From 7774f0e83155ed3e4b399421f32a58c7b9fa6e80 Mon Sep 17 00:00:00 2001 From: ritchie46 Date: Fri, 15 Mar 2019 13:56:10 +0100 Subject: [PATCH] add bayesian introduction training --- training_bayesian/1_intro_bayesian.ipynb | 1327 +++++++++++++++++ training_bayesian/data/votes.npy | Bin 0 -> 8128 bytes training_bayesian/images/2d-continuous.png | Bin 0 -> 115304 bytes training_bayesian/images/2d-discrete.png | Bin 0 -> 10293 bytes training_bayesian/images/PyMC3_banner.svg | 83 ++ training_bayesian/images/bernoulli.png | Bin 0 -> 2978 bytes training_bayesian/images/cdf.png | Bin 0 -> 14582 bytes training_bayesian/images/conditional_prob.png | Bin 0 -> 19476 bytes .../images/conditional_prob_continuous.png | Bin 0 -> 35698 bytes training_bayesian/images/dieprob.png | Bin 0 -> 33854 bytes training_bayesian/images/gauss.png | Bin 0 -> 14321 bytes training_bayesian/images/marginal1.png | Bin 0 -> 10646 bytes training_bayesian/images/marginal2.png | Bin 0 -> 13512 bytes training_bayesian/images/marginal3.png | Bin 0 -> 93035 bytes .../images/random-variable-1.svg | 35 + 15 files changed, 1445 insertions(+) create mode 100644 training_bayesian/1_intro_bayesian.ipynb create mode 100644 training_bayesian/data/votes.npy create mode 100644 training_bayesian/images/2d-continuous.png create mode 100644 training_bayesian/images/2d-discrete.png create mode 100644 training_bayesian/images/PyMC3_banner.svg create mode 100644 training_bayesian/images/bernoulli.png create mode 100644 training_bayesian/images/cdf.png create mode 100644 training_bayesian/images/conditional_prob.png create mode 100644 training_bayesian/images/conditional_prob_continuous.png create mode 100644 training_bayesian/images/dieprob.png create mode 100644 training_bayesian/images/gauss.png create mode 100644 training_bayesian/images/marginal1.png create mode 100644 training_bayesian/images/marginal2.png create mode 100644 training_bayesian/images/marginal3.png create mode 100644 training_bayesian/images/random-variable-1.svg diff --git a/training_bayesian/1_intro_bayesian.ipynb b/training_bayesian/1_intro_bayesian.ipynb new file mode 100644 index 0000000..43aad23 --- /dev/null +++ b/training_bayesian/1_intro_bayesian.ipynb @@ -0,0 +1,1327 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": 1, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [], + "source": [ + "import matplotlib.pyplot as plt\n", + "import numpy as np\n", + "from scipy import stats\n", + "import seaborn as sns\n", + "from IPython.core.display import HTML\n", + "import pymc3 as pm\n", + "import theano\n", + "import theano.tensor as tt" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "# Random variables and probability distributions\n", + "\n", + "![](images/random-variable-1.svg)\n", + "\n", + "* Random != unpredictable, but only means we are uncertain of its exact value\n", + "* We express our uncertainty of the possible values of x in an probability distribution\n", + " * Discrete probability distributions\n", + " * Continuous probability distributions\n", + " * Probability functions $P(x)$ map $x$ to a probability of x being equal to that value.\n", + " * A probability distribution spans all possible values of $x$, which means the total probability == 1. $$\\int{P(x)} dx = 1$$\n", + "\n" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/html": [ + "\n", + "

Discrete probability distributions

\n", + "\n", + "\n", + "\n", + "\n", + "What is P(x <= 5)\n" + ], + "text/plain": [ + "" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "HTML(\"\"\"\n", + "

Discrete probability distributions

\n", + "\n", + "\n", + "\n", + "\n", + "What is P(x <= 5)\n", + "\"\"\")" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Continuous probability distributions\n", + "\n", + "![](images/gauss.png)\n", + "* Maps continuous values to a probability **density** Pdf(x)\n", + "* Examples:\n", + " * Length of people\n", + " * Housing prices in Amsterdam\n", + " * Duration of waiting time at dentist\n", + " \n", + "How de we get probability mass outputs?\n", + "\n", + "Try in python:\n", + "\n", + "```python\n", + "from scipy import stats\n", + "norm = stats.norm()\n", + "```\n", + "\n", + "$\\mu = 0$\n", + "\n", + "$\\sigma = 1$\n", + "\n", + "What is $P(x > 0)$, $P(x > 0.02)$, $P(x < 0.69)$?" + ] + }, + { + "cell_type": "code", + "execution_count": 14, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "P(x > 0.02) 0.49202168628309806\n", + "P(x < 0.69) 0.7549029063256906\n" + ] + }, + { + "data": { + "text/plain": [ + "0.4954" + ] + }, + "execution_count": 14, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "x = np.linspace(-3, 3)\n", + "\n", + "norm = stats.norm(0, 1)\n", + "\n", + "plt.plot(x, norm.pdf(x))\n", + "plt.plot(x, norm.cdf(x))\n", + "plt.show()\n", + "\n", + "\n", + "print('P(x > 0.02)', 1 - norm.cdf(0.02))\n", + "print('P(x < 0.69)', norm.cdf(0.69))\n", + "\n", + "# monte carlo\n", + "n = 10000\n", + "(norm.rvs(n) > 0.02).sum() / n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Two dimensional discrete distribution\n", + "\n", + "* Two processes $x$ and $y$\n", + "* Only discrete values for $x$ and $y$ possible\n", + "\n", + "![](images/2d-discrete.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Two dimensional discrete distribution\n", + "\n", + "Properties:\n", + "$$P(x, y) \\ge 0$$\n", + "$$\\sum_{x=0}^1\\sum_{y=0}^1 P(x, y) = 1$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Two dimensional continuous distribution\n", + "\n", + "* Two processes $x$ and $y$\n", + "* An infinite number of values for $x$ and $y$ possible\n", + "\n", + "![](images/2d-continuous.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Two dimensional continuous distribution\n", + "\n", + "Properties:\n", + "$$P(x, y) \\ge 0$$\n", + "$$\\int_{x=-\\infty}^ \\infty \\int_{y=-\\infty}^\\infty P(x, y) dx dy = 1$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Marginal probability: discrete\n", + "\n", + "* Reducing a the dimensionality of a probability distribution. **ND -> (N - 1)D**\n", + "\n", + "![](images/marginal1.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Marginal probability: discrete\n", + "\n", + "Answers previous sheet:\n", + "$$P(x=1) = P(x=1,y=1) + P(x=1, y=0) = 0.4$$\n", + "\n", + "$$P(x) = \\sum_{i=1}^{N_y} P(x, y=y_i)$$\n", + "\n", + "Sum the probabilities in the margin\n", + "\n", + "![](images/marginal2.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Marginal probability: continuous\n", + "\n", + "$$P(x) = \\int_{y = -\\infty}^\\infty P(x, y) dy$$\n", + "\n", + "Can be approximated by sampling:\n", + "\n", + "![](images/marginal3.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Conditional probability: discrete\n", + "\n", + "![](images/conditional_prob.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Conditional probability: continuous\n", + "\n", + "![](images/conditional_prob_continuous.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Bayes' formula\n", + "\n", + "Jointly distributed events can be written as a multiplication of a marginal and conditional distribution.\n", + "$$P(A,B) = P(B) \\cdot P(A|B)$$\n", + "\n", + "And can be written for both **\n", + "$$P(A,B) = P(A) \\cdot P(B|A)$$\n", + "\n", + "$$ P(B) \\cdot P(A|B) = P(A) \\cdot P(B|A)$$\n", + "\n", + "divide by $P(B)$\n", + "\n", + "$$ P(A|B) = \\frac{P(B|A) \\cdot P(A)}{P(B)} $$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exercise: Conditional probability, breast cancer mammogram\n", + "\n", + "* **C** Individual has cancer\n", + "* **NC** Individual does NOT have cancer\n", + "* **+** Individual has been positively tested\n", + "* **-** Individual has been negatively tested\n", + "\n", + "Prior probabilities:\n", + "\n", + "$P(C) = 0.01$,    $P(+|C)=0.9$,    $P(+|NC)=0.08$\n", + "\n", + "Posterior probability:\n", + "\n", + "What is $P(C|+)$?\n", + "\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exercise: Conditional probability, breast cancer mammogram\n", + "\n", + "\n", + "$$P(C|+) = \\frac{P(+|C) \\cdot P(C)}{P(+)}$$\n", + "\n", + "Working out marginal probability $P(+) = \\sum_x P(+, x)$ \n", + "\n", + "$= P(+, C) + P(+, NC)$\n", + "\n", + "$= P(+|C) \\cdot P(C) + P(+|NC) \\cdot P(NC)^{**}$\n", + "\n", + "\n", + "$$P(C|+) = \\frac{0.9 \\cdot 0.01}{(0.9 \\cdot 0.01) + (0.08 \\cdot 0.99)} \\cdot 100\\% = 11\\%$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## A Simple model\n" + ] + }, + { + "cell_type": "code", + "execution_count": 43, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "(array([ 12., 54., 118., 178., 234., 187., 133., 66., 16., 2.]),\n", + " array([2.48806141, 3.01859083, 3.54912026, 4.07964968, 4.6101791 ,\n", + " 5.14070852, 5.67123794, 6.20176736, 6.73229678, 7.2628262 ,\n", + " 7.79335562]),\n", + " )" + ] + }, + "execution_count": 43, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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d/cbuvqC713L0MoN/6O4t/UsLY6iqM6rq2ceeJ3lJkvvmnYo5dfe/JXmoql4wLV2Z5DMzjsRquT4uVeO7HkxyeVWdPt346sokD2xlhzu2ZSxGdV6SfdPdT34gya3d7ZbBwCLnJrnt6J9N2ZHk3d39gXlHYgX8RpJ3TZcmfSHJq2eehxVQVacn+aUkr517FlZDd3+0qt6b5BNJHkvyySQ3b2WfbiENAAAMxeVqAADAUEQOAAAwFJEDAAAMReQAAABDETkAAMBQRA4AADAUkQMAAAxF5AAAAEP5f9Ad2Qvh6yF3AAAAAElFTkSuQmCC\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "np.random.seed(2)\n", + "# Central Limit theorem states: that the means of a subset of samples of any distribution will approximate a gaussian distribution given enough samples.\n", + "\n", + "# Uniform distribution between 0, 10\n", + "uniform = stats.uniform(0, 10)\n", + "\n", + "# Sample 10 samples 1000 times and calculate the mean.\n", + "means = np.array([uniform.rvs(10).mean() for _ in range(1000)])\n", + "\n", + "plt.figure(figsize=(14, 4))\n", + "plt.hist(means)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exercise: Fit a gaussian distribution\n", + "\n", + "Fit a gaussian distribution on the `means` array.\n", + "\n", + "Hint: A gaussian has two parameters.\n" + ] + }, + { + "cell_type": "code", + "execution_count": 45, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "" + ] + }, + "execution_count": 45, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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rnAyv4wBAu0apAYA4EApLt8zOVI+0el04qNLrOGjUKyOsy4ZU6PXiFH24ni8/BQCvUGoAIA48tSxVRdsDunFUmVL8XqdBU5MGVqpfRkg3zc5Qdb3XaQCgfaLUAECM21JjumdBug7rXKvvdqv1Og52kuxv+O6aFeUBPVyU5nUcAGiXKDUAEOPunp+hipDpptFlMr7EPiYd2qVOp/Ss1oNfpGtFObvSAKCtUWoAIIbNLwno2eUp+ln/Kg3I4timWHbjyHIl+5wmz8qQc16nAYD2hVIDADHKOemm2RnKTXa6YmiF13HQjM6pYf1qeIU+2pCsN9Ykex0HANqViEqNmU0wsyIzW2pm1+3i/ovMbJ6ZzTazGWY2NPpRAaB9eWV1sgq3JOna4eXKTmLTfzw4p3+VhuXUacrsDJXXcawgALSVZkuNmfklPSDpBElDJf1oF6XlaefcCOfcaEl3Sfpj1JMCQDtSXmf6/dwMjexQp9P7VHsdBxHym3TbmDJtqPbrIYYGAECbiWRPzXhJS51zy5xztZKelTSx6QrOue1NFtMlsUkRAPbBA1+kaWO1XzePLpOPDf5xZUzHkE7rVaW/LE7T6gqO8gaAthCIYJ3uklY3WS6WdODOK5nZpZKulpQk6ZhdPZCZTZI0SZJ69eq1t1kBoF1YXubXY4vT9IPeVRrbMbT7FQumtl0o7JX/G16hN9ak6I55GXrgoO3N/wIAYJ9EsglpV9sIv7Unxjn3gHOuv6RrJd24qwdyzj3qnMt3zuXn5eXtXVIAaCdunZOhZL/TtcMZDhCvuqaFddGgCr1enKLPNwe9jgMACS+SPTXFkno2We4hae0e1n9W0kP7EgoA2qv31iXpvfXJumFEmTqnhr2Og31w4cBKPbc8VbfOydA/jymRLxp71vLP2/fHAIAEFMmems8lDTCzvmaWJOksSdObrmBmA5osniRpSfQiAkD7UFPfsJemX2ZI5w6o8joO9lFqQLp2RLnmlgT18qoUr+MAQEJrttQ450KSLpP0lqRFkp53zi0wsylmdkrjapeZ2QIzm62G82p+1mqJASBBTV2apuXlAU0eVa4kzi9PCKf0rNHo3DrdNS9dFSEmPgBAa4nk8DM5596Q9MZOt01ucv2KKOcCgHZlQ5VP/29Rmo7rWqOj9qv1Og6ixGfS5FFlOu39XD1SlKarh3GeFAC0BrYFAkAMuHNeuurCpt+OKvc6CqJsbMeQJvas1iNFaVpTyccuALQG3l0BwGOFWwJ6aVWqfjGwUr0z6r2Og1ZwzYiGsnrnvAyPkwBAYqLUAICHwk6aMjtTXVLqdcngSq/joJV0TwvrwkGVmr46RYWbIzryGwCwFyg1AOChf65K0ZySoK4ZUaH0wLe+AgwJ5MJBleqSUq8pczIV5j81AEQVpQYAPFIZajiXZlSHOp3aq9rrOGhl6QGna0ZUaE5JUK+sSvY6DgAkFEoNAHjk4aJ0baj2a/KoMvmY9tsunNqrWiM71OnO+RmqDHmdBgASB6UGADywptKnR4rS9L2e1RrXib9u24uGEc/lWl/l16OL07yOAwAJg1IDAB74agrWdSMY4dze5Heq00k9qvVwUbrWMeIZAKKCd1MAaGOFmwOavjpFFw6qVPe0sNdx4IHrRpQr7KS75jPiGQCigVIDAG0oHHaaMqdhhPOFgxjh3F71TA/rFwMr9fKqFM3awohnANhXlBoAaEOvzFnDCGdIki4eVKm8xhHPjpcCAOwTSg0AtJHK2pDufLOIEc6QJGUEnf5veIVmbQ1q+mpGPAPAvqDUAEAbefjDZVq/vZoRztjh9N7VGpZTpzvnZaiKIXgA0GKUGgBoA2u2VemRD7/U90Z1Y4QzdvhqxPPaKr/+wohnAGgxSg0AtIG7/vWFJOnaCYM8ToJYc2BenU7oXq2HitK1oYqPZQBoCd49AaCVFa4s0Suz12rSEf3UowNb4/Ft148oV72T7pqf7nUUAIhLlBoAaEXhsNOU1xaqS1ayLjqyv9dxEKN6ZYR1/oBKvbgyVXO3MuIZAPYWpQYAWtErc9Zozuptuua7g5WezB+r2L1LB1eqU3JYN8/OVJgRzwCwVyg1ANBKvhrhPLJHtk4d093rOIhxmUGna0aUa+bWoF5eleJ1HACIK5QaAGglO0Y4nzxUPmY4IwKn967W6Nw63T43XWV1vGYAIFKUGgBoBU1HOOf3yfU6DuKEz6RbRpdpS41Pf17I0AAAiBQHeANApAqmRrzqXZ9mSeFkXdttrlQwuxVDIdGMyg3ph32rNXVpqn7Yt0r7Z9V7HQkAYh57agAgygq3BPTK6hRNGlipHulhr+MgDv3f8HKlBZxunp0px9AAAGgWpQYAoijspCmzM9U5pV4XDa70Og7iVMdkp6uHVWjGxiS9tTbZ6zgAEPMoNQAQRa+sStackqCuGV6h9ACb2NFyP+lXpcHZId06J0NVIa/TAEBso9QAQJRUhqQ752doZIc6nda72us4iHMBn3Tz6DKtqfTr4SKGBgDAnlBqACBKHi5K1/oqvyaPKhcTnBENB+XV6Xs9q/VwUZpWV/CRDQC7wzskAETBynK/Hi5K08k9qpXfqc7rOEggN4xoKMm3zsn0OgoAxCxKDQDsI+ekybMylORz+u2ocq/jIMF0TQvrsiEVenttsj5avMnrOAAQkyg1ALCP3lyTrA83JOvqYRXqksoIZ0TfBQMq1ScjpJtfXaDaEK8xANgZpQYA9kF5nWnKnAwNzanTT/tXeR0HCSrZL00eVa5lmyr0t4+Xex0HAGIOpQYA9sG9C9O1ocqn340pU4B3VLSiY7rW6tjBnXXfO0u0cTvT9QCgKT6CAaCFFmwL6G9LU/WjftUa05EvEkHr++3JQ1VX73T7m194HQUAYkpEpcbMJphZkZktNbPrdnH/1Wa20Mzmmtm7ZtY7+lEBIHaEnXTjzEzlJDldO5zhAGgbfTql6xdH9NXLs9aoYMVWr+MAQMxottSYmV/SA5JOkDRU0o/MbOhOq82SlO+cGynpBUl3RTsoAMSSZ5enaNbWoG4YWa7sJOd1HLQjlx69v7pmp2jyKwtUH+a1BwBSZHtqxkta6pxb5pyrlfSspIlNV3DOve+cq2xc/ERSj+jGBIDYsbnadOe8DB3YqVan9eLcBrSttKSAbjhxiBau265nPlvldRwAiAmRlJruklY3WS5uvG13fi7pzV3dYWaTzKzAzAo2bWLWPoD4dPu8DFWETLeNLZOZ12nQHp08sqsO6peru98uUklFrddxAMBzkZSaXX1k73J/t5n9RFK+pD/s6n7n3KPOuXznXH5eXl7kKQEgRny6KagXV6bqFwMrNSCr3us4aKfMTLecMlxl1SHd/XaR13EAwHORlJpiST2bLPeQtHbnlczsOEm/kXSKc64mOvEAIHbUhqUbZ2Wqe1q9Lh9S4XUctHOD9svUOQf11tOfrdL8NaVexwEAT0VSaj6XNMDM+ppZkqSzJE1vuoKZjZH0iBoKzcboxwQA7/11cZqWbA/oltFlSg14nQaQrjp+oHLTknTz9AVyjqEBANqvZkuNcy4k6TJJb0laJOl559wCM5tiZqc0rvYHSRmSppnZbDObvpuHA4C4VFxSqT8vStfx3Wp0XDfOYUBsyE4N6toJg1WwskT/nL3G6zgA4JmItjU6596Q9MZOt01ucv24KOcCgJhy8/SFDZejyzxOAnzT6eN66KnPVun3b3yhY4d0UVZK0OtIANDmIvryTQBoz/69cIPeWbRBVw6tUPe0sNdxgG/w+Uy3ThymLeU1+t1ri7yOAwCeoNQAwB5U1oZ08/QFGtQlU+cPqGz+FwAPjOyRo0lH9NdzBav1QRGntgJofyg1ALAHf353qdZsq9Jtpw5XkHdMxLArjxugAZ0zdP1L87S9us7rOADQpviIBoDdWLyhTI/9Z5nOGNdDB/TJ9ToOsEcpQb/+cMYobdherdteW+h1HABoUwwlBYBdcM7pxpfnKyMloOtPHOJ1HKBBwdQ93j1a0oUD0/VQQbFOSJ6vo7vuZlJf/nnRzwYAHmJPDQDswguFxfpsxVZdN2GwctOTvI4DROzKoRUakBXS9TMzVVprXscBgDZBqQGAnZRU1Or2N7/Q2F45OjO/p9dxgL2S7Jfuzt+uTdU+3TY3w+s4ANAmKDUAsJO73vpCpVV1+t2pI+TzsaUb8WdUbkgXDqzUtBWpen8dexoBJD5KDQA08dnyrXrms9U675A+GtI1y+s4QItdMbRCA7NCuq6Qw9AAJD5KDQA0Kq2q01XPzVav3DRdefxAr+MA++Srw9A21/h06xwOQwOQ2Cg1AKDGaWf/nK/126t131mjlZHMcEjEv5G5IV00qFIvrEzVexyGBiCBUWoAQNJLM9fo1TlrddVxAzSmVwev4wBRc/mQCg3KCul6DkMDkMDYFAkg8TXz3R4ry/2a/E4Hje8U0sWZM6SCGW0UDGh9yX7p7gO26/vvddCUORm654AyryMBQNSxpwZAu1YXlq74LEt+k+4dv11+NmQjAY3oENLFgyr1IoehAUhQlBoA7dqfF6Zr9tagfj+2TN3Twl7HAVrNLxsPQ7uuMFOllXVexwGAqKLUAGi3PtsU1ANfpOn03lU6uWeN13GAVvXVYWhbany65bUFXscBgKii1ABol0prTVd9nqWe6fW6eXS513GANjGiQ0iXDKrUSzPX6J2FG7yOAwBRQ6kB0O44J/1mZqY2VPl034HblRF0XkcC2swvh1Zo8H6ZuuHleRyGBiBhUGoAtDsvrkzRa8UpumpohUbnhryOA7SpJJ909xmjtKWiVre8ymFoABIDpQZAu7Ki3K+bZmfowE61umhwpddxAE8M756tS4/qr5dmcRgagMRAqQHQbtSFpSs+ZXwzIEmXHTNAg/fL1PUvz9O2ylqv4wDAPqHUAGg37luYrjklQd0+rkzdGN+Mdi4p4NPdZ4zS1opaXf/SPDnHuWUA4helBkC78Enj+OYz+lTppB6MbwakhsPQrp0wSG/OX6/731vqdRwAaDFKDYCEV1pruuqzLPXOYHwzsLNfHN5P3x/dTff8e7HeXrDe6zgA0CKUGgAJzTmnG2ZmalO1T/eN3670AIfYAE2Zme74wUiN7JGtq56brcUbyryOBAB7jVIDIKFNKyzW68UpunpYhUYxvhnYpZSgX4+cM06pSQH94skCBgcAiDuUGgAJa/nmCt08fYEOyqvVhYMY3wzsSdfsVD1yzlit21aty56epVA9wzQAxI+A1wEAoDXU1Yd15bOzFPT7dO8BjG8GvqFg6i5vHifpttEpuqYwrN9PfVGTmzsHLf+86GcDgBZgTw2AhHT320WaU1yqO04boa6MbwYidmbfap27f6UeX5qmaStSvI4DABGh1ABIOE9/ukqPfLhMZx/YSyeM6Op1HCDu/GZkuQ7Jq9VvZmZq5hYO6gAQ+yg1ABLK2wvW68Z/ztPRg/J0yynDvI4DxKWgT3rgoFJ1SQ3rwv9la30Vfy4AiG28SwFIGIUrt+qXz8zSiB45euDHYxX08xYHtFSHZKe/HLJNFXWmCz/OVnW914kAYPfYpwwgdu3mZOZdWbrdr/Pf76BuKWE9PnqJ0uYubsVgQPswOLtefxy/XRf9L0c3FGbqngPKZAzdABCDItqMaWYTzKzIzJaa2XW7uP8IM5tpZiEzOz36MQFg99ZX+fTT/+Qoye/05OHb1DGZL9gEomVC91pdNbRcL61K1V+XpHodBwB2qdlSY2Z+SQ9IOkHSUEk/MrOhO622StK5kp6OdkAA2JPSWtO5M3K0vc409dBS9Uxn0hkQbb8cUqkTulfr93Mz9OH6JK/jAMC3RLKnZrykpc65Zc65WknPSprYdAXn3Arn3FxJ/DUBoM1U10uTPs7Wl9v9evjgUg3vEPI6EpCQfCbdfUCZBmbX65efZml5md/rSADwDZGUmu6SVjdZLm68DQA8U++kqz/L0qebk3T3Adt1WJc6ryMBCS090DA4wG/SBR9nq6yOk2sAxI5ISs2u3rVadMC6mU0yswIzK9i0aVNLHgIA5Jw0ZXaG3liTohtHlmlirxqvIwHtQs/0sB44qFQryv268rMs1Yc5fw1AbIik1BRL6tlkuYektS15Mufco865fOcuY2avAAARsElEQVRcfl5eXkseAgD0UFGanvgyTb8YUKkLBlZ5HQdoVw7pXKebRpXr3XXJuuftIq/jAICkyEY6fy5pgJn1lbRG0lmSzm7VVACwG9NWpOiu+Rma2LNa148s9zoO0C6d079KC0sDevCDL5WREtAlR+3vdSQA7Vyze2qccyFJl0l6S9IiSc875xaY2RQzO0WSzOwAMyuWdIakR8xsQWuGBtA+vb8uSdcVZuqwzrX6wwHb5eOQfsATZtKtY8o0cXQ33fWvIt3x5hdyjkPRAHgnoi/fdM69IemNnW6b3OT652o4LA0AWsXsrQFd8km2BmeH9NDBpUqK6Fu2ALSWoE+698zRykgO6OEPv1RZdZ1unThcPrY2APBARKUGALy0vMyv82fkqFNKWFMPK1VmkC3CQCzwzfybbushZW1L10OfrlL52sW6+4DtCu7tRof881olH4D2g1IDIKZtrPbppzNyJElPHLZNnVP4OiwglphJ146oUGbQ6a75GSoPmR44qFQpfJUNgDZEqQEQfQVTo/IwpbWm82Zka3O1T88cWaJ+mfVReVwA0XfJ4EplBcP67axMnTsjR48dUqoM9qoCaCMclQ4gJi0r8+vU9zpocWlADx5UqtG5Ia8jAWjGT/pX60/jt+vzzUH9+KMcldRwfg2AtkGpARBzZmwI6vvvddC2Wp+eOmKbju5a63UkABGa2KtGjxxcqkWlAZ35YQdtqOJPDQCtj3caADHlyaWp+tmMHHVNDeuVY7dqfF6d15EA7KXjutXqicO2aW2lT6d/0EGryvlzA0Dr4l0GQEyoC0s3zszQ5NmZOnq/Wr14dIl6pjMUAIhXB3eu09NHbFNZnen0DzpocSmTAwC0HkoNAM+V1Jh++p8c/WNZmi4aVKFHOMEYSAijckN6/sgSSdKZH3bQnK3MJwLQOig1ADy1dLtf33+vgwq3BHXPAdt13YgK+Tm3GEgYA7Pr9cJRJcoMOp39UY7+tzHodSQACYhSA8AzH6xP0qnvdVBFyKdnjijRD3pXex0JQCvolRHWC0eVqFtaWD+bkaN31yZ5HQlAgqHUAGhzzkl/XZKq82dkq0d6vV45dqvGdWJkM5DIuqSG9fyRJRqcHdKF/8vW08tS5DjKFECUUGoAtKnasHT9zEzdOidTx3er0QtHb1P3NAYCAO1Bh2Snp47YpoPz6nTDzCyd999srWfkM4Ao4J0EQJvZUmP6yUc5enZ5qi4bXKGHDt6u9ACbaoH2JDPo9MTh23Tz6DJ9silJx7+dqxcKi+XYbQNgH1BqALSJolK/Jr6bq9lbg7pvfKl+PbxCPgYCAO2Sz6Rz96/Sv47fqsFZIf162hxd8ESBNm7nvDoALUOpAdCqnJPeLE7Wae93UE1Yev6oEk3sVeN1LAAxoE9GvZ49apt+e/JQzVi6Wcff+5H+OWsNe20A7DVKDYBWs3S7Xz+bka2LP8lWv8x6TT+mRKNzGQgA4Gt+k35+WF+9ecXh6p+Xriufm60L/16oTWVs/AAQOUoNgKgrrTXdMjtD3/13rmZtDWryqDK9dHSJujIQAMBu9MvL0LSLDtENJw7WB4s36Tv3fqjpc9ay1wZARCg1AKKmPuz01KcrdfS/OupvS1P1w77V+mDCFp0/oEpB3m0ANMPvM006or/euPww9eqYrsufmaVLnpqpzeXstQGwZwGvAwBIDJ8s26JbXl2oReu2a3ynkG4aXa5hORxqBmDv7d85Uy9edLD+8p/luvffi/Xp8o9068ThOmlkV6+jAYhRbDsFsE+KSyp16VMzddajn6i0slb3nz1Gzx25jUIDYJ8E/D5dfFR/vXb5Yeqek6pLn56py56eqa0VtV5HAxCD2FMDoEWqauv10Idf6pEPv5SZdNVxAzXpiH5KTfJLBV6nAxBXCqbu9q6Bkl4+UHqkKE1/mrdWH3+xRufuX6mf9K9SbvJO59vkn9e6OQHELEoNgL3inNOrc9fp9jcWaV1ptU4e2VXXnzhE3XNSvY4GIEEFfNKlQyp1TNca3TEvQ39cmKEHi9J1eu8q/XxAlfpm1nsdEYDHKDUAIjZ/TalueXWBPl9RomHdsnTfWWM0vm+u17EAtBNDcur1xOGlWlzq12NL0vT8ilQ9tSxVx3er1aSBlRrnnMz4Vl+gPaLUANijqtp6vbVgvZ4vWK2Pv9yi3PQk3X7aCJ2Z31N+H388AGh7A7PrdVd+mX49vEJPLk3V379M1dtrO2jMso/1i8P76bvD9uP9CWhnzKv57/n5+a6ggAPvgVjknNPs1ds0rbBYr85eq7KakHp0SNUZ43rq3EP7KDs1uOcH2MPx8QAQbZUhadqKVP11VRet2lqpXrlpOv/QPjojv6fSk9l+C8QzMyt0zuU3ux6lBkgAUSoRmwadrZdnFWtaQbGWbCxXStCnE4d31en5PXRQ347yRbrlk1IDwAP1Y8/Vvxeu16MfLdPMVduUnRrUjw/spXMP6aPOWSlexwPQApGWGjZfAO1cXVh6f32Snl+eqvdfelf1YaexvXJ0+2kjdNLIrspKaWavDADECL/PNGF4V00Y3lWFK7fqLx8t10Mffqm//GeZJo7urh8e0FNjeuYo4OcbLYBEQ6kB2qnFpX5NW5Gql1elaHONT3kp9brg8L46Y1wP7d850+t4ALBPxvXO1bhzcrVic4Ue/+9yTSso1guFxcpKCejwgXk6amCejhyUp86Z7MEBEgGlBmgn6sLSgm0Bfb45qNdWp2hOSVABczq2a43O7FOtI/erVcC3RVqlhh8ASAB9OqVrysTh+vV3B2nGks36oGijPijapNfnrpMkDeuWpaMG5emoQZ3ZiwPEMUoNkKAqQqZZWwL6bHOSCjYHNWtrUFX1DefEDM4O6bejyvT9XtXquPOX1wFAAspKCerEEV114oiucs5p0boyvV+0UR8WbdLDHy7TA+9/yV4cII4xKABIBAVTtbHap8LNQX22OaiCLUEt3BZQvTP55DQkJ6QDOtXpgE51yu9Ypy6pYa8TA0DMKK01/Xdjkj5Y3/Czsdov6eu9OIcPyNOQrlnNT34EEHVMPwMSWKg+rBVbKjVzZYk+X7FVnxet0Iryhh2vyT6nMR3rdEDHOuV3qtPYjnXKDLI3BgAi4Zy0qPsPduzFKVxVovpww3voflkpGrhfpgZ2ztDA/TI1qEumBnTJUFoSB74ArYXpZ0Ccq6qt16qtlVq5pUIrt1Rq5daGy1VbK7WmpEqhxg/ZDmlB5efU6+y+VcrvVKfhHUJK4pBwAGgRM2lotywN7ZalS4/eX6VVdSpcuVWLN5Rr8foyFW0o05PLtqg29PUe7565qY0Fp6HoDOySqX556UoJ+j38lwDtS0SlxswmSLpPkl/SY865O3a6P1nSk5LGSdoi6YfOuRXRjQokltpQWNsqa7W2tFort1Ro1ZZKrWxSYjaW1Xxj/ayUgPp0SteI7tk6eWRX9e6YrrG9ctSvU4Z8M//mzT8CABJcdmpQxwzuomMGd9lxW33YadXWShWtL9OSDQ1FZ/GGMn1QtGnHBiefNQwp6NkhTZ0zk5WXmdx4maLOWcnKy0hW56xk9vIAUdLs/0lm5pf0gKTjJRVL+tzMpjvnFjZZ7eeSSpxz+5vZWZLulPTD1ggMxBrnnKrrwiqprG34qahTSWWttlXWamvj9YafOpVUfLVOrSpq67/1WF2yktU7N11HDsxT745p6tUxXb1z09S7Y5py0pI8+NcBAHbm95n6dkpX307pmjB8vx2314bCWrGl4htlZ11ptYrWl2lzec2OwtNURnJAeY2l5+vik6xOGcnKTA4ovfEnIzmg9GR/42VAQaa0Ad8QyeaB8ZKWOueWSZKZPStpoqSmpWaipJsbr78g6X4zM+fVCTuISc45OSe5r65LjcsNt2un5bBzCruGdevDDdcbbmu8Hv76en3YyTW5HgqHVVfvFKoPKxR2qqsPK1Tf5PYd9399vT4cVk1dWFV19aqqq1d1Xb2qausbl8Oq3nG9ye219aoO1WtPr/TMlIA6pCWpQ3qSOmYkaf/OGQ3LaUF1SE9S58zkHVvzUpM4VAEAPFcwtUW/liRpYOOPcht/GoWdVFJr2ljl06ZqvzZW+7Sp2vf1ZZlPizb59GG1T+Wh5gtLcsC3o+A0lB7/juspAb+SAj4lB3wK+k1JAZ+Cfp+SAj4lNV4G/d+8ntx46fNJfjP5fSafz3Zc/+rH17gcaHK/zyf5rOE+U8MhfGbWcKmG+8waLtV4/9frfv07alwGWiKSUtNd0uomy8WSDtzdOs65kJmVSuooaXM0QrampRvLNfH+GW3+vPvS9lpaFd0enrW5x3Q7XWn6WDsKyTcez+24Ld6qrd9nSgv6lZrU+BP0KyXYcJmXmfz1cpJPaUmBHfflpAV3lJXc9CTlpCUpJy3I1jQAgHwmdUx26phcryH69p76pipD0pYan8rrTBUhn8r7fkcVNfWqqAmpvCa04/Lr6w33ba2o1aqtlaqpC6u2PqzaUMNPXeMGvnizo+jo67JjTe4z7VSA9rC4c1f61u/uZaYW/W7Lf7XNTTqiv644boDXMfZKJKVmV/8Ndv4/I5J1ZGaTJE1qXCw3s6IInr+tdFIclDDEHF43aAleN2gJXjdoCV432GtXSp2ujJ3XTe9IVoqk1BRL6tlkuYektbtZp9jMApKyJW3d+YGcc49KejSSYG3NzAoiGRcHNMXrBi3B6wYtwesGLcHrBi0Rj6+bSI6L+VzSADPra2ZJks6SNH2ndaZL+lnj9dMlvcf5NAAAAADaQrN7ahrPkblM0ltqGOn8uHNugZlNkVTgnJsu6a+S/m5mS9Wwh+as1gwNAAAAAF+JaDi6c+4NSW/sdNvkJterJZ0R3WhtLiYPi0PM43WDluB1g5bgdYOW4HWDloi7141xlBgAAACAeMasWQAAAABxrd2XGjObYGZFZrbUzK7zOg9in5n1NLP3zWyRmS0wsyu8zoT4YWZ+M5tlZq95nQXxwcxyzOwFM/ui8X3nYK8zIfaZ2VWNn1HzzewZM0vxOhNik5k9bmYbzWx+k9tyzezfZrak8bKDlxkj0a5LjZn5JT0g6QRJQyX9yMyGepsKcSAk6VfOuSGSDpJ0Ka8b7IUrJC3yOgTiyn2S/uWcGyxplHj9oBlm1l3S5ZLynXPD1TDoiSFO2J2/SZqw023XSXrXOTdA0ruNyzGtXZcaSeMlLXXOLXPO1Up6VtJEjzMhxjnn1jnnZjZeL1PDHxjdvU2FeGBmPSSdJOkxr7MgPphZlqQj1DBlVM65WufcNm9TIU4EJKU2fn9gmr79HYOAJMk595G+/f2SEyU90Xj9CUnfb9NQLdDeS013SaubLBeLP06xF8ysj6Qxkj71NgnixJ8kXSMp7HUQxI1+kjZJmtp42OJjZpbudSjENufcGkl3S1olaZ2kUufc296mQpzp4pxbJzVszJXU2eM8zWrvpcZ2cRvj4BARM8uQ9KKkK51z273Og9hmZidL2uicK/Q6C+JKQNJYSQ8558ZIqlAcHAYCbzWe/zBRUl9J3SSlm9lPvE0FtK72XmqKJfVsstxD7J5FBMwsqIZC85Rz7iWv8yAuHCrpFDNboYZDXY8xs394GwlxoFhSsXPuq73BL6ih5AB7cpyk5c65Tc65OkkvSTrE40yILxvMrKskNV5u9DhPs9p7qflc0gAz62tmSWo4iW66x5kQ48zM1HB8+yLn3B+9zoP44Jy73jnXwznXRw3vNe8559hyij1yzq2XtNrMBjXedKykhR5GQnxYJekgM0tr/Mw6VgyYwN6ZLulnjdd/JukVD7NEJOB1AC8550Jmdpmkt9QwGeRx59wCj2Mh9h0q6RxJ88xsduNtNzjn3vAwE4DE9UtJTzVufFsm6TyP8yDGOec+NbMXJM1Uw8TOWYrDb4hH2zCzZyQdJamTmRVLuknSHZKeN7Ofq6Ekn+FdwsiYc5xCAgAAACB+tffDzwAAAADEOUoNAAAAgLhGqQEAAAAQ1yg1AAAAAOIapQYAAABAXKPUAAAAAIhrlBoAAAAAcY1SAwAAACCu/X/eAYP5f8purwAAAABJRU5ErkJggg==\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "mu = means.mean()\n", + "sd = means.std()\n", + "\n", + "m = stats.norm(mu, sd)\n", + "\n", + "x = np.linspace(0, 10)\n", + "plt.figure(figsize=(14, 4))\n", + "plt.plot(x, m.pdf(x))\n", + "sns.distplot(means, kde=False, norm_hist=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## What dis we just do?\n", + "\n", + "The gaussian we fitted is actually a model that explains the data we've seen.\n", + "\n", + "The models has two parameters $\\theta$, the mean $\\mu$ and the standard deviation $\\sigma$.\n", + "\n", + "We fitted the model on a frequentist way. Our model would have a really bad fit, if we only drew 5 times." + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Cumulative distribution\n", + "\n", + "* A cummulative distribution shows the integral of the probability distribution.\n", + "* $Cdf(a)$ = $P(x \\le a)$\n", + "\n", + "```python\n", + "plt.plot(x, m.pdf(x))\n", + "plt.plot(x, m.cdf(x))\n", + "```\n", + "![](images/cdf.png)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exercise\n", + "\n", + "Given our model **m**\n", + "\n", + "* What is $P(x \\le 4|\\theta)$\n", + "* What is $P(x > 8|\\theta)$\n", + "* What is $P(5 < x < 6|\\theta)$\n", + "* What is the probability of our data, given our models parameters? $P(x|\\theta)$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exersice: answers I\n", + "\n", + "Using the cumulative density function:\n", + "```python\n", + "print(f\"\"\"\n", + "P(x <= 4) = {m.cdf(4)}\n", + "P(x > 8) = {1 - m.cdf(8)}\n", + "P(5 < x < 6) = {m.cdf(6) - m.cdf(5)}\n", + "\"\"\")\n", + "```\n", + "```text\n", + "P(x <= 4) = 0.1495479734480526\n", + "P(x > 8) = 0.0003465131086946016\n", + "P(5 < x < 6) = 0.3527724808375644\n", + "```\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Exersice: answers II\n", + "\n", + "$$P(x|\\theta) = \\prod_{i=0}^{N}{P(x_i|\\theta)}$$\n", + "\n", + "Where $N$ is the number of data points. \n", + "\n", + "The following code returns `0.0` due to nummerical underflow. $P(x)^N$ leads to very small numbers.\n", + "```python\n", + "np.prod([m.pdf(x) for x in means]) \n", + "```\n", + "\n", + "### Log probability\n", + "A trick used is converting to log space. \n", + "Hint: $ln(x \\cdot y) = ln(x) + ln(y)$\n", + "\n", + "```python\n", + "np.sum([np.log(m.pdf(x)) for x in means])\n", + "```\n", + "\n", + "```text\n", + "-1316.6759133098722\n", + "```\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Likelihood\n", + "\n", + "A distribution is plotted by varying the data $x$ given constant $\\theta$ parameters.\n", + "\n", + "$$P(x|\\theta)$$\n", + "\n", + "We could also vary the parameters $\\theta$ given constant (observed) data $x$.\n", + "\n", + "This is called a likelihood function.\n", + "\n", + "$$\\mathcal{L}(\\theta|x)$$\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Equivalence principle\n", + "\"The probability of data conditional on a parameter value equals the likelihood of that parameter value given the same data\"\n", + "\n", + "$$P(x|\\theta) = \\mathcal{L}(\\theta|x)$$\n", + "\n", + "Note:\n", + "\n", + "The likelihood function is not a probability distribution.\n", + "\n", + "$$\\int_{x=-\\infty}^ \\infty P(x) dx \\neq 1$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Bayes' model definition\n", + "\n", + "\\begin{equation}\n", + "P(\\boldsymbol{\\theta}\\ |\\ D) = \\frac{P(D\\ |\\ \\boldsymbol{\\theta})\\cdot P(\\boldsymbol{\\theta})}{P(D)}\n", + "\\end{equation}\n", + "\n", + "Where:\n", + "* $P(\\boldsymbol{\\theta}\\ |\\ D)$ is the __posterior__: the distribution of the parameter(s) after taking into account the observed data.\n", + "* $P(D\\ |\\ \\boldsymbol{\\theta})$ is the __likelihood__: the probability of observing data D, given model parameters $\\boldsymbol{\\theta}$.\n", + "* $P(\\boldsymbol{\\theta})$ represents the __prior__ (initial belief) about the distibution of the model parameters $\\boldsymbol{\\theta}$.\n", + "* $P(D)$ is the __evidence__ of observing $D$. This is a marginal probability. Since this factor is the same for all possible model parameters being considered, it does not influence the _relative_ probabilities of different model parameters.\n", + "\n" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Bayes' model definition\n", + "\n", + "\\begin{equation}\n", + "P(\\boldsymbol{\\theta}\\ |\\ D) = \\frac{P(D\\ |\\ \\boldsymbol{\\theta})\\cdot P(\\boldsymbol{\\theta})}{P(D)}\n", + "\\end{equation}\n", + "\n", + "Note that:\n", + "The prior and the likelihood are functions, where the evidence is just a constant (Needed for normalization)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Example\n", + "\n", + "I observe two coin flips [H, H]\n", + "\n", + "Is this a fair coin?\n", + "\n", + "We can model a coin with a Bernoulli distribution. \n", + "\n", + "$$ x \\sim Bernoulli(p) $$\n", + "\n", + "![](images/bernoulli.png)\n", + "\n", + "So we are interested in the parameter $p$ of the distribution.\n", + "\n", + "Let's restrict our model to 3 parameters.\n", + "\n", + "| $\\theta$ | $\\mathcal{L}$ | prior | unnormalized posterior | posterior |\n", + "|------------|----------|-------|------------------------|----------------------|\n", + "| 0.3 | 0.09 | 0.33 | 0.33 * 0.09 = 0.03 | 0.03 / 0.326 = 0.09 |\n", + "| 0.5 | 0.025 | 0.33 | 0.33 * 0.025 = 0.083 | 0.083 / 0.326 = 0.26 |\n", + "| 0.8 | 0.064 | 0.33 | 0.33 * 0.064 = 0.213 | 0.213 / 0.326 = 0.65 |\n", + "| marginal p | - | 1 | 0.326 | 1 |" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Solution in code\n", + "\n", + "```python\n", + "prior = np.ones(3) / 3\n", + "likelihood = stats.bernoulli(np.array([.3, .5, .8])).pmf(1)**2\n", + "unnormalized_posterior = prior * likelihood\n", + "normalized_posterior = unnormalized_posterior / np.sum(unnormalized_posterior)\n", + "print(normalized_posterior)\n", + "```\n", + "\n", + "```text\n", + "array([0.09183673, 0.25510204, 0.65306122])\n", + "```" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Practicallity\n", + "\n", + "In the previous example we restricted the models parameters. In practical models we can have thousands of parameters, each having an infinite domain. \n", + "\n", + "Computing $P(D)$ is therefore often impractical / impossible. \n", + "\n", + "As $P(D)$ is only a normalization constant, algorithms can still approximate a posterior. This is due to posterior being proportional to the prior * likelihood.\n", + "\n", + "$$ P(\\theta|D) \\propto P(D|\\theta) \\cdot P(\\theta)$$" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## PyMC3\n", + "\n", + "* Approximates posterior probability by sampling (for now it's magic ;) )\n", + "\n", + "![](images/PyMC3_banner.svg)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Same example in PyMC3" + ] + }, + { + "cell_type": "code", + "execution_count": 147, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [p]\n", + "Sampling 4 chains: 100%|██████████| 22000/22000 [00:03<00:00, 6271.39draws/s]\n" + ] + } + ], + "source": [ + "coin_flips = [1, 1]\n", + "with pm.Model():\n", + " p = pm.Uniform('p', 0.001, 0.999)\n", + " \n", + " likelihood = pm.Bernoulli('observed', p=p, observed=coin_flips)\n", + " \n", + " trace = pm.sample(draws=3000)\n", + " \n", + " " + ] + }, + { + "cell_type": "code", + "execution_count": 148, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[,\n", + " ]],\n", + " dtype=object)" + ] + }, + "execution_count": 148, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pm.traceplot(trace)" + ] + }, + { + "cell_type": "code", + "execution_count": 156, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "name": "stdout", + "output_type": "stream", + "text": [ + "p: 0.3: 0.08795\n", + "p: 0.5: 0.25275\n", + "p: 0.8: 0.63875\n" + ] + } + ], + "source": [ + "for p in [.3, .5, .8]:\n", + " print(f'p: {p}:', (trace['p'] < p).sum() / trace['p'].shape[0])" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Same example in PyMC3\n", + "\n", + "* Do we really have a uniform prior when we have a coin flip?\n", + "* Update your prior with a Beta distribution (Tip: Google beta!)\n" + ] + }, + { + "cell_type": "code", + "execution_count": 161, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 161, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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9U2TU7o5unxBPNz8fXtyQZzqKcDApd2GzljYrL2Xkc0l8L8bEyTFbd9QryJ+5Y2P4YOdRjlY1mI4jHEjKXdjsw13HOFrVIKN2N3fqDKeXO854Ep5Jyl3YxGrVLNuQy4DIYKYO6GM6jrgI0T27MWtkFG9vO0JlXbPpOMJBpNyFTb44WMqh47UsmZJIxzVrwo0tmZxEQ0sbb2yRhbQ9lZS7sMmyDblE9+zG1cOjTEcRdpAaGcz0QX147ct86ptbTccRDiDlLjq143AF2wsqWZiegJ+P/Mh4inumJFFZ3yKLeXgo+U0VnVqxMZ/Qbn7MuSTGdBRhR2PiwhgT14uXN+XTZpUZQzyNlLs4r4LyOtbuK2H++DhZQs8DLUpP4EhFPZ9klZiOIuxMyl2c18ub8vGzWFhwqSzG4YmuGNyXuN7deXGjTAfsaaTcxTlV1DXz7o5Crh0VRZ/gQNNxhAP4WBQLL0tgZ2EVOw5Xmo4j7EjKXZzTm1sP09hilWl9PdyNY9onFFu+UaYk8CRS7uKsGlvaeGNLAVMHRMgEYR6um78P88fH8en+4+SX15mOI+xEyl2c1fvfHKW8tplFk2TU7g3mT4jHz8fCy5tk9O4ppNzFd1itmhUZeQyNDmFCYm/TcYQTRAQHcP2oaN7NLOJEbZPpOMIOpNzFd3xxsJTcsjoWpctUA95kYXoCTa1W3tx6xHQUYQdS7uI7lm/MIyo0kJnD+pmOIpwouU8w0wb24Y0tBTS2tJmOIy6SlLv4N7sKq/gqv4IfXCZTDXijhemJnKhr5h9fHzUdRVwk+e0V/2ZFRh7BAb4y1YCXGp8YxrDoUF7KyMMqUxK4NSl38a3Cino+3lvCLeNiCQ70Mx1HGKCUYtGkRPLK6/jsQKnpOOIiSLmLb726uQAF3DEx3nQUYdDMoX2J7tmNFRlyWqQ7k3IXAFQ3tLBy+xGuHt6PfqHdTMcRBvn6WLhzYjzb8ivYXVRlOo64QFLuAoCV249Q19wmUw0IAOZcEkNwgC8vyTqrbkvKXdDSZuXVzQVMSOzN0OhQ03GECwgO9GPu2BhW7ynmaFWD6TjiAki5C9bsKaa4upGF6QmmowgXcsfE9p+H1zbL6N0dSbl7Oa3bpxpIjAhi6oA+puMIFxLdsxszh/XjnW2FnGxsMR1HdJGUu5f7Kr+CvUdrWHhZIhaLTDUg/t2i9ARONrWycnuh6Siii6TcvdxLGXmEBflz/eho01GECxrevydj48N4dXMBrW1W03FEF0i5e7HcslrW7S/ltvFxBPr5mI4jXNTC9ASOVjXw8V5ZZ9WdSLl7sVc25ePva2HBBFkfVZzb9EGRJIQH8VKGrLPqTqTcvVRFXTPv7Sji+lHRhPcIMB1HuDCLRfGDyxLYVVRNpqyz6jak3L3Um1sP09Rq5a7L5PRH0bkbR/enZ3c/Vsg6q25Dyt0LnVofdcqACFJkfVRhg27+Ptw2TtZZdSdS7l5o1c5j7eujylQDogsWXBqHn8XCK5vkoiZ30Gm5K6VeUUqVKqX2nuNxpZR6XimVo5TarZQabf+Ywl6sVs3yjDwG9Qvh0iRZH1XYrk9wILNHRvHujkIq65pNxxGdsGXk/how4zyPXwWkdHwsBl64+FjCUTYcKiOntJbFkxJkfVTRZYsmJdLYYuXNrYdNRxGd6LTctdYbgYrzbDIbeEO32wr0VErJ4psuavnGPPqGBHL18CjTUYQbSo0MZsqACF7fIuusujp7HHOPBk6/Nrmo43PfoZRarJTKVEpllpWV2eGlRVfsKapmS94JfnBZvKyPKi7Y4vREymubef8bWWfVldnjN/xs/29/1isdtNbLtdZpWuu0iIgIO7y06IoVGXn0CPBl7thY01GEG5uQ1JshUSGskHVWXZo9yr0IOH015f7AMTs8r7Cjosp6Vu8pZt7YGEJkfVRxEZRSLJ6USG5ZHV8clHVWXZU9yn0VsKDjrJnxQLXWutgOzyvs6NT6qHdOlIuWxMWbOawfUaGBLJeLmlyWLadCvg1sAQYopYqUUncppZYopZZ0bLIGyANygBXAvQ5LKy5IdUML72xrXx81qqesjyounp+PhR9clsBX+RXsKpR1Vl2Rb2cbaK3ndfK4Bu6zWyJhd29vk/VRhf3NuSSG59ZlsyIjjz/eIpe3uBo5ZcLDNbdaeXVzPhOTZX1UYV/BgX7cMi6WNXuKKayoNx1HnEHK3cN9uOsYx2uaZKoB4RB3TIzHohSvyDqrLkfK3YOdWh91QGQwk1Pl1FNhf/1CuzFrRBQrtxdSXS/rrLoSKXcPlpFdzoGSkyxMl6kGhOMsTE+kvrmNt7bJlASuRMrdgy3fmEdkSACzR8r6qMJxBkeFkJ4SzqubC2hqlSkJXIWUu4faU1TNppxy7rg0AX9f+TYLx7p7UhJlJ5v459cyJYGrkN96D7VsQy7Bgb7cNl6mGhCONzG5N8OiQ3lxYx5tMiWBS5By90D55XWs2VvM/PFxBMtUA8IJlFLcMyWJ/PI61maVmI4jkHL3SMs35uLnY5GpBoRTXTmkLwnhQbywPpf2axuFSVLuHqa0ppG/7zjKTWP6ExEcYDqO8CI+FsXdkxLZc7SazTknTMfxelLuHublzfm0Wq0sniQXLQnnu250NH2CA3hhQ47pKF5Pyt2DVDe08NbWI3x/eBRxvYNMxxFeKMDXh4XpCWzOOSETihkm5e5B3tx6mNqmVpZMllG7MGfe2FhCAn1ZtiHXdBSvJuXuIRpb2nh1cz6TUyMYEiUThAlzggP9mD8hjn9llZBbVms6jteScvcQ7+4oory2mXumJJmOIkT7xXM+FlbIYh7GSLl7gNY2K8s35jIqtifjEsJMxxGCiOAAbk6L4e9fF1FS3Wg6jleScvcAa/aWUFjRwJLJSTJBmHAZiyclYtXIdMCGSLm7Oa01L6zPJSkiiCsGRZqOI8S3YsK6c/Xwfry19TBV9c2m43gdKXc399n+UvYX13DPlGQsFhm1C9dyz5Qk6prbeHVzgekoXkfK3Y1prXnus2xiw7pz7cgo03GE+I6BfUO4ckgkr2zOp7pBFvNwJil3N/bFwVL2HK3m/qnJ+PrIt1K4pqXTUjjZ2MprMnp3KmkEN6W15rl12fTv1Y3rRstiHMJ1DYkKZfqgSF7elMfJRhm9O4uUu5vacKiMXUXV3Dc1GT8ZtQsX98C0FGoaW3n9ywLTUbyGtIIbOnWsPbpnN24Y3d90HCE6Nax/KNMG9uGlTfnUNrWajuMVpNzdUEZ2Od8cqeLeqUmyhJ5wG0unpVBV38IbWwpMR/EK0gxu5tSoPSo0kBvHyKhduI8RMT2ZMiCCFRvzqJPRu8NJubuZL3NPsONwJfdMSSLA18d0HCG6ZOm0FCrrW3hz62HTUTyelLsbOXWGTN+QQG6+JMZ0HCG6bHRsL9JTwlm+MY/6Zhm9O5KUuxvZkneCbQUVMmoXbu3B6SmcqGvmra1HTEfxaFLubuT5z7LpExzAHBm1Czc2Ji6My5LDeXFjHg3NbabjeCwpdzfxZW45W/MqWDI5iUA/GbUL97Z0WgrltU1y7N2BpNzdgNaaJ/51kH6hgdwyLtZ0HCEu2tiEMNJTwvnT+hxq5KpVh5BydwP/2lvCrsIqHroiVUbtwmP8dMZAqupbeFHWWnUIKXcX19pm5alPDpLSp4dcjSo8ytDoUGaNiOLlTfmU1shqTfYm5e7i3t1RRF5ZHT+5cgA+Ml+78DA/+l4qrW3tF+YJ+5Jyd2ENzW38/tNDjInrxRWDZZUl4Xniegdxy7hY3tleSF5Zrek4HsWmcldKzVBKHVRK5SilfnaWx+9QSpUppXZ2fCy0f1Tv8+qX+ZSebOKnMwbK2qjCY/3w8hQCfC08/ckh01E8SqflrpTyAf4EXAUMBuYppQafZdOVWuuRHR8v2Tmn16mqb+aF9blMG9iHsQlhpuMI4TARwQEsTE9k9Z5idhdVmY7jMWwZuY8FcrTWeVrrZuAdYLZjY4kX1udS29TKT2YMMB1FCIdblJ5AWJA///vxAbTWpuN4BFvKPRooPO1+UcfnznSDUmq3Uuo9pZRcQnkRjlU18OqXBVw3KpqBfUNMxxHC4YID/bh/ajJf5p4gI7vcdByPYEu5n+1g75l/Wj8E4rXWw4F1wOtnfSKlFiulMpVSmWVlZV1L6kWeXXcINPzHFammowjhNLeOj6V/r2488a8DWK0yer9YtpR7EXD6SLw/cOz0DbTWJ7TWTR13VwBjzvZEWuvlWus0rXVaRETEheT1eNnHT/LejiLmT4ijf6/upuMI4TQBvj786HupZB2r4cPdxzr/AnFetpT7diBFKZWglPIH5gKrTt9AKdXvtLuzgP32i+g9tNY89tE+gvx9uW9qsuk4Qjjd7BHRDOoXwhMfH5ApgS9Sp+WutW4F7gfW0l7af9NaZymlHlNKzerYbKlSKksptQtYCtzhqMCebG1WCRnZ5fzH91IJC/I3HUcIp7NYFI/OGsKx6kb+/IVMS3AxlKl3ptPS0nRmZqaR13ZFDc1tTH9mA8GBvnz0w8vw9ZHry4T3emjlTlbvLmbtQ5NICA8yHcelKKV2aK3TOttOGsRF/OmLHI5WNfDY7KFS7MLr/fyqgfj7Wnj0wyw5NfICSYu4gILyOpZvzOO6UdFywZIQQJ+QQB6cnsL6g2V8uu+46ThuScrdMK01j36Yhb+vhZ9fNdB0HCFcxu2XxpMa2YPHPtpHY4us2NRVUu6GrdtfyhcHy3hwegp9QgJNxxHCZfj5WHh01lCKKhv483p5c7WrpNwNamxp49EPs0iN7MHtl8abjiOEy5mQ1JtrRkSxbEMuR07Um47jVqTcDVq2IZeiygYenTUUP3kTVYiz+uXMQfhZFI99lGU6iluRRjGksKKeF9bncs2IKCYk9TYdRwiX1Tc0kKXTUli3v5TPD8ibq7aScjdAa82v3t+Lj0Xxy5mDTMcRwuXdOTGBpIggHv4gi9omuXLVFlLuBvx12xE2HCrjZ1cNpG+ovIkqRGf8fS08ccNwjlY18N+r95mO4xak3J2soLyOxz/aT3pKOPPHx5mOI4TbSIsP4+5JSby9rVAOz9hAyt2J2qyaH727C18fxZM3Dpel84ToooeuSGFg32D+8709VNQ1m47j0qTcnWj5xjx2HK7kN7OH0i+0m+k4QridAF8fnrl5JNUNzfzq/T0yNcF5SLk7yf7iGp759CAzh/Vl9sgo03GEcFuDo0J46IpU1uwpYdUumff9XKTcnaCptY2HVu4ktJs/j187TA7HCHGR7p6UxJi4XvzX+3sprm4wHcclSbk7wbPrsjlQcpInbhgm87QLYQc+FsXTN42gpU3zn+/tlsMzZyHl7mCZBRW8uCGXuZfEMG1QpOk4QniM+PAgfvn9QWRkl/Pm1sOm47gcKXcHqqhr5sGVO4nq2Y1fXT3YdBwhPM6t42KZlBrBf6/ZT9axatNxXIqUu4M0t1q5580dlJ5s4g/zRtEjwNd0JCE8jlKK3900nF7d/Vn0eiZlJ5tMR3IZUu4O8uiHWXyVX8GTNwxnVGwv03GE8Fh9ggNZsSCNivpm7nlzB02tMvc7SLk7xF+2FPDWV0dYMjmJa0dFm44jhMcbGh3KUzeOIPNwJf/1/l55gxWQYwV29mVOOY98uI9pA/vwkysHmI4jhNe4ZkQUh46f5A+f5zCwbwg/uCzBdCSjZORuR4dP1HHvX78mKSKIZ+eOxMci57ML4UwPTU/lyiGRPL56HxsPlZmOY5SUu52cbGzhrtczAXhpwSUEB/oZTiSE97FYFM/cPJLUyGDu/+vX5JXVmo5kjJS7HbS0WXngnZ0UlNfx51tHE9u7u+lIQnitoABfVixIw9fHwsLXM6n00gnGpNwvUlNrG/e99TWfHyjlkVlDuDQp3HQkIbxeTFh3lt02hqKqBuat2Ep5rfedIinlfhEaW9pY/MYOPtl3nEdnDeE2mZ9dCJcxNiGMV26/hMMn6pnz4hZKqhtNR3IqKfcLVNfUyp2vbmdjdhlP3DCM2y+NNx1JCHGGy1LCef0HYzle08TNL26hsKLedCSnkXK/ADWNLcx/+Su2FVTw7JyRzLkk1nQkIcQ5jE0I482F46iqb2bOi1vIL68zHckppNy7qLL9LXq0AAAIkUlEQVSumVtXfMWeo9X86ZZRzB4pFykJ4epGxvTk7cXjaWy1cvOLW8g+ftJ0JIeTcu+Cosp65q3YysHjJ1k+P40ZQ/uZjiSEsNGQqFBWLh6PAuYs38rXRypNR3IoKXcbfbDzKFc9l0FRZQOv3nEJUwf2MR1JCNFFKZHB/O3uCXT39+GmZVt4/rNsWtuspmM5hJR7J2oaW3jwnW944J2dpEYG8/ED6UxMltMdhXBX8eFBrF6aztXD+/HMp4eYu3yrR77RKuV+HtsLKrjq2Qw+3F3MQ9NTWbl4PDFhcoGSEO4utJsfz80dxbNzRnKw5CRXPZfBP78p8qgJx6Tcz6KlzcrTnxxkzotb8LEo3l0ygQemp+DrI/9cQniSa0dFs+aBdAb1C+ahlbtY+s5OqutbTMeyC5kV8jQNzW38LbOQ5RvzOFrVwI1j+vPIrCGy0IYQHiwmrDvvLJ7AC+tz+P26bDYcLGXBhHjunBhP7x4BpuNdMGXqf0PS0tJ0Zmamkdc+U3VDC29uPcwrm/I5UdfMmLhe3H95MlMHyJumQniTrGPV/OGzHNbuKyHA18LcS2JZNCmR6J7dTEf7llJqh9Y6rdPtbCl3pdQM4DnAB3hJa/2/ZzweALwBjAFOAHO01gXne05XKPfCinre+uoIb249TG1TK5NTI7h3ShJjE8JQSqbrFcJb5ZTWsmxDLu9/cxSA2SOjuXNiPEOiQox3g93KXSnlAxwCrgCKgO3APK31vtO2uRcYrrVeopSaC1yntZ5zvuc1Ue5V9c1syT3BppxyNueUU3CiHouCmcP6cc+UJIZEhTo1jxDCtR2tauCljDze3naExhYr4T0CuCy5N5cmh3NZcjhRBkb09iz3CcAjWusrO+7/HEBr/dvTtlnbsc0WpZQvUAJE6PM8uaPKvbGljZLqRkpqGjle00hJdSPF1Y3sOFzJ3mPVaA09AnwZnxjGxORwpg2MlCl6hRDnVVHXzGf7j7M5p5xNOSe+nWUyMTyIsQlh9O/VjciQQPqFdqNvaACRIYEOW9PB1nK35Z3CaKDwtPtFwLhzbaO1blVKVQO9gXLb4tpu/cFSHl+9nzarpqXNSptV02rV7fdbrZxsav3O1wT5+zA4KoQHp6VyWUpvhvfviZ+c+SKEsFFYkD83pcVwU1oMWmsOHa/99gjA2qwSKs9yhk03Px8C/Sz4WCz4WhS+Pgpfi8LHopg3NpaF6YkOzWxLuZ/tANOZI3JbtkEptRhYDBAbe2GTbQUH+jEgMhgfy///Q7X/o1nwsSgigtv/avYNCXT4X1AhhPdRSjGgbzAD+gZzV8c6rY0tbd8eKSjp+G/pySaaW60dg0/rt4PQVqsm3Aln4dhS7kVAzGn3+wPHzrFNUcdhmVCg4swn0lovB5ZD+2GZCwk8Jq4XY+J6XciXCiGEQwT6+RDXO4i43kGmo3zLlmMT24EUpVSCUsofmAusOmObVcDtHbdvBD4/3/F2IYQQjtXpyL3jGPr9wFraT4V8RWudpZR6DMjUWq8CXgb+opTKoX3EPteRoYUQQpyfTZdeaq3XAGvO+NzDp91uBG6ybzQhhBAXSk4ZEUIIDyTlLoQQHkjKXQghPJCUuxBCeCApdyGE8EDGpvxVSpUBhy/wy8NxwNQGLk722TvIPnuHi9nnOK11RGcbGSv3i6GUyrRl4hxPIvvsHWSfvYMz9lkOywghhAeSchdCCA/kruW+3HQAA2SfvYPss3dw+D675TF3IYQQ5+euI3chhBDn4dLlrpSaoZQ6qJTKUUr97CyPByilVnY8/pVSKt75Ke3Lhn3+D6XUPqXUbqXUZ0qpOBM57amzfT5tuxuVUlop5fZnVtiyz0qpmzu+11lKqb86O6O92fCzHauU+kIp9U3Hz/dMEzntRSn1ilKqVCm19xyPK6XU8x3/HruVUqPtGkBr7ZIftE8vnAskAv7ALmDwGdvcCyzruD0XWGk6txP2eSrQveP2Pd6wzx3bBQMbga1AmuncTvg+pwDfAL067vcxndsJ+7wcuKfj9mCgwHTui9znScBoYO85Hp8JfEz7Snbjga/s+fquPHIfC+RorfO01s3AO8DsM7aZDbzecfs9YJpS6mxL/rmLTvdZa/2F1rq+4+5W2lfGcme2fJ8BfgM8CTQ6M5yD2LLPi4A/aa0rAbTWpU7OaG+27LMGQjpuh/LdFd/citZ6I2dZke40s4E3dLutQE+lVD97vb4rl/vZFuaOPtc2WutW4NTC3O7Kln0+3V20/+V3Z53us1JqFBCjtf7ImcEcyJbvcyqQqpTarJTaqpSa4bR0jmHLPj8C3KaUKqJ9/YgfOieaMV39fe8SmxbrMMRuC3O7EZv3Ryl1G5AGTHZoIsc77z4rpSzA74E7nBXICWz5PvvSfmhmCu3/d5ahlBqqta5ycDZHsWWf5wGvaa2fVkpNoH11t6Faa6vj4xnh0P5y5ZF7Vxbm5nwLc7sRW/YZpdR04JfALK11k5OyOUpn+xwMDAXWK6UKaD82ucrN31S19Wf7A611i9Y6HzhIe9m7K1v2+S7gbwBa6y1AIO1zsHgqm37fL5Qrl7s3Lszd6T53HKJ4kfZid/fjsNDJPmutq7XW4VrreK11PO3vM8zSWmeaiWsXtvxsv0/7m+copcJpP0yT59SU9mXLPh8BpgEopQbRXu5lTk3pXKuABR1nzYwHqrXWxXZ7dtPvKHfybvNM4BDt77L/suNzj9H+yw3t3/x3gRxgG5BoOrMT9nkdcBzY2fGxynRmR+/zGduux83PlrHx+6yAZ4B9wB5grunMTtjnwcBm2s+k2Ql8z3Tmi9zft4FioIX2UfpdwBJgyWnf4z91/HvssffPtVyhKoQQHsiVD8sIIYS4QFLuQgjhgaTchRDCA0m5CyGEB5JyF0IIDyTlLoQQHkjKXQghPJCUuxBCeKD/A0407MSZhBYJAAAAAElFTkSuQmCC\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 1)\n", + "plt.plot(x, stats.beta(4, 4).pdf(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 162, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [p]\n", + "Sampling 4 chains: 100%|██████████| 14000/14000 [00:02<00:00, 6167.84draws/s]\n", + "The acceptance probability does not match the target. It is 0.8795086571448326, but should be close to 0.8. Try to increase the number of tuning steps.\n" + ] + } + ], + "source": [ + "coin_flips = [1, 1]\n", + "with pm.Model():\n", + " p = pm.Beta('p', 4, 4)\n", + " \n", + " likelihood = pm.Bernoulli('observed', p=p, observed=coin_flips)\n", + " \n", + " trace = pm.sample(draws=3000)" + ] + }, + { + "cell_type": "code", + "execution_count": 163, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "data": { + "text/plain": [ + "array([[,\n", + " ]],\n", + " dtype=object)" + ] + }, + "execution_count": 163, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "pm.traceplot(trace)" + ] + }, + { + "cell_type": "markdown", + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "source": [ + "## Who will be elected?\n", + "\n", + "There will be a new referendum about a possible 'Dexit'.\n", + "\n", + "People have to vote $1$ for staying and $0$ for leaving.\n", + "\n", + "Maurice de Hond has done a survey and gives a probability of \n", + "\n", + "\\begin{align}\n", + "f(x)= \n", + "\\begin{cases}\n", + " 0.2,& \\text{staying } \\\\\n", + " 0.8, & \\text{leaving}\n", + "\\end{cases}\n", + "\\end{align}\n", + "\n", + "Meanwhile the first votes are coming in. What is the probability of a 'Dexit' occurring?" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "array([1, 1, 1, 1, 1, 1, 1, 0, 0, 1])" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + } + ], + "source": [ + "votes = np.load('data/votes.npy')\n", + "votes[:10]" + ] + }, + { + "cell_type": "code", + "execution_count": 3, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "data": { + "text/plain": [ + "[]" + ] + }, + "execution_count": 3, + "metadata": {}, + "output_type": "execute_result" + }, + { + "data": { + "image/png": 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\n", 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" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "x = np.linspace(0, 1)\n", + "plt.plot(x, stats.beta(1.3, 3).pdf(x))" + ] + }, + { + "cell_type": "code", + "execution_count": 4, + "metadata": { + "slideshow": { + "slide_type": "slide" + } + }, + "outputs": [ + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [p]\n", + "Sampling 4 chains: 100%|██████████| 42000/42000 [00:06<00:00, 6487.09draws/s]\n", + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of data points: 2\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [p]\n", + "Sampling 4 chains: 100%|██████████| 42000/42000 [00:06<00:00, 6164.67draws/s]\n", + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of data points: 10\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [p]\n", + "Sampling 4 chains: 100%|██████████| 42000/42000 [00:06<00:00, 6377.00draws/s]\n", + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of data points: 50\n" + ] + }, + { + "data": { + "image/png": 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\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + }, + { + "name": "stderr", + "output_type": "stream", + "text": [ + "Auto-assigning NUTS sampler...\n", + "Initializing NUTS using jitter+adapt_diag...\n", + "Multiprocess sampling (4 chains in 4 jobs)\n", + "NUTS: [p]\n", + "Sampling 4 chains: 100%|██████████| 42000/42000 [00:07<00:00, 5921.57draws/s]\n", + "/opt/miniconda3/lib/python3.7/site-packages/matplotlib/axes/_base.py:3455: MatplotlibDeprecationWarning: \n", + "The `ymin` argument was deprecated in Matplotlib 3.0 and will be removed in 3.2. Use `bottom` instead.\n", + " alternative='`bottom`', obj_type='argument')\n" + ] + }, + { + "name": "stdout", + "output_type": "stream", + "text": [ + "Number of data points: -1\n" + ] + }, + { + "data": { + "image/png": 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3xLs9B7eAI+LqnpAxWlrIGF70J6KZ48P9RhqaH4HwVGf8iMht1+d6TsxQxHP03K71tDb9DVIDuc8dTyUbTE50jrKWQ1s4TWdkht8dPTH2UOKOpYYNJvUiolECJJg9vRNefbo5DD2bMJ/5C9mdhSYdBHKpTUZzMzsONLN709oZPmsi0jSxdzzojayP0vkMtD4OQ/u8pkSTUxdHHe3R45ZzoCszuTS/vm1j+0Oa3jF3olF6kj1o1qEc1PExe8NMc2B4N5sHN7Ohb8PECNRYV7uZv1/q0cco2zp9BsTTzWEODhaZSugY3r7o945F02CStfuHpl3c55gEWx+GgWmO3WFi585ffyo+JRVTSkl7oh3HdQqtOgUp5cSoVjr3PYb2jUWaxhAC9DjRXQ8SNOMT3nqs6zHWdq0dF8dauODnGbZDMjuLKbCpIa9hSCFBB8QzJvfu7GPHNFFJy3GJaN4+bB1O0zQ0hOW6E9I1U2aKvSN76c7sJ+N44s5wpu73fOG5vnc963rXYbs2+xPPkba8/eW2b4GhPVgj3nPtkXuwozEy27eP2Rvt7MWORGjoe5yFw+uPZK8cMUpgKRTPBylJ/fwzdH/he7hlgj+8+7OcdN1FvH/t2/jV3l9xxaoruO+f7+OrL/sqi6tKOy+VEIIl730vq+/8A9lAI2/7cxk3PpviyZ4nee+9b2U4M1xS+xSKw8CWUiZmXuwEoWez56APTXRqTVcfd176dxDs3UjMHCJjjzvcctRJy0RwdX3W6yKCupeC2BttJul4ERopOXRaVO494xAiaaZUnh3dMVK6NSFF0nbcceE1TRvstGFDIie6BvfMEE3KbTcv0ialLJyiOHwAhg/guBJt61Z2b93EQCZKSrfGIzK2Pp6yV2BEvlgMyyGle1GGPSN7eLb/GXSniEGy1rXQvwPHdYgbE536YiOcMndkCkUURollzKlRxgKpcK4raR1OY9gOWac4oSBkLrqSGjz0gvmYGs7+fWRTWQYnpQLaeXaNpmJKx0FvbqYn2c2ByAFa461jyxyMHswJ06n7yzh4kPS6dbhagWMxchBrYABtw3gNFHoC3bQpN4pL43U1DSc1LlzXHQyz7mAB8WWkxsW4lAxqU/dVwbb+bu48neZY9MW9fdcdzYyl/I6tahjsvedhuvvjGLaD7bqUGVFEz+bx7Qkx9ntlu+NRskTGYlPvfhKGZ/Om7dt5ZNNEkee6LkkzienqJHq34iSTMNIKZmbioXBM7BFvfz7VHKbr9z9Ce/iviMOoyZstVBdBheJIsXSSN72Hvjv3YdSVcft7P0ts1RP87bmtnNlwJj/4px9wzoJzSm3lFKrOO5ezH7qfbR/8OCc9vYOfRB0+84Yu3vO3N/GzN9zOqfPVvFmKY569Qoh3A34hxKnAJ4ENM6xzXJI0kxSaNtWVDvsTz7E6ejKnAVhZ/Ol+ujO9JCzBK0Iv8xaUkFi/m+DyFNbeOL7qKq8d+OSIyRHimgkSRgInz4HR3ElNGaRDwPZqp6RpEhyKAoEpHy2lxNm+FX+okYJfOkdFfz/pHa08ccmrALh4TQNL6ip4tGkIy7K4slqnfHLUQUp82QxuZRWOdNFdi1RmiOBzTyGq51Nx7rmH/qKJPqhbxsb2KMMpHVEtqd7ZjG/VGlgKDO1lKKmzsb+Gpfu7yTgG0ZZ9mPGd+Fp2457VxcV1J9E4On/XaLpbzhk3XZsDyTArR794vAu33EUkUzCpI/XGtghiKMV5i+eNvXYwuZlz5v0TG9sjnL28njVAxjGpkHLMlRaWJ4okElwLXBfHlYdsGpG3A6e84kukKdptTeTV+kgJQhDPWCQNi650EivQxKVVK2bcjHAlxv4OQmeeUrQDm33wlzg9PYQDdZhn1/CGk13caCd7sg1EO6JYroFmJfBLl6gepaongtHcgp2thZqJ6Yaj9YUSiUCgWRq2a1NXXocdiSD1OA9vb8eqaeBq4RIY7e5nG2ORFas/F5UUPpBM6/zbrg3SHfueqSfXga1Tl5uXWLccKLRu8yPe/5e8lbZ4G82xZs5fdD6FhngjaROzzqUs4GP0GDvSJaXHqQ/VM5jQ8QlYWOu1vfdpaYRlwqStWT09WPEk1ZlIbgBFEDLCUA7J9CD1TJ2XbJTn2iO0pXcQMTu4cvUbCAxsoxGAidfk6MBMfVsX6eAzVFYW2Fj/Dljx0rwXXC/9dMHqaT9/rlARLIXiSMhESX7ltfTduY9YXQ23fPgdrK+6mebYQb5yyVf449V/PCbF1SiBhgYu/vPv0K7+F+bvhe/9uYJAKsm/3/92trQ9VGrzFIqZ+ARwFmAAfwSSwPUltWgO6Eh0sL53PSORME52chqN51gNZ6emU/kHd5D5x28nvGaNeGk97mgKU/uTsPduwOvc98MNd/FE18RCcVe66LZO00jThDSeoUR2zCncoXfxbN+zYyPivrROJquRMMdH2udFd1M18AiPNx1A376Tij1N1EXbxj8oNQAjrexrH6a7pZvQgb2IaSJLlZE4VV1dCGdcQEXS3gi5P93P8u13YOzbhdk/cWS/rK+bqh2b8KVTPBLbx4HMIH1GHGvPU2O1WNJxcLPZiaLTtvHvOIC961GwTYZTOo60aR9JE+uP4T8wXp/VE/Nqm0ajS/5YhvLOVgw7Da7LkJnEzRpjjuIT657kqT/cg2k77Ij0sHawjXg2F2ExUmi7Wig72DJlH2Qtb9/09x6gYst+cF2EtAlYaWzXYnffMCNGnHWJgzSnOj1BkxhPldRMHbd3GwzsZO3uXra1DiNmavWeszngjEeA/PGZ0wCFZWL19QGSmJ3hwegeMlYG1zSxH13Lsm0HELloSNqZvltiTI/hSAdh6DiJNNmDXd4bduF1LMclnPLeMwe8iIYYjTwO7SW6fz2DPa3otkN/to1U63oGM21s6niG1Gj0J5sEI0lXoovtQ9sn7Q5JOj3AUxtu4tmepwDQtDA7Oh5DhjcD0DJUOHXTaB2NiAkk0Ne5iQODXhpq1h7fv4/2rmNt7NC1bjWbvGYXfak+kmYSKSXDySxbu6K4rhzbnlfX5ZIYGSFlpJCRGFb/ftpbmtjaObGe65HhbWzo30AkG2FTR4TnWsNkd+8G06Bq52Yq9xVIz8y7ZhzpRZNHaUl0oJkZ3BmUvO1KHtg93vkymUripJIEe6ZJGc19phVJkFi/+5DbRjv6rd1VBEuhOFxiXSS+8Wb6H9bpnzePH39oJR3iT1y6+FK+/rKvs6hqUaktLAoRCHDh97/DrlWrmffzH/Ffv6/l1rcl+egzn+XmTJiXv+TfS22iQlEQKWUG+K/c3wnLaMpMencrwWAVvGjciREI/LpJ5eZ9sGiG6EshcjU+ma1/Yrd1MilDJ5yZmNa1b2Qfj7c1kcxaXLxqkFOqL2YpkBpqp1YEkPNqMeXEgviyPf0kMmkSL9GotSyk4xAyImy2ukkOP8eF2Rp82hBlxjxc06Ji+0H0+gj46mjPnEc1UJntp2o4BmUu7kAUasFwLPzpIea391EmyyBQD1ISiI6AyJLYsZ5KMvgGRqBmKbYjsaTD6GxJ/pS3LwPxKJQXFhPZ7dvRB/vx/9Pl7OlLcMayekTGi/oYfWEC0sWRNnvjnlOb1K1Dto4XOVESNHM1K1mT1J59hJbVUX461HVvxTc4QKrmMjTLwmcGMJs2UnXKZTjSxTVtoAzwohWm43rPXBfNTjCSiePTEwS6ItSnLRq0LI9V1xDM6PhrU/iAtlQvtD3K6dkUZtcQAT3FNivConSWBTUhePKvLLIjVMyvoM1fwZnTZTBoYQadOL3D93OyzM1Jpg1DzdRFq9JdaNWrAAg1N5EZklSfexK9hrcfIskuFht1Y/uoIqLBgsJzQGmmxvefvYcV8ypw7XqW5GIbSOnVDI120wO68lrCb++OUeur4fUvXpxbXIIPLNfg6e2t1GzfSePyARJVp+fscJi/6wEqg5VY5zV4583ATjBMWPFSBns2gDs+p1pfuo/I0B5YsoBMOs7OnjjVuY54mhWmnEnzk01pHJE7b1wXX3cnC8NRMgv/SnLZxP3vIpkuYdZwMvjsJI5by3BmmN6BTbx0R4TBA3vgxadg5aU/6rbN7v19dOzfTEVWcka6gsqRg1hLs6QNG83SqMrfuO2QiY8gzCDVW57FXNUAZeNppQOxLpbPX0HQPz4fmcxFwMJJgxUVIEZjOK7Fns5eao0Qqyt0yipjlJmVOHX13vdwvTS/Ay0tnL54fL675qf+xMmRNGVOBmtpY8F9MBoNnfQiuC7+PLHKgU6yZ63CcHRGr6m5RgksheJwGNhF6sa30f+Yj8759fzPdWAEO/naRV/j2lOvndUJPY8W53zyQ+xfuYLKL3+Rj/2uijvfmuXj3MSPtAivvOTTpTZPoZiCEOJJCuQsSSkvL4E5c06hcd8yM0rdcB+OMzEVLqhlEY6L68qJKSpCoNsOu3ojnJcyWJB7uWkwyTx2QFUlBweSOPIB/MsvgNolDKS6SWtp8JWzo3eQSEUnlxsm5XoYzZ2P6eYc2kgbUIbI1RvZpsPeviTp5+6gf6SH2mUrAahKtkPUc8gCWYuavjA+I0PASpNqHK/pKcs54nrTEIOpGMGTyxDdcfRTNIJWmgrbIuQLoQ/1E2o7iKwpQ6/1E2wfj4ptTbaB1s8p1inYroUjHQJAeVcb/szE+aFSZopn2x/kpLY+hjJDNDcZnGw7BeefytopGg92YtXkUp5sA/b9nUEjwbAzsSxQGA5+0lRmB8iwAHK1WHZCI54JE3aSLAJwbQzbJBSXhJMuTlqjzWjmJMsB5oPrsrc/Qa+R5aTVUNm0ix5zgFoqvG6D1COQDDtxyjMmC/cOUlauYZ/npRC2JVo5vWwRZm+Yci3G/FgvZqPX8r4qFw2LZUziGY1T501NOTN7etA7eui0vTrdrmSn94ZjU7mzD3te3kTLLY9RH++gPr6XvuVXIyyTnYO7CXYMUSNyrfozUaTPE1hlZgqJD9uRDCazgDfJcVwzEMCg7kUXe+M69aEUjJ25TBBXTtaYUOeVyZrUVrhTSr80O8FQeoRK6WLHYwR9vQjpELA1yuM61Fg4hoHpGJ600S0Cra1YZSMw0oKorkaSiww5JtGMSY+hUTHcyskZHduRE+RQ1rKpCAYAr3Yv6PcRH45iuX4akn1QUQkSyvQY4UyK8t4tUDcffIUnUs7nQHITK4xeYDlSCLAdkuEhHMuGVO7adFxCO1voWt3IvFykMDmUgJAPX9YTfYOZfp7oGuAM32KW5M7R8mcextbWUe33Bm8GE1n2yyTldpwyXwX7Dz5D5NSzuHDxhRNsEox3chwj2U9NSuKkO7DOeinB3mEaow7hc1+MZQbozRyk3IxQmemlJjV+DZvSpmugBxbOBzPN3p5nJmy2P5ElGtFYM7+KqK1R7S/HMiG+dz115yxk8eDESNsuq5OBvnW8vfaaGfftbFCUwBJCvFhKuXeujVEojmla15K+5X30rq2iq6GKr/1bmpWLzuD7r/4+q2pXldq658WZ//wGOpYsof9jH+P9fzSp+mfJp/gV39OGueKK/ym1eQrFZD6T9zgEXAscpVktS0fV5m7M5XXQAA3DG6nM9CKyPgbS/SySDobpsLipnTIZJUyARYATH3f6w6k4fdpBxEA7r8WLivi6BxGROFx2Pn5HxzUz+LueJdlbRSDxBPVBQbThXGxXkrRGyGRdQHLA6kW3KgkFfJAZQTrzqNw9QBJvlD+RNWnt7ySimZy1DHyWA0EDcjGl+q4odn091FdQ1pvgmaUtkKsbkz4f4JLNWOiWn0AuMmGNxCk3YuCvQ7g2wvAEUFjrIWrrBPIiBqa0wXF5onMfHQuDLNR6OY3Ck7inzCRQy1DGS0WSSK+Vuz48ZbC7LbmDU8LdBPtTaFUrsbUYuDYbeg/Q70hWMF4r4rgufunmCeTxR1uHdzDgRFhECNG/Db+TRUhv30SzWQhCzNaA+VPsdaST15lt4tZXbd+CI2qw/H40wyZg2wz1D7IvWM6S3HKhdJLMpIBAPOM527bjkr73t9C4EuP8czi4/Ze8qLMOJzmMb56DG/RPWE+YDsH8VLi8zo8+PY1fS0OmE2tjJyJUC2fX562bIGglMalnOKVThkGj3xNYeza1dsZ9AAAgAElEQVQ+SkV2gJqXv2ps+WBao3xw3AHXLYekbrGgMkh620F8toAVIXTLYenGJ1ieuRe/uGRs+ar4EKHkApJumg57CMMOsVIuo0rz6sNEuVfU09W9G1tLsaTapbJ1AGocZINFpFYDqr1mEOEDOLbt7bcql4q2/eihDPHMxAYR+/qTXLiqAS06wP62bqzyenyOQXnHQRqqgbwBko1aG69wl2EHNKiqm9ZBD1spqv2ewA/YGWTPZiIO1O9soTeepRzwt3bjRCKY0Tg9bUPMSx9gtGKvPBKGsiGQUN4fIzwvTNROkzIGOC2dRC6EQDwLwRBlRgyzfB598SxDZb3UZIY43XSJuOeSMLx045G0QTx3jfrtLNXpTkTolInnCTBgh3GGdxG1Q5iuRd32rcjBebBs6VjKsS+v+cV2s50l2UFqnXkw3ISeMiiXJ4+9H82lBkugx4jhF4KqrHd+mc27vehjCSk2gvULIUQZ8FvgD1LK+AzLKxQnFnvuIvvr/6T7iQYGaoJ8890GV73krXzh4i8QCkxfvHk8seal5xL665/Z+2/v5z1/66fijUE+w/3c8pjDZa+9qdTmKRRjSCm3TXrpWSHEUyUx5ihT1puAF+eeCIFwLYYyQ2h6GBlbBBKCGRM3NOp4jzvg2cGtVGVGSGrDpNu7SS9s9MQVUGYmcH0BbOkQxEc6laasN0ZVZZDAcAd+V1Lrj9FdtZB6piJ1z5nx5dXERDTvNZHSWNA0SHxVA5KqgnX5+biGgZ61pyRGBUfSZCd9J+Fa2PF9+MtAyvEJ2/3xLCnDxi3zlnWlm2sIMHGrqaxFIjQxfWvZow/gc6oYSGgEV57qSRwhMNrbWbGtiYA9morm0hc3SfSOULFvkPLFtV7KYt73byx3EUBXJMOqUDk4DnZcp/zgeNOH0QH/6sEkBEL4bJ3uWAYnbZASvdj2uMvVMaJRlSncct+f0PBbDm7QIZF1iKYMMo5GhaWTZdyRr8z0kck1KfC5Fm5+tMSxGenZw+5djyH8F+K3MxjxOJruUpeMETulEYwkpMNQuwjDdgj4fSAlwykDayCOiKeQtdX49End9ByHRNbi2bYwr17UiD+aq0US4Eo54dBUZL12/yNxL+0uFEvS0DWETyxjwEqwxKqifTCF5boYQxpt6R58RhWsWIbpSMrTw+CrmPDx5UaM1dufhcB4MlyfNTjmCGdcg6BRQUUmA7FO7GCukYOlo2Ucno61UpmNQqB8SmOQUGYAkfGOqc+wCA72g5SIoQhyeR161qBa6yBWfh51iQOAC9XVxIcHEDj4nAxSuti7OohpksjJqzjjJYtIxbMYCx3M0ZpGI8UDfQc8XVb3EgK2hm5VktE06LBo0MePs2sYxDQLV0r6tS6WVXn7w0kOIOcvQjguZUMxFui7aD5zvhdNAzojGguTOvg0an2dmOXjzVTKzARQQzw2gh5pZbu2hO3JKAvDOouA8lw6bH18L8HFQaB8YofKdJi4HG+QEUhmmDjuMXHHuhJ6Y1lqLR+NB8MslP7x4zrpByI/cpZt6cYfLjBJ81GcCasogSWlvCzXqen9wFYhxGbgN1LKx6ZbRwixAvgdXqsRF7hVSvljIUQD8Ge8OUs6gbdLKQ9vhjeF4miy/XcYd36a1icXEQ8JbvxXP5+/8ltcc/LRCTMfTZactIKyu//Ic+96P2+9r5VyvYxPy39w62N+znutimQpjg1y95FRfMAFTG5rdYKQNix6YhpuZQDbzetKlkNKCa5D++AIqxYYBG3PIZ3iRlhZIlYMISXppnZa2ntZIMe3VZnpJV29mvv7DmAKk7MOGugBl+rBJNU0YVQsJFBewcRCDdBtb+Je2TOx1bTfyFKZ6SdbsYCmxAEqgTLNhCqITzN3T8PQBuxEE4P2CJV9MFpBMZ1LFDTj1Mf2EPZ7dSpBMwG+AAcGU/jtqa2ya6I7cIVAzxsTG0pn6SODTEUpM3WCZSGylk1QeNEwGfPEjR1L4TRPbTgB0L6nk7RhEzBtZMduJOPOnsSLprkS4s2dLK/yvMnAUBTp8zzEhD4u8AacGItGdsICQdo2cQJBWlM7WJWrdTOGWqi1M9iBSm8iWkunanc/nNRIqDeCDgSt0eYT460YI06Kk/CiagB+w8b1Cyozg6SrV4/taJnspl9LY9guVmyY+nLPTexLp/AFcilm0SHKfRJhGySyFn4hYO/dPOe8jJWbmsZSUwNLKunPtjLaGzDrWqR0i7js5OFdHVxiTkxvHXLiNPprEe54JHJo6xOwYBmhRBJcl5SMEU9HGbL9NCxqBN2kZ18rWsDGlZkpotx0XLKORZfh1RwK6U5IJUw7mQkDBglNI5btpsIxsIw4pmHjM6PE/ZVo8Sxnt+9mKKWjAQGfYNGuPjIXrSCkhxltlFfT3kUgdQBRlcA3MILRXe2luQF1sb2Q13txwIoRzE0t4EvogB+QzOvoRzYE8G3rYbPbTqrc4bTMEKHwAbQlo9EeGyEd73oSQLIPguM14JvvX0ey3DsXhOugkxvwQBLVDPBDUmYRQEU8BRULvdMgfxJjKTFdnTLf+EWTklncaBfU15Fte4zByir0TJYGN0TAzozVHgop8ScPPR3B5KkawtYIharxBhI6jeR1XEwP40ovDTqmjf+epNwsNb6KsYYarfYgZA0CbgUzT/4wuxRdgyWlbBFCfBnYCtwMnCe8gpMvSSn/VmAVG/h/UsrtQogaYJsQ4jHgvcDjUsobhRBfAL4AfP75fhGFYk7Y+HPsv3+JfU8vxRIuP76uge+/42ecveDsmdc9Tpm/uJGX33UHj7/nQ7z50V0E9CD/ecl9/Hqt4IzXfKfU5ikUANtgrPrbBjqA/yipRXNEImUwT9okdYuoZbKwJkTaMYg4KYIZE+E6Y6O0Xb1NlBsJrx4DoGcT+HM5braeN5ibi+rYUydQHTbGhUn+iHDATCLLx5cLZC1CZNDnVRIY0ehNTuxE1rjpaSKuSZmZJCs9VyOgW6QCGSbjuC6m4zKkt+HqnTi+MqrjLnow56ondfD50PRxx9vRhxhsv5+YnaJCBCgnQK8TQThQbS6gHMcr8s/zqTptLwVwYSiEIyU+IRhxUyBtBlt3Ivv7qF1+xsS6edc7zaSUkBkdCx6dbNmzR8uONwcZ0JpZ4zt1rH6rN9tKhZshFA9iS8/Z9wuBlIXdL0NahO0UFbGJ7+8wvW6FZWaUkD7siSLD+1yRcybtyU3TpaQy04tE0GINcGrW50UVg34aD0zszOZzTYKWhha1Gch6KX9lUY2q/hSicjEZd9xRzpoWupRjwsSRkvSuVgKrTyflZhEIqn0hRO9T+IWLE3Jzc4mZmLZLpdOHZtcSzXXGrBpIoi2sJptJkRrooLFsEwD+pnbKtCFWVkYIMkwwaxILLaXSlV7EC0jaGhEnSsiXazPuShpawiCDQAUH+uOITGKib503Z5hvUmax39HxOzo2oA+lxuZ78udqk/Q8QTA6P1p5KouLS37yZGWmF1/U62TZ1BtneaM3JuSb1BQmf/Cgqm0EahblWrfb+Lq8ypyWeAuLWUXWymI7eWm28b34Hd2zcRpv3k2mCenDlEkHrWq8lEG3HZiY7Ykp8wY+pMSQNhGZZiDbzvLgYmqMNoR0yUoTEbao6Yzi96dYWRbE8ZfTE/AR0tJj61f0RKhwHKzqcnqdiQ10/I5ORXaQlByV394B6jZ7WMM8LJn32yShPKkjgXI9jJ8RUgNZWODlubZrUYJVXlqy6ehIJJuH4izwe3V+g9kUi90QR1tgFdWmXQhxthDih8B+4HLgTVLKM3OPf1hoHSnlgJRye+5xKrfuMuDNwO25xW4H/vl5fQOFYq7Y8BOcB77Ic88uw5d1+d371vCT9911QourURrm1/Kav/yaraddwtVPW7zlWR8f7rqHzqdvLLVpCgVSyjVSypNy/0+VUr5OSrm+mHWFEK8XQhwUQrTmBvkmv/9DIcTO3F+zECKe9951QoiW3N91s/mdprGVsniauDsxGvN0opk2a5BQfGLrYT3nIAkp6TNixCyNvmiM9pE07SNpMpMiBhYOWp7jXJ5Ks2hXH37dyqvxmYib1dBcnapwmrruGH7DJpkxxzqWjTqMw/ZoRGvchSxLG/Ro4yl0PkeHeDcRzaQ3liUrPYfb7+barufsHU01HBV8tnTpcyKUa97ofNaysVwXFxcHF2mOYNpubsLjAt9BSiJpg3BK9zoR2uOiL5Un4izHxcw54E3hGAdad0yoEanIDqK7OgPOeBJOldZV8ENr+7zapJSr05QZAPvQbaPLUuOplv7cRK2VwykW7erLs9VrvQ1Q1xUlbUx0Yhft7kfYbq4ZOCRyNSn+SZPEBiyNykw/QStBWNNxc0ItGMtiOi7tI+kJ4m00QkGe2HBSGeo3PsqQE2fQiZF2dUAScLJENJNE1iKpmyza3Q+upDyVod8ZF+X+rEV9R4SRoU52jWxgxIiBYZLBoErroUyb2HAk5WQQSY30fm/ybd1yybgmvoxBMGOSyF0zYiROvzHNnOQCAub4+S+mts0Ze1QRy1A9mCRZIPq6oK0TXVoMWuOfY2d6GM5L7TSsideTlJKu7MRBiZRu05tr9R+ws2S7vPPKdlwy2QzRbJghc9IEzkUQsDMEJ9k94kxtsT9o9BN2EjTu98R3wtWIuZ5gqko2I6SLzzXRpTl2PMJuEpD4HQPhmmPnVkrqCN30rrW8KNboxOBBy/sefif3nuvisxxWbNnF9sgetpnjtXYBJ0MokcV1XfyugXAyhNPG2CjIqI2G7dU7DjsJkjJLm+1NsJw27LF5+o5egmDxEayfALfhRavGfhWklP25qNYhEUKsBs4DNgGLpJQDufUHhBALp1nnQ8CHAFauXFmkmQrFLLHp/zAf/i8e3bqCNSMOD3zgHL770V9TGSw0s92JybzaSt5458+4798+ztXPbgDp50Pydn5X2cjiCz9QavMUL0CEEG851PvTZFPkr+8Hfgq8FugFtggh7pNSjk02I6X8dN7yn8C7d42mJX4NuBDvPr0tt+7cpbi7Ep8zNeIT0UysAnPK5AuumKvRaThEMibVvhC2dMZG/bOO55DsSvThODFOEouo7xpG+jzxU54yaLcTVPunugix8C5knqAQjks6oSM1k4qgf8wuOcGVKezWlGcGodKLsFUPJLH9PkaDZALw2Q6Wz8ntivFtjDpU+ejmuAPrt5I4udqrQmPWiezEKELQTuHP+e8p3aY6Z7FhuxiORp0b8kSUA5PvAPmCqzATxUw2J5bQwohp7ieTj211yote1QyMO9cBO0NWT4ylUU5XCVwzkCS5wos1tenDBZfx500M3eOMC+BgQkd3JfGx1yaeD7Jn4qnfYbSPHb9BZ+ploedERlnGpCI2UTA1HBweiwjNbw6TcodYFFwyLuYYjxgBuJaJGBzBmBQREtmpnR91y8WVhdNSK0fGzyUxqeWgPkkUVQ0VnvcraCWw/PVj859J6TLget9/Id50ApE8gWhKm247TFnKN6XDuCNB4OB3jLEBhYpkkljrZhbEvIhYXZcnzKzctWNL10tRnBQzsaWNcLzIj5jyeyELPm2zh1hUcE40UfBaGh3UqcgOEDDz44GSgGETMxi7xiF37VV728tn6c52yg1vUGZe2wjx1fMxar2zKaQPgw5UTW2v7hYpnDrsIcrSjQT7WuDMGRaeJYoVWFcBWSm9mJ0QwgeEpJQZKeXvD7WiEKIauBu4XkqZLLaNtZTyVuBWgAsvvPBoik7FC50tv0J76PPctX8lF3fa7Pz3S/nsDbfiEy+8ebnn1VRwzR0/5d5//yRXb3gG4fj4kPwev69aSN2ZJ14NmuKY502HeE8ChxRYwMVAq5SyHUAI8Se8rIrpZvN8F56oArgSeExKGc2t+xjweryJjueGSDNlMa8RwGhnunjGJJExx0ZvU7qNoxWebDWZNXFxSboTRZpwdG+U1/RRhbfjKvLmECrLRYzsPIfTS53K4hrhCc6M33SoCntOataamnIYtNIEx4MuYxGX0e80Kpyqhgs7r6NiaqRAy/R8nDxbY26a6rEUPImwx9MowYtM5SPMBI0Hpq8VGSggFkbxO4eORI1Gn0bJF551PTEILsGWE/db/iStAVsj4GSR/on3n9A0Ymkygbz6riNxpA41Oexkoepzpx7/QngT/o77gpbjThAak4XOxM+YXtD6HBdf76RJaXPbMu2p2yyfVB80VYQUT9xNj+1fO29Px12N8hGTspWLxzLyRkWh5boFRUvFpMnDQ/Esdl53wtGBlNH//a4nTFxcWq0BVvgbKfcF6dMOUq11ja3XbYepK/B5jrSB4FikczrKE8VP1jvkTBM1xDunxQydbuo7Ixi1E4cNvEj2+B6LOiniubTf2DS/gfnMaxuhejgLr5lx0VmhWIG1Fs+kUalfCTwKvPxQKwkhgnji6s68kcUhIcSSXPRqCVDcr4RCcTTY+UciD32G3/Qs5+o9Nv1vvpR3femXpbaqpMyrDnHN7Tdz93XXc9Wmp8D18Sn3c9xatZCylZfMvAGFYpaQUr7veW5iGdCT97wXeGmhBYUQq4A1wBOHWHdK3+/ZzL4YifST1G3qYSzdxXRcFu3uJ3rKgrHndmKo4M18cgH5KAs7d5OUDlXhwp876khNGcHXukhMqvOZ3iktPJia38baduWMwqlYzEmiKZ2rmZFCUBmbPq0qKSc6jV4kACx5hF3/haBHOzBWqF9mTiPOcrvNdG26nWkORI6FeweOzBa8jpIzcSjRkr9fp6bQjdOcHCFoTe9Uz8SUZm/TkC8sD1i9TJ4tSpPjosmSNsI8Oq26LZy8M378y4zkao9OSkyNukpZvOitbw5PiATlY08SK8NughVi/tR6rzwV68rxVhsZJ0V9T4pIXaH+oFCd7sTxzyv4HnipsofD6DWWb0zAmjrAMlkAA2MiUHdNIkPdY6LVLlYcH8VwTbECKySlHDs7pJRpIcQhc6VyDTB+BeyXUv4g7637gOuAG3P/7z08kxWKOaL5Ubr/8Ul+Gl/Ge591SL3qQi7/n1tLbdUxQUNNiGt++0Pufu8NXLVlHS4+vizfx43vfARfvUrhVRx9hBBXA2eRlx0lpfzGTKsVeG26W+47gbtGMzeKXXc2sy+sQ2SfNbSOOymBGaIok5kcMTGLFBMJd2q6oijWMy4RPsfbicVGJwK57oOZXD1Y0Z5/HkG7cDSuEDOJq6PBTFG4seVMm8rwVKEA0KnNfqZsfg3TZHzSwje1UeQEuuwwWTNDxaEXO0wEhX8yxl8fO3fy8HV4YVzDNadcf/k4kxuV5LAdl3BKL0ofGNIiLQ0qM4c+JqPd98qMOGVWnKrNgmxDYde+UMrnFKa5VmYS+bUD4bG6y2LpdSKg+2decApH7/eq2JwnTQhx/ugTIcQFjHdQnY5LgX8DLs8rGL4KT1i9VgjRgpcHr6rmFaWndyt77nk/3zAW8q8PO5jnnMmFt/wK4XvhpQVOx6LaCt70y++x9oxX8cYtkpotgpvvegsYhW+4CsVcIYT4BfAO4BN4ns3bgFWHXMmjF8a6RgMsB/qnWfadTEz/O5x1ZwVhO9R3RmZe8HnS5xz5Z1SOFPZyA/ax8bsQMsIEdINQagZvfBoKjaLPxHRRq6RuMqSnsVz3SHTbMUFN/5FHqcYprlRkcnTxSKiIFn/cR9vmHwkzpbyFc5GsHidCxJ1egIcPkVp3OKdMIUE0ndApszwhK6SkMnJk1wkcRhQpHwlVyaOXyCacozcffbERrOuBvwohRm8mS/BubtOS6+g03dl6RZGfq1DMPSMtbPzzO7hJ1PFff5f4Vq7kRbf9Fl9Z4XD8C5kVDVVc9X838ej7P8Vbn93IHWVZ/lLxVt7+rgdBiVHF0ePlUsqzhRC7pZRfF0J8n5nrrwC2AKcKIdYAfXgi6t2TFxJCnA7MA57Le/kR4DtCiNFcmdcBX3w+X2ImAtHiIyGlIr/GZzaxD1GHc7iUpzOII035Owx8pnPI0XrdcqekXR4NhO2ycN/hpxnOnQYcnWHh2OL51GDNRMLVJqQvloKqaaKPpUQgi64nnMzkbpjFII+1CJaUcgtwBvBR4GPAmVLKbXNpmEJxVMjGWPvHa/lyIMT/+wtU1DZw2q9/g7+2duZ1X6CcvKiWV9/6AzasPJd/fdJl86ZunvrHR0ptluKFxejQdkYIsRSw8OqlDomU0gY+jieW9gN/kVLuE0J8QwiR37XlXcCfpByPM+SaW3wTT6RtAb4x2vBizjhewxyzwOSaqudD0M5QpfXO2vam4/mM/s8l81tKn4aYT33n3F42c8nzcdAPlRr4QiVoxglqR6dO7mhT9ETDwEXA6tw65wkhkFL+bk6sUiiOBq7D3//0Vm4KOvz3HT7muWWc9MtfEly6tNSWHfOcuWwemZ//mM0f/DD/8egBbg2sp7Hhe5x16WdKbZrihcEDQoh64LvAdrwh8duKWVFK+SDw4KTXvjrp+X9Ps+6vgV8fgb2KEhI6zCL8Ew1/wbbbRfDC1feKo4RP2t7w2FFCP4Ko15FS7ETDvwe+B1yGJ7QuwpsLRKE4brnznn/nG84gn7vbz/KYZOUtNxM644xSm3XccMHJC1n2gx+zc+EaPvCQ5Jf3/Yq+gw+U2izFCwAp5TellHEp5d14tVdnTBZJCsUYx1422nFB5kiFmUJxjDJdZ9W5oNiiiQuBS6WUH5NSfiL398m5NEyhmEtue+R6/je1i8/e5+f0Hotl3/k21ZdeWmqzjjtec+5K/N/+Ec3zl/D+++HHv/scifD+UpulOMERQuwSQnxJCHGylNKQUs5G5f2xR5HzCikOTdkstYJXzB6+w+wap1AcbxQrsPYCi+fSEIXiaCCl5MdPfZmbBx/n/z0C5zZbLLjhBure/OZSm3bc8vZXnMbAF35Ab/083nOv5Ps/ewdmdvr2ugrFLHANYAN/EUJsEUJ8Rghxws0X4ConVHGCEiww75FCcSJRrMBqBJqEEI8IIe4b/ZtLwxSK2UZKyXc3fJNfdt7LDc9YXLzDYd673838D36g1KYd93z06nPY9vHvE6uq4M13W/zoJ1cjZ7ELmEKRj5SyS0p5k5TyArwugGcDHSU2a9aZqfWzQqFQKI5Nim1y8d9zaYRCMddIKfnelpv4fetfuWF7lpc+W0bNa69g0X99CSFUgv7zRQjBF995CZ+P/y/X/voGXvnHKL9qeDsf+I+7Sm2a4gRFCLEaeDvelCEO8LlS2jMXBPtUJFihUCiOR4pt0/4U0AkEc4+34HVuUiiOeaSUfH/r9/nd/jv4xH6Ni9eGqDz3XJZ+97sI/5HMBK4ohN8n+NYHL+c3//I1AlJw6q37uPe+L5TaLMUJiBBiE968Vz7gbVLKi6WU3y+xWQqFQqFQAMV3EfwgcBfwf7mXlgF/nyujFIrZYlRc3d50Ox/qSHPpg5WEVq1i+c9+ii8UKrV5JxyhoJ+bPn0N/3flp6jLQsVN97Jh029KbZbixOM6KeX5UsobpZTtpTZGoVAoFIp8iq3B+k/gUiAJIKVsARbOlVEKxWwgpeQH237A7U23897eNFfcV0mwdh4rbr2VwLx5pTbvhKW+soyvfu7f+NWr3smSGIx86Sb2tz1TarMUJxBSygOltuFooKYhUigUiuOTYgWWIaUca2ckhAigfvsVxzBSSn60/Uf8dt9vefuAyRv/Xo7PV8HKX95G2fJlpTbvhGdFQyUf+eL13P2yV3JyP+z7xIcZiHaW2iyF4rhC04/iDJwKhUKhmDWKFVhPCSG+BFQIIV4L/BW4f+7MUiieH7ftuY1f7/01V0Z8vPteF9coZ+Wtt6qJhI8iZy2t44rPf4unLjqVs9olT33wGpL6iTldkUIxF6geggqFQnF8UqzA+gIQBvYAHwYeBL48V0YpFM+HO5ru4JYdt3BhooaP35PCTJax4ie3UHn++aU27QXHK05dwOLrf8bu8+o5Z5/F/R+9EsNWk34qnh9CiEohxFeEELflnp8qhHhjqe1SKBQKhQKK7yLoSilvk1K+TUr51txjlSKoOOa4p+Ue/nfL/3JyZhFfv7ef7Eg5S//3Jqpf+cpSm/aC5S3nLyf6H7+i/cUBzn8uwV8++yYc1ym1WYrjm98ABvCy3PNe4FulM0ehUCgUinGK7SLYIYRon/w318YpFIfDwx0P87UNX2OJtZKb721F66tg0Ze/TN0bry61aS94PnLFmex6x0/pO1Vy4UM9/Pnb70GN0SieBydLKW8CLAApZRZQE9opFAqF4pig2BTBC4GLcn+vAG4G7pgroxSKw+Wpnqf44jNfpEGu4mf3HUDrrKDxYx+i4T3vKbVpCryJiD9/7St49o1fZXCVwzl37uLun19farMUxy+mEKKCXLMlIcTJeBGtEwpDqiYXCoVCcTxSbIpgJO+vT0r5I+DyObZNoSiKLYNbuGHdDdT4VvDD+zuwmsuY97Y30fgJ5cAfS/h9gs+97x1sueI6Rpa6nP6TR3ngjyqrS3FEfA14GFghhLgTeBz4XGlNmn2katarUCgUxyWBYhYSQuR3B/DhRbRq5sQiheIw2Duyl48//nEqxEK+cl+Y0D6H2n+6kEVfvxEhVMbQsUZFmZ//z957h8t1lYf677f79H56b5LOUZdsyZJtScYCYxvsABdsEjrYQCA3AZyQ3F8SEi41kMRASAKBxHQIJIQL2Nhgg8GxHdx7k23ZsmzVo9PLlPX7Y++ZM3P6OSpHZb/PM8/s2W2+tWbvPd+3vrLe+fvX8L3hF+j5+S+o//g3uTmW5oKL373UovmcQiilbhKRe4DNuKGB/1spdXCJxTrm2GL6XiwfHx+fU5B5GVjAZ8uWc8CzwOuPuTQ+Pgtg15FdvPvn70ZTYd774wINDxwhelYbdV/4N0Sbb/Srz4kmGbK4+P2f4ddjb6b15ocI/9m13BqNcv65b1xq0XxOciYN9gG86L03iVgFVuIAACAASURBVEiTUuqeEy3T8SSgBRnL+1Mb+Pj4+JxqzMvAUkrtON6C+PgshD0De7jqxqsYzwpvvCHBuvseJtKTou6rP0R0fanF85mDplSQ1e/9Mruzr6Xq5r1of/RRbvunIFs3XL7Uovmc3Hx2lm2K0yx0XTQHfAPLx8fH55gwbiVO2HfNN0TwA7NtV0r97bERx8dnbg4MH+BdN76LvrFhLr6xk1fc/VvC7Q71X78eMc2lFs9nnqxqTHD47dcxmnsN4VsG6H3/n3HnV4JsWvHypRbN5yTlTBvsC2o2vUsthI+Pj89pwrgVPWHftZAqgu8B6r3Xu4Fu3DwsPxfL54TRN9bHVTddxb6hg2z9+Uqu/O3/EGqA+q//GAn6l+KpxrbuRg6/4d9QW3Uy/YqD7/0j7nr610stls9Jjog4IvIBEfkPEfmBiPyhiDhLLdexRhPfG+/j4+NzrNi3vPWEfdd8Daw0sF4p9UGl1AeBDUCDUuqvlFJ/dfzE8/GZYDg7zHt+/h6eObKbrb9Yy7vv/A3BmjwNX/0WWrJ+qcXzWSSXn9PDfZd+CbbkaX6pwLPvfQ/37fntUovlc3LzNaAH+DzwBdwBv68vqUTHAd03sHx8fHxOSeZrYDUB42Wfx4GW2Q4Qka+KyH4ReahsXVJEbhKRJ733ExcM6XNKM5Yf4w9u/gMeOvgw23++mvfe+RtCNWM0fv7v0JrWLbV4PkfJ21+5hesv+AJqU46eZ/M88P63c8/eu5ZaLJ+Tl2VKqXcopW7xXlcBXUstlM/pR14PLLUIPkvIweXVSy2CzynKfA2srwP/IyIfEZG/BO7EHUGcjX8DLpq07sPAL5RSnbjzlnx4AbL6nKFk81k+9MsPcedLd/Lym3q4+rd3Eq4foeFj16CtunSpxfM5BogIH/xfF/LNrZ8hvy7HWY/muP1Db+POvXcstWg+Jyf3isjm4gcR2QTctoTy+Jym5IyZI09HkqFFnbOgWYsV56Sivz6+1CIcd/KWzmDticvb8ZlKVE7NQY75TjT8MeBtQC9wBHibUurjcxxzK3B40urLgOu85esAv2SYz6xkC1k++KsP8cs9v+RVP+viHXfdS6RxhIY/uxpt63uWWjyfY4iha/zFWy7hi5v/L3TnuOCeHLf8+bv4zQu/WWrRfE4+NgH/LSLPisizwO3ANhF5UEQeWFrRTjwjgdqlFuGUYSQRXND+Mstcz0OZxRlYY3ay4rNjaoTt+c2aY8hUtU2fx5yP6bA9P+EWQDa4dEWlCsaJC58t6CfPtC8JbXHX3GIYDx37a2YxGDL9vbG/5+R+7i3kqgkC/Uqpa4E9IrKYTLFqpdSLAN571Uw7ishVInKXiNx14MCBRXyVz6lOtpDlg7f8Mbc89wte+5N23nTPI0Sbh6n/g9chF/jOz9ORoGXwiXe9hs+c9zEK7QUuuy3HTz/xHm5+7ualFs3n5OIioBXY5r1agYuBS4FXLaFcS8TRT6o+bs7fG2HOoPAcC3LO8VPa86ZOtHqB+br6hLdpsCZaYaDlHZN9a+rJWwvrj7xe6RWLOhbBeZ6jTksRkQAZPUbMU7ateRgbmgijsRPjCTC0yutRHYfr5UBPzYL2P9RVxaGuGVXOmRFhLHr86+dkIvP7jrgWPs6STNDXfOKyePobZn7+xLSFDYoU0Y7+sXhUzMvA8sIC/wT4U2+VCXzjeAkFoJT6klJqo1JqYyaTOZ5f5XMSkivk+MNf/DG/eu4m3vkfDbzhgceJtw1R984LkUs+DfMYsfM5NYkFTT579eV86oKPU2iEN/08x/Wf/QNuePaGpRbN5yRBKbUb6AdiQKr4Ukrt9radcRytElvQT44pLvqaFqbULcQgc0yHjO6Ge4078zM29MCEQjtUHaG/Ic5AbZSButiC5JwPw6mp3onhdKVCbYlOtREnpgXRFzRGDs+smzrLgWNOnENb4PnK/4cdY7ZjJ9yA2gL/u4Ny9F6UnBHCCAYJhxb3mxXMCQM2d5xy8ubqlaKX+mg1n6FQ05z7jFuusVPe7iKJ42TgLdSzDMzZGeWDFsVw3rPqty78exbJfO+m3wFeDQwBKKX2srjy7PtEpBbAe9+/iHP4nObkCjl+/8ZruGP3TXzo2xle/sRuUt0D1Lx1B/Kafwbt5HHX+xwf4kGLa9/9Kj728o+RqxPe/rM8N1z7Qb772HeXWjSfkwAR+SjwAPA53MmHPwt8Zp7HXiQij4vIUyIyrStcRF4vIo+IyMMi8q2y9XkRuc97/egYNGVO5qv0FlXYTMSpUJrnzQyhcJO9LTCh1xiikTGnVwV6W1MLl4GFhWPlLYNRZ+4B2GJ/lIcaqXkOb4d0t31Hmr2wPk0YroownJmfojluxdnfUzPFICtIpWFYCBjoXRkCk5TagfrFGQXT9kuZcXNweTXJkEXUsQiIhYY2xVOgCVNCFzvM6cOyRISgeew9VSFtZs9O1p6fUj5uxYnO4QVRsxh+ybKwvAOty49LO+cirx+bcD01TYjpZIoG1rHEFrM0uAGQNSfdP5O6v/z5ka+Z/lky228G4FgT91J/fYzDHWletr5nnhIfPfN9ko0rpRTeI1hEFhsE+iPgLd7yW4D/WuR5fE5TsoUs7/rpB3nwmZv4i6/H2Pj8S1RvOELVlTuR134F9BP/YPNZGhIhi8+/5xL+8pV/w3CtzdXXF7jtS3/NF+/9Au7jyOcM5vVAu1Jqu1Jqh/e6YK6DREQH/gF4JW5p9ytFpHvSPp240RpblVI9wB+WbR5RSq31Xq8+Zq2ZAT06/3FMmfQ+mdFwbFbvkNLmn9Ni4O6b0WJUG9MbANnQRGhdRo9RoycYCdQxFGqc9dwFa/5yHO5Ik53BwANwxCIVtrGnCaGb3E/V+vRKZcF71pS3Zz40Ga6BM27FUYbOuJcDNdlgLSrrufo6kkELQ1+4jyJoV7ZPiUbOqFTTRpdVGlx528DwBistMWgzqzEnTQuQCjsVSupczDX2WRVxGJsUCjdXa4Myfb/3RzsZik8N+RufnGsmQkGbMGaDM+S6KWbWLaRMymxgZkOnfGCjXq80Cpr0DImQNa98uYgzm55TeXy7UVO61sqPL37PqFPNSGD6SogBU5/iAZ5rcEZbpA8tqYVLIa0ABc2etUJjYZJHNDZd7tkcgyQVWzUhe4JzyuZrYH1PRP4ZiIvIu4CfA1+e7QAR+TZu4vEyEdkjIu8APgnsFJEngZ3eZx8fAEZzo7z+P9/NS4/9gk/+q03XoSPUbzlM8vKL4DVf9o2rM5BU2OZL77mQj7zy0xypDvPun+Z54mv/yP/9778kX8gvtXg+S8dDwGKGWc8GnlJKPa2UGge+g1t8qZx3Af+glOoFUEotaaSFIdqcOSCaBqNOGpi54IHShNFEkKEyz8uoU4UlBjkjSF535hwRLpLQwtToCUJl4VLmJM9T+bnCK7pxzKMPrRq3EtToCer0JGMRpxTCFLYNxuomRscNTajXU9hiTO0P73MmUqm4BzxFXonGyvBEfk8qMGFALjPqSGtTDbrBmvkZwrrIFO9AMOH2Sz41s6dqriImM/3mQ6FGhkKNjEUd8l7+VX9tFQN1MQZDzeSSQe/8dfTFVlTKZRoIlcbFTPqs65mo3GhP8tBN9sxNR6LMiC2GEppiUKXHSoa05XkhiwbklOIgZWLEE0H2d1ezf1kLAM3JEFZrZYGRIjXGbB7XiZOWFz0paBZZM0aVHiMqgZLBCmBPE7Ib0Mx5ZTcEyjxkk+8rTYQa3R0occRCREp9UkTXNHRNaNRT5IxAaaqB6X6D0XiAIy3lfeIKOBysm7KvAKF5zOeeKrtHyn8flSivxihodqXBMzkctpyWQIJWo9IgS2uRiusTXINzoj+ETGTpCnXMt4rgZ4DvAz8AlgF/oZT6/BzHXKmUqlVKmUqpBqXUV5RSh5RSL1NKdXrvk6sM+pyh9I70c9F33kzovjv5+Nc0ago5WnbsI3r5Fb5xdYaTDtt87fe385nXfJqXatJcfX2BoW/9gA/9/PcZy48ttXg+S8MncEu1/0xEflR8zeO4euD5ss97vHXldAFdInKbiNwhIuXTjThe8aU7RGTaKrjHtkCTwsFkqGpuBb7oGelwPCUkEqbZmBomNlgWqpYzggzteBWjdsb7Nvc5W1RmNQFTE/avdBX8sG2giaABYc0BXWMo1cNIoLqkOB5cVkV/Q5yQ7nC4I+0adEEHo/QMdzVUJfpU79MM2mexcl7OCBLWHCwxGSgzqGxTJ92c5MAK1zDSrDj56LKJ46cJOyxXXIsFPlqMapqNGqpCE4peIjghY0IPk9GnGkKjiSAHl01fQMHyvqcqYhE1J5RTpemIgPJG6osGadyIVBgnrakQju2eu78+XuqjnBFCoVCzuI2U6CjRGaqaaM9AXYLhTBilGWS99VkzQkF3CGtBAqZB1DEJeV6UOqu8vRO/z2g8QM7bx2JqHlx5rk46FiUyQ66crmmkzBDxoEVtpIa456lwbKNkREW1IDnDNQYnK/jleTZZM8yYlWQ4WMeoU41hamSsBGNR75ymTrY+XgoP3de0pnRsWJt5AKBmsnfT64a8bjFuRUrhh2aZ10UTbcZwyoWga1Ov37Dm0G7U0KBPbywCZEMmtjcdwOTbasQzrBWKoapwhVexuKsSnfp4oLQ8HrJp1CufJ8XfZDIxc6qxWgjYFFrKjTaF7t3XRW+fHSjzUpUJPRKopToaKO1fJKPHaDdrKsKopbyxok8xwE4kcxpYIqKLyM+VUjcppa5RSn1IKXXTiRDO58xg16EXecW3r+Sc2x7hT79fIJbQad3xHIHXXgOX/r1vXPmQCFlc9+7z+OoVn+Tx+kbe8osC8e/9mqv/6w30jfUttXg+J57rgE/hRkF8tuw1F9P9206ONzWATmA7cCXwLyJS1LCalFIbgTcCfy8i7VNOdgwLNNUlI0Q85a0rkSAdsam340QD0yurxTyf8ajDwZbVmGLMWM56zE5S0DVqG9aiTQkPdFWDdNghHY8Sj9gYmhC0XOW7HDUp5C3vmIykQthikA3ZFQadAo40ToxC5wxXCS8WSBgOp6fI2WpU02m7htP+zjYGw22AIl8mR0/bRVC9qvTrpowEWStOv2dk6SJkIk6lsqUmPDLjdpx02MYQDUOMKVXwiK1ELVRP8/q9/OJqCycwQgGaEkGUuB6isY40401xVNxVMrV4O/We4mzommuEbb6YsYjDSCrI8vNWls43tKyeg8urKJSVS1cijFmVCu5IbGZFvLxKooaGbWo4pl7qKVub+P/Vy/qlrzlJlRGnxXCNP9Eg7xilMFRhIs8sv25d6bhs2P0+y/vNA5ZGUyxSMkSV12OysZHq6uWl4zJhh1Gn0ojNGiEok2/MTjMSzFDQLHKGaxwUc7gCVZW3akGz6G2pZe+6tpIhN/l3b9TTbLa7iMxifIEi6phkIg6mppGJOMS8+1MXKZXHLy+vn53h/q0owR4wGQ/bGJoblKeLTq0+EeIrIiDCQKSD2DTGazxgEXNMGhMBEmXft7+rmf7G4m8kFYbMuBUnFJ94ZhX7YyjYQF36QjLJyZUbNRLJ8yrW2IZGXrMZCjVUrB9vdM/riEU86F4DK8wG0nqEgGax2e4iWtb+cHLCeBuMtFWcaywWYCzqTCmsMmVAKdHCUjKngaWUygPDInLsS+b4nPHcvOtBfvd7r+c9P3yWN9+SJ9am03L+bsw3/C1s/xO/WqBPibBt8C/vOIfr3/RR7mjq5vW/KbDmB0/wpn9/Jc/3P7fU4vmcWA4qpT6nlLpFKfWr4msex+0BypOAGoC90+zzX0qprFLqGeBxXIOrWOAJpdTTwC+BdRxHwvU9qHAb6wLdtDhp1oeb6Fl2PkHT4EhLknzZhLV71q8olQvXDJusGaY3uY68PjWHZbA2StaMkrdMImaMxqCryI45SZToFDTTzcWwQuDEScQSJL38BX1SjlDIy9GZbJO0GZXKWNgxWV3Vxmgswr5Vdby4pp28bjPmZIjGU14o0YRKUizSoItGY7yobCmyVqzCUBqNhdHNEMob/e4wa4no7rKpVY7Mm5MUskTIJhYwaUgESqFMKjRVmU45TWyyOyvWKRHa0iHssv5IhCyqIg6OrpNd3kzB0DG8/7B2p4qUHaI2GQLb9FoDytTJ1kQhlIa6dcTDzWii4YhF3vMQKdvmSFsKRAikJjx3TjBCwdQZWVmLvq2D3roGhkLN5MzKfJX+SCc0nE1DPECjp7jGghaR2vUQq2d1vetZ0DQpGTrLgzV0h+oq+ro5UqkGVmlRtPZmAIKmzngiyHBZeOVwqJ5E60ra1l0AgThYIYaL3ljP8lS6RsC7jkOpLrJeCKWyDFpTVaXvt019qsdENIhMGF2ZsE3B0OmvryoNBBQN3LFoS8WhI4EaLE2jL76CUSeDAizdvZZjVpQ2oxpbm7tC5XAqRjJolQxGSbWTj7vf5Zga6yNNdNj1aKKVjMfhTJj+9RMGyJjtGsQpPUqHWUujnaBQNrnxaLiJhFVbUfCj0NYACDkzQiJYeY+bolNTs4ZU2zpMXSMWsAiaBkHvXi1+X2V/1GGG00i00og90pTiUHsjhUwTqbBNtsN1+CuEcSuGZkYYCtVXFM9oSQdBMxiNBagyohQMHSvk/u7ljwlbzImy8yJkE+7yaCxQsWPRg6eqUxzuSHOkJUlkfQNtXrjzmJ0ga8amraopQHUgRLtRTYexsNL+R8t8c7BGgQdF5Csi8rni63gK5nP687nbrucz338rH/vaYTY9pajaOEb9eYNob/sP2Pi2pRbP5yTEMXW++Oaz2f3ej/D/2rdw0d2KK77Ty9u++yru2+NPSHwGcbeIfEJEzhGR9cXXPI77LdApIq0iYgFX4BZfKueHwA4AEUnjhgw+LSIJEbdmtLd+K/DIsWrQtOgGY04GKS/qIlIqRjDmZEhGeqgJ91TkPEXqukqKad50lcTR2IRyOlqW01UeUpPXAwyFGlEiRByrJAM1KyFc5X20aFrljlqrRJT6RICaiFMKuSsWlDDKCibEAxY1UYeWeJq8ZjIQ66A/3kZtoI2cGUKMAEHLqDAGiwpbQZuaQ1EeKnSkoZrg9u0oe0IZLlZci5gJiE/Y08mQhS1WKXxNpUNYQYt0MI5t2eQ7msB2ZZhprq9i0QUVqoHAhEcha4UxNY0mO8nmdBMoRe/yKoI71xMLmGWV5xRDW1ZNe+54qIpU2PUW9q1qZLi7xpNlah+M2RlSeoSir8kxNPrrJzxVyTKvVtgxQISaWIBAuonmVIjm6jTN6R5WVa2pyDMr4mgmwXiUmO6QNV1lv9FJoMJBDrenGbfirM6kkXjELf0dqWa0PsVIoMprJYytbCO7qYf2eDsEUziJqdOn5oMWycZ6ukN1JEI1WNFVmJFOLlx/NUlnwhDQDLcPBiJtjARqCNkGmfDE9TIWdbANGwTMhhRNiThaopXBqm0AhIzKcFQlGkaZdzdnhmkKxaiKOChxQ/waEpXG9kjA/T2q7bJzebdmur0FwlUo0wCZ3mvcYCfJ2knGw3bF/VqYZMilzlvHWFmupJKJ0hLF3DQVCzMQ6QCmjkMvd2ppqV6LXtNY2l68Btx2TApd1ISRWJjYuT3oLe4xpmdojSaDDKdibNq5mfDGHuyk2/aRYC3RhrPJZmpQYpIzIqUcKtvQObKxm/76OGkjTItRRdC7jx0x0QWy1sTzKOUN3tSHY+xbU09fS6XHtTrqgOHQ0LWOZXF3oMPUNSxdp6UmTTSRYcyevoDPmsQy1sTryOgx0np02n2OF/M1sH4C/DlwK3B32cvHZ8GM5wq85Xuf49nv/jGf+PowdXmTlu0HSJ1bh1z9S2jbvsQS+pzM6JrwkctXkf7T/49/XH0Za3fBH39jnA/88N3ccPcXl1o8nxPDOmAz8HEWUKZdKZUD3gf8DHgU+J5S6mER+WsRKVYF/BlwSEQeAW4BrlFKHQJWAHeJyP3e+k8qpY6vgVWUu1yDMoNl63UKVasYP/cV1ITaEM+NJMaEwjYSybBvZR39dVVoCGN2kkM1a+mvSXGgo2lKjsJ4KMBzG9bQffGlEEziGJ4xZpQp+QIDm7Yx1LEaEGwveT6jx7CnmQ+pw8v10UQQFFkzghIdS3NoDvWwon4TRryZVk8htMQgasRLCpEeCxF1zIoCA8Gi904ELej2SdEQGI01MXDOdsbrm+iuWkvYM7iKHqyUHgGlGGtPs27jZtpi7WiWCZGJvu0KVNEWSRL0vCbDQdfjYIrBZruL5nQYohM5JQXLYHRZhlTtKizNYE19ioaqMEbIIRWy0AKuvOPNkyqnBRJQ7ZaOPqv6LAxNo7k6RmMmTCricFb3lWzrchVix9CgeSt9sW7GPYUyKDaEq0u/S5F40CLjhaeVF03AjrJh49W8rPUV1ISq0T1DcqypMgyrhAg5I8S4VyxAxSPkokGW96wvFaXQnBrEijBWvZaxaJih2ijDK1sYS8ZQnqHene6hK9HJcNidh6lYnTBkmKAUlvcbjZy9DdnxDqxIpRHQmVxGd2oZBc0iFY+xoiZaUswBxoIR6kINKK8TuhLL2NC8jUCggWXRs6kOVoasAbRnQjQlJ37fppUXkazbiJ7ZhhIDS9epXr6FF2svZCjUQF53aAutojOcpsOsJWeEStdkIpDm/Hd8lOHNU8uANyeDxBtWULPj93juvHOnzC+V152K3y5mBAiHmyumEtDFQkXD2GX5WAXPkBMvFLEgZsW8YeGtW8k2lXltphTfnTi/uWkF+WSUdTXraQwuI1W7gRov/87UNcIBCz08cX+YYqH1bGG0yy3CmjMcBsq8bgXbpDexirGajQymNpTWp7QIuh0i+spzWL7z7aRCNsUmJc0gr2w8n8FQc4WUbStaoHYNqbVbCGsO0bKQzeD21xKpd0OLj8RX0ptYTV9r2usXoGb6wYwTwazJLSLSpJR6Til13YkSyOf05plDR7j6mx/gTTfewcanFFazRfPa3RjnXAkXfwasxc3Y7XPm8fZzW7kp+Ud88m/TfPD26/j4dTk+MfhFdr9wB1dd8lXEz907bVFKTZ0xdf7H/hT46aR1f1G2rIAPeK/yff4bWJJ/6zE7CeyFeDNoOug2JW1JBDSNaqeF+tRKzOQQY12N8KhbQyqnBzmcWY6RG2JrIcqvbIOCZtLXOKF4jXR2c/jIEZLP7kXTDNpTWwl3NcGdj2LOECbVW7XRXdhzXyk+MKYFOSvYzuHCGONmjI58DUPhNqAwa/ss3WZl7Vnszu+DnFsgYU3bcp5+pJ+s7qDZFk4wRNpuYLwuRiyyF9sYYHi88jwD4RZ6E4Lj9clYSwf2gXESRpDB/BhaZgVH0meReuwZ8KoahnWbQQCBVDyB1TcI/aPUx0IEt17KC48dcdubWEVw30ul75pc3Q0gHwsgA1FU/UZCxiAXJ1dRnB69NpAgeG41ebNQUijDtkEhEAcrzAVNF2DqJtGX74RHBlmrxrl38DniqXZMzc2l0TWBaC2FsjmRIloAvHyjVMgiadUwkJu+8GU6kObs2rNLn7Oqv7Q83tCMejEJfQcnDghmQFLkB3aR94yZ5Q0J9lqjwIT3U0RIOAme8Q4bro6A6Dh6gITjGoKWZxCPOykKYmDqGlURh5Vxz6tV5VYxVNaEV8pZvgzuvRmAkBnC1uFI93ICiQHiQLYmiX6wj72rl2PmUgQlREhLEYm3YYYDWG1tsHsYRw9R7gQOxNajKzcPrMo2OSiudyd8zjaafnUrjRmLQvpsyA3R2LGSkX0DPJOIsPfICMX7rq06zoN9o+QNA7LjEEwhlgX6hPFU/Eoj3U4ykAZj+pLzEdsAFSDmmIzn3Xslm1zB/s5eUo89jaXb2LpDobEOHt4FQOv6nTz54u0Mj7vVdBucBAc0g9rhXCkU0RVi+ilNGvQUI/Zg6bNpeSHAYqB5htuacAN37NtHXWzCoHG83zFmpsh5v//+Zc1o+QKj8SCNei/EGiZaLxpKM8npQYz8MKOBGohmCQRtwrZBPmBSKCgCpk5NzOElp5bxoX4YnYjcDqSSWJdeMm077M5l5Pfe6TZVM6hPhHk43IlmVz4cMmGbA4MntijWXBrID4H1ACLyA6XUa4+/SD6nKz+4/0H+69vv5yM37SM6KmQ2jpDqGUZe/a/QM21BLh+fWdnZXU3rx6/mo39bxTtu/CIf+3ofX9l5Nx88tIX/++pvEUx1LLWIPscJEbkE6AFK8W5Kqb9eOomOHwORdiTyIirkFYGI1TMUhNjB/sodRTAbqsA0aEmHWJa36B1upV8ziYUa2Z/poL0wyv6xJwkFh3nu8DAg5KpqyI14ipOVwTYiBM0gzdEWIlaE3kmTnJrdy2HEXY7svJChx3rRfrIbgKBmMyQFBu0k6WwfEmwBe0Jpb06F2DWUK31OlIWyadXV1A48TU0kD3aEkUA9fSu3QpXNWmcZg1YNY401tK3cwhO3forecVfRVwpaY63cJwdnz9u1HLZ0t3D4ubM4wh5gQsGkcROt52xj+MA/ke0H6tZhrt6B/sR/en1baVBtTHaTDyZ5gd8CkDaSgFcYWSvmpQmGZpADzLJCIoJQFw/AWI6hYp96hmxRSY8RYHt8GXjrpzPoANJalEEgaYQY0UxAleajSjkZDgzuKe0btirLYOvRspApEZg8gW6yGfpHgV0MZcIE4g2EapLoQ7MXFnJMg3gowVvWXowzyVujizBuJ2i2DUxNx2neil5TDY88RvCsjYQOwdC4e33YHR3k1y1Hu/dRAAoNjWRDeeyAqzznMwmGdiTo232Y1mAP6YhD3XiEczqrCBbzknYPT5FPzDAxAox7HpzagFsAQwy3/bomiBUAyzUsuqojvBAPM2AHqLW836O5gz0OhHfvRdWuKhmIFQSLhsnMwWKJgI0ZsaHfnZZE93IAG8NtPB7dQzY6jpP3Bp41DVZ3MD4IhUgdXdURsgUFBxyqnDhdUo96/s5SXKPm/QAAIABJREFUGCFAwSk36iaMLUez6K5ZxnPaAIOFCWPESLrheSoaw9IO0Z4OQ1mp82VVUZKbzueJgQb6gbWNcYL2pfSPZHm47zYCmRawwsAAglvEhKE8w8F6ogNPljyMJWINaH176KmbGqYa00L0FYbQJ4Vc2phAvqJwCEA2U03r+g6GX3yQ8c48VY0JAvWrkOh+YokQzanFTuG7OOYysMp7Ygb/sY/P7IyM57nmW//A6v/6Mn/6aI7xlEbHeS/hrNsKl/8jxCZXSfbxmT8dVRE+/5Er+bPmBs7+9ue46obHufX5Qd468io+s+lDNG14x1KL6HOMEZF/AoK4uVL/ArwO+J8lFeo4UtAdwq+9inx/PyMPPACawUg4QYx+sunqikHq4uh1vCZB+MgYTqKbFbGJ6nyvWduG0MbXHvwhQEl5KYaKhYw4RfOn6H14WfPL+BVuDZGCbWA0N8FjruKq2TaY5aP2rtrQH+1gzE4yGqgGJgysZNDixSwMj+forApXlO/u2nghgXueI+24o9ejgSqy8TQwUNkhhkXQ0jE9z1lBKVakVvBEOgxP/pJcy8zqim3qRCJRGBBPfq+qXUfXtBVro45FWybM/ZPWVzlJiEzkd7WZdWxJ1jNsJigcHkZmKp8+j8IJJYKzzc3kyWc4nN9+CUeevIEXCjnMSJDetE3t8CBVUsNAMMAub9+uRFelKM7ccxoVGQ1WEarJgG5CeqIEfnMyyODzlXbtWGoFzSu2TTGuADqrw2jROOniJk3HamtHSyQxEgnOTebpHR6vLLftEV+zGp66Z9rzomlEulfwynm2pxga2xZvI9WQJ1cooAUCWC0tWM1NDP7q1or9RzYupzlfYIOWgaE1kGmFgccAUEagNMvyOXXnsCvwHEOhOIWObjj8NHrTMnIHDmBUVZEYrGZ/pJ28ZRDjeTrsanaXfY9Vm4aGjYSHojQElwFPATBe2wA8iVgm+zt20EZxviug1i0331Qo0OtsxQkaGGn32snVpVGORc0DRzD7JgypfE87wfYagi/cz+BImYGVSrH+916LY2vw5NNsi3chjdvdjUphGRr167eQyayioBSOqTOSzfP4mHuPTi52M3li4vFlXeTsfRMronXQt4fpyOhRMloEvWxwImIbrDTryIR1Yp7nNlebIhuwGW1qw+7spO7IMM9khqnvXIeVboI+L2cu1XFCC6fNZWCpGZZ9fObF7U/v4Zuffy9v+uWTBMfAWDPE8rUmcvE/wOo3+FUCfY4JUcfkc1fv4KvdTXzz2i9w5cM/o2sv/Nnhz3L1kz/hvFd9GUJzKys+pwxblFKrReQBpdRfichngf9YaqGOJ1oggBYIMGqaKBTVmQjPb+gmmWoo/ZGnyyZqxbGJXXohufteoD4e4IUjrstJn6QBFRXZ5bFNBEMWec0mx1SCRpCpvoAJzNZ6xgeryh7p4oYDVX5Z5TlXr8HY/wL5PtcTZ+oW7T3/i749N5c1XJu+uD5QFXMohJ1SdTQ0jYGtF9CYDNJ72JXWWdENj15fLkSZAEkk1UJs3aZZWoZbpW26/yo7TGdmO3sKDoy43qvAym5sLYQ8c8PU/ZdfCs/fXPpuVAEtVDVzAGV7WSRs/fopWtiahrgrVriKePfv8LK8za/0A4wM/ZqR6gbkrnEMMVmV2sjmlgYMbYFh00YAt8YZlPot3QWDz5R2SYVt1jQEeG5gwqtVMIOVOXtl2IaOU5eEfZXToBoJb/JcU6e2LCQtETTpw+3+tkyYTfkULw4P0hprZbwwzmhulJLncA6KxWEEQUS4qPUiNMOgz9iF5XmZAivdHKrghvUUBgcrj9c112tiOKXrYdzzUmlh1zuYcBLUX3QFd+3ajzXaB7EG9Hic0CY3NPMyewsPvtDDI32/cgttoFEIBdCKzui69ZBoQYb6CBtun4SMOH0t7bD3Sbd/vWIw4fPOJbd/P6OPPwG4Bld1bZrgxo2Il5eICPlUjI5AFSMjZR5vy0R03Z18eAScsoIf8ViwFFoYqttYkffpfnFNqWriZMoLkxS/PxEw6fP6qxCLMd5Y7lUT10AMxGGkt2T4jqVWAPdNue+W1UwtVNFTt5a7Vw9R5Xjzpplp1iR20JP2Bu9r10I4A86JLYY+V5GLNSLSLyIDwGpvuV9EBkSkf45jfc5gcvkCf/WNf+Gp913C71//JCqiaH35ATp/9zLkf/8W1lzhG1c+xxRNE965rYMrPv9XfO7iP0Qbi/Kn31T8+meP8aWvbCX/8A+XWkSfY4cXoMawiNQBWWBqibJTnMCaNYQa61m5oqm0LrRpE6FVa6hJR8hEvYlAPc3bsaYq0K9eU8fGllnmQZonXYkOgrpFrio8ZduFHZexee0ODq55JZmwzer6ODu7p59k9dzG86iKBHD0IOH2ZsLnnYfmlCnjobRbHh4YWdaDssoV9TILo2oFdqad5lSwZCS2Z8JEHZM1DRMTw1oN9dSs7cESndrQJJlSndBUaVzZk4tQTMOYnYKk5yVLn0UkMjFfk2gaenhSH1WtcIs3lU00vHL5dlZe8LaS52NONNP1HpVh6hpG8Xh76qTNqbBFbdxhU3PTrMaV7vVfpmnmedtUMUyr3AOnGaVcNkrhdm3UBBupCk4/8XJ3qptVL7+SQMfUohPT0ZIO0ZQMlc4f8IxpW7dZk1mDVgoTm1uf6AnW0RWoJunEyETsab1kRczaWuzOidL8k8MrAYJGhPF0mtC27ZhVE+0Vx6EQLA9Hm7hu02GbHcuqCFsRhoN1ZJPtLL/kjbS3dU85v60HWJFYTUCfaH+5xHosht3ZSfjcrRjenHtKKbRQaNa2lc/pFguYNCWDhOxJ14cIrHodpMvC7IvX2Ay5ZGsSO2iLN09Z31EdYUtbqmIOPcszErVQ0DVYwxP3XW2gjcbEavLdbYx1TyoakvG8p7oFUdeAqg/X0x3bWmrzhuYEm1rLDL10xwk3rmAOD5ZSavpakz4+s3DbY4/zq0+/j8v+Zw8CjG8cYtPODcgrPuqW+/XxOY6srI/xt594B5/5z3XE/vVz/M7td/PcU8JfH7iG31/1faouudb3Zp36/Nib/PdvgHtwNZgvL61Ixx49HGbTqy+oWKcFAqxct5M9z9yAZbgKRVMyyDMHh4g6BjnP/1RUPGdTtGDGHHgAQps3kTvkegeczg7aEwd5zBkjakWhzJ9lWUGsFa/gEoCHHgVVKIUNuvkgE18SMoK8efVlKKVKsoW2bCF3uLf0WY9GyPcPsGbDcg4MjCGHPeWyXNhgaoqXZGX99EqUpel0h+owKkbip2+4HpghbK6sGw9mNs/ooSmhGVDwfIF2FAKVRm7q3O3uwrM3eNLMP0ioszrsGVbZabevT23j3JYUI4/eRF0sOGP+VhER4bK19fBIgvvPbiJ4T2XIVmMiQLClHTLdrmHZ73pM6L7MfX/qp2gIEcdgYMzinIaVZYZPJS2xFgByXlVFsaZX1ou4eWwTnZ8JZHj6yNOkAhPP8JZUiIw5x++BmwfXEaiiqj6Eyhdmv/jnwbLoRsbzBbTQwnN7uuPrORzcQ8FJUBuuZTSSYoz9yDSDJC6KfdXnk42EJ5yKHno8jtPTw+Avf4noM6vtIoKpWeiWTV2iFqN5LRx5tKJ/Z31e1K5xQ/oC05dEX1YTQfaUHe/1r6YJjqnTWRWmsyrNwWhNyWANb91KYXwcBp8FoC7u0Kk3sbklxa/7A7TWTTL6Y41w4HFo2zaj0dSQODmKpflltnyOGUeGh/nHT32Irdffwu/0w/62HBt21BD+nS9Ax8uWWjyfM4iQbfCXV5zNHWdfyxf+7hu84b+v44p/H+H/PXo3XU+dzXmv+AtY96b5jx77nFQopT7qLf5ARH4MOEqp2TPvTyOKymtN1GF1IkFjMsjqhjg8aAAG7fF2GiONs5+kjB3Lq7jlIVdZH2toKa030mmMtJu/ZXe0YxeeYosVKhVxmBURXrmy1g1U2PXgNJsnFDEtGMQKTihFoXPPhXyemGnSkAgy0nuUE4mL5obkAVrALYm9YetrkJrpvSwLoTUd4r7nj3h5QWXBfssvcQ3NPVPnvw6ZR5dsHy0WLkg1wcC+Kdt1zcDSrZKbd940nQMDuyCuQWx5KcrE1DV3XrRMZQ4XZQZxY2YNkomxfNnyGY2rcoxYmEB7PeaqhQ26pgIpLm67uGJdOmyzoWZ6L21N1OGl/lGijgFe3JWzciWjDz9SUfFvvsg8bLLSpT2LrbK8JsFd52ynKuJeM/bylehqCLNhqgeoSM6MUDBsYGo1PD0cwlnWhdkws2fQ0IQ3rtpJoqEG25sfb0P1Bp49/FhFHtiMaDpEFjFZb1m1SRAywQmjSSwL3bJK9WZsXWP7Mve+3Llh2eQzuaGEq163cBmWAN/A8jlqlFL82zf/lvh1/8rlz+c5kFZor0+x7c1/De0X+KGAPkvG5rYUaz77Pr7w022MXff3XPbInYw+ZfHtXR/lkrO/RvSya32v6imEiJwFPK+Uesn7/GbgtcBuEfmIUmp+yRinCSJCY3LqaO2y5DSKyTQEDTefIeqYYJgMbL1gjiMqmZzPNZmZ8jTmQjStYvBDAm4Y2vKmNM/OMAHwrCy/BHrvcM+l68Qumb7kcxEtYGO0tEyWatp9w15olalPMrD06YtZ7GzeObcBYgYhO1vGm0fduoqPsYBrkHZVTw1nm4ng2WeVqucRroLMctAfACs8p3epSPj88wGYGuQ2gVlTTfalMmOwaTNWE2AuoOjHIgh7hpUI0PUKGO3DijVgNc5/AAJcPWehFMJRGNqPHo9P2RZxTHZsnAi/k5qVmImmKV6Zyd862x1XHtJYZEVqBbv7J8yndNjBKOvzUPuF9LRuZ/dzP5+9MfNg8px65VtItkLf8xOhtWcAvoHls2iUUvzkh59j6F+/wuYnsgw5ioMvi3LuH34KrWO7b1j5nBQELJ1rLl/Lrq1f4Np/vZ5NN/496287zIMP7MW46xLOfs3vIjv+ZElitH0WzD8DFwKIyPnAJ4H3A2uBL+FWE/SZB5urz+ORwjyU+Bm4dHXd3DsVKRobi/xPsDs70aNRYjU1pXLG7fF27t9//5whkMCCQ8EiG5bB8sqy25va08SJ8dDemRyl8/sOc5LhVR+q5/mB5yuNrs6dE+GF0xDevg2VnRoeKCJsaJ4+fGtGeaoqvXir0qugJwwvDuD09JB98SV6MqsINU0U3NBEo6Bmn9tsMoH163FyZW2KzS8Hi/YLYNfMv/Gq9Cp29e0iHUhPu72rOkIur2hJhUDXpuaqAVZz05xhfuur17O7fzeBkeDkCL0ZwztVMk1kVfP8qjWKzPgfFA0YvDTtlrlpjbXSGmtlqKEAzsGpO2gaaPMzpGeimAdYPuBSGwvw5FiOWEMHgZZmN1ev6xUzn8TLuzyd5kL1DSyfBVMo5Pn5f32MA1//HmsfzTNuwNObY5x/zaeI9GxbavF8fKalPRPm2mtex02XnMffXffPvOrOH9Dx6yC3P/Qf1P7nv9Pylj9CNr1zxgRen5MCvcxL9QbgS0qpH+CGCt63hHKdPIRmLlRQjmME0GXxE2/O5b2qoOkcSLxYmhB3oYgIZk1laFIm4LZzpomQy9HjcbRQEHv58jn3JVILvc+WwiD1RJx87xFqYoGKcvRFTM9LF7AMmLb+4uysTK9keXJSWJ0+taBFOVOKaBxDGqONqPUNUJgwoCzDIlD2222t38rBkWmU9VkQTZu3R6yCYNItgjADjuHQk+qZcbupa6xpnOpBKiewau75wyNWhJXplYzvmchP66gK88iL/ZizhJovpBT+TNTFAzxxtCexghNGzDGmLR0qvRcnVLi4YzvWssrrZlaSra584aMP2z1Z8A0sn3kzPHyQn3z3jxn+yR1seFhRrcNTG1Ns+j+fZ93ydXOfwMdniRERXt5TwwWf+HO++9vf5e+/8xF+5+57SNwq3HvvtdSt/SJVV/9/aBv8KQROUnQRMZRSOeBlwFVl286o/7MtdVs4PDYpIrLnNYu+boseqR8/sHeGPY7ifjADaLWdFA4cWFTey9EihkFkx465dwS3THZVd8nACW3ePK23qEjUMdnSnia5LwQjk30b85BNZIpXa6kREdB1VD4/7faIFSFiTfUEnWl0VkforD4+/WCbrtHmeoeE9nSYSMjmhd4FZ9bNi7AVZnB8cO4dp0HThI5J1UVj9iIiQk4j4wrOsD8kn8Xx6JM/5dbv/w3xX7/E6qdh3IAn1tSy+v98nstWzTxy5ONzsmLoGr+7uYPXbriO6+68l3//0Ud59V1PEPh1ngN3foR4z99QfdUfYm3/Pd/QOrn4NvArETmIW6r91wAi0gGcMUUuAOJOnLgzaWR+lpH0sG0wODazh6XokaqKOEScaVSDohchNTXPo4L6DbDvIbewRBnBdWvJ9fYekxH944qmVYQpia7PWpkNIBOxYX/xAP95cawJb98GMxh7pysdmTCOoRPba0FB0VMfQ3R90QZWKc9uhmfE5trNDIwPTLvtVKA5FaI2dnI9W3wDy2dajgzt54ZffJwXbriZ1fdnOf8QDAWEu7euZs0ffYLXrDztppzxOQNxTJ2rz93IO7f8kC/dcTPfu/Gz7Lj/WTbdP8zgez6O0fRpat54BeErP4jYJ9fD+0xEKfUxEfkFUAvcqCYyzzXcXCyfGdjWlSFflotUG3d45pBJ+6SR53PaZ5jCQDfmV70r0ey+JiGWhVk99xxTC2Uh5c2PBfXxAEemK6Wd7oTnDk2b47OUWM0zV6WbE08ZN+vrj5E0i+N4hkSerGia0JQKMhgKkR+Y8CwZenH6hYWdz1m9Gj22GyM1/f1t6VZF6ftTjbVzhIEuBb6B5VOib7SPX93zFZ664d9JPNDHhicVa/LwQpXDrZe+mvPf/z5+r3l+8f0+PqcSuia8Z8vLePc5F/CN+27l/9z+Bdbf+wg7782R++Q3KFz7DWKbu0m944M4G86ZX2K9z3FBKXXHNOuOOkXhdMfQtYo/fNvQ2bHs1A3JKVYsm09J8GNJbUMrtS3TGIqxhpOufHTs0tmrJc6FiBB9+c7jXunvVGTWSYo9IyhkH304bHDzZvK9vSUv6prGGImgSTo897xf5WiWNW2VQZ/jh29gneEcGD7Ab+7+Fs/c+H3Cjxxiw5OKznEYDgj3d7Yy9Or3c/lrd3DhSeZ69fE5HogIb1q3jTet28Zdex/h2v/+Cs7dN7H1kRwbbn2YgVveQT5pEX/5hWR+793YHf4flo/PUmDqJl2JLmrDtdNu39qR5uDg4ot4TMsSGlDbGrfRP9Z/wr93UYUpTmM0b8oALRqdcZ9kyOLs1iRVkaPXmzTbRisr8GIb+nHL+/I5tvgG1hnGeH6ce/f+lodu+RbD/30HTU8M0/UiLFcwasPTDVU8vuF/seY1l/P6VbXYxolPSPbxORnYWNfN11/3WQZeNcCX7/0Bf/7g92h5ZDfnPTRO93d+ysB3fspY0sbetImGN76d8Iaz3Pl7fHx8TggdiY4Zt6XD9oJH+Y8Hx8rbHTJDRz1Bsc/RY6RShM/dihabvYhDbWxxFTN9Th98A+s0ZyQ3woNP3c4zv/4RI3f/lsjTvbS9qNiSdWPXezMaD/TU8GzPq2h4+at5+ap6Xhv1vVU+PkUidoQPbH4rH9j8Vl4YeIGvP/ADfnDvf1L/+H42PjlOz89uZc/1tzIW0BjvaCB87k6aX/MGQgucyNLHx8fH5+RnuomDfXwm4xtYpxHjI8PseuQ29tz7G3rvvwvz2RdI7xsj3Q+rgbymOJJW7O9wOJBezr7NV9C1cRMXdaRJhPwwAB+fuaiP1PPhrX8AW/+A3tFebnzyRv7x7u9hPPwEq57Ks+qp55AHv8Jz//gVhmLCWFMKe8Uaolt30njeTgLB02cSRR8fn7kJGkH68n1HVeXex8fn1EPUAmc4Xwo2btyo7rrrrqUWY8lRhQKjBw/x0tNP8+wT93P46Uco7H6CwL4DxA4Pk+wroHk/Z06DwwlFNlkgFwswWruCoTUXk169jdXNVb772sfnGJIr5Hii9wluffR6nrnrJgJPvEDHc3lWPKcIjrv7jFuKgYyQrQqg1dYQallBaPlaUs0dpGpa0CPVs5bZPt0QkbuVUhuXWo7jif/f5TOeH6d3tJfq0LGvoOjjc7JRGBkBkZN/OoajYL7/XUtiYInIRcC1gA78i1Lqk7Ptf7r+SWXzBfp7B+jbd5DB/Yfo2/8iA/ueZ/zAc2R790H/YYz+PoIDg4QHxokO5TEmTQUxbMGhBAzHCkhEocdC2LWtRLrOI9K1mYautcRCvjHl43MiUUrx3MBzPLj3Xp6642dkH36IyPNHaHwxR9MBMArufgWgP6YYihfIRRX5oI6KBNBicYxUNYHqZhLJBhKJegKJakLJWuxolTvj/SleydA3sHx8fHx8TjXm+991wkMERUQH/gHYCewBfisiP1JKPXK8vnN4pJ/8wACqUKBQyKEKBfeVz1MoFFDFdcpdV9peyPPCoQHu3rUfcllCQy8RHt6LlstBLovKZ1G5LCqXh0IWcjl3MrxcDsnm0MZy6Nks+ngOI5vDyBYwswXMrMLKKqwsJYPJBNLeq8iQDQMB6I3AoXpFNgQqrKNFAkQTSdK1zbR1nMWaptUY6U4IJk95pcvH53RARGiONtMcbYbll5fWHxw5yLP7n2D3I/dw6OH7yD/9DM5LvaQPjJF5seB5u0aBl7zX/YxYsMuBEQdGHUXWhjEHxi2hYAh5Q6dgaijDIG8aKNME00bZDmKYKN105zAyLEQzwTBBtxDDBtNCdAtNM9F1DUQn7SR59bKVrjdNNEQ3JuY1EgERxLbR/OpiPj4+Pj4+07IUOVhnA08ppZ4GEJHvAJcBx83AuuYTF/C+7w0t6tgosGMRx42aMGpNvI+YkA1CzoS8KeRNDWUKeUcjFzDRQg5WJEwgHieSriKdaSCTrKcrXE8k1ohEa91Rax8fn1OWdCBNujkNzVvglZXbCqrA4UMvcGj34/Q9v4uB559ndO+L5HoPQX8/xuAwweEx7MM5AiN5rHGFlVNAzjvD+DGT88k5tld9+E9IvfWtx+z7fHx8fHx8TidOeIigiLwOuEgp9U7v85uATUqp903a7yrgKu/jMuDx4yhWGjh4HM9/MuG39fTkTGnrmdJOOP3b2qyUOq1nLheRA8DuozzN6X4dLBS/Pyrx+6MSvz8q8fujkmPRH/P671oKD9Z0MWxTrDyl1JeALx1/cUBE7jrdcwGK+G09PTlT2nqmtBPOrLaerhwLA9K/Dirx+6MSvz8q8fujEr8/KjmR/bEUJav2AOUTxDQAe5dADh8fHx8fHx8fHx8fn2PKUhhYvwU6RaRVRCzgCuBHSyCHj4+Pj4+Pj4+Pj4/PMeWEhwgqpXIi8j7gZ7hl2r+qlHr4RMsxiRMSiniS4Lf19ORMaeuZ0k44s9rqMzP+dVCJ3x+V+P1Rid8flfj9UckJ649TYqJhHx8fHx8fHx8fHx+fU4GlCBH08fHx8fHx8fHx8fE5LfENLB8fHx8fHx8fHx8fn2PEaW9gichFIvK4iDwlIh+eYZ/Xi8gjIvKwiHzLW7dWRG731j0gIm84sZIvnMW2tWxbVEReEJEvnBiJF8fRtFNEmkTkRhF51NvecqLkXgxH2dZPe+seFZHPich0UyScNMzVVhH5OxG5z3s9ISJHyra9RUSe9F5vObGSL5zFtvVUfC75LJ753P+nOiLSKCK3eM+ph0Xkf3vrkyJyk3dP3yQiCW+9eM+zp7x7YH3ZuU6p58BsiIguIveKyI+9z60icqfXtu96RcIQEdv7/JS3vaXsHH/qrX9cRF6xNC05ekQkLiLfF5HHvOvknDP5+hCRP/LulYdE5Nsi4pxp14eIfFVE9ovIQ2Xrjtk1ISIbRORB75jF6U9KqdP2hVtEYxfQBljA/UD3pH06gXuBhPe5ynvvAjq95TrgRSC+1G06Hm0t234t8C3gC0vdnuPVTuCXwE5vOQwEl7pNx6OtwBbgNu8cOnA7sH2p23Q0bZ20//txC+QAJIGnvfeEt5xY6jYdp7aeUs8l/3XirpNT9QXUAuu95QjwBNANfBr4sLf+w8CnvOWLgetx59TcDNzprT+lngPz6JcPeP/HP/Y+fw+4wlv+J+A93vJ7gX/ylq8Avustd3vXjA20eteSvtTtWmRfXAe801u2gPiZen0A9cAzQKDsunjrmXZ9AOcD64GHytYds2sC+B/gHO+Y64FXLlTG092DdTbwlFLqaaXUOPAd4LJJ+7wL+AelVC+AUmq/9/6EUupJb3kvsB846kkjjyOLbiu41jpQDdx4guRdLItup4h0A4ZS6iZv/aBSavjEib5gjuY3VYCD+2dkAyaw74RIvTjm09ZyrgS+7S2/ArhJKXXY64ebgIuOq7RHx6Lbego+l3wWz0Kvk1MSpdSLSql7vOUB4FFcJfIyXMUa7/1yb/ky4GvK5Q4gLiK1nHrPgRkRkQbgEuBfvM8CXAB839tlcn8U++n7wMu8/S8DvqOUGlNKPQM8hXtNnVKISBRXmf4KgFJqXCl1hDP4+sCtAB4QEQMI4g60nVHXh1LqVuDwpNXH5JrwtkWVUrcr19r6Wtm55s3pbmDVA8+Xfd7jrSunC+gSkdtE5A4RmXLDicjZuIrqruMm6dGz6LaKiAZ8FrjmhEh6dBzNb9oFHBGR//BCL/5GRPQTIPNiWXRblVK3A7fgPnhfBH6mlHr0BMi8WObTVgBEpBl3xO3mhR57knA0bS3fdio8l3wWz6l2XR81XvjSOuBO+P/buZ/QOqoojuPfA7EVK2hVFDSKBkXcVakQ8U9r1YIiFaGLQCVW3YkLFyJIXairLiR0oYhQURRBaK1pQcGFbv1blFaq1fiH9mnVbox/Vqk9Ls55yfB4qS8z85L35/eBIW/u3BnmXG5m3p135nKJu5+AGIQBF2e1xdplkNprF/A//Ch6AAAD+0lEQVQkcDrXLwT+cPdTuV6MbT7u3D6b9QelPcaAk8Cred/ebWZrGNL+4e4/A88Dx4h7+yxwkOHtH0V19YnL8nNr+ZIM+gCrXc5k67z0I0Sa1UbiSfFuMzt//gAxkn0DeMjdT9O7qsT6KPCeux+n91WJcwS4FXgCuJG4cG/v1onWoHSsZnY1cB0wSlwYNpnZbV0816o6ibVpAtjr7v+W2LcXVIk1DtA/1yUpr9/6dSVmdi7wNvC4u/95pqptyvwM5X3FzO4Ffnf3g8XiNlX9f7YNRHsQ97gbgJfc/XrgHyL9azED3R75XtF9xIO3S4E1wN1tqg5L/+jEUtuglrYZ9AFWA7i8sD4K/NKmzn53n8ufSY8SX1ibP02/CzydPyv2siqx3gQ8ZmY/EU9GJs1sZ/dPuZQqcTaALzLl5hQwTVy4e1WVWO8HPs40yL+JHOLxZTjnsjqJtWmChfTApe7bC6rE2m/XJSmv3/p1aWZ2FjG4etPd92Xxb/kgoflAoZn+vFi7DEp73QxsyfvxW0Tq1y4irWkk6xRjm487t59HpE4NSns0gIa7f5Lre4n79rD2jzuBH939pLvPAfuId66HtX8U1dUnGvm5tXxJBn2A9RlwTc6usor4snKgpc40cDuAmV1EpFz9kPXfIfI29yzjOZdVOlZ33+buV7j7lcSvO6+7e6/OWFU6ztx3rZk131nZBBxZlrMup0qsx4ANZjaSX142EO829KpOYsXMriVeRv2oUPw+sNnM1ubTvc1Z1qtKx9qH1yUpr6N+0u/yfZBXgK/dfaqw6QDQnNXrQWB/oXwyZwYbB2YzHajfrgNtuftT7j6a9+MJ4EN330akfG/Naq3t0WynrVnfs3zCYha5q4gHb58uUxi1cfdfgeN5PQS4g7hvD2X/IO7t42Z2Tv7vNNtjKPtHi1r6RG77y8zGs40nC8fqnPfAbCDdXIjZQ74l3lPYkWXPAVvyswFTRAc9zMIsLA8Ac8CXhWXdSsfTjVhbjrGdHp5FsGqcwF3AoSx/DVi10vF0I1ZiBrKXiUHVEWBqpWOpGmuuPwPsbLPvw8RLujNE2tyKx9ONWPvxuqSl3n4yaAtwC5F+c6jQp+8h3hP5APgu/16Q9Q14MdvkMLC+cKy+ug500DYbWZhFcIz4AjwD7AFWZ/nZuT6T28cK++/IdjpKiVnQemUB1gGfZx+ZJh48DW3/AJ4FvgG+IlLFVw9b/yAyO07k/bABPFJnnwDWZ/t+D7wA2FLP0fJAIiIiIiIiUtGgpwiKiIiIiIgsGw2wREREREREaqIBloiIiIiISE00wBIREREREamJBlgiIiIiIiI10QBLRERERESkJhpgiYiIiIiI1OQ/TeDSU6XO2xYAAAAASUVORK5CYII=\n", + "text/plain": [ + "
" + ] + }, + "metadata": { + "needs_background": "light" + }, + "output_type": "display_data" + } + ], + "source": [ + "for n in [2, 10, 50, -1]:\n", + " with pm.Model():\n", + " p = pm.Beta('p', 1.3, 3)\n", + " pm.Bernoulli('likelihood', p=p, observed=votes[:n])\n", + "\n", + " trace = pm.sample(10000)\n", + "\n", + " print('Number of data points:', n)\n", + " pm.traceplot(trace)\n", + " plt.show()" + ] + }, + { + "cell_type": "code", + "execution_count": 5, + "metadata": {}, + "outputs": [], + "source": [ + "np.save('data/votes.npy', stats.bernoulli(0.68).rvs(1000))" + ] + } + ], + "metadata": { + "celltoolbar": "Slideshow", + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.7.2" + } + }, + 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