LFni4ZKJiL7gIgHr7rvvLi4ufuGFF9asWRMTE9PW1vbhhx8+9thjt99++5edBk1EdMU+bw/sAADR0wOLBaWlbtsDsXgxjEa5aBEAHx+kpcFgwCXsoEdENOEuFLDa29v/9a9/bd269a677nJc0Wq19913n1arveWWW44dOxYfH++RIolo+uvtRUkJiovR1wcAoqMDFossKxPDw85DhUBCAlaskHPmANBokJ2N/HyEhnq8aCKiL3GhgDU4OCil1Ov1TtcNBgOAPsdPQSKiq9PRgaIilJdjaAgAREODVBQcPgwpnXde8PUVWVkyPx/h4TjfHqjTISDAC2UTEV3AhQKWVqu95ppr9uzZs3jx4rHXP/vss+jo6CVc40BEV6epCYqCmpqR9kBVXZ1UFNTXuzk9MDAQeXkiL08GBACIjITBgPR0qC+pUYeIyNMu9MNJCLF169YNGza0trauXr06Nja2tbX1n//853PPPffOO+9c5SGIRDRjSTnSHnj8OADAZkNVlVAUtLW5iVbh4SI/H1lZ8PWVwLx5MBqxZAnbA4loUrvIRqOzZ88+e/bshf+ILVu23HPPPeNa1aXiRqN0BbjroBe5tgeKsjJZVCRG9mX/4mCtVoxpD0xIQH4+rnjlJ6f8jMUpPzNN9o1Gf/nLXw64bd4ZIzs7e/zqIaLpyWpFeTmKitDZCQA4d05YLLK0FIODzgutMNIeiEWLJODjg/R0GAyIivJ81UREV+giAeuhhx7yTB1ENF319sJiQUkJ+vsBAGfPiuJilJW5nh7oaA8U59sD/f2RnQ2dju2BRDT1cIEoEU0Up/ZA1NcLkwm1tW5OD/TzQ1YW8vNlWBiA4GDk5LA9kIimMAYsIhp/joOYa2ogJSClqKuThYXi1CnXkTIwELm5QqdztAdGRY20B/r4eLxoIqLxw4BFRONGShw5AkXBiRMALtIeiIgI6HSj7YHz58NoRGIi2wOJaDpgwCKicWCz4dAhKAqamgBADA6itFQWFYmeHjej4+JgNMqkJJxvDywowPz5Hi6ZiGgCMWAR0VWREhUV+OwzdHUBAHp6UFoKiwUDA242tZo3TxQUyMREAGr1SHtgZKSHSyYimnAMWER0Vf7f/0N5OQCItjaYTDhwADab0xipUom0NGkwIDpaAv7+I2vYuTkREU1XDFhEdOXq61FeDpw8KUwmWVvr5iMrPz+RnS3y82VoKIDQUOTnIzsb3O+TiKY3BiwiukLSLi1b68QbhTh1CoBzugoKkjk5ON8eGB0NgwFpaWwPJKIZgQGLiC7b8MDwvq37zL8zt9e2u7k9ezYMBixb5ghTCxfCYEBCAtsDiWgGYcAiossw0DFQ8kqJ5QVL7+le17ty7lxhNMolSxztgSnJMBgwd67nyyQi8jIGLCK6JD0tPaWvllr+YBnodD6fVAIiPh46HRITJaBWIyMDej1mz/ZKpURE3seARUQX0XqgtfjF4sq3Km2Dzu2BPn4+yetSVcsLDndEDQwgJASZmcjLQ3CwVyolIposGLCI6Eud+PSE8oxy5F9H4HJ4oCZUk31/dv5D+SFxIQCkxOAg/P29UCQR0STEgEVEzqRd1n1Yt3fz3oaiBte7QTFBOd/PyX8o3z/i8zwlBNMVEdHnGLCI6HPD/cOVb1Waf2c+e+Ss693IpEjDzwzpd6X7aLjXAhHRhTBgEREA9J/tL3mppPjF4t5WN+2B84zzjI8YE29JFCrutUBEdHEMWEQzXdfJLvPvzeV/Lh/qHXK6JVQi8RuJxk3GecZ5XqmNiGiKYsAimrlaKltMvzUd3H7QPmx3uuWj8Um/K93wM0NkEo9iJiK6bAxYRDPR8U+OK88oRz8+6npLE6ZxrGEP1nKvBSKiK8SARTSDSJusfr9a+a3SXNbsejd0bqjuIV3297I1oTyKmYjoqjBgEU1b3d2QEqGhEAJDfUOVb1aaf2/uONbhOjIqNcrwM0PanWk+fmwPJCIaBwxYRNPN8DD27YPZjDNnACBU3TevueTE9uK+M32ugxdcu8CwyZCwKkHwKGYiovHDgEU0ffT3o7QUFgt6egBAdHbCbD5XUVE95KY9MGl1kmGTYW4+j2ImIhp/DFhE00FXF4qKUF6OwUEAQHOzMJlQXQ27c3ug2l+97NvL9D/Vz07kUcxERBOFAYtoajt9GiYTqqpgcxzEXF8vFEXW1rqO1IRqMv53hvERo+P0QCIimjgMWERT1YkTUBQcOQIpAbtdVFdDUdDSAsB5OVVYmNDn/3hbln+YnzcqJSKacRiwiKYYKVFTA0VBYyMACJsNVVXYswdn3ZweKKOjkZcnMjKS0nz8wzxdKhHRjMWARTRlDA+jshIm00iUEn19srhYFheL/n7XwXLePFFQIBMShBChYbjhBk9XS0Q0kzFgEU0B/f0oKYHFgt5eABAdHdJkkpWVYnjYeagQSE6G0Yg5cySg8UNWFr7yFfj7e75qIqKZiwGLaFLr7BxpD7RaAQBNTVAUWVMjpHQaKdVqkZEh9XrMmgUgKAh5ecjLQ0CAx4smIprxGLCIJim37YFw1x4IjQYZGTAaZUgIgIgI6HTIzoavr0cLJiKiUQxYRJNOfT0KC1FXBykh7HZUVQmTCadPu46UYWFCr5eZmfDzAxAbC70eaWlQqTxeNBERjcGARTRZ2O2orobJhKYmAIDVKioqYDaLri43o2NipF4v0tKkSiUEFi+G0YhFizxbMRERfQkGLCLvGxoaaQ/s6AAA0dsrLRaUlGBgwHWwXLRIGI32+HghhMoHqakwGhET4+maiYjoAhiwiLxpYACVlVAUnDsHAOLsWZhM2LfPtT1QCoGUFGE0Qqt1tAdmZsJgQBh3tyIimnwYsIi8o7MTZjMqKkbaA0VLizSb5YEDbtoDfXyQmiquvVbOni2B4GDodMjJYXsgEdHkxYBF5GktLVAUHDwIux1SSnHkCBQFJ086n28DIDBQ5uaKvDwZGCiB2bNhMGDZMqg5cYmIJjf+nCbyHOf2wAMHVCYTWltdR8rwcOj1yMyEr68EtFrk57M9kIhoymDAIppwjvZARUFzM4CLtAfKmJjRvRaEQEICDAYsXOjZiomI6OowYBFNoKEhVFTAbB5pD0RPDywWlJa6bQ9EfDyMRsTHA/DxQVoaDAZER3u0YCIiGhcMWEQToq8PxcUoLkZfHwCgvX2kPXBkX/YxVCqkpEiDAVotAD+2BxIRTX0MWETjrKNjpD1waAgA0NAARRGHD8OlPRC+vsjMhF4vw8Nxvj0wN5cHMxMRTXkMWETjprkZioLq6vPtgXV1UBRRX+86UgYGirw8mZuLwEAAkZHQ69keSEQ0ffDHOdE4GNseCJttpD2wrc3N0IgI6PXIyJC+vmB7IBHRNMWARXTl7HYcPAhFQUsLAGBwEGVlKCoSjn3Zv0hqtcJoREqKFEIIJCbCYMCCBR4umYiIPIEBi+hKWK0oL0dRETo7AUD09MiiIpSWisFBp5ESwOLFwmjEokUS8PFBejoMBkRFeb5qIiLyEAYsosvT24uSkjHtgWfOwGSS+/e7bQ+UqanCaJQxMRLQaJCRwfZAIqIZgQGL6FJ1dKCoCOXlI+2B4tQpqSiittZNe6Cfn8zMFHo9wsIcpwfm5ECn4+mBREQzBQMW0SX59FPs3QubDZBS1NZKRcGpU25ODwwKknl5yM1FQIAEIiNhMCA9ne2BREQzC3/qE11cSQk+/RSw2VBVJRQFbW1uolVEBHQ6mZUFX18A8+fDaERiIoSboURENM0xYBFdnGn3oFBKZVGR6OlxvSvnzIHRiORkCCEEliyB0Yh58zxfJhERTRYMWEQX0nu6t/jlks5nLBgYcP0oSs6bJwoKkJgIQK0eaQ+MjPR8mURENLkwYBG5d/bI2eL/Li77U9nwwLDTLalSISkJRiPmzJGAv//IGvaQEK9USkREkw4DFpGz+sJ6ywuWmv+pkXY37YGO0wMdey2EhiI/H9nZ0Gi8UCcREU1aDFhEI6RdHv77YeUZpaGowfWuT1iwLUeHnBzp7w8gOhoGA9LS4OPj8UKJiGjSY8Aigs1qq9pWVfh04ZmaM653I+IjdD/SZX03+9gp9fHjUKkQH4/Fi9keSEREX8qjAevQoUM7d+6Mjo5evXp1gMuWi8eOHSsrKxt9+vWvfz08PNyT5dEMNNAxUPpqqeUFS0+Lm/bAuflzDZsMSauThEoAWLIES5Z4vEQiIpqCPBewPv744w0bNtx7770ffvjhc889pyiKr6/v2AG7du36zW9+o9frHU9zcnIYsGjidJ/qLnq+qOy1Mus5q/M9gcRViYZNhgXX8ihmIiK6Ep4LWL/+9a83b978/e9/f3h4OCMj44MPPli3bp3TmPz8/O3bt3usJJqZzhw889mbn1W+VWkbdD49UOWrWrphacF/FESl8ihmIiK6ch4KWN3d3SaT6b333gOgVqtvvvnmf/3rX64Bq62tbdu2bdHR0QUFBX5+fp6pjWaOE5+eMP3WVPdRHVy6AzWhmuzvZef/OD8kjnstEBHR1fJQwGpqalKpVDExMY6nWq32wIEDzqWo1SqV6p///GdFRcXQ0NAnn3wSFxd34T+2tbX1r3/96+HDhx1PAwICHnjgAXFpa4+Hhobsdvtlfh80JUm7PPrRUdMzpiZLk+vdwOjArO9l5TyY4x/hD2BwcNDjBZIncMrPWIODg/wX+wxktVqldPnH9CVTq9U+V9clPom6CDdu3Lhx40YAdrt97dq1TzzxxOuvv37hL7Hb7T09PZ2dnY6nV/NXSdOSbdBW836N+Rlz++F217vh8eE5D+RkfCdDHTCJJgIREU0DHnpf0Wq1dru9ra0tNjYWwOnTp7Va7ZcNVqlUq1atumi6AhAbG7t+/frbb7/9CkpSqVR2u13DDSKnqf6z/SUvlxT/d3Fva6/r3XnGecZNxsRvJDraA2km4JSfsaxWK1/3GUgIIaX04kvvoYAVFhaWl5e3Y8eO++67z263f/TRR48++igAq9V66tSp+Ph4x1/E6G/3TCZTfHy8Z2qjaabrZFfJKyWlr5YOdrn8sk8gcVVi2nfTln5zqTdKIyKimcJzvxn55S9/+e1vf/vEiRP79+9XqVRr1qwBcPjw4fT09J6enqCgoNtvvz0iIiI2NrasrKy0tHTv3r0eq42mqO5u7N+Pjg4EBCA9HbL5tPJb5eC7B+3DzkttfDQ+6XelG35qiEyOPHfunFeqJSKimcNzAWvVqlX//ve/P/7449WrV69fv97xqd2CBQu2b9/u7+8P4MknnywsLOzs7Lzrrru2bdsWFhbmsdpoymlrg8mE/fthc+y0cPy4YlJw9Kib9sAwTc79ObqHdCFz2B5IREQe4tG1venp6enp6WOvhIaGjm7WkJqampqa6sl6aCo6eRKKgro6SAlIKerq5J49orHRdWRQTFDO93PyH8p3tAcSERF5DJunaGqQEocOwWTCqVMAgKEhVFYKsxkdHa7L1KNSogw/M6T9rzQfPx7FTEREXsCARZPd8DD27YPZjDNnAEAMDqKyUhYWih43pwcGJc+7+df5yWuShQ/bA4mIyGsYsGjyGhhASQksFjiilOjslGazrKgQQ0PO6UkIuWQJjMbl352bovNCqURERGMxYNFk1N2NoiKUlcGxrbo4fVqaTKiqEq47cfv4yNRUsXw5IiNDQrBsmeeLJSIicsaARZNLaytMJhw4MNIeKI4dk4qCY8fc/MLP31/m5ECnQ3CwBGJisHYt/LmcnYiIJgEGLJosTpyAyfSF9kDs2YPGRjfRKjhYZmcjP9+Rp7RaGI1ISYFK5fGiiYiI3GHAIi+TEjU1UBQ4dloQQ0OiokKazTh/xOQXREdLg0GkpTnC1OLFMBrBPf+JiGiyYcAirxkexsGD2Lv3fHtgXx+Ki2Vxsejvd/3USi5YAKNRXnONEAICiQlYsQJxcR4vmoiI6BIwYJEXDA6iogKKAsehNaKjA472wOFhN+2BSUkwGh1hyleN1FRcey1mz/Z81URERJeKAYs8qqsLZjPKy2G1AoBoboaiyOpqIaVztFKrkZEh9XrMmgUgKAh5ecjNRWCg56smIiK6PAxY5CGnT0NRcPAgbDZIKVXHjkFRcPw4AOdoFRCA3FyZl4egIACzZkGvR0YGfH29UDYREdEVYMCiCVdfj8LC8+2Bdrs4eBCKgtOnXUfKsDCh18vMTPj5AYiNhV6P8yvaiYiIpgwGLJoodjtqamAyjbQHwmodaQ/s6nKzhj0mRhiNSE2VKpUQI+2BixZ5umYiIqJxwYBF429oCJWVMJtx9iwAoLdXFBejpATu2gOxaBGMRhkfDyF8fJCaCqMRMTEeLpmIiGg8MWDReHJqD8TZs8JslpWVGB52GimFECkpMBqlVgtA44fMTBgMCAvzeNFERETjjQGLxkdnJ0pLUVqKgQEAEE1NUBTU1MClPVCq1SIzU+j1MiICQFAQcnORl8f2QCIimj4YsOhqtbSMtAeOHMRcXy8UBbW1riOlRiMyMkRBgQwOBjB79kh7oJr/GxIR0fTCdza6cmPbA4XdLqqqpKKI1lY3Q8PDZX6+yMqSvr4AtFrk57M9kIiIpi0GLLpsdjuqq6EoaG4GMNIeiC9pD0RMjBzda0Eg4RoYjVi40LMVExEReRYDFl2GoSE4olRHBwCgtxclJaK4GP39roPlvHmioMCekCCE8PHB0qUwGNgeSEREMwIDFl2Svj6Ul8NiOd8e2N4uzGbs2+faHgiVCikp0mCAVivZHkhERDMSAxZdREcHzGZUVGBoCABEYyMUBYcOQUrnob6+yMyEXi/DwwEEB0OnQ04OAgI8XjQREZFXMWDRl2ppgdmMAwdgt0NKKY4fFxaL2/ZABAbKzEyRn+9oD4yIgE6H7GyeHkhERDMUAxa58YXTA202HDggTCbR1uZmaEQE9HqZkQFfX8n2QCIiIgAMWOSkrg6ffIKWFgDnTw80mUR3t+tIGRMzehSzEEhIgNGIBQs8XC8REdFkxIBFnyssxK5dACB6emRREUpLMTjoZueFMUcx+/ggLQ0GA6KjPVwsERHR5MWARSPOnsXu3cCZM8Jslvv2CZvNeYRKhdRUaTAgNhaARoPsbOTnIzTUC9USERFNZgxYNKJ8R7P9f4pw4ICb0wN9fUV6OgwGOWsWgJCQkfZAf3+vVEpERDTZMWDNdFLKuh11lhcsx3Ydc/1toAwMRG6u0OlkQACAyEgYDEhP5+mBREREF8L3yZnLZrXtf2e/6VnTmZozbm7PmgW9XmRkSLVaAvPnw2DAkiUQbtZkERER0RcwYM1E1nPWijcqTM+auhvctQfGxo7utSAEkpbAYMD8+Z4vk4iIaKpiwJpZzjWeK/pDUdkfywa7B53vCSy+4RrNV411wwutVvj6jrQHRkZ6o1AiIqKpjAFrpmirbjM9azrwlwM2q3N7oMpXtXTDUsPPDDHpMQDsdnR3IzSUm4USERFdIQas6a9+b73yW6V2Ry1cDg/0C/bL+m5W/o/zw+Z/fhSzSoXwcI9WSERENM0wYE1b0i4P//2w8lulwdzgejcoJkj3I13u/8n1j+BeC0REROOMAWsasg3a9m3dZ/qdqf1wu+vdWQmzDD8zLPv2MrU/X30iIqIJwbfYaWWgc6D0lVLLC5aelh7Xu3G6OOMjxqTVSULFvRaIiIgmEAPWNNF9qrvo+aKy18qs56zO9wQSbk4wPmJccC2PYiYiIvIEBqwpr7Wq1fRb04H/e8A+ZHe65ePns/RbS42bjFGpUV6pjYiIaGZiwJrCTn52UnlGqfuozrU9UBOqcbQHhs7lUcxERESexoA1NQwMYGgIISEAIO3y0N8OKc8ojcWNriODtcG6H+lyvp/jH872QCIiIu9gwJrUpERtLcxmnDwJKRERYrtmsOrE24VnDrk5PTBicYTuh7rs72WrA/iyEhEReRPfiScpmw3798NkQlsbAKC/X5SWdlgspb29roPnGeYZHzEmfiOR7YFERESTAQPWpDM4iNJSFBXh3DkAED090vF8cNA5PQkkrkrUPaSL/1q8FwolIiKiL8GANYmcO4eiIpSVYWAAAERrq1QUWVUl7G7aA1PXpxY8WhCVwvZAIiKiSYcBa1Joa4PJhP37YXMcxFxfLxRF1ta6/sJP+vmJzMyNWwxzktgeSERENEkxYHlZfT0UBbW1kBJCSlRXC5MJTU0AnNKVDAkR+fnIzp4Tr5mT5JViiYiI6JIwYHmHlDh8GIqCU6cAQNhsqKqSe/eKdjenB2LWLOTlITtbqtUaDW65xcPFEhER0eVhwPK04eGR9sAzZwBA9PfL4mJZXCz6+tyMnj8fRqM9IUEIoVIhORlf/zrCwz1cMhEREV0eBizPGRgYaQ/scRzE3NkJs1lWVIihIeehQmDJEhiNcu5cAH6+yMiAXo9ZszxdMxEREV0BBixP6O4eaQ8cHAQAcfq0NJlEVRVc2gPh4yNTU8Xy5TIyEkBgIHJzkZeHoCCPF01ERERXigFrYp09C4sFZWUYHgYAceyYVBQcO+ZmP1B/f5mTA50OwcESCA9Hfj6ysuDn5+maiYiI6CoxYE2UkyehKKirg5SAlKKuDnv2oLHRTbQKDpbZ2cjPh7+7+fPKAAAT10lEQVQ/AK0WRiNSUqBSebxoIiIiGg8MWONMShw6BEVBQwMAYGgIFRUwm9HZ6WZ0dLQ0GERamiNMLV4MoxHx3JWdiIhoimPAGjc2G6qqUFh4/vTAvj5RUoLiYrhrD5QLFgij0X7NNUIICCQmYMUKxMV5uGQiIiKaEAxY46C/H6WlsFg+bw8URUWyvBxu2wMTErB8OebOlYDGD5mZyM9HRITHiyYiIqIJw4B1Vbq6UFSE8vKR9kA0N0NRRE0N7HbntVZqNZYtk3o9Zs8GEBQ00h4YGOjxoomIiGiCMWBdodOnUVyMfftG2gNx9KgwmXDsmOtI6e+P8+2BON8emJ0NX1/PVkxERESewoB12errUVjopj3QzdAvtgfGxkKvx/kV7URERDRtMWBdKilRUwNFGYlSYmgI5eWiqMhte6CMjhZGI5YuZXsgERHRDMSAdXHDwzh4EHv3nj89sK9v5PTA/n7XwXLePFFQIBMSIIRgeyAREdGMxIB1If39KCmBxYLeXgAQHR3SZJKVlWJk4dXnpBBIThZGI+bMGW0P1Ot5MDMREdFMxIDlXmfnSHug1QoAaGmB2YyqKuFyeqD08UFqKpYvR2SkBIKCoNMhNxcBAZ6vmoiIiCYFBixnp0/DZEJVFWw2SCmFoz3w+HE3QwMCxh7FHBEBnY7tgURERMSANcaxYzCZcPTomPbAzz4TTU2uI2VYmMjNRU6O1GgAxMXBYEByMtsDiYiICGDAAmC3o7oaJhNGopTVOtIe2NXl5mDm2FgYDEhNlSqVEEi4BgYDFi3ycMlEREQ0qc3ogDU8jEOHxrQH9vbCYpElJWJgwHWwXLQIRiMWLwbg44OkJBiNmDPHwyUTERHRFOC5gNXW1vbzn/+8oqIiNTV18+bNcS5bF9jt9mefffaDDz4ICQn5j//4j+uuu27iiunrQ3GxsFh8HDstiLNnpcnk2Jfd6VMrKQRSUoTRCK0WgJ8fMjNhMCAsbOKqIyIioqnNcwHrzjvvnDt37ptvvvmnP/1p9erVJSUlTgNeeumlLVu2bNmy5ciRI7fddltFRUX8xGzNWVmJjz5Cf79KSqluaZSKgkOHhJTO43x9ZUYG9HpEREggOBg6HXJy2B5IREREF+GhgFVTU1NYWNjW1hYcHPz73/8+JibGYrHodLqxY1588cXNmzfn5eXl5eV9+OGHr7/++ubNm8e9kro6/P3vkBLi6FGVUoiT9W4WWgUGyjFHMc+eDYMBy5ZBPaN/oUpERESXykORYf/+/cnJycHBwQB8fX2zsrL27ds3NmANDAzU1tbm5eU5nup0up07d05EJYWFkBL45BNVYaHrXRkeDr0emZmOvRbmzoXRiKQkCDcpjIiIiMg9DwWs1tbWiIiI0acRERGnT592GgAg/PzG564D3Kqurn7wwQc3bdo0+lX//ve/VRfcLKGhwc9qFX4V5U7XZWzssE5nT0qCSgVpv2b+QH6+bd48O4Cenot/gzSF9PAVnZGGhobsdrt1ZO9gmkE45Wcmq9UqpbziKe/v7+97ddtaeihghYaG9vX1jT7t7e0N++Iq8dDQUAB9fX0hISEAenp6wi/hlJmEhIQHHnjgpptucjzVaDRhF1t8PmsW2tqAWC2OHh25tHixNBgQH68GfHyQlgaDAdHRl/Hd0ZTj+N+MZhRHwNJoNN4uhLyAU34GcgQsL055DwWshQsXHjt2zG63Oz5eOnLkyMKFC8cOCA8PDw8PP3LkSExMjGPAggULLvrH+vr6xsTEXNZa+GXLsGsXsGaNVBQ5NCSyshAbC0CjQXY28vMRGnpZ3xkRERGRMw9tPV5QUBAQELB9+3YAO3fu7OjouP766wGUlJT8+c9/doy58847X3rpJQBnzpx5991377zzzomoRK9HUhIQGGhfudJ+ww2IjQ0Jwde+hocfxvXXM10RERHROPBQwPLx8XnjjTd+8pOfLFmy5O67737zzTf9/f3xxYD1q1/96vjx4wsWLEhMTNywYcPKlSsnphKsX48NG5Ca2puY2HXbbXjoIRQUwN9/Iv5rNBmdPHnS2yWQF3R1dZ09e9bbVZAXcMrPTJ2dnd6d8kK67v80YYaHh5uamrRa7QUWjjU3NwcFBYVe2kdJ69atW79+/e23334FxTz77LMtLS3PPvvsFXwtTWkhISFtbW3+zNQzzNNPP93Z2fn00097uxDytMDAwK6urqtcsExTzlNPPdXX1/fUU095qwCP7uykVqvnz59/4TFardYzxdhsNrvd7pn/Fk0qfOlnJr7uM5bNZvPkRwk0SXh9ynvoV4REREREMwcDFhEREdE48+garHFXUFAQFRW1ZMmSK/hai8XS29s7oUdK0+T0u9/97kc/+hEXZMw0ZrN5cHDwK1/5ircLIU979tlnH374YR8fH28XQh6lKMrw8PCKFSuu7MtzcnKubIX3qKl9ut7atWvb29uvbAe57Oxsq9U6dn95miHWrVsXzZ1kZ56cnJzh4WFO+RnojjvuiIyM9HYV5Gl5eXk2m+2Kp3xQUNBVFjC1P8EiIiIimoS4BouIiIhonDFgEREREY0zBiwiIiKiccaARURERDTOGLCIiIiIxhkDFhEREdE4m9r7YF2A3W7funVrUVHRwoULH3zwQbd7ZZnN5m3btvn5+W3cuDE5OdlxcWBg4NVXX62pqcnIyPjud7+rVk/bv6Lpqrm5+eWXX25vb7/pppu+8Y1vON0dHBzcuXNnYWHhwMCAXq+/4447HNsPVlZW7ty5c3TYvffey72ypha73f7WW29ZLJZFixY9+OCDwcHBTgN27dpVVlY2+nTTpk0qlQpAf3//K6+8cvjw4czMzPvuu49Tfsppamp6+eWXOzo6brrppltuucXp7smTJ7dt2zb2yu2337548eKKioqPP/549OLGjRujoqI8US6NB7vdXlVVVVZW1tra6na+A5BSvv322yaTaf78+T/4wQ9CQ0Md1+vr61999dWurq5bb731+uuvn7gip+0nWL/4xS+ee+45nU5nsVhuvvlm1wGFhYU33njjokWLgoODDQbDiRMnHNfvvPPOHTt26PX6d9555/777/do0XTV+vr6DAZDa2trZmbmAw888MYbbzgN2LVr19NPPz1r1qzExMQnn3zyO9/5juO6xWLZsmVLx3nDw8Mer52uyqOPPvrCCy/odDqTyeT6LgvgH//4x44dO0Zf4tHrGzZs+Oijj/R6/VtvvfXggw96sGQaB729vXq9/syZMxkZGffff//WrVudBgwNDY2+6NXV1T//+c8dGdpsNr/11lujt2w2mzfKpyt04sSJVatWvf/++48++mh3d7fbMU888cQzzzyTl5dXXl5+/fXXO3b97OjoyM/P7+vrS09Pv/vuu99///0JrFJOR93d3SEhIfv27ZNSWq3WqKiovXv3Oo259dZbf/Ob3zge33PPPZs2bZJSHjp0KCAgoLOzU0rZ3Nys0WgaGxs9WztdlTfeeCMnJ8fx+K9//WtiYqLdbh87wGq1jj4uLy9Xq9X9/f1SyldffXXdunWeLJXGUVdXV3Bw8MGDB6WUg4ODs2fPNplMTmN++MMf/upXv3K6ePDgwcDAwO7ubillQ0ODRqNpaWnxTM00Ll577TWdTud4/N577yUnJ19g8K9//WvHG62U8qWXXtqwYcOE10cTqaurC4Dbt+ne3t7w8PCysjIp5dDQkFar3b17t5Ty+eefX7lypWPMli1bRt8vJsL0/ARr//79/v7+6enpAHx9fa+99trCwkKnMYqirFy50vF45cqVjgGKomRnZ4eFhQGIjY1NTEy0WCyerZ2uiqIoo+dLXnfddbW1ta2trWMHjD2CsKurKzAw0M/Pz/H06NGjjz/++Msvv9zS0uKxgmlcVFRUhISEpKSkAPDz81u+fLmiKK7DLBbL448//sYbb/T29jquKIqSl5fnWEIQFxcXHx9fXFzsycrpKhUWFo7+JL/uuutqamra29vdjpRSbt26dePGjaNXjhw58vjjj7/yyitOPyVoGqiqqhJCZGVlAVCr1StWrHC8yxcWFo59jygrKxsYGJigGqZnwGppaRl78lRUVFRzc/PYAVartb29fXTM6ADXL2xqavJIyTQ+mpubRxdShIWFaTQap5d+1MDAwMMPP/zYY485FuJERkbm5uYGBgbu3r07OTn5wIEDniuartpFpzyAhQsXJicnazSat99+Oy0tzfE23NzczCk/pY2d8hEREWq1+sum/O7duzs6Om699VbH06ioqJycnICAgF27diUlJVVXV3uoYvKIL/uZMHbKR0dHSym/7H+Yqzc9l3P6+fkNDQ2NPrVaraOr2xzUarWPj8/oOhur1erv7+/2Cx3XaaoY+wra7fbh4WG3r6DVal23bl1SUtKmTZscV9auXbt27VrH4/vvv/+pp55yWhhLk9mlzNyf/OQnjge/+MUvli9f/sorr/znf/4np/xU5zTl7Xb7l72Cf/7zn++6667Ru+vWrVu3bp3j8Xe+853Nmze/8847HiiYPMN1agcGBjquj33rBzBxU356foIVFxfX0tIy+pfY0NAwZ86csQNUKpVWqz116pTTgLi4uIaGhtFhDQ0NcXFxnqqaxsHYV7Cpqclut2u1Wqcxw8PD3/rWt9Rq9datWx0thE5yc3NPnjw54bXS+ImLi2tubh5dp+w65ccSQuTk5Dhe4rlz53LKT2ljp7zjgeuUB9DV1fXBBx/ce++9bv8QTvnpJy4urrW11RGh8CXv8qdOnfL19Z24hvHpGbAyMjIiIyN37NgBoLGxsbCw8Jvf/CaA5ubmTz75xDHm1ltvdXxEYbfbt2/fvnr1agA33HBDXV2d47PioqKirq6uFStWeO3boMu3evXqHTt29PT0ANi2bdtXv/pVx4q64uLi2tpaADab7Z577unr69u2bdvY9Vjnzp1zPBgeHv7ggw+WLVvmjfLpCmVnZ4eGhn700UcAGhoazGazY4eOpqam3bt3O8aMvsQ9PT07d+50vMQ33nhjdXX1oUOHABQWFvb39xcUFHjne6Arsnr16n/84x+ORXXbtm372te+FhQUBMBisdTV1Y0Oe+edd1JSUjIyMkavcMpPS/v27XMs8Fi6dOmcOXP+/ve/A2hpafnss88cvx1evXr13/72t8HBQQDbtm275ZZb3P4ze3xM3Pp573rvvfciIyPXr18/f/78Rx55xHHx3XffnTdvnuNxfX39/Pnzb7zxRoPBkJOTc+7cOcf1Z555RqvVbtiwITo6+o9//KN3qqcrZbfbb7vttpSUlLVr10ZFRRUVFTmu33DDDU888YSUcvv27Y65l31eQ0ODlPLaa6/V6/Vr1qxZvHhxRkYGW8mmnHfffdcx5efNm/fYY485Lv7lL39ZuHCh43FsbOx111136623xsTErFq1anBw0HH9v/7rv0an/Ouvv+6d6ulK2Wy2b37zm6mpqWvWrImKiiouLnZcX7ly5ZNPPjk6LDMz8+WXXx77hUaj0WAwrFmzJj4+Pisrq7W11aN101UzGAyOxJyenp6dnW2z2aSU99xzz/333+8Y8Le//W327Nnr169fuHDhww8/7Lg4NDR0/fXXL1u27LbbbouJidm/f//EVSiklBOV3bzt1KlTZWVlixcvTktLc1zp7u5uaWlJTEx0PO3t7d27d69GoykoKBj7Ycbhw4dramrS09Pj4+O9UDddHSmlxWJpbW01Go2zZ892XDx58mRAQEB0dPTZs2ePHz8+dvzSpUs1Gk1PT09FRcWZM2fmz5+fmZnpWPlOU0t9fX15efk111yzdOlSx5Wurq7Tp087pvyZM2cqKyt7e3sTExNHNxZ2OHTo0KFDhzjlp6jRKV9QUDBr1izHxRMnTgQFBTnWv9vt9oqKipSUlICAgNGvOnfuXEVFRXt7+4IFCzIyMjjlp5yKigq73T76NCsrSwjR2NgohBhdIdDY2FhSUhIfH+/YVcDBbrebzeaOjo6CgoLw8PCJq3A6BywiIiIir2BmJyIiIhpnDFhERERE44wBi4iIiGicMWARERERjTMGLCIiIqJxxoBFRERENM4YsIiIiIjG2fQ87JmIaKz+/n6z2Wy32/V6veMoFSKiCcWARUTT3KeffnrHHXcMDAwIIXx8fP7yl7/cdNNN3i6KiKY5/oqQiKaz1tbWNWvW3HjjjW1tbW1tbTfeeOO6detOnDjh7bqIaJpjwCKi6ezFF1/s7e39wx/+oNFo/Pz8XnvtNQDPP/+8t+siommOZxES0XSWk5MTGhq6e/fu0Ss333zzkSNHamtrvVgVEU17/ASLiKYtKWV1dXVCQsLYi0uWLDl69OjAwIC3qiKimYCfYBHRtNXf3x8YGKjVaufMmTN6saWlpbGxsbm5OTY21ou1EdH0xi5CIprmFi5ceO21144+tVgsjY2N/LclEU0oBiwimrb8/f39/f3T09Offvrp0YubNm3as2dPeHi4FwsjommPa7CIaNoSQiQnJx8/fnzsxWPHji1atCggIMBbVRHRTMCARUTT2U033bRnz55z5845ng4MDOzatYsbjRLRRGPAIqLp7Ac/+IGvr+9Pf/rT4eFhm8326KOPWq3WH//4x96ui4imOXYREtE0t3PnzvXr16vVah8fn97e3rfffvu2227zdlFENM0xYBHR9NfV1bVnzx6bzbZixYqIiAhvl0NE0x8DFhEREdE44xosIiIionHGgEVEREQ0zhiwiIiIiMYZAxYRERHROGPAIiIiIhpnDFhERERE44wBi4iIiGicMWARERERjbP/D4TZOHy1OA+xAAAAAElFTkSuQmCC", "image/svg+xml": [ "\n", "\n" ], "text/html": [ "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot( θ_range, x -> pdf.(message1, x), color=\"red\", label=\"Prior-based message\", xlabel=\"θ\", ylabel=\"p(θ)\")\n", "plot!(θ_range, x -> pdf.(message2, x), color=\"blue\", linewidth=8, linestyle=:dash, alpha=0.5, label=\"Likelihood-based message\", legend=:topleft,size=(800,400))\n", "plot!(θ_range, x -> pdf.(posterior, x), color=\"purple\", label=\"Marginal posterior\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The pdf of the marginal distribution lies on top of the pdf of Message 2. That's not always going to be the case; the Beta(1,1) distribution is special in that when you multiply Beta(1,1) with a general Beta(a,b) the result will always be Beta(a,b), kinda like multiplying by $1$. We call prior distributions that have this special effect \"non-informative priors\"." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "#### Multiple questions\n", "\n", "Of course, in practice you would be evaluated on multiple questions, which are essentially more samples from the underlying distribution that is your skill level. We are going to add question outcomes to the model. For now, we will still work with right-or-wrong questions (i.e., binary outcomes), denoted $X = (X_1, \\dots, X_N)$. The generative model becomes\n", "\n", "$$\\begin{aligned} p(X, \\theta) &= p(\\theta) \\prod_{i=1}^{N} p(X_i \\mid \\theta) \\\\ &= \\text{Beta}(\\theta) \\prod_{i=1}^{N} \\text{Bernoulli}(X_i \\mid \\theta) \\, , \\end{aligned}$$ \n", "\n", "The factor graph for this model is:\n", "\n", "\n", "\n", "Specified in code, this is:" ] }, { "cell_type": "code", "execution_count": 11, "metadata": {}, "outputs": [], "source": [ "@model function beta_bernoulli(N)\n", " \"Beta-Bernoulli model with multiple observations\"\n", " \n", " # Allocate data variable\n", " X = datavar(Int64, N)\n", " \n", " # Prior distribution\n", " θ ~ Beta(3.0, 2.0)\n", " \n", " # Loop over data\n", " for i in 1:N\n", " \n", " # Likelihood of i-th data points\n", " X[i] ~ Bernoulli(θ)\n", " \n", " end\n", " return X,θ\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "You may have noticed that the prior distribution changed; the company now assumes that you must have _some_ skill if you applied for the position. This is reflected in the prior Beta distribution with $\\alpha = 3.0$ and $\\beta = 2.0$.\n", "\n", "Now suppose we have two outcomes, $X_1 = 1$ and $X_2 = 0$:" ] }, { "cell_type": "code", "execution_count": 12, "metadata": {}, "outputs": [], "source": [ "X = [1, 0];\n", "N = length(X);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Running the inference procedure is nearly exactly the same, except now we have to provide the sample size parameter $N$:" ] }, { "cell_type": "code", "execution_count": 13, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = inference(\n", " model = beta_bernoulli(N),\n", " data = (X = X,),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We now have two likelihood-based messages:" ] }, { "cell_type": "code", "execution_count": 14, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=1.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message1 = @call_rule Bernoulli(:p, Marginalisation) (m_out = PointMass(X[1]),)" ] }, { "cell_type": "code", "execution_count": 15, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=1.0, β=2.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message2 = @call_rule Bernoulli(:p, Marginalisation) (m_out = PointMass(X[2]),)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Taking their product gives us a total likelihood message, i.e., \n", "\n", "$$\\begin{aligned} \\mu_3(\\theta) &= \\mu_1(\\theta) \\cdot \\mu_2(\\theta) \\\\ &= \\sum_{X_1} \\delta(X_1 - 1) \\ \\text{Bernoulli}(X_1 \\mid \\theta) \\cdot \\sum_{X_2} \\delta(X_2 - 0) \\ \\text{Bernoulli}(X_2 \\mid \\theta) \\\\ &= \\text{Beta}(\\alpha = 2, \\beta = 1) \\cdot \\text{Beta}(\\alpha = 1, \\beta = 2) \\\\ &= \\text{Beta}(\\alpha = 2, \\beta = 2) \\end{aligned}$$\n", "\n", "Let's verify that manual calculation using RxInfer:" ] }, { "cell_type": "code", "execution_count": 16, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=2.0, β=2.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message3 = prod(ClosedProd(), message1, message2)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "This product of messages is the result of passing the two likelihood-based messages through an equality node (see [Bert's lecture](https://nbviewer.org/github/bertdv/BMLIP/blob/master/lessons/notebooks/Factor-Graphs.ipynb#Equality-Nodes-for-Branching-Points)):\n", "\n", "$$\\begin{aligned} \\mu_3(\\theta) &= \\int_{\\theta'} \\int_{\\theta''} \\overrightarrow{\\mu}(\\theta'')\\ f_{=}(\\theta, \\theta', \\theta'') \\ \\overleftarrow{\\mu}(\\theta') \\mathrm{d}\\theta' \\, \\mathrm{d}\\theta'' \\\\\n", " &= \\mu'(\\theta) \\cdot \\mu''(\\theta) \\, . \\end{aligned}$$\n", "\n", "You don't have to worry about explicitly managing equality nodes; most packages automatically perform these operations (or functionally similar ones) under the hood." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "What would be your likelihood-based message if your data was $X = [0 \\ \\ 0 \\ \\ 0]$?" ] }, { "cell_type": "code", "execution_count": 17, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Now that we have a likelihood-based message, we can combine that with the message from the prior distribution, $\\mu_4(\\theta) = \\text{Beta}(\\alpha = 3, \\beta = 2)$, to get the marginal posterior for $\\theta$:\n", "\n", "$$\\begin{aligned} p(\\theta \\mid X_1, X_2) &= \\mu_3(\\theta) \\cdot \\mu_4(\\theta) \\\\ &= \\text{Beta}(\\alpha = 2, \\beta = 2) \\cdot \\text{Beta}(\\alpha = 3, \\beta = 2) \\\\ &= \\text{Beta}(\\alpha = 4, \\beta = 3) \\, . \\end{aligned}$$\n", "\n", "Let's check with RxInfer:" ] }, { "cell_type": "code", "execution_count": 18, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=4.0, β=3.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message4 = Beta(3.0, 2.0)\n", "posterior = prod(ClosedProd(), message3, message4)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "That should also be equal to the inferred posterior:" ] }, { "cell_type": "code", "execution_count": 19, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Beta{Float64}(α=4.0, β=3.0)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results.posteriors[:θ]" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Great. That checks out.\n", "\n", "Let's also visualize the messages and the resulting marginal:" ] }, { "cell_type": "code", "execution_count": 20, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n" ], "text/html": [ "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "plot( θ_range, x -> pdf.(message1, x), color=\"red\", label=\"Message for X₁\", xlabel=\"θ\", ylabel=\"p(θ)\")\n", "plot!(θ_range, x -> pdf.(message2, x), color=\"blue\", label=\"Message for X₂\", size=(800,400))\n", "plot!(θ_range, x -> pdf.(message3, x), color=\"purple\", label=\"Total likelihood message\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Message 1 and message 2 are direct opposites: the first increases the estimate and the second decreases the estimate of your skill level. The total likelihood message ends up being centered on the average, i.e., $0.5$. If we plot the prior- and likelihood-based messages as well as the marginal, we can see that Bayes' rule is really a weighted average. " ] }, { "cell_type": "code", "execution_count": 21, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n" ], "text/html": [ "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Plot prior-based message\n", "plot( θ_range, x -> pdf(message4, x), color=\"red\", linewidth=3, label=\"Prior\", xlabel=\"θ\", ylabel=\"p(θ)\")\n", "\n", "# plot likelihood-based message\n", "plot!(θ_range, x -> pdf(message3, x), color=\"blue\", linewidth=3, label=\"Likelihood\", size=(800,400))\n", "\n", "# Plot marginal posterior\n", "plot!(θ_range, x -> pdf(posterior, x), color=\"purple\", linewidth=4, linestyle=:dash, label=\"Posterior\")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 2. Score questions\n", "\n", "Suppose you are not tested on a right-or-wrong question, but on a score question. For instance, you have to complete a piece of code for which you get a score. If all of it was wrong you get a score of $0$, if some of it was correct you get a score of $1$ and if all of it was correct you get a score $2$. That means we have a likelihood with three outcomes: $X_1 = \\{ 0,1,2\\}$. Suppose we once again ask two questions, $X_1$ and $X_2$. The order in which we ask these questions does not matter, so that means we choose Categorical distributions for these likelihood functions: $X_1, X_2 \\sim \\text{Categorical}(\\theta)$. The parameter $\\theta$ is no longer a single parameter, indicating the probability of getting the question right, but a vector of three parameters: $\\theta = (\\theta_1, \\theta_2, \\theta_3)$. Each $\\theta_k$ indicates the probability of getting the $k$-th outcome. In other words, $\\theta_1$ indicates the probability of getting $0$ points, $\\theta_2$ of getting $1$ point and $\\theta_3$ of getting $2$ points. A highly-skilled applicant mights have a parameter vector of $(0.05, 0.1, 0.85)$, for example. The prior distribution conjugate to the Categorical distribution is the Dirichlet distribution. \n", "\n", "Let's look at the generative model:\n", "\n", "$$p(X_1, X_2, \\theta) = p(X_1 \\mid \\theta) p(X_2 \\mid \\theta) p(\\theta) \\, .$$ \n", "\n", "It's the same as before. The only difference is the parameterization of the distributions:\n", "\n", "$$\\begin{aligned} p(X_1 \\mid \\theta) =&\\ \\text{Categorical}(X_1 \\mid \\theta) \\\\ p(X_2 \\mid \\theta) =&\\ \\text{Categorical}(X_2 \\mid \\theta) \\\\ p(\\theta) =&\\ \\text{Dirichlet}(\\theta \\mid \\alpha) \\, , \\end{aligned}$$\n", "\n", "where $\\alpha$ are the concentration parameters of the Dirichlet. This model can be written directly in RxInfer:" ] }, { "cell_type": "code", "execution_count": 22, "metadata": {}, "outputs": [], "source": [ "@model function dirichlet_categorical(α; N=1)\n", " \n", " # Preallocate variables\n", " X = datavar(Vector{Int64}, N)\n", " \n", " # Prior distribution\n", " θ ~ Dirichlet(α)\n", " \n", " # Likelihood\n", " for i in 1:N\n", " X[i] ~ Categorical(θ)\n", " end\n", " return X,θ\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Suppose you got a score of $1$ on the first question, a score of $2$ on the second question and a score of $2$ on the third question. In a one-hot encoding, this is represented as:" ] }, { "cell_type": "code", "execution_count": 23, "metadata": {}, "outputs": [], "source": [ "X = [[0, 1, 0],\n", " [0, 0, 1],\n", " [0, 0, 1]];\n", "\n", "N = length(X);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Compute the likelihood-based message towards $\\theta$. I've given the three messages below:" ] }, { "cell_type": "code", "execution_count": 24, "metadata": {}, "outputs": [], "source": [ "message1 = @call_rule Categorical(:p, Marginalisation) (q_out = PointMass(X[1]),);\n", "message2 = @call_rule Categorical(:p, Marginalisation) (q_out = PointMass(X[2]),);\n", "message3 = @call_rule Categorical(:p, Marginalisation) (q_out = PointMass(X[3]),);" ] }, { "cell_type": "code", "execution_count": 25, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The company thinks that applicants are more likely to get the answer partially correct than entirely wrong or entirely right. This is reflected in their prior concentration parameters:" ] }, { "cell_type": "code", "execution_count": 26, "metadata": {}, "outputs": [], "source": [ "# Prior concentration parameters\n", "α0 = [1.0, 2.0, 1.0];" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The inferrred posterior is a Dirichlet distribution with higher concentrations for scores $1$ and $2$: " ] }, { "cell_type": "code", "execution_count": 27, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "Inference results:\n", " Posteriors | available for (θ)\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = inference(\n", " model = dirichlet_categorical(α0, N=N),\n", " data = (X = X,),\n", ")" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Visualizing a Dirichlet distribution is a bit tricky. In the special case of $3$ parameters, we can plot the probabilities on a simplex. As a reminder, a [simplex](https://en.wikipedia.org/wiki/Simplex) in 3-dimensions is the triangle between the coordinates $[0,0,1]$, $[0,1,0]$ and $[1,0,0]$:\n", "\n", "\n", "\n", "Every point on that triangle is 3D vector that sums to 1. Since the triangle is a 2-dimensional subspace, we can map the 3D simplex to a 2D triangular surface and plot the Dirichlet's probability density over it." ] }, { "cell_type": "code", "execution_count": 28, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Load pre-generated triangular mesh\n", "mesh = Matrix(DataFrame(CSV.File(\"../datasets/trimesh.csv\")))\n", "\n", "# Compute probabilities on trimesh of simplex\n", "pvals = [pdf(Dirichlet(α0), mesh[n,3:5]) for n in 1:size(mesh,1)]\n", "\n", "# Generate filled contour plot\n", "tricontourf(mesh[:,1], mesh[:,2], pvals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The yellow spot is the area of high probability, with the contour lines indicating regions of decreasing probability. These prior concentration parameters clearly indicate a higher density in one corner of the simplex. Let's inspect the posterior concentration parameters." ] }, { "cell_type": "code", "execution_count": 29, "metadata": {}, "outputs": [ { "data": { "image/png": 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" }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Extract parameters \n", "αN = params(results.posteriors[:θ])[1]\n", "\n", "# Compute probabilities on trimesh of simplex\n", "pvals = [pdf(Dirichlet(αN), mesh[n,3:5]) for n in 1:size(mesh,1)]\n", "\n", "# Generate filled contour plot\n", "tricontourf(mesh[:,1], mesh[:,2], pvals)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The distribution has shifted to the upper right edge and has concentrated more (i.e., the probability contours drop off more rapidly). " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Add some more data to the model. What scores lead to a yellow blob in the exact middle of the simplex?" ] }, { "cell_type": "code", "execution_count": 30, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "### 3. Continuous-valued score\n", "\n", "Suppose the company wants to know how fast applicants respond to questions. The interview conductor also has a stopwatch and measures your response time per question. Each applicant is assumed to have some underlying response speed $\\theta$. Each measurement $X_i$ is a noisy observation of that response speed, where the noise is assumed to be symmetric, i.e., the applicant might a bit as faster as often as they are a bit slower than usual. The Gaussian, or Normal, distribution is a symmetric continuous-valued distribution and will characterize the assumption well. The likelihood is therefore:\n", "\n", "$$p(X \\mid \\theta) = \\mathcal{N}(X \\mid \\theta, \\sigma^2) \\, ,$$ \n", "\n", "where $\\sigma$ is the standard deviation. The conjugate prior to the mean in a Gaussian likelihood is another Gaussian distribution: \n", "\n", "$$p(\\theta) = \\mathcal{N}(\\theta \\mid m_0, v_0)$$ \n", "\n", "with $m_0, v_0$ as prior mean and variance. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Write down the full generative model using the above prior distribution and the likelihood of $N$ observations.\n", "\n", "---" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "In code, the model is:" ] }, { "cell_type": "code", "execution_count": 31, "metadata": {}, "outputs": [], "source": [ "@model function normal_normal(m0, v0, σ; N=1)\n", " \n", " # Allocate data variable\n", " X = datavar(Float64, N)\n", " \n", " # Prior distribution\n", " θ ~ Normal(mean = m0, variance = v0)\n", " \n", " # Likelihood\n", " for i = 1:N\n", " X[i] ~ Normal(mean = θ, variance = σ^2)\n", " end \n", " return X,θ\n", "end" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The interview conductor cannot stop immediately after you have responded. From previous interviews, the company knows that the conductor in front of you is typically off by roughly $2$ seconds. That translates to a likelihood variance of $\\sigma^2 = 4$. " ] }, { "cell_type": "code", "execution_count": 32, "metadata": {}, "outputs": [], "source": [ "σ = 2.0;" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Your response times on the questions are:" ] }, { "cell_type": "code", "execution_count": 33, "metadata": {}, "outputs": [], "source": [ "X = [ 52.390036995147426\n", " 74.49846899398719\n", " 50.92640384934159\n", " 39.548361884989717]; \n", "\n", "N = length(X);" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The company designed the questions such that they think it may take the average participant 60 seconds to respond, $\\pm$ 20 seconds. That translates to the following values for the prior parameters:" ] }, { "cell_type": "code", "execution_count": 34, "metadata": {}, "outputs": [], "source": [ "m0 = 60;\n", "v0 = 20;" ] }, { "cell_type": "code", "execution_count": 35, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(54.61030279130141, 0.9523809523809523)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "results = inference(\n", " model = normal_normal(m0, v0, σ, N=N),\n", " data = (X = X,),\n", ")\n", "\n", "posterior = results.posteriors[:θ]\n", "mean_var(posterior)" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "Ah! It seems that you are a bit faster than the average participant.\n", "\n", "Let's visualize the prior message, the total likelihood message and the posterior again. First, we want to get the likelihood message:" ] }, { "cell_type": "code", "execution_count": 36, "metadata": {}, "outputs": [ { "data": { "text/plain": [ "(54.34081793086648, 0.5625)" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "message = @call_rule NormalMeanVariance(:μ, Marginalisation) (m_out=PointMass(X[1]), m_v=PointMass(1.5^2))\n", "for i in 2:N\n", " message_i = @call_rule NormalMeanVariance(:μ, Marginalisation) (m_out=PointMass(X[i]), m_v=PointMass(1.5^2))\n", " message = prod(ClosedProd(), message, message_i)\n", "end\n", "mean_var(message)" ] }, { "cell_type": "code", "execution_count": 37, "metadata": {}, "outputs": [ { "data": { "image/png": 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", "image/svg+xml": [ "\n", "\n" ], "text/html": [ "\n", "\n" ] }, "metadata": {}, "output_type": "display_data" } ], "source": [ "# Range of values to plot pdf for\n", "θ_range = range(50.0, step=0.1, stop=65.0)\n", "\n", "# Prior\n", "plot( θ_range, x -> pdf(Normal(m0, sqrt(v0)), x), color=\"red\", label=\"Prior\", xlabel=\"θ\", ylabel=\"p(θ)\")\n", "\n", "# Likelihood\n", "plot!(θ_range, x -> pdf(message, x), color=\"blue\", label=\"Likelihood\")\n", "\n", "# Posterior\n", "plot!(θ_range, x -> pdf(posterior, x), color=\"purple\", linestyle=:dash, label=\"Posterior\", size=(800,300))" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "The prior is quite wide, indicating the company has a lot of uncertainty about participants' response speeds. The likelihood is sharply peaked, even after only 4 questions. Note that the posterior is a weighted average of the prior- and likelihood-based messages. In this case, it is closer to the likelihood because the likelihood variance, $4$, is much smaller than the prior variance $20$. " ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---\n", "\n", "#### Exercise\n", "\n", "Suppose each question was timed by a different interviewer, and that the interviewers differ vastly in how precise they record response times. How can we incorporate this knowledge into the model?" ] }, { "cell_type": "code", "execution_count": 38, "metadata": {}, "outputs": [], "source": [] }, { "cell_type": "markdown", "metadata": {}, "source": [ "---" ] } ], "metadata": { "@webio": { "lastCommId": null, "lastKernelId": null }, "kernelspec": { "display_name": "Julia 1.9.3", "language": "julia", "name": "julia-1.9" }, "language_info": { "file_extension": ".jl", "mimetype": "application/julia", "name": "julia", "version": "1.9.3" } }, "nbformat": 4, "nbformat_minor": 4 }