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MCMC Introduction
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| { | |
| "cells": [ | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "\n", | |
| "## Introduction to Markov Chain Monte Carlo (MCMC)\n", | |
| "---\n", | |
| "\n", | |
| "**Likelihood**: <br>\n", | |
| "The apriori assumption specifying the distribution from which the data are assumed to originate. Assuming losses follow an exponential distribution within unknown parameter $\\theta$ is equivalent to specifying an exponential likelihood. Symbolically, the likelihood is represented as $f(x|\\theta)$.\n", | |
| " \n", | |
| " \n", | |
| "**Prior**:<br>\n", | |
| "Sticking with the exponential likelihood example, once we've proposed the likelihood, we need to specify a distribution for each parameter of the likelihood. In the case of the exponential, there is only a single parameter, $\\theta$. Typically when selecting prior distributions, you want to choose a distribution having the same domain as the parameter itself. For example, when parameterizing the exponential distribution, we know that $0 < \\theta < \\infty$, so our prior distribution should also be valid on $(0, \\infty)$. Valid distributions for $\\theta$ would be gamma, lognormal, pareto, weibull, etc. Invalid distributions would be any discrete distribution or the normal distribution. Symbolically, the prior is represented as $f(\\theta)$.\n", | |
| "\n", | |
| "**Posterior**: <br>\n", | |
| "The expression which encapsulates all of the power, simplicity and flexibility of the Bayesian approach is given by:\n", | |
| "\n", | |
| "$$\n", | |
| "\\mathrm{Posterior} \\propto \\mathrm{Likelihood} \\times \\mathrm{Prior}\n", | |
| "$$\n", | |
| "\n", | |
| "The posterior is represented as $f(\\theta|x)$, so the above expression becomes:\n", | |
| "\n", | |
| "$$\n", | |
| "f(\\theta|x) \\propto f(x|\\theta) f(\\theta).\n", | |
| "$$\n", | |
| "\n", | |
| "We can update the proportionality to direct equality by the inclusion of a normalizing constant, which ensures the expression on the RHS integrates to 1:\n", | |
| "\n", | |
| "$$\n", | |
| "f(\\theta|x) = \\frac{f(x|\\theta) f(\\theta)}{f(x)}.\n", | |
| "$$\n", | |
| "\n", | |
| "\n", | |
| "### Conjugate Priors\n", | |
| "\n", | |
| "The are a small collection of likelihood + prior combinations that result in analytical solutions for the posterior probability. \n", | |
| "A [conjugate prior](https://en.wikipedia.org/wiki/Conjugate_prior#cite_note-beta_rate-7) means that the posterior distribution is from the same family as the prior distribution. For example, if we select an exponential likelihood with a gamma prior, the posterior distribution is also gamma, with a specified parameterization. \n", | |
| "Further, many of these conjugate priors have analytical expressions for the posterior predictive distribution, which represents the modeled target output of our analysis. \n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "\n", | |
| "### Metropolis-Hastings Outline\n", | |
| "\n", | |
| "Suppose we have a working collection of $\\{\\theta^{(1)}, \\dots \\theta^{(s)}\\}$, to which we would like to add a new value $\\theta^{(s+1)}$. We generate a sample from our transition kernel $\\theta^{*}$ which is nearby $\\theta^{(s)}$.\n", | |
| "\n", | |
| "* If $f(\\theta^{*}|y) > f(\\theta^{(s)}|y)$, then we should include $\\theta^{*}$ in our working collection with probability 1. \n", | |
| "* If $f(\\theta^{*}|y) < f(\\theta^{(s)}|y)$, we will include $\\theta^{*}$ in our working collection with probability determined by the acceptance ratio. \n", | |
| "\n", | |
| "We can compute the acceptance ratio without having to compute the normalizing constant:\n", | |
| "\n", | |
| "\n", | |
| "For $\\theta^{*}$, the posterior is given by\n", | |
| "\n", | |
| "$$\n", | |
| "f(\\theta^{*}|y) = \\frac{f(y|\\theta^{*}) f(\\theta^{*})}{f(y)},\n", | |
| "$$\n", | |
| "\n", | |
| "\n", | |
| "and for $\\theta^{(s)}$, the posterior is given by\n", | |
| "\n", | |
| "$$\n", | |
| "f(\\theta^{(s)}|y) = \\frac{f(y|\\theta^{(s)}) f(\\theta^{(s)})}{f(y)}.\n", | |
| "$$\n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "Next, compute the acceptance ratio, $\\alpha$, as $\\frac{f(\\theta^{*}|y)}{f(\\theta^{(s)}|y)}$:\n", | |
| "\n", | |
| "$$\n", | |
| "\\alpha = \\frac{f(\\theta^{*}|y)}{f(\\theta^{(s)}|y)} = \\frac{f(y|\\theta^{*}) f(\\theta^{*})}{f(y)} \\times \\frac{f(y)}{f(y|\\theta^{(s)}) f(\\theta^{(s)})} = \\frac{f(y|\\theta^{*}) f(\\theta^{*})}{f(y|\\theta^{(s)}) f(\\theta^{(s)})}.\n", | |
| "$$ \n", | |
| "<br>\n", | |
| "\n", | |
| "\n", | |
| "* If $\\alpha$ >= 1: We add $\\theta^{*}$ to our collection of samples, since it has a higher likelihood than $\\theta^{(s)}$. Set $\\theta^{(s + 1)} = \\theta^{*}$.\n", | |
| "\n", | |
| "* If $\\alpha$ < 1: Set $\\theta^{(s + 1)} = \\theta^{*}$ with probability $\\alpha$.\n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "\n", | |
| "### M-H Pseudocode:\n", | |
| "\n", | |
| "1. Generate sample from proposal distribution / transition kernel $\\theta^{*} \\sim J(\\theta|\\theta^{(s)})$.\n", | |
| "2. Compute acceptance ratio $\\alpha = \\frac{f(y|\\theta^{*}) f(\\theta^{*})}{f(y|\\theta^{(s)}) f(\\theta^{(s)})}$.\n", | |
| "3. Sample $u \\sim \\mathrm{uniform}(0, 1)$. \n", | |
| " - If $\\alpha \\geq u$, set $\\theta^{(s + 1)} = \\theta^{*}$.\n", | |
| " - If $\\alpha < u$, set $\\theta^{(s + 1)} = \\theta^{(s)}$.\n", | |
| "\n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "### Example: Conjugate Normal-Normal Model with Known Variance\n", | |
| "\n", | |
| "Assume:\n", | |
| "\n", | |
| "- $\\{y_{1}, \\dots, y_{n}\\} \\sim \\mathcal{N}(\\mu, \\sigma^{2})$.\n", | |
| "- $\\mu \\sim \\mathcal{N}(\\mu_{0}, \\sigma^{2}_{0})$\n", | |
| "- $\\sigma^{2} = 1$\n", | |
| "- $\\mu_{0} = 5$\n", | |
| "- $\\sigma^{2}_{0} = 10$\n", | |
| "- $y = (9.37, 10.18, 9.16, 11.60, 10.33)$\n", | |
| "\n", | |
| "\n", | |
| "<br>\n", | |
| "Because this model is conjugate, we have analytical expressions for the posterior parameters $\\mu_{0}^{'}$ and ${\\sigma^{2}_{0}}^{'}:\\\\$\n", | |
| " \n", | |
| "$$\n", | |
| "\\mu_{0}^{'} = \\frac{1}{\\frac{1}{\\sigma^{2}_{0}} + \\frac{n}{\\sigma^{2}}} \\Bigg(\\frac{\\mu_{0}}{\\sigma^{2}_{0}} + \\frac{\\sum_{i=1}^{n} y_{i}}{\\sigma^{2}} \\Bigg); \\hspace{.50em} {\\sigma^{2}_{0}}^{'} = \\Bigg( \\frac{1}{\\sigma^{2}_{0}} + \\frac{n}{\\sigma^{2}} \\Bigg)^{-1}\n", | |
| "$$\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 11, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "muPrior: 5\n", | |
| "\n", | |
| "muPost: 10.0274509803922\n", | |
| "\n", | |
| "s2Prior: 10\n", | |
| "\n", | |
| "s2Post: 0.196078431372549\n", | |
| "\n", | |
| "Posterior distribution: dnorm(10.027, 0.196).\n", | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "# Compute posterior mean and variance using closed-form expressions. \n", | |
| "s2 = 1\n", | |
| "muPrior = 5\n", | |
| "s2Prior = 10\n", | |
| "y = c(9.37, 10.18, 9.16, 11.60, 10.33)\n", | |
| "n = length(y)\n", | |
| "\n", | |
| "# See https://en.wikipedia.org/wiki/Conjugate_prior.\n", | |
| "muPost = (1 / (1 / s2Prior + n / s2)) * (muPrior / s2Prior + sum(y) / s2)\n", | |
| "s2Post = 1 / (1 / s2Prior + n / s2)\n", | |
| "\n", | |
| "message(\"muPrior: \", muPrior)\n", | |
| "message(\"muPost: \", muPost)\n", | |
| "message(\"s2Prior: \", s2Prior)\n", | |
| "message(\"s2Post: \", s2Post)\n", | |
| "message(\"Posterior distribution: dnorm(\", round(muPost, 3), \", \", round(s2Post, 3), \").\")\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "Let's imagine that closed form expressions for this model were unavailable, and we needed to use Metropolis-Hastings to approximate the posterior. The acceptance ratio comparing $\\theta^{*}$ to $\\theta^{(s)}$ is:\n", | |
| "\n", | |
| "\n", | |
| "$$\n", | |
| "\\alpha = \\frac{f(\\theta^{*}|y)}{f(\\theta^{(s)}|y)} = \\Bigg(\\frac{\\prod_{i=1}^{n} \\mathrm{dnorm}(y_{i}, \\theta^{*}, \\sigma)}{\\prod_{i=1}^{n} \\mathrm{dnorm}(y_{i}, \\theta^{(s)}, \\sigma)}\\Bigg) \\times \\Bigg(\\frac{\\mathrm{dnorm}(\\theta^{*}, \\mu_{0}, \\sigma_{0})}{\\mathrm{dnorm}(\\theta^{(s)}, \\mu_{0}, \\sigma_{0})}\\Bigg).\n", | |
| "$$\n", | |
| "\n", | |
| "\n", | |
| "An implementation of Metropolis-Hastings in R is provided below:\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 12, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Acceptance rate: 0.269.\n", | |
| "\n", | |
| "Analytical posterior mean: 10.02745.\n", | |
| "\n", | |
| "MCMC posterior mean: 10.00881.\n", | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "# R implementation of Metropolis-Hastings algorithm for Normal likelihood \n", | |
| "# and Normal prior with known variance.\n", | |
| "# Aim is to find the posterior distribution of the unknown parameter mu. \n", | |
| "# For demonstration purposes only. \n", | |
| "\n", | |
| "y = c(9.37, 10.18, 9.16, 11.60, 10.33)\n", | |
| "\n", | |
| "nbrSims = 10000 # Number of simulations.\n", | |
| "s = 1 # Standard deviation of likelihood.\n", | |
| "s0 = sqrt(10) # Prior standard deviation.\n", | |
| "mu0 = 5 # Prior mean.\n", | |
| "sProp = 2 # Standard deviation of proposal distribution.\n", | |
| "\n", | |
| "samples = rep(mu0, nbrSims) # Vector to hold posterior samples.\n", | |
| "accepted = 0 # Track accepted samples.\n", | |
| "\n", | |
| "for (ii in 2:nbrSims) {\n", | |
| " \n", | |
| " # Get most recently accepted proposal.\n", | |
| " theta = samples[ii - 1]\n", | |
| " \n", | |
| " # Generate sample from proposal distribution.\n", | |
| " thetaStar = rnorm(1, mean=theta, sd=sProp)\n", | |
| " \n", | |
| " # Compute numerator and denominator of acceptance ratio.\n", | |
| " numer = prod(dnorm(y, mean=thetaStar, sd=s)) * dnorm(thetaStar, mean=mu0, sd=s0) \n", | |
| " denom = prod(dnorm(y, mean=theta, sd=s)) * dnorm(theta, mean=mu0, sd=s0) \n", | |
| " a = numer / denom\n", | |
| " \n", | |
| " # Generate random uniform sample.\n", | |
| " u = runif(1)\n", | |
| " \n", | |
| " # Check whether thetaStar should be added to samples by comparing a with u.\n", | |
| " if (a >= u) {\n", | |
| " theta = thetaStar\n", | |
| " accepted = accepted + 1\n", | |
| " }\n", | |
| " \n", | |
| " # Update samples vector. \n", | |
| " samples[ii] = theta\n", | |
| "}\n", | |
| "\n", | |
| "acceptRate = accepted / nbrSims\n", | |
| " \n", | |
| "message(\"Acceptance rate: \", round(acceptRate, 3), \".\")\n", | |
| "message(\"Analytical posterior mean: \", round(muPost, 5), \".\")\n", | |
| "message(\"MCMC posterior mean: \", round(mean(samples), 5), \".\")\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 13, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Warning message:\n", | |
| "“\u001b[1m\u001b[22mRemoved 3 rows containing non-finite outside the scale range (`stat_bin()`).”\n", | |
| "Warning message:\n", | |
| "“\u001b[1m\u001b[22mRemoved 2 rows containing missing values or values outside the scale range\n", | |
| "(`geom_bar()`).”\n" | |
| ] | |
| }, | |
| { | |
| "data": { | |
| "image/png": 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Ha7vbKyUnUhSDxpaWlCCL4tIwyNGjWqrKxMiK/KFoulSZMmtT0a18Hb7Xa7XC7V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\n1zZCCA1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GHZvr3zbbclR8b9+8sXX0ha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\ndrv+sw8mq0gXkS5nh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| |
| "text/plain": [ | |
| "plot without title" | |
| ] | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "height": 480, | |
| "width": 660 | |
| } | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "# Comparison of generated samples vs. conjugate posterior. \n", | |
| "library(\"ggplot2\")\n", | |
| "library(\"data.table\")\n", | |
| "options(repr.plot.width=11, repr.plot.height=8)\n", | |
| "\n", | |
| "xl = 7 # quantile(samples, .001)\n", | |
| "xu = 13 # quantile(samples, .999)\n", | |
| "df1 = data.table(samples)\n", | |
| "df2 = data.table(x=seq(xl, xu, length.out=1000), stringsAsFactors=FALSE)\n", | |
| "df2[,y:=dnorm(x, mean=muPost, sd=sqrt(s2Post))]\n", | |
| "\n", | |
| "gg = ggplot(df1, aes(x=samples, y=after_stat(density))) +\n", | |
| " geom_histogram(colour=1, fill=\"white\", bins=31) +\n", | |
| " geom_line(data=df2, aes(x=x, y=y), linetype=\"solid\", color=\"red\", linewidth=1) +\n", | |
| " xlim(xl, xu) + \n", | |
| " theme(\n", | |
| " axis.title.x=element_blank(),\n", | |
| " axis.title.y=element_blank(),\n", | |
| " plot.title=element_text(size=16)\n", | |
| " ) + \n", | |
| " ggtitle(\"Metropolis-Hastings samples with posterior density\")\n", | |
| "\n", | |
| "gg\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "<br>\n", | |
| "\n", | |
| "Trace plots are graphical tools used to diagnose the convergence and mixing of Markov Chain Monte Carlo (MCMC) simulations. They help assess whether the MCMC algorithm has properly explored the target distribution and whether the samples are representative of the posterior distribution.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 5, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "image/png": 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QblnFhA6XsMFEK5jErX3+1fmVUolWnEXaC0rVqVG5hQVozdbOoPDZSXP/UCJamP\n/oh+obQc0Uookbb9HlC2lVDup5QMn2mFsrxxu0CgVDHzkayyxd0Sbyhz0sf+LbsYG2QMAv0z\n9lCuDBrKycFAGcA0Qkr+Ad995v1CuZ1DWbYIPoYPKN9u2S6ARbjCoZxnQol/Myh3FraWH3rM\nDqWcJvZZ6GiFUnxKh/xBmdPlys3i+HcbGIfGT+Ux/jvJB5Q9HFBuYVCO5U8UGJTdFShb2jtK\nqOFQPu/2r8zKtR5Q2qqFIJRLBZSFY1fLREPpBuWsNfy3DcpjDMrdEkp/k09kb803qkEcyhkA\nO835uZtZoPxDXEQoZ7AXboHyAMz286JEfEHpZ3DmQTwsQSiPgmjxWxcklPgFvxzq2q4OFMpJ\nTij313C5Za/S/DdCmS+A2TGU+IWyJv4cZJ6CaOsCZR58jBhXKFMtbdk2gEW4wgeuzJNTTpxl\nf6+AL7ygHJiisgKl+lEclW1Nh/wUI/WA0oDMH5SCHy8o+WcyO46gPMigdN3rU6HMqUD5sTeU\n9TWU/3hD6aM/oguUFcVH0d96RHsMfiMmlBtv+BmFnV1UiDSh3GFOO2uFUp6YqAtlJZTqlhMg\nlJ+5XOsXynK4zeaYgyON4gDKd4OGciLHSM0ae9UXDEL5558CShyNulrt7rfpZz9P8jf47uHk\nhFJ5Idtw2Y4sKpsbH8MHlEui2/h5apn/BJSy7uVZ1qd4OXz+BnxTyLrJBg6lWOEP+amx96I/\nKL82z1U9mcf47ySwDHD/AUR93R6OgTQb4AdyDfjsUAFC+ZQCZbT9/J+ag/gGNYljKCvRL8Gl\novbaIwylxyFqbKAUH1B/644ah3IXg3IfbLzuB8ps0XztHYhQ1h8+HWC7K5TnwOiMgVBOd4Py\nBT8vSiQIKEtj18Ecsy1QinfIBmUi/8/NoFzqhDKQXjMUyvHg6K+xxl71BYNQdoihJCOUOMgq\nkdp1q/YEl7vIXIoNlG3sUM4pWyYXPkZ7MsYdytZ+nlrmP9xBolDKMeVn2HmU5VAeHFCmHKb+\npUD5DHRQoTwiV/i7gHKxvOpJs2O6FcqdKySU3R1QdrZAyUspvJBHuUGat+x3eUrpiBFtb61R\nw6Hs5/avzL3NHjOxhLKuCWWh2FXHe2ig/HuNF5RJfHTcdoGygjuURwWUeLDsBWULO5TbzPm5\nrVCeFRfrQhk3KPcHAmWW2ENZCqHMzqAUVPuAsjhC2dD3gOb6+AX/FtSxXV03QCjHgmOewU/c\nZjzoWYqQ1q0ElNiBNUw90VZjvMtdZGIHZYZssp4TleRNBmUOfIx2pLoblG9Ft/Lz1DJOKPE8\nynIoSA81vKCUBTgplOp31hF5qHHIvRgpixPKXsvJJgNKo/fAEyaUEy1QdqgHoh3KCWUbBiWW\nqL5YZ1hgUD4poaTWRXlD6TrjeWZRsAjjAeXOzyyd5xHKJRpKLyh9dB9ygbK8+Cbrb/WHQ7mT\nQbnXA8rmHMoBDMph0wC+NqFs6hPKaaxERnp1y9kPs/y8KJEs9lJ8LF+6jmL/pyrruVkKz18g\nlIcllGtNKNW3ikFZ3Hd7EoPyzSChXA5jYgFlK4Qywx2SDxuHQ1Uoq/qD8i8/UI7lUJoHjG3M\nfXwqybOXyOyyZbLjY7QjVdygXBzV0nGlM//y4bvz5AigM+w8ynLIT6EsaN1krVAOSK5AGWOF\nUnyDHnItHcXzYg77NSWHUyj58e9Ws9n8cV9QxtSTvdJ9QTmKjJ76A3QRUM7Ko9zAN5TjE31L\nouwHIWo4lK4T+WaCIcZlFcqP5L6vTFNYCG+POmZeUamOCWXBRw/KMQjlpTVebXlBQYn+7JWN\nYUesUF7zU9cna4SEcp+A8itXKM8CnKG/mi8mpI4DyvpYqPAuoNziCuVJ+Al/MSizBQIlztlU\n3Hd7EoPy9aChHA2OFslPWNWXW/wAS7ZpMShbYmvoQpIPv6FC1RNtlVUov6282PJ4F8F3V9Cx\n7MSRAmVr86uLSgJzKZSls+FjtCWVXY5xU70ZFe240hkBpVGt8QxrHlwO+QSUJ8y+iylsUFby\nCaVYMWIHZQlvKL9Vbh5Tl5XvoHnKMTS7NYXyKoWyY3eEktec8YDyCQHl87CNtKjjc7Gxxekd\nCqVrt65MYI5szOEfynnwknrqolJtCqVY3TSUvpLEx8meqbZ55GjKiV1+BuVvxjiVI4BzK3zD\n2vT2eEDZjB8P9edQTgX4EoxTtVYocbRPlWkIZWm6LCqUibBHzD7f/eHNZIF15J2c9lIH7lCe\ngB/xlxuU4oj7DyeUxTygfFHVsyMAACAASURBVA1q264OFMqRTihXMyh7DcWfazKKKxHKlgzK\n6SQfvvEWKCsqGwxpAt3+Uv70D2UJZMEK5Rl5mUI5i8wuUzor9i11h/KxNwKC8jLv261AuZjg\nq88LsL3A44TUMBfAAaWcWsYBpVgxDrmWjuIxoZy4hf4YO42UGKZAaTSbdzP7W06IBZTfUyhH\nUii/h84Cypl5lBv4hvI5hNK+yqhhUDZ2nXYtk1IzIsdY83oB5YIx8gqEcpoFylocyu/CN5MC\njyqUn3hBmThwKMsaUK4j5H9GI+FhBuUOCeVVP1BmaaJAWQ+h3OILSuxyVHkqh3IKQnk+pfgM\nE5UksYByBiNXzRZrHRiRE3zkRUncZrO+gNuZgPLTIKHEBt1XA4Fy5ynHVcthuAuUrDdPDCv8\n/WaouLJnSQ7lOzCF5MWvrhAVynIqlCkBiih/UuT8QAkl6M+BplOtFCi/Avrmv1CmdBZ8jDbu\nUL4eFcgkPhJK2RZ6BvDc9nLII6CslN24KYdSnq/ob0LZB9qrE7IekUdCh1wrovCYUBYaS3/U\nakqKq1AaBzk+oWxfF0TVK19QjmBQdnKFcrH9Lo+Lrr0IZXNvKF1nE8oE5sjGHGPN6wWUzxlN\nIU3gZRhjgbImh/JDug49qlD+9YnXSY/EPtowXaAsg20j/bfTA4S1hPwSFJSNOZTPcyinAGwG\no8J6k3LG7SiUeDiPUNZmUP6NhSIklMUJQumzP7zydHRBpzs+Sncoj/N+cnEL5QInlM4h0PWc\nDYnLYZgDymmjGZTtGZSLnFBOJHlxQS1QllGhTAFgOeL80y+UaOrAPPLvnADmF46AslRmfIw2\npJIrlC2UyQRvLv3N/Wku80Ewr0iQf4dm5Lt6SyAXwLYC3egesQll8qH76/5Nsojepb6hPCzX\nW39QzrVCWUNAeUO8POO7u6tPKOuwgnA0T/qEssNTCCWvEDNDrevmD8qvSfNaPhcboaRvWGPX\nSTIygTmyMcdY83oJpbGHj1COVE9dVKRQviWgzP/oQTn63kCZ+QUJpWwkPMSg3M5g2Q0brviB\nMnMjFcqhFMpNrlCeEVAWOU2hLEUmI5QrDShxG94bOJT2IjLuUP6PbwglcecmixVK4aMVymJI\nVTHbGcorp42LDMr5oK71C+nBfR0nlHXHOq5aDkPtUF6FIuzcS3tWz/bVEHE1QhnNoBx3MwMu\nnwXKUn6gvHkGXLqCnuANFXYoE5Xi+/gsXwooM+F70todykUtapp/HQLXbkoL0nUVUMrn+R2a\nYmFAoC5vy9+NkArZjBsnH7oc3iOJW/LRDAFAedC1IgrPXAPgQnhEWq0JKTaMbDSgNFZJBcrx\noJz+IO1rG1A6qqIhlFfornGHp74LFMpuCpSRNe3/VeIXSnMMY46x5vUfcij7+YLy+n8Va3Ao\nP0AoYzcn3EMD5UUJ5Vb3I6H9DUN8HJq7QFkaG5EZlJ/ifJ0mlHjsqEDpu6Ru5ga8hf05DuVk\ngA2+oER8K9OPwYByBYjPMAw7k7hBedzxdHRBpwUI5S98QzCgPAif8uO82EA5xxw8U88JZeFX\nA4VyGQy2Q3kFCiOUVysyKOcZUJaQUI45xw6nLIMBiqtQJgfIrvz5VFMXKC+F8jPYYwE73kso\nz5NEta1QziCzypTKiO9JK3coX2thfpp083a+RIJzcdbmowWNSRE5lHMhO0LZlZDyVihnkUQp\n+RHk88kqytkP+0A7K5RiRu2DrgP9eUwoCyKUVW1QGkX/u5jdiKxQtqvNKmcSNyhbwXf00xpG\nYp5EKDns0wODsh9C6TYAS2Y/gxJXgXb2gf2ZgPU4n4fz5GYfS34rKTrBSSgNAJrQb6IRJpTP\nRlesTqFMiVBOfnShXC08W+rWxRY7+vlqw3SBshRCmWkWhXINh/LWDDzJcpBBuY1BuQs2/OcH\nykz1FSjrIpSfm2ulFUp8zEr0Y6gFJckkK5R4dLzXuXjHQ/6wXcOhtBeR+cJaglXkZziKv0og\nlJkZlOKs6RoTSrU5l0FZ1Abl9EqLZCeSethFwAblfFco64x1XLUMBoGte/kVKIRHyvuAQfmi\nE8qRZ51QFvUDZdvqLlCeF11kLVBuf4yE1eH7+CxbOJQlM+DtfUC5sHlZ86/9DMod9loOI6CW\ngFIy8js0oVC+ANkAvkYoy2U1bpyMQjmTJErBd4ysUIYqD3pYzKgdGygrNyZFhxpQfmkWVPUH\npSi99IRfKDu4QZl6sf0uXQOHcnTjceFY0riEfbcyI7Buzp2wKYBCeVDW3/qQ9/hUoXxRhfLx\nBhWrmVDme0ShvCChXGJ85BtVJiiUPg7NXaAsiWfbGJSfYInnWeQkqzsgocTuI15Q1uP69MNK\nT3WHTgL4zISysQVKnOazEt0b5FBeUqHMQ7Ax1LF4R8HaEvZ3hiR0HXHOOu0O5U9wBH9xKGcx\nKLkZa6SPNiiRKgeUFUvIdgcG5TxQj6MKvRI4lAPsUP4HhdC1vRzK2RLKHhRKPMH8Dgw7y1Z+\nCw+FVSiTWaFsU9UvlDiqUEC5KYyE1XWBMj12eG1JKrr07H7sVSuUyNGcTLYbjYCafFj1y/II\nF6FcCzMgK4UyXxdCyqpQLkMokzugfNoOpeh3fdB1oD+PDcqKAkqu1ZcMt4uLVhLS2YRyXCyh\nHEraP/GtAeU0C5SOcnhdxRgIhDKius/FxneyFZQPx3qDxe1jHTIC673XCctZUigPyGoJEkqj\nzdgGZbdHHcpRVihl89S1kI+VG/mG8nlPKGdSKPFAjUP5tYTyX3coj2ClwUxipu2+BpTrXKH8\nHQCnaJRQTuRQduP/DMO1d488wjJzwAYlfRAGpb2IjDuUP8Ih/MWgpK+RPproVm9Aed4FSlvn\n4GkVSsgXr0B5O2OKi2TJZVLoJXcoxziuWgb9nVAWNKH8vaEBZXEO5dsw+Cw7OFChvPLYWOUR\nnFA6R2GeEy9aQMk3740cyl/ljb4Aum7MLFMyHZ51c4cypQ1KHKcy2w7lcBcoG1Mop0FmgK0I\nZRlzEl4BZVK+Y/RcsopyUq+noa0K5SExUSxdLd2GZfHYoKwQToqoUGJ/1LexdrQFyqPKA7St\nzUoM0zzhqLOLUP4HQwSUfPSFB5RdVCgz+JwU7duDHEqsDuMCJeuU0hHLWTIoxRDcD7ygrF+x\nKiGLBZR5H1Eo/5RQviWh/A/eV270FvjouH0enBKVMKBcLaHEg64DCpQ7fUI5CqtYZ6zFO7dx\nKIdMBFhrHuf4grIEh3K5ASWu5S5Q7jY3ZfkgVHRn/e0v4F/izA98qvG7hLJ8cRcor+D+ccgG\nUojev46znq2E8tpsY5a5ZfCcHcp/oQC6todBuRzk2mZCOeAMfufdUfejzlvaBpMCZFP+bFPZ\nL5TYECyg3BBKwurxxhAWDmXpEmkRymh3KBdEWqDECTdfcEJZg9efeFl6dJpBORkyUSjzUglK\nK1AOWUb3Y8OS8O3dCmWI8qCHxPyHfqGcY0KJhJdrZIPym3fJEqz018k8+2WDsqbcjB73DeXj\nJpRT1QKYvqHsS1fWZs49FJlOkfuhJZQLx7G8xe1zimQENmCnI5azzF5i4wE5QEBA2VfugVMo\n58Jws8WtW72KVTiU78Pk3kkfVShXif6Gi+Wq8a8FysW+oPxVQjnEHJBYHPtvZZxJnsM+ZD/S\nBz4hoMTD5K2snx2F8rL7tF+jsIp1xpocymcRyjoI5ae+oDxOf1WkX7A1KZQTrFDi9DC7ofBZ\nYs12sHZIPC2gtA+wM6H8YYt57fdYS5i+RuypklGF8hN3KItyKL8psFq5clq54vLF18Pv91cY\nlBfoq7kDH5FCFLLavqE8BOnlVcugnzuU/6sP2ED1rgXKFgzKzmfwo3SH8s0C15xQVgoWys0C\nyjTYRhJNKrhBOT+yjPnXPgblrIy2Gw2H6hzKl6RHpyGcQjkBMiKUVIJS5kxASTmUifn2/lyy\nCiaUbaxQ8vkPKZRuw7J45hhvBIOyTCNSeCjZIKDcAq+MboBQ/kE6mlCOtUP5Hr/kBuW3FMrB\npN3jxyBGdAHxgLKzBUrHLoBMTLN9EE2hxJEXxZxQsgE7HbHHWjbou19253KBcg4kMaHsWq9i\nZQpBCoRyUil4RKH8w4BSrhqX5SdMc3T/YvDRcfuEhLKuWYrCB5T7FSi/8QnlSIQygxXKCVQy\ns3pluAXK/xEVyr8Qyq78n2EhNxBKowbKBkH9ly5QrnYpAmZC2VJppPsOh58rUO4HsaF9Io9S\nbFDi51207nLL2fepZe1QYsv8DoCht+EdUnCmK5S1R/PfByCdvOpd6GuH8jIUCMMKHQzKt21Q\nXjnyNrQ5gx+lBcpzEspR+AYmsULZuqJfKHH49QAO5eccypPyRptx3ZhRukRq/KCi3KGcZ4US\nZyZ2QDkMqvFCPTYox0F6gK8QypIMyiu4Lggow/j23i+pbyhFV6SD9rlilJhQFsA3v3RDK5Qv\nj6qPx1o2KI8oD9DGD5QtGZSDSLtux6C9gHIKQjlNnH/xD2VTP1A23QdRFErsJ+cCJRuw0xGb\nzbPBs/tlLwUTytW8/0djCqVyDrdr3QomlCXl3kiAeRigHGmB8k25avyjQNkpwieUv0go65il\nKIrhB82g/BgPVWdQKLcQCeVXEsp//EFZg0P5jAHlagnlaRJuHqxR43AeUw5lcTLeCiWuVRRK\nOYfgWHH8u9nclOWDMCjt52Q3G1BGKY1b3/KZRBiUGWa6Q6l2OWVQFqmzXJ5kZZlaprjsQlTX\nhHL2Y5DkFiwlBadzKPcWJWoklPtVKJ8BWwmMfyB/GBlfgEO5xISyGEL5RmoK5e9o9m1XKEe6\nQVkB1G41PGfFi0Yo+z8+gO8HUShD6ytQbuJQFn8MoWzhDuUrVihxCsWZvqGUhzunoRGFchSk\npVDm6UShZEfrU7DiXNIhOEozLJT7SKGUk3r1tkI5TEzrFRsoSzYkhYZQKLlWW+AlCWUHtmAn\nLxEXKFfyS90cU9wglP9SKNvaoXxCvAGp37DfpZN46mcZlFPt/5Zp32QftIByjXCvz4RyFy96\nlAGYwx1xa8gGz+yTDVESykhSl1e+tkNZp0Il6oOGku/xvCnPH/4tP2GaDk0X4wlM8t8Fx71/\nNKA0u+oXNaD8SIVynwLlSvjcF5TYgzl9dTuUqwSUP4X+HV42v+xAQo3DkrMIZQ0K5TjczpeZ\nUF7Bs0awU9x4bB3+exNr1zSDUK4ikxyb8WbjbWyhQHmMlxRnUKYPHMplskmMRYUSW4xeZlDO\nygGJbyKUUzmU65JblseEMq28yhXKfKGkVwoO5WILlM2jX020FFr/jo1bvqC8SEhiG5Tl/UA5\nBvKTyBoCys9CSGgDMN9dCWVKfI99QDkswgIljkycYYdyKFTlFc1eksuFUH4K3SENwJcIZQkG\n5dhk5OOuSRiUoRBBln9og7K1uumVFrPVUCht5cWUGFDOSo6NAsUbqFB+AS+OZFCe51CuZP30\nbVDWADHFLoPyE7X3A4dyIGnb9SiFkrdZT2ZQioMENyh5+QGEsokfKBvvg+YSSlkB+ltx+i4D\n7w/REceCZYOn98njq/d5naNnI+XBYWOYrULZpU6FihzK92BSiUcVyvMfCyjfkM3ilxQoYwSU\n0Vkd9/7WgNJstCiCn0SGGU4ocRP6krWJ1IHP/zahXGJWyBNQVuPjyvqgSrUHjwf4iLV277h4\nBP4IL5tazuYtoKxA15uKUExCKc7zheJZawrlN+KRJZQbYw+lsitylB/KG1DuA7FHslquUz6g\nVHvgTCldTB6eCyixr8eMPJD4OkI5SUBpnYJBQrlPhbKPHcq/IV8I6ZGMQ/mGFcqo+fAWQjkN\noVROYTigVD/n1uU8oGxmg/K4vNFGoNvy9NLFU2BplOakvEuZnhSdI0qbf+0FHKg93QllFV6o\n5yW5XKehIYWyEKSmUObuSD8NdhcKZT9ITKGcRj/7ZqQT/eru6xPKUvI1HwgEysas9bRYA1JQ\nhXLuyHocyhiEchGreGeFsrUVyqnqEnAoB5A2FMp2FijFR+qEsmOAUIYjlGUbdaOXi0oo5RdC\nBrZmkA7Yczcb9N4rtwYJZQSp+6R4zS+A0tmlS20NpQLl6yaUK4ybxDRZjO3ypLZzkoEjBpTd\njOsolDHjGJQf4smPGeQ420T2KlDWQiiNASztzDIXvqD8kEGZeMYRON+IQil2balxWPSMQnkI\nKJRjbVD+i2eNQPaiGCvGU28wN2WW3+jr/5hMNDbjO1P522eH8nzzG+wFs0P5Ynnoj3TeUN5M\nC3foO1J7GYxWnnJKKQnlykImlNMKQOJrsIQUmEBfdHtC1lqgfD3/KH5hrweUeUPIk0k4lIsA\nRE2k7kUv7W0eNQ9eg9ancQu7BR+YRXPOSjRGIJSJrFC2KusXynykaXUB5XonlLXen166WHI8\n5+cDyo5OKKd5Q/kbg7IgpALYglAWy8AWJinpC4kHcygb/tmxK4NSzlXjG0pbeTElc+QThjMo\ni9S3QjlnhArlawzKMXBYeQAK5XJ+qasLlMcUKPlewyQ8r/+4+EhTuUB5figOF3sWvqKOTbH/\nW6Zdo70QSaHEQysFysexmYpCyaZz7oDHMFmh117Wyk9UKMXBoRPKChTK5AjlxOKPIJQjEMpz\nH4vOBq/L84d/yU+YYJvHmwzKKs5JBg5KKGt3Na4r3JPU6smg/AChnG6BcguDsiZ8fsmEsq0y\njG0kDvVIJ6B8mkM5DuB91ogTMoVBmUpCSY3DomcUyt0cyosMyo8Z+qH4NlAo5UckofzcA8rL\nYr6uzfAPucl6D3MoD+Kjk8N8D9UPlOdUKP8FCeUI5SmnlCzGbvPvy1lYZ42XGJRTi0Ciqwgl\n3fms5YAyNQQE5SXIC+RxuleIm8NCBcqxIfWjXoaJCOUUsuV36Gby5x/KMqD2P+Q5I170GMhL\nGkso11EoG4Lc8PAbCaDj9FLFkiGUke5QdmhmgRJrw03LYLvREKjMK5q9KL/Ff4MGDMqUCGUH\nqgG7y2iEMoxBGQKQriMVtG+S8iaUrdRNr6SYhIFCucaxWDKzrVAWqkcKDKHrD9+t+wJmj6iL\nrRvnSHvc81zIRpPaoKzOa7NTKLE7zhQ7lJehP2nd5Qi0DQzKDvA1KzXwjAHlLeW/89OLg0CE\nMoJCiXsMBpQHgPcczQCsCbIDrnFZoede1spPTCibyYPDxjCLfoCjZPXBLrU0lAqUiySUF1Uo\nG7/JPCznhHIfiCMABcpCPUnNHhTKfgjldwxK3HvZw6D8gp1l8w3lCAZlVTuU7zEoYbIDSix6\nVgG+olAW5VC+C50fZ2XCQrHoGoVSjuEeK4YJfm5uyvJB4CMywShLeFmcJ0coV4XhXqQK5SG+\nh8qgTDsTN25xSLNafvm6QFm49rvMAHL1K7Y3MqUEh/IbevCInTVegmr05+QSkOgKQtlAQGmp\nLJ5SQrnHnCbnHejthDIPkC5hHMoFCpQjoVbUi9ARoZxMSr4EXcwVUYHyArbtWqEsrUK5qw57\nQBXKRtUH8P6N68AdSvoyTlEoy7lB2V6Fcg8rvj3VCWUlAaVcOSWUySmUuSiURViHKQPKqQhl\n4g7tLVD2olAqJUdLyF38gKBsxN78ghTKwQaUm2H2cBPKP/9yg7KVHUplCaIZlM9boJyI72Q3\nCaVj/vUOsJX1PkIow9G922mUzkiD5Hnwtg33QjMo2xDP4xSR9fr2A28mzwCsCbIDrnFZofse\nXojaJ5RGyZDONSvQA783kmNj7MRijyqUZw0oZW/fC/ITpmmHUFIPczuhnGRAaY4AKNSDQpl+\nOoXyfSuUx4kC5V8+oMShHmmr8M+nN0JZa/BYgJUI5R2YfBjOIZRiNm8BZXn4ahdCOUZA2Y1N\naxqKI7+/AWNo4hgB5Wf8O/Rq20vGg1ig/EeB8j22UTRnn9kBxvMh/pFTKMuUTjtDgXKVK5SX\nAW5TKHO35uVS3+AdAicXL8Z2P7+hB48mlBPLQNi/CGUJNyiTSSh3W6G0nvGhRwJ54E6nEA7l\nPBPKIiMolHMhBlr9RjeYErOgs1wRf+i4nkF5DXssukBZSoXyXT5hjAllHtJAQrkWSEgjkHso\n+I0E0GFaqaJJbpOTEOEOZbtmpcy/9rDi21PcoGSlHxUo61MoC0AygC9yxdD3l0E5Kik9Jg0b\n/I6AMqY13ex9QlkcRv3MPskDcrIGlyhQjiTkeOK6JL8K5QsSynbZSOqCr7KeWjYoq4EYHdDF\nN5Sdj0AbsTF4QBkDX7GBYQaUN9RSLgMNKBtwKHFnUoWS9RxND6wJskNVglA+tYcXosb9RPY+\nPNNMtqI1hpnAuhjz2KA094sCycMD5UfiTX5NNhD9qUDZNpxDmZp9gjfUkQxDJZS1zP5aBXuQ\nGhzK9/Bsj4RyN4Nyswml0d2wjQPKyiqUgyiUy7G1+zaDsqEJ5a/AqkM6oGSTUIVi93MKpRxx\nM0aMp17PN+XTcgJm+iDwIRlvlCWUUG6iUK50QHmQr5pFs2zMkDY5h5K3cSlQKvVDBJT0KVif\nnlf5Fj+5WFF2mx3wGIPyRQblhAoQdplCmV9A+akFyiSskyF7H1PtF2cqJZRnqhsnJP6C3HAn\nBjiUL1ugrBk1G3IilBNJ8WnQSf7rbRiOUL6b8hqHMhTAHOhCjxBLqFC+44SyvgplOD+9xoJQ\nxlAo6ap1Epq5Q9nWCeVkO5SDoaKAUn6LI5RrKJRJBZSF2JvLoAwdjLWJKZSJ2kcxKOVcNb2g\npcpUMRhZk53wPQDqUABrDCgb4pu/H2xQzhpWB6E8i1CGZF3AoBzNh7iKUCjf4ZcYlJP5EvRi\nrYsI5T/wHGmlQDkB38mu4rvPDcov2XgHhLIR7iBet0IpTu+0qb8XmkCZhhX+UqDcZ0DJmiA7\nVCYI5ZO75WYgoWxK6nAEJZTYVBZdknSuUb6cAWXRRxDK4fhunJFQLpRQ/iG/ComAcoqEckfI\ndfPeQwwozYmoC3Qn1RUop5H/MYQklDjSuoaE8i08ZdRGGcbGoEwjoOxlQLkMobyFUJ5FKMVA\nfgPKL3diWe7RuJ2/A526skmoQvHUjguU6/imfErOAoVQzokJV6DkPS830T3SlazUmgrlAb6H\nWhTfNTwBtscTyuO/MCgRTHoszIq9Ti5alN3YhBK/38dVhrB/6C5n/uL0RbejUFoK5oZJKOl3\nAhQgTzXsj6+1F4Nyj9n56CLkgtvtBJQv8mc9eYJBWaPFC5ASoZxAik+iUIoy4G/DMITyFfpy\nXaEsDspJ/3d4ee8zYjd6DOQmdasJKD+1QfkZXYr2COUIcoJB6ZxzIXnrphYocbd7khuU7G17\nUa6cv0E9CmV+SAywOSf9SinIoByZhEIZwqCkz5yoXaQ/KIvCyKqsvc8C5brHLqnPPFu+EQzK\nfVCH5EMoefm9TTBZQtk26x2gUOLmYYWypSuU9dnBbzRdcf6BfqRVp8OBQtketrBuvH1MKJVS\nLiaU9fZCYwolrpmFJZT0G511sU/PB9XEVCJYiPWJ3bLQsAmlODhsDDNwtZ2YmG7uNTKTThzK\nZAjlBA3lQrmWnlegbCOgTMU+wc3qNK4mlObcBfm7k2rdGZQrnVBuElB+dpFBWQuPjCxQ4t5g\nmkoSytcQyjEA7yKUN2ESQllGhRK1o1B+Y4GSTRkQivuXO8AYcTNG1KVay1tlTuBde3fiUD4O\nobBIbEZWKLEwhgrlfv54RekdrFB+LAd52qHsEMmhxNZOAeWkIhLKlGycBIdyTFUI/dsnlCES\nSvqdADlJklLZfUPZWkA5l0PZLFxAORNSQKtfEcpxJpRLJZR/kWG4qx5ig7KYFUpWY+x3AeVo\nCmXtav35wJQ1cAeh/EnelkE5tVQRGE6PKZqSsm5QthJQHsfO/bvZLAUT7VAOggr8bZsrofyV\nQjkZ8kEiAWUBdnprRBK6qxUyyICyCd3sk5QzoYyWrxhTBEZUwSJ+ViiXsLXziDzxZkDZwBXK\nPkNrkzc5lLchy3x3KN/mlzrjRJw2KFfQda0LaUmhbC0Or8bjO+kDyu1/MijxcKcPfEmhnGhA\nyTdIE8q6eziUaxQo9xhQdsNfMRUIQvn4blnt6D3+PjzTREIZzqEciZtA9UykU3WE8vVkWHZm\nQpFHFcrfJZSvynHE5+RXIU3rRm+yU2YcynXqpFsGlDU70C17EFsT81fqlat7+mkUyhXYQVtC\nucsVSqw+1doBZUUOZU9o/NOGmgjl29jafUNA+ZgNynIMysJklICyS14KfcMQ3OoplHLEjYTy\nU74p/4J3rVVGQhkiO46Tv0UXdYRyBYMyUkCJB/z7+OMVheIGlPxkgE8o29QkhfA9xs1rvgEl\nu7GA8u8KDMrRNSD0LwFlTTuUt0GeN6cvFXKQxE9mw53BngLKifJ2F+jR9a1oehM8tzmbQxle\nl3QvPByqt5gByaHlrzCeFB9JoRRnTJfCUDwD/DJ981yhLKpC+bYdylykpgplY5BtXtjGAdCO\nQ/k/X1BGN8WZjch25vpuNkvBxPS2Gw2C8rxs81xJ6K/0ILgxh3JTDgplfhNKoFBOZlC2RSgT\nl5NTMPS0QlkYofxo9VX6sa4yr32LrZ2vyhNkL9igrE3yDqb+SyifkFC2yXoTocSPYpQVyqq8\nkqaAchKHsh5rJYyC5RTKVqRlx8PQSoWyi4RyEVFT4lXSDr6gK+c3YbhSN8TP/BqHsirbVgdI\nKFvX2QPhUKYB7iMWlmWo6IrKxiKl58bFYJe8LNB1l+z3udKEkreihcN0XG1HYC87hLJa+bIc\nysqPMpQfijfZgPKs/CokCOUbCpSvu0MZgwWY2YFLPtxM01mgRPZ2sfOhG9mQKQrlBbZu1MTu\nZa2V0RnD8bA5dUU+jKAHNO6Xs+ag0QBLEcrrCOUZhFKUhjoF7MCBQrkDoRzJoezYJTd248Gx\nZQjlFvHIo0UBvzV8U/4J7yqh7ArsjA6LCeUlCiXu6USy9Xs/g3Iv39yLMCinszGSFijvrD2m\nQvkPhTI3hxKLF8/n4O6ABQAAIABJREFUW/ykwhzK7XQPrw92Yocq9K+RNSHkIoUyn4ByjVoH\n8oYDyqzIVg83KG+2EFDO4lA2qsWgrNZiGkJ5im4wxYZBRzFHFoVyCIfyDw4lWKGMLmKFkrW7\nqFBWl1B+AnfADmXbqflyMCibuEMZ1aQkf69x49zNZimY4BtK+R+EMpxCGYZQlr/1XRg7vTWc\nQ/k2TL5DnzmsTWNPKEfDZ/RjtUCJa6cTyvr45u+DWiTvIAXK2oMYlGdI66w3IMs8AeVBuiEc\nl29eFV4gzoCSLYEJ5d8UyuiOhyiU/AQgeye7JCMro6/iPBmWt6HYPArlZirOGuBQTjCgLMYq\n0gyQPSsRykYCykISyt0GlGyHMQbPC2SBLnYo+zQmtXkrmgpltUykowFlUphQ+BGEcpgFygVy\nHPEZBcpWDd9gfQtSsY59tVUoBxtQNl5wtRs9evv+Y5JXQNkXll+iCEylO28I5U4FyuoIJa4b\nNbGIiRPKCgaUz2StOZBCuQQbca7BRAplAxcotwgo/8RNuWPnXHh2GnsCU4qMUwgmlGwexR/w\nrjXLsAfxAyW+lSqUe/i+bhEo4YCSjYb/jbKDUF5jX/K3v6VQZuRQ4miieXyLn1ioCLvxdgoX\nhzJp9otkeB0IueALyqsGlPSlQnaS6CkBJX4mu00o/4QcTiirk6cYlFMhmYByEHSAmwPZsHUD\nynNkqIAys/LE0YVBWWWX8nYXE8qcpJoKZRPeD4FlHX2kNlPoj+F0DWhCyrhB2YJDuVGBcrwd\nyoFQjlcjnStXzl/pQXBDyMuhhN938H4AwxPTY1KEchKDsjWFso8KZZTch8YUguGVKQJr7VDi\n+Z0FsieBFcq9FMo8JpQbATrVElBmuQ5ZXmEfBYMykSz2aULZCaGcaIVyGV3XWpLoDiaUTfCd\n7JyMgv+bA8qi80hb2ERl5FA24FCyFviibKS4AWWr2nugIZS2QrkL+OCw9MBKCMfgNpcFOu90\ngZIfrYfDNFxth+MmgFBWLV+GQ5nkEYbytIRyvlwXf5fHDMSE8jEGZQ11LpnBID6dmiHwdVeK\nwdjCJA+DciqFshost0O5QUL5J4cSx+a3skOZSkDZHcKfzlRz4CiA2QjlVQNKMaGXCSUFsRAZ\nIaHMwaE8x6CUm6eE8hO+KX/LoCytQClqUf8tBj1upFAud0C5m4/9KwIlDSg/2VbhP5zFjtl3\nEgYxKPexe66im3IrASU2F0goCxZhfeK3U7ieZsObcEDL0HoQ8idCWcwFyv8MKOlLgmwkUfcs\nrlD+QaG80VxAOZOu55TxRlXJU4WGQ5UWkyGpgHIAhfJGPtajeSkM5lCeYVDesUNJF57MlZ0j\nEcozEVNPi4ZZhLJK1f44MGXBT6vhNjR1h/JnunW6QhkpocS9mF1sOpdxTijLukDZgEIZCrAx\nO/y+HVLjtcMklJ03IpSt/EJZEKEcbodyMatHsED29H9BvhH1OJQ1OZTYHHP6Dn2SGAFlqyxX\nITOHciRCGSahjKoCYnLuTrhHYIPyXZ9Q9nGD8hUK5UZK5CcCympNrtmh/LEbXmhVaw808AVl\nOmDFYWJS/oFzoHTaKbsz+YaSHgpVzUg6VmFQJkUoxxeSw98CzMMEJfduvhz1oULZssEbrG+B\nPyhrAGxlUBZiUD7FoCwC848wKHHF+UZAid/ZFEo+0q8mdm60QIkz3aQqz6FsC+G9M9RAKCMR\nyisw8RD8boUSm6LLwpZtCpQdOmfnUJ5lqsiz2aOr8d+reYeIo3hXC5SiFvUlC5R4wKxCuYt3\njDGgpOvfJ2/haCMDyoHs9Pde7MWJlXOhVQYOJY73eYVv8RMLuEE5pD7dCYbFHMq2VHS1vNlx\nYBUjiIQyrEfKKdfehu4CSmP6wj8guwVKCKdQVhJQToIk0PIk3WA4lHkZlEs4lC/BaQrlH04o\nC1Ioc8gG66X0cGIbVDWhzEEqcSjzv45QRoLsboJnzQBaI5TDKJTh7lBGNMGJwelawaHE6VzG\n2qEcQKFk1UjnyJXzV6hNd/LyYMOyAuVQCSUUZFCGI5Rl5RQMNigLIJTD6MvYjzWufhUljxaz\nQRELkm7vxhoTnVDmllBmWU+hbF8Th9P/TqG8AplfBuzONRL774TJiiNRlXndIyuUdRUoo0lU\nzEFoKZprGuM72Qmh/NUBZZGXSRsK5RcCyvqQCM5d5VAWYVDmgcmfpiR9vyIta+6G+gglpa+Q\nrNe304CyDv5qj59TZuj4jR3KcFKL2xoOUzmUfzMoO1QpRzeWRSaUIxwn5X3noYHytw+Ed/Nk\nZ+bT8piBJlpCyTr2VVehHKRA+VVXuEjGFCS5Ecq0CGVBK5TYf/FzCSWfuqUGnmFppYzOYFA+\nVo4Xt2kC4T3T1Rg4EqAZtmj+BxMYlCkllCcllF9QKAuS4QLKTtnY2EqsU7TNHFowSkC5ivcL\nOqRC2cUCJR8dvpGyv5xxF8HW7/24T/jPFn6kXdgFSmbfCQbloW/2GFC2TI9QpsmKQ3MklPmL\nsP792xQo/3clphHdCaYbVl43KI8ZUNKXBFlJWC+A6LfhKTuU5ymU1xFKPLOKUDYipGF5CuUw\nqNJ8AoUyGqEsilBez8NWdQPKX8kQ+hJv26CMKkChzC7bYZbQD/9rqKJCWV5CuYpCOQZkrys8\na0a/JSYzKH+iUJZ2mUA7WdPGFiix3PvYdLYbDYAyAkq5cp6iUNbjUG7IDqe3sVHWAsqBFEr8\nqg5tSaF82oSyB7RQocwPwyrDUIg8z6DMJp7zTXbCcUGSWfycFYNy92uUNoRyD9RAKNczKNN+\nvAGgnYCyZZZ/IfNLJpShTihZodwJAkrWkzEK3qHrWhSDMlpAGc6gTCqgNOYNZ2FQbqDHPQjl\nFgplGJwVUBZmJTUSQfW3U5KsM0nLGgzK+khfQQnlN8DHXxlQfodQxhhQrjCh5HcJB/ySo18m\ndEWuQqGsLKFMDOMLUigjBzk+Tp95GKAc6g7lbyqU9d9gfQsklMpcMk4oC5BcBpT5Yd4R+n8O\n5Q4Fymrw2e8cSjzd21KBchhCmVJA2RjCe6RmUDZBKP9FKE/Xp1CKquUmlF9zKP/AfZ4OnbJw\nKH9nqsjDoFFV+e+P+aZ8QIWyM74JoqS7CuUydnoKoey9bR999OOhIXx9KgylgA3rpFCuXoyd\n6C1Q9mm3h91zGYeS7uHkbIrD817mUE7IJ6FMitUBGZS/LIRu1HYBZQ2EUi1GcVRC+VordrYl\ntDdAvaVuUGaD65ECyhkCyrLkqYLDoFLz8XQvhEP5PMTAtdwCyoEcypMUyl/OI5TYsXuqOIkf\nlR/gTjYTyv+sUGa/FcqhzLfoYwrleBuULTmUP9LFcIWyCYfycwblTjadyxgnlKV5kT0Fylqk\nDuAXMmzIZkA5JDF5mkOZE6GMRigTWaDkp69O/fIHnnEcVgmG0K9RBmU6cbD9JjvqmZ94Jj9n\nxaAcUQyhHM6hzDVQQJkGoWwrocx8GaHEXgojEMoQCWWLyiCq7zqhbCGgbMGg5J1wG/mD8iXS\nmkK5QEBZD0INKAsJKGFESpKFQll9N9SDUlYod9ih/BahbK9AyZognm7EBjsQA8qhuCJrKAWU\nv34g5lp6JbW4+lfZuEITVf91BcpqrlBWp1B2gQtkTH4B5RQKZV6Yh7Pd/czY28HG4H0mofyN\nfYnWqEx31cqqUObDCkNlDSi7P1ZjwIhMYQzKyxzK0iqUONZVQjmMQxnTMTOH8jSDUq60EsqP\neBfbfXhXhPKkhFJUKkYoL3xvg/IOTKNQ3lklz/kUphsvg3Ing/I3nMXOB5TR6RiUzTiUbNdo\nQt7CrDfWNrqHJ6H8+ZUS1+lGZ4dSdu4/Aqy0DiG9c7BdvtCnGZRP2qE8R6G8pkLZkEJZSkA5\nEqE8QTcYCmV7uJbLgHI09uWkB//wRNtbAsqotuLDz+sKJT+DNQqyXwcOZV4K5S2YALIDM2En\nHaI5lF/6grKxE8rRdij70y8lDqVcORHK2pDLhJKVtRqSiEG5FHAaWwiN4lDKyuIGlHsBMtDF\nFVBu2A8zI7emEz2x3uBQJhJQzmJQFjWgrM6hxJ4QDMo2NRDK0yQ68z+Q6UU2WyWDEhQoRWUL\nVlF8At+nlVC+Tde1FqRF+wMGlA3xneyYlL6OUw4oC79IofwMYK2EMgTOXuG9egsyKMPodymF\ncgaJrrYb6npCeQyhbLdDdmfyDeVfhFTOQDpUylKKQ5mIQxkx0PFx+sxDCGUqcfUpBcoW9V5n\nfQtSstXJJ5RfIpSj8xH8Pn+SQvks/c5XoNzOzmx+xprLq8H6UwzK6hVwyiRldAZCuZZDOeON\nxtDoyRQUyvBUjXH/8x9I8jKH8gy/sYCyDGzeiqNVDCgzXrlxgC5E7kn47WtAiV1w1mc99BHv\nYrsb71pDQNlJgfIv+qH2z4dQXqTQ4blqCuVtmEKh/No4QrdB+StCyXYST0B/utI/3XYPuydC\nGZUWoczFoHxJQJmHQ/k1JEYosSsThKcoeYPu2itQrqZQXk0hetscllD2ysahpEeZdRHKpOy1\njJfv3znIClftUJYQUGalh2sMyiLPUSiv5mRQvgUDOJS/kMHQKUpC2UKFMqtssH6LKrEVqvxm\nQJmNQvk8Fs/Js+gjuOmEchKDcgpdDFcoG4UXJ2ytwBMIO1kppVFuULL+L3MSi6Grp6AmqcWh\n/DwrnP6aQznYgDIzQtmC7kv3VqFszqHcCnjqNg8MrQR07f18P3SBKWnFebM32FHP/LCZ/OT+\nLHwjhhfB+qnD8V2uRnIyKG8Mv5rmo88BWhlQXoJMcwWU+5V5NlpUgjfufI1L3QGhHO8GZXMK\nZZSAsoEJ5akyiRxQtoL1AO+uZlDWxbYlCSUrqUGhHJZCQlkHoaT0FWgv7r4deL2kdMCqaDEo\nM0FbB5QN2WAHglBO5lBeZFDGVMTNdFESBmUBhLKa+zRabnlooDz1voDyZQnlSbrFvifmebFC\nWVWdnXCgFco/yei8BHd5nkyDUOaEeYcUKHGvYb2E8gSHMtVx0skCZV48ZiuD92j1TDg0eiJp\n9QHDw1OFI5R/Y6+u3xQoTxhQfoVQDhVQdsjQbQhCCdF0czIq1DIoX4X1H3IodzEoSylQiiJV\nCGXfHNhudpG8yyoGNUMoJ+6D85uMmxWiiyihXLUYv/9tUO5m93xXgRLHMQsox+cpzDoZqFAW\nAITyFH3b8xQVUIbiS97Hl+qQAWVWJlnIMwzKJ+xQnoUsJpTYEa4B3fxSLnuq4FCo0DyNAWU/\nCuWVHOxsgQHljxTKFlE3JZRtxIef2wrlZSpNZQuUVRiUuRmUE8Gc1xr3fKIQyqFkMoWylBuU\nDa1Q4nhOFyhLCijlYyOUNVUoWbUWCmVvDmUGE8oyDii/grUMykShdFcaoexMoRTNwW+wAZjz\nQ2cIKFOtoGukBcpa0+bBv7/BjwzKljXI6whlVKa/EEp8kOEUSrMqcvOK8PpB1vKqQllHQLmU\nrmvNSfN2CCVHpz5C2SEJQvkNgA3KuRzKd5xQFmBQhgIMSUEyzyBRVXc5odwmoEwroTyKULbZ\nLqFcbkBZk39FNoJJFigrQElCXmNQjmNQQm3H5+krDwOUQwSUfBDcS7I27wl4k5JIP9eTL19r\nXvd1dsrMHUourAFlHpLdgDIbvMKhxBVnOzS/hn1GTrLHWP8/DiV8KaBcy4vjcChL4z2iEMpu\niSmUjVM3wltfYlDWK51CgRJ7gUkoh2DPySUUynRteuxne2lUZGOSvZGV2Xuz/gM+Tx7raUuh\nPJWM3rAj3lpUKv4LtpFnbVDeugXjJZSsWIgBJV2fV72Jr8knlC3SMCgjOJTsGHJ8bgllIizM\nz6DMB6UYlG8ilJeqtOFQXpJQHgR4gvUe7YW7SxlJyLMAdZbC425QXolQoKyP40q6P1kAoUxN\nD9eijiOUfRHK7ALK/hzKY3h80MIBJfXodhbZYL3YDmXWawLKXK99yKE0Cn8hlC0klA3coazP\noVzPoPyGjeccaYfyeSjBp5SZbUJZg645OdmnkRV+28przQ0yoExH/xHS3Apld4iEG+TSjGkv\nwDr6nrEGzgH0axShnJxWNAe/zkZtzQuZwfsKzwJ69DS0MPYdHobvclXcCaiNUP6QGqGMro5Q\n/kahvACZ5hhQ3lKhXLQHz9dZoWSjrSWUkWlWQAsJJb6TFMrecIoeKi+0vA2F5pCWsM6Asg5C\n+R+HMj+DMgRgMIeyyi6oBaXq2aFkheUElO1w9c8ERZfYoWxAavJPXkA5BEdxVKJQlpNQhsG4\n/PToMAK/gwPMQwPlSQNKWUntON1iq+BX8HTYaUDJDlCqqA9vQElF+rIzQpn7r6wMyskUyiwI\n5WQB5Ta287mOdcCgUP4soPyCdISS/2wgz2avFkXIjzny4jEbg7J5Hwpl19DqA4Y1TtMQb/0X\nnoNjUIopNk0ovwTIL6FsH5O2dVcGZS36RMbcUQzKBbDufb4p7xRQYj8iDqUowGlCeYFCh+O7\nGZRj9sJ57J8H6bDnSCEoC6yvPYfyBE7OZEA5i0GJ90Qom6cmBSSULwoocxVmK60KZV4oTY06\nyaHMBwaUe/lS4R4yW4F7ZmJQQl+6yUood5lQnoGUHErsgjJNQvkUQlk+UoWyHfyXTUD5PG5C\nc6ljCOUN9vAKlDmtUP5Dd8kolLz6lgJlTgeUuEE3n8ignEQXww3KpHkaWaBEUkaktd3ICeVJ\nCmU1DuXTWQwoBzIoS/QCnCICQiLDDpJeicrISb04lJ+FZisC6+l7lktAuX4fPZyYnFYMPnqd\njSuaFzLdgPIyGVpIQLmLQ1kTLksoowSULTL9CRnnsErwCOVNFyhjsPfiOBXK5rCErmuRJBJm\nGVDWw3cyBqE86R/KLxiUv//HB9TmYyU1KJSDUpBM00mLyrvoUpZkUObnUN754AsFyjsbb7XD\nkziZcqZqa4Oytx3KwdiVpFJ6Ur8MlLBA2QxbdQLMwwflixLK/8EblMQbWL7+m8g6r7OW4BQM\nysrqww9QoNzSmR76stlv6d4PgzITtD9I//+ThHI0tj8KKH9kzTLVYDNCuRgu9MyWqjAeg+VB\nKEvhPSKebgSNOkPh/sOapGmAUF5EKH+1QpnjwpRhdBNkUA6WUKZuHWNCKSuQjcR6KRTK9/hY\nBHa6j0KJZ32ggwLlRfiaqs2hfIf1nWRQjqRQYinawuzMZSEoZ0D5MetU8gEfLX+csjOL9G5D\noZzz4e3XDShzR+BJQgHluJyF2LfxVnoo3EZAmZtBeZxDmRGvXhWiQImvh80s2DMj4NkI6Eeh\nXGJAiV3kjmH72hn63/9UKOsZUJaLTIUHwwhl4b7QlkLJju0WSyg3IpTNJZTNJZTUhtuZZYP1\nYvibQlnpVwPKLFcplFiNLMdrH8B13LaObBUVOhQoJ1IoSxodtcwkTd6oGP5ep0A5nEP5XG95\no+egOJ9SZrZE+CRUp58sNvFAzyyw6jNelHNgGKFIQn7AyucQEkFXrV5hNijXJ+uaHz6jWztT\n9nkDSrFVLmLd5efBNN4FjkE5pBBOXcKgrIJHSzXg8q8I5Wf0W6Uah7J5pvOQcTaDchg9BLhh\nQBlZEV7bDb36HfcL5UwKJZ/ktK4B5Q+fOqCcjQWHAN5exaCs7YAS5edQVhJQfmxAeRwrXLBj\ntrR0q/gFdrdDIDNFl22LHeQxCpSt2RWN8FsPofyDkIrpSapSEspQGJfvkYXyPQmlHOb6C4Py\nOhYb3RERKyir4wC6J1IjlBngMQ4lHv5+bYXyewHlJtIBSr4O557IlrIw7lrkwWM2BmWT3hTK\nTpCz/9AmaevjrS9giwmDUsxFfJw+0y+P0Z2xTVvosevJxySUyWuE78OXVROhlFOiSChX8g4R\nOwSUBwwoRQFOhPIZO5Q3YTiFEisslmVQFpRQ7vAB5S74s9lg1hoemYpByXpTzBVQ5ijE5uPb\nCqFQmHeOp1CWEVDmLkoyOKDE18MK4fRMTy+lvwPP0e8BK5Q1cAX/HaFspkJ5cVcDiCmYf4iE\n8n8whhR+hkL5b1YrlBvw+KD5dRuUzRHKTBLKNymUXyKUy2dhQ4AFyvcplPQVH5lZgd8WN+hI\nDuUE6rUrlMkklNjJ+Rs2k+owDmXJ/PJGz0ExFyircCh7ZMaSJgzKARzKfIAFfRHKTaS7Fcrr\nZF2KJ/PA53RrZ3em7+G6ffRwYnIaUYFtEesuPw+mKlAOLnhpswPK71MhlM0llBnPQcYXWN1O\nhPK60dwTWQEW7oau8IGEkrWS1hZQvkXXtQh6CDsDmgso6zAoE1Mou2ewQ1nwBQrlGiuU/3Io\n8yKUOFKgP4ey4i66lAJKfmbmZ+w9bkD5A+xoh0BmjC7XxoTyY/zVuz6p2Ypd0QjPzJlQpiyJ\nUC5M/MhCORjfjRPviUFwc00oX6ckXuNQ1l7EoWRN3pXYaBXMlDdNKKsyKM/TTafpUwaUaSHl\nARuUr7IuvVVg/bcCyo0I5SI41ylr8kIIZW6EsgTeI5xC2bAj5Og/tGna8njrPxHKU3WtUP6U\nEvLAJnpgkW83G7T4FrRrD1CRwlKlbE36REal/xEVCValWLeCQ7ldQLnfgFLUlWNQZuNQTmID\nD5silEP2wjksHFae7RVYoGSdSt63Q/lH00HsRFnEYyqU7KzEuORZHFDmhDK3KPsIZRETyr8k\nlHuBDbIhpEc6dviPe0MUyq6s8x6HsmoU4XNK/iuhxKEVdQfQHbJ6QKEsG/mYBcrLWQSUz+Em\n5BPKbAC3Mi0Wb+KbcIlD2Zh1EhgJma9AZQZl9oUCysPTRTEo3KAjcGMb4gnlWgblDjaT6lAB\nZV55I4SSNcIpUFajq6EBZUfWR0qBMgn+pxlsOh4aVlpuzU9BBIVybcoeOWAD3dqxIR33ytci\nlJPSiL7oHMpXYAqHciaWMhlUcHnOmgjlTqhMshlQfkhXhggG5a+3GmQ8q0J5zYSyPELZBSbc\nao9QjnVC2YxCOZ1Cyc+b1kYo2yemr6NzSgeUs0iUDcrTAso8WF8GoXwuBck4nTSvsBOqW6H8\nCfv6GFB+B9vbYTcmCmVrCeUyE8qWX+CaZkA5hpAK6UmK4lBcQjk27yMP5RxZD+BnBuVVrKG3\noxlC+YwTypb9LFB+0RlqzRoFzTiUk8gzkBRSHKC7qhzKreyTGi2hPCKg3EBioMRrcLZN1qSF\ncNfChLJBr4bQMAay9x/StBRgI84f2LRsh/IHhHIjQrldgbIChXLLpBoIpaxlL6Bcu4K3yrDT\nfdVLcihjLFBuFVD+SfKx8htN4eYNGCSgrCCgLI9QTlhFn/Qj1qnkfT5a/jhlx4CS7a03E1Bi\nt7M5AkpIkr/3HbKgA4RAIQFlDihrQpmeQQkIJZ/pDKtk8cbzHmkRytvQn+4wW6Gs0oK4QYkD\npBiUZRiULRiUfRDKzALKfvjBzOFQRl4TUEbyAzDSPCuFMuNi8Sa+AX9xKPnZ/5GQSUKZbeF7\nFEq6OR6aJrrFfowvnkM5Hur6gLKhBUqcOlJAWSKXvFE/KMqhfEGFsiLrLQk9MuHXHIOyfxjp\nyaFMhP9pChuPgB3KNY89nQU2JsKZWjmUn+6jd6dQUsG+2ExeY93lX4FJvAsch7LAu9lr4pRH\nO6ES3q06/MOgXE+hrIoTXf76CmT8HTLOYlWWhtJvtqsGlBHl4dXd2Ev3s/Z1iAllN/bGwmIG\nZTN6oB8poKxlQNkpOfDBCTRH2NhPBuUnAEs5lLU4lFvwX7kRShwp0M+AspqAMh+H8gf8ChuJ\nbTNpKJTHYFs72O8KZa96pEbLpTjkXEA5COh2UyEdSV5UQhkioZQ76955aKA8bkAp6wH8BIso\niVc4lLXo6tCYQsnODVY0oexL+qtQdgKIHgnNutMHfJxBCZBiP4MST6hwKEcJKNftZ+3XVeFz\nAWXVLIkL4RaTGxu3iuOqVq8nhbI9ZOs/pNk6BuV5/H47VbdUclY1kGBDKsD3KelR68bNAHm3\nSCjbUc72GlDKuqwSyuV81dgmoGTH6O3xhxjPfAG2bu+TFTtB/0nyCCi/vwH998A5LBxWUUBZ\ngV6uA805lD8rUPYTUJ5vIqBMSfID5GnOoZyJY+PGYm3uf0m3/AqU2RiUP8MbHMrWCA1CWYAv\n1W40Dy/0wDMVaW/jiQgFyrFEQIkzAF1uqkBZpy8UgLqQD6HEtrsWv1AoCz0NbeCfTGyXZTH0\n5VB+jl97DEqs+2hAmQWhFONLKJQXyRaoiKOZsJMAhfI/AWVWCuV5BuWUkvy2CpTj6LKXcIey\nKP7+VECJVSmHCChzyBshlC/ufccCZVVSwYQyhrU/kOc5lHkBqwrhYC4blM3oJ/5JqmczmFD2\nNaGkH8sTXSiU3xLyYlGYCJfwUIJC+TcZmP+dbDXsUH7HoGzKoZwGGfdBhpkI5c0OFMorKpQL\ndmPns499QdmUgjPVgLImvpPt7FD2YbX5C8ykd7FC+dtlDmUuhBI7wPZNTjJOo/uxO6EqlKiL\nYyMElN9j6/HgsH0IZU1yBL5ui90pKJSt2NwSxAJl9FL0uhGMw/doIEJZPs3XyYpAMQPKPBTK\npo8klCvF2I7ZEsof4TUO5STY3lRAmVxA+feJ7OykYLQCZRUDyggGZSoOZXKE8kcG5VeA1U9H\nsbEPFMpPBZSfkfZQYiGcqZwljEGZy4CyNkLZFrI8P6TZegblOYTypA3KdSkgF4dyA0K5Kgba\nUijLUyi/pFBWBqM4zAhsOqNQLuNQfs2hvDzQgFKMPrkAH0AjA0ocVd4UProOz1EosR5OJQZl\nAQZlDojkUP5kgXIm6dV6J5xvPJBB2TSFCeVsYL3ux2LdGwolVu6UUGaFcnSf4EcKZS4LlOID\nwQkgWL+O7tjQmOYW9gGssYQe1ZlQVm5OOJT/IJTYV2+KhLIOQllKQjmaFMJZrv/OyKB80wJl\nxFUblJH02PZWBp9QZqRQPofVyLIsXAlsMMfBycXlbemLHy+grOgKZZKkViixwNNgPlCxuDHD\nWT8oDC8OK4n/4KihAAAgAElEQVRQipJgJyiU5TmU3TPip8ehDGVQ5gFWfR4aw4bDNihfJatT\nP58mZFMYThdD8yzAmn3UWQrldUIe70AW4nn1CIDxwGoYMSgHSCi/oS+C3q0ag/IxhLJJFbI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cQBlvZCgoa66nHtfJVVVQ0gn+ojlIC/cSKH0B5TIHKDtTwu0Kyj8UlHuohQllmQVl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\n", | |
| "text/plain": [ | |
| "plot without title" | |
| ] | |
| }, | |
| "metadata": { | |
| "image/png": { | |
| "height": 480, | |
| "width": 660 | |
| } | |
| }, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "library(\"coda\")\n", | |
| "\n", | |
| "coda::traceplot(as.mcmc(samples))\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "<br>\n", | |
| "\n", | |
| "# Rstan\n", | |
| "\n", | |
| "- Documentation: https://mc-stan.org/rstan/\n", | |
| "\n", | |
| "\n", | |
| "---\n", | |
| "\n", | |
| "RStan is the R interface to Stan, which is a powerful probabilistic programming language used for statistical modeling and Bayesian inference. Stan provides a framework for specifying complex statistical models and performing inference through methods like Markov Chain Monte Carlo (MCMC) and Variational Inference.\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "The following losses have been realized:\n", | |
| "\n", | |
| "\n", | |
| "$$\n", | |
| "100, 950, 450\n", | |
| "$$\n", | |
| "\n", | |
| "\n", | |
| "which are assumed to originate from an exponential distribution with parameter $\\theta$ (*exponential likelihood*).\n", | |
| "\n", | |
| "Further, let us assume $\\theta$ is gamma distributed with $\\alpha = 4$ and $\\beta = 1000$ (*gamma prior*).\n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "The posterior predictive distribution of an exponential likelihood with parameter $\\theta$, whereby $\\theta$ has a gamma distribution, is a **Pareto II distribution**, with density\n", | |
| "\n", | |
| "$$\n", | |
| "f(x) = \\frac{\\alpha \\beta^\\alpha}{(x+\\beta)^{\\alpha+1}}\n", | |
| "$$\n", | |
| "\n", | |
| "and k-th moment\n", | |
| "\n", | |
| "$$\n", | |
| "E[X^k] = \\frac{\\beta^k\\Gamma(k+1)\\Gamma(\\alpha - k)}{\\Gamma(\\alpha)},\\; -1 < k < \\alpha. \n", | |
| "$$\n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "\n", | |
| "By setting $k=1$ (first moment), we get our *prior expected loss*:\n", | |
| " \n", | |
| "\n", | |
| "```R\n", | |
| "### In R ###\n", | |
| "priorAlpha = 4\n", | |
| "\n", | |
| "priorBeta = 1000\n", | |
| "\n", | |
| "priorMean = (priorBeta * gamma(2) * gamma(priorAlpha - 1)) / gamma(priorAlpha)) # 333.3\n", | |
| "```\n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "For our data, the mean loss is $500$, which is higher than the expected loss given by our prior predictive distribution ($333.33$). \n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "\n", | |
| " \n", | |
| "\n", | |
| "\n", | |
| "> **Question: How should we update our opinion of the risk in light of the data in order to estimate expected future losses?**\n", | |
| " \n", | |
| " \n", | |
| "<br>\n", | |
| " \n", | |
| " \n", | |
| "\n", | |
| "We can solve this problem analytically, since the prior and posterior parameter distributions have a conjugate relationship.\n", | |
| "As stated above, it means that the posterior parameter distribution comes from the same distributional family as the prior, here a gamma, with updated hyperparameters to reflect the data. The posterior distribution and hyperparameters, given our data ($n$=number of data points, $c_{i}$=claims in year $i$) is:\n", | |
| "\n", | |
| "$$\n", | |
| "f(\\theta|x) \\sim \\mathrm{Gamma}(\\alpha +n,\\, \\beta + \\sum_i c_i)\n", | |
| "$$\n", | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "The *posterior predictive distribution* is a Pareto II distribution with updated hyperparameters. \n", | |
| "We can calculate the posterior predictive expected loss amount using the same expression above via the updated \n", | |
| "hyperparameters: \n", | |
| "\n", | |
| "\n", | |
| "```R\n", | |
| "### In R ###\n", | |
| "losses = c(100, 950, 450)\n", | |
| "\n", | |
| "posteriorAlpha = priorAlpha + length(losses) # 7\n", | |
| "\n", | |
| "posteriorBeta = (priorBeta + sum(losses)) # 2500\n", | |
| "\n", | |
| "posteriorPredictiveMean = (posteriorBeta * gamma(2) * gamma(posteriorAlpha - 1)) / gamma(posteriorAlpha) # 416.7\n", | |
| "```\n", | |
| " \n", | |
| "<br>\n", | |
| " \n", | |
| " \n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "In summary:\n", | |
| "---\n", | |
| "\n", | |
| "* **Likelihood**: Data is exponentially distributed with scale parameter $\\theta$ $\\hspace{.25em}(f(x|\\theta) \\sim \\mathrm{Exp}(\\theta))$.\n", | |
| " \n", | |
| " \n", | |
| "* **Prior**: $\\theta$ is gamma distributed with parameters $\\alpha, \\beta$ $\\hspace{.25em}(f(\\theta) \\sim \\mathrm{Gamma}(\\alpha, \\beta))$. \n", | |
| " \n", | |
| "\n", | |
| "* **Posterior**: After accounting for our experience, $\\theta$ is gamma distributed with parameters $\\alpha + n, \\beta + \\sum_{i=1}^{n} x_{i} $ $\\hspace{.25em}(f(\\theta|x) \\sim \\mathrm{Gamma}\\big(\\alpha + n, \\beta + \\sum_{i=1}^{n} x_{i}\\big)$. \n", | |
| " \n", | |
| " \n", | |
| "* **Posterior Predicitive**: Given the likelihood and prior, the posterior predicitive distribution is $f(x_{\\mathrm{new}}|x) \\sim \\mathrm{ParetoII}(\\alpha', \\beta')$. \n", | |
| "\n", | |
| "\n", | |
| "\n", | |
| "The posterior predictive distribution uses knowledge of our experience to update the estimate of expected future losses.\n", | |
| "It accounts for uncertainty about $\\theta$. To obtain the posterior predictive, randomly sample data from the specified likelihood using the posterior samples. The distribution of these posterior predictive samples approximates the posterior predictive distribution.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "<br>\n", | |
| "\n", | |
| "Unfortunately, most distributional relationships used in practice are not conjugate. However, we can demonstrate that when using the same likelihood and prior assumptions, and the same loss data ($100,950,450$), MCMC will yield distributional estimates of the posterior predictive distribution very to close to the analytical distribution.\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 14, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A data.table: 10 × 3</caption>\n", | |
| "<thead>\n", | |
| "\t<tr><th scope=col>rate</th><th scope=col>ypred</th><th scope=col>lp__</th></tr>\n", | |
| "\t<tr><th scope=col><dbl></th><th scope=col><dbl></th><th scope=col><dbl></th></tr>\n", | |
| "</thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><td>0.0053174556</td><td> 106.40434</td><td>-49.95096</td></tr>\n", | |
| "\t<tr><td>0.0026821548</td><td> 989.42936</td><td>-48.15333</td></tr>\n", | |
| "\t<tr><td>0.0014230133</td><td>1297.87491</td><td>-49.44238</td></tr>\n", | |
| "\t<tr><td>0.0011792165</td><td>1855.45348</td><td>-50.14838</td></tr>\n", | |
| "\t<tr><td>0.0030052005</td><td> 36.11703</td><td>-48.16488</td></tr>\n", | |
| "\t<tr><td>0.0030052005</td><td> 30.10367</td><td>-48.16488</td></tr>\n", | |
| "\t<tr><td>0.0004849644</td><td> 22.75040</td><td>-54.63246</td></tr>\n", | |
| "\t<tr><td>0.0012268644</td><td> 164.39857</td><td>-49.99022</td></tr>\n", | |
| "\t<tr><td>0.0023159468</td><td> 652.79949</td><td>-48.26542</td></tr>\n", | |
| "\t<tr><td>0.0017804255</td><td> 381.35090</td><td>-48.76738</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/latex": [ | |
| "A data.table: 10 × 3\n", | |
| "\\begin{tabular}{lll}\n", | |
| " rate & ypred & lp\\_\\_\\\\\n", | |
| " <dbl> & <dbl> & <dbl>\\\\\n", | |
| "\\hline\n", | |
| "\t 0.0053174556 & 106.40434 & -49.95096\\\\\n", | |
| "\t 0.0026821548 & 989.42936 & -48.15333\\\\\n", | |
| "\t 0.0014230133 & 1297.87491 & -49.44238\\\\\n", | |
| "\t 0.0011792165 & 1855.45348 & -50.14838\\\\\n", | |
| "\t 0.0030052005 & 36.11703 & -48.16488\\\\\n", | |
| "\t 0.0030052005 & 30.10367 & -48.16488\\\\\n", | |
| "\t 0.0004849644 & 22.75040 & -54.63246\\\\\n", | |
| "\t 0.0012268644 & 164.39857 & -49.99022\\\\\n", | |
| "\t 0.0023159468 & 652.79949 & -48.26542\\\\\n", | |
| "\t 0.0017804255 & 381.35090 & -48.76738\\\\\n", | |
| "\\end{tabular}\n" | |
| ], | |
| "text/markdown": [ | |
| "\n", | |
| "A data.table: 10 × 3\n", | |
| "\n", | |
| "| rate <dbl> | ypred <dbl> | lp__ <dbl> |\n", | |
| "|---|---|---|\n", | |
| "| 0.0053174556 | 106.40434 | -49.95096 |\n", | |
| "| 0.0026821548 | 989.42936 | -48.15333 |\n", | |
| "| 0.0014230133 | 1297.87491 | -49.44238 |\n", | |
| "| 0.0011792165 | 1855.45348 | -50.14838 |\n", | |
| "| 0.0030052005 | 36.11703 | -48.16488 |\n", | |
| "| 0.0030052005 | 30.10367 | -48.16488 |\n", | |
| "| 0.0004849644 | 22.75040 | -54.63246 |\n", | |
| "| 0.0012268644 | 164.39857 | -49.99022 |\n", | |
| "| 0.0023159468 | 652.79949 | -48.26542 |\n", | |
| "| 0.0017804255 | 381.35090 | -48.76738 |\n", | |
| "\n" | |
| ], | |
| "text/plain": [ | |
| " rate ypred lp__ \n", | |
| "1 0.0053174556 106.40434 -49.95096\n", | |
| "2 0.0026821548 989.42936 -48.15333\n", | |
| "3 0.0014230133 1297.87491 -49.44238\n", | |
| "4 0.0011792165 1855.45348 -50.14838\n", | |
| "5 0.0030052005 36.11703 -48.16488\n", | |
| "6 0.0030052005 30.10367 -48.16488\n", | |
| "7 0.0004849644 22.75040 -54.63246\n", | |
| "8 0.0012268644 164.39857 -49.99022\n", | |
| "9 0.0023159468 652.79949 -48.26542\n", | |
| "10 0.0017804255 381.35090 -48.76738" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "# Demonstration using Stan to fit data using exponential likelihood \n", | |
| "# with gamma prior. \n", | |
| "suppressWarnings(suppressPackageStartupMessages(library(\"actuar\")))\n", | |
| "suppressWarnings(suppressPackageStartupMessages(library(\"data.table\")))\n", | |
| "suppressWarnings(suppressPackageStartupMessages(library(\"coda\")))\n", | |
| "suppressWarnings(suppressPackageStartupMessages(library(\"foreach\")))\n", | |
| "suppressWarnings(suppressPackageStartupMessages(library(\"ggplot2\")))\n", | |
| "suppressWarnings(suppressPackageStartupMessages(library(\"parallel\")))\n", | |
| "suppressWarnings(suppressPackageStartupMessages(library(\"rstan\")))\n", | |
| "options(scipen=9999)\n", | |
| "availableCores = parallel::detectCores()\n", | |
| "\n", | |
| "# Loss data and hyperparameter initialization.\n", | |
| "y = c(100., 950., 450.)\n", | |
| "N = length(y)\n", | |
| "a0 = 4\n", | |
| "b0 = 1000\n", | |
| "\n", | |
| "\n", | |
| "# Create stan model string. \n", | |
| "modelStr = \"\n", | |
| " data {\n", | |
| " int<lower=1> N;\n", | |
| " real y[N];\n", | |
| " real<lower=machine_precision()> a0;\n", | |
| " real<lower=machine_precision()> b0;\n", | |
| " }\n", | |
| " \n", | |
| " parameters {\n", | |
| " // Prior parameter(s).\n", | |
| " real<lower=machine_precision()> rate; \n", | |
| " }\n", | |
| " \n", | |
| " model {\n", | |
| " rate ~ gamma(a0, b0);\n", | |
| " for (i in 1:N)\n", | |
| " y[i] ~ exponential(rate);\n", | |
| " }\n", | |
| " \n", | |
| " generated quantities{\n", | |
| " real ypred;\n", | |
| " ypred = exponential_rng(rate);\n", | |
| " }\n", | |
| "\"\n", | |
| "\n", | |
| "# Pass model string into stan_model constructor. \n", | |
| "modelSpec = rstan::stan_model(model_code=modelStr) \n", | |
| "\n", | |
| "# Specify data for use in model. \n", | |
| "modelData = list(N=N, y=y, a0=a0, b0=b0)\n", | |
| "\n", | |
| "# Sampling.\n", | |
| "modelFit = rstan::sampling(\n", | |
| " modelSpec, data=modelData, iter=10000, warmup=2500, chains=4,\n", | |
| " cores=availableCores, seed=516\n", | |
| " ) \n", | |
| "\n", | |
| "# Bind reference to posterior and posterior predictive samples. \n", | |
| "postDF = as.data.table(modelFit)\n", | |
| "\n", | |
| "head(postDF, 10)\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 15, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "name": "stderr", | |
| "output_type": "stream", | |
| "text": [ | |
| "Number MCMC samples : 30000\n", | |
| "\n", | |
| "Mean of analytical posterior rate : 0.0028\n", | |
| "\n", | |
| "Mean of MCMC posterior rate : 0.00278767293045957\n", | |
| "\n", | |
| "Mean of analytical posterior predictive distribution: 416.67\n", | |
| "\n", | |
| "Mean of MCMC posterior predictive distribution : 417.500278419702\n", | |
| "\n" | |
| ] | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "message(\"Number MCMC samples : \", nrow(postDF))\n", | |
| "message(\"Mean of analytical posterior rate : \", 7 / 2500)\n", | |
| "message(\"Mean of MCMC posterior rate : \", mean(postDF$rate))\n", | |
| "message(\"Mean of analytical posterior predictive distribution: \", 416.67)\n", | |
| "message(\"Mean of MCMC posterior predictive distribution : \", mean(postDF$ypred))\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "source": [ | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "#### Create a summary table of analytical and simulated percentiles:" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 16, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A matrix: 3 × 11 of type dbl</caption>\n", | |
| "<tbody>\n", | |
| "\t<tr><th scope=row>q</th><td>0.005000</td><td>0.010000</td><td> 0.05000</td><td> 0.10000</td><td> 0.2500</td><td> 0.5000</td><td> 0.7500</td><td> 0.9000</td><td> 0.950</td><td> 0.990</td><td> 0.995</td></tr>\n", | |
| "\t<tr><th scope=row>analytical</th><td>1.790835</td><td>3.591984</td><td>18.38632</td><td>37.91337</td><td>104.8841</td><td>260.2238</td><td>547.5341</td><td>973.7387</td><td>1335.319</td><td>2326.744</td><td>2829.158</td></tr>\n", | |
| "\t<tr><th scope=row>mcmc</th><td>1.641492</td><td>3.791636</td><td>18.41353</td><td>37.68443</td><td>104.6822</td><td>261.4861</td><td>550.7296</td><td>983.1344</td><td>1339.464</td><td>2304.745</td><td>2773.372</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/latex": [ | |
| "A matrix: 3 × 11 of type dbl\n", | |
| "\\begin{tabular}{r|lllllllllll}\n", | |
| "\tq & 0.005000 & 0.010000 & 0.05000 & 0.10000 & 0.2500 & 0.5000 & 0.7500 & 0.9000 & 0.950 & 0.990 & 0.995\\\\\n", | |
| "\tanalytical & 1.790835 & 3.591984 & 18.38632 & 37.91337 & 104.8841 & 260.2238 & 547.5341 & 973.7387 & 1335.319 & 2326.744 & 2829.158\\\\\n", | |
| "\tmcmc & 1.641492 & 3.791636 & 18.41353 & 37.68443 & 104.6822 & 261.4861 & 550.7296 & 983.1344 & 1339.464 & 2304.745 & 2773.372\\\\\n", | |
| "\\end{tabular}\n" | |
| ], | |
| "text/markdown": [ | |
| "\n", | |
| "A matrix: 3 × 11 of type dbl\n", | |
| "\n", | |
| "| q | 0.005000 | 0.010000 | 0.05000 | 0.10000 | 0.2500 | 0.5000 | 0.7500 | 0.9000 | 0.950 | 0.990 | 0.995 |\n", | |
| "| analytical | 1.790835 | 3.591984 | 18.38632 | 37.91337 | 104.8841 | 260.2238 | 547.5341 | 973.7387 | 1335.319 | 2326.744 | 2829.158 |\n", | |
| "| mcmc | 1.641492 | 3.791636 | 18.41353 | 37.68443 | 104.6822 | 261.4861 | 550.7296 | 983.1344 | 1339.464 | 2304.745 | 2773.372 |\n", | |
| "\n" | |
| ], | |
| "text/plain": [ | |
| " [,1] [,2] [,3] [,4] [,5] [,6] [,7] \n", | |
| "q 0.005000 0.010000 0.05000 0.10000 0.2500 0.5000 0.7500\n", | |
| "analytical 1.790835 3.591984 18.38632 37.91337 104.8841 260.2238 547.5341\n", | |
| "mcmc 1.641492 3.791636 18.41353 37.68443 104.6822 261.4861 550.7296\n", | |
| " [,8] [,9] [,10] [,11] \n", | |
| "q 0.9000 0.950 0.990 0.995\n", | |
| "analytical 973.7387 1335.319 2326.744 2829.158\n", | |
| "mcmc 983.1344 1339.464 2304.745 2773.372" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "qq = c(.005, .01, .05, .10, .25, .50, .75, .90, .95, .99, .995)\n", | |
| "losses = c(100, 450, 950)\n", | |
| "aPrior = 4\n", | |
| "bPrior = 1000\n", | |
| "aPost = aPrior + length(losses)\n", | |
| "bPost = (bPrior + sum(losses)) \n", | |
| "meanPost = (bPost * gamma(2) * gamma(aPost - 1)) / gamma(aPost) # 416.7\n", | |
| "\n", | |
| "summDF = data.table(\n", | |
| " q=qq, \n", | |
| " analytical=qpareto(qq, aPost, bPost), \n", | |
| " mcmc=quantile(postDF$ypred, qq),\n", | |
| " stringsAsFactors=FALSE\n", | |
| " )\n", | |
| "\n", | |
| "t(summDF)\n", | |
| "\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": 17, | |
| "metadata": { | |
| "tags": [] | |
| }, | |
| "outputs": [ | |
| { | |
| "data": { | |
| "text/html": [ | |
| "<table class=\"dataframe\">\n", | |
| "<caption>A matrix: 3 × 10 of type dbl</caption>\n", | |
| "<thead>\n", | |
| "\t<tr><th></th><th scope=col>mean</th><th scope=col>se_mean</th><th scope=col>sd</th><th scope=col>2.5%</th><th scope=col>25%</th><th scope=col>50%</th><th scope=col>75%</th><th scope=col>97.5%</th><th scope=col>n_eff</th><th scope=col>Rhat</th></tr>\n", | |
| "</thead>\n", | |
| "<tbody>\n", | |
| "\t<tr><th scope=row>rate</th><td> 0.002787673</td><td>0.00001054038</td><td> 0.001055778</td><td> 0.001123645</td><td> 0.002018755</td><td> 0.002656199</td><td> 0.003414303</td><td> 0.005211702</td><td>10033.04</td><td>0.9999379</td></tr>\n", | |
| "\t<tr><th scope=row>ypred</th><td>417.500278420</td><td>3.18861756550</td><td>487.050972996</td><td> 9.246018581</td><td>104.682170551</td><td>261.486058310</td><td>550.729631192</td><td>1741.335758054</td><td>23331.57</td><td>1.0000053</td></tr>\n", | |
| "\t<tr><th scope=row>lp__</th><td>-48.659083505</td><td>0.00679920570</td><td> 0.721120960</td><td>-50.707246928</td><td>-48.828523635</td><td>-48.380273029</td><td>-48.199264906</td><td> -48.147441645</td><td>11248.64</td><td>1.0002120</td></tr>\n", | |
| "</tbody>\n", | |
| "</table>\n" | |
| ], | |
| "text/latex": [ | |
| "A matrix: 3 × 10 of type dbl\n", | |
| "\\begin{tabular}{r|llllllllll}\n", | |
| " & mean & se\\_mean & sd & 2.5\\% & 25\\% & 50\\% & 75\\% & 97.5\\% & n\\_eff & Rhat\\\\\n", | |
| "\\hline\n", | |
| "\trate & 0.002787673 & 0.00001054038 & 0.001055778 & 0.001123645 & 0.002018755 & 0.002656199 & 0.003414303 & 0.005211702 & 10033.04 & 0.9999379\\\\\n", | |
| "\typred & 417.500278420 & 3.18861756550 & 487.050972996 & 9.246018581 & 104.682170551 & 261.486058310 & 550.729631192 & 1741.335758054 & 23331.57 & 1.0000053\\\\\n", | |
| "\tlp\\_\\_ & -48.659083505 & 0.00679920570 & 0.721120960 & -50.707246928 & -48.828523635 & -48.380273029 & -48.199264906 & -48.147441645 & 11248.64 & 1.0002120\\\\\n", | |
| "\\end{tabular}\n" | |
| ], | |
| "text/markdown": [ | |
| "\n", | |
| "A matrix: 3 × 10 of type dbl\n", | |
| "\n", | |
| "| <!--/--> | mean | se_mean | sd | 2.5% | 25% | 50% | 75% | 97.5% | n_eff | Rhat |\n", | |
| "|---|---|---|---|---|---|---|---|---|---|---|\n", | |
| "| rate | 0.002787673 | 0.00001054038 | 0.001055778 | 0.001123645 | 0.002018755 | 0.002656199 | 0.003414303 | 0.005211702 | 10033.04 | 0.9999379 |\n", | |
| "| ypred | 417.500278420 | 3.18861756550 | 487.050972996 | 9.246018581 | 104.682170551 | 261.486058310 | 550.729631192 | 1741.335758054 | 23331.57 | 1.0000053 |\n", | |
| "| lp__ | -48.659083505 | 0.00679920570 | 0.721120960 | -50.707246928 | -48.828523635 | -48.380273029 | -48.199264906 | -48.147441645 | 11248.64 | 1.0002120 |\n", | |
| "\n" | |
| ], | |
| "text/plain": [ | |
| " mean se_mean sd 2.5% 25% \n", | |
| "rate 0.002787673 0.00001054038 0.001055778 0.001123645 0.002018755\n", | |
| "ypred 417.500278420 3.18861756550 487.050972996 9.246018581 104.682170551\n", | |
| "lp__ -48.659083505 0.00679920570 0.721120960 -50.707246928 -48.828523635\n", | |
| " 50% 75% 97.5% n_eff Rhat \n", | |
| "rate 0.002656199 0.003414303 0.005211702 10033.04 0.9999379\n", | |
| "ypred 261.486058310 550.729631192 1741.335758054 23331.57 1.0000053\n", | |
| "lp__ -48.380273029 -48.199264906 -48.147441645 11248.64 1.0002120" | |
| ] | |
| }, | |
| "metadata": {}, | |
| "output_type": "display_data" | |
| } | |
| ], | |
| "source": [ | |
| "\n", | |
| "# Get effective sample size.\n", | |
| "summary(modelFit)$summary\n" | |
| ] | |
| }, | |
| { | |
| "cell_type": "markdown", | |
| "metadata": {}, | |
| "source": [ | |
| "\n", | |
| "<br>\n", | |
| "\n", | |
| "This is a relatively simple model. The expression for the correlated log normal chain ladder is slightly more complex (see below). Here is a great blog post that walks through applying the correlated log normal chain ladder model to Schedule P data from the CAS Loss Reserving Database:\n", | |
| "\n", | |
| "- [Correlated log-normal chain-ladder model](https://magesblog.com/post/correlated-lognormal-chain-ladder-model/)\n", | |
| " " | |
| ] | |
| }, | |
| { | |
| "cell_type": "code", | |
| "execution_count": null, | |
| "metadata": {}, | |
| "outputs": [], | |
| "source": [ | |
| "\n", | |
| "cclModel = \"data{\n", | |
| " int <lower=1> len_data; // number of rows with data\n", | |
| " int<lower=1> len_pred; // number of rows to predict\n", | |
| " int<lower=0, upper=1> origin1id[len_data + len_pred]; \n", | |
| " real logprem[len_data + len_pred];\n", | |
| " real logloss[len_data];\n", | |
| " int<lower=1> origin[len_data + len_pred]; // origin period\n", | |
| " int<lower=1> dev[len_data + len_pred]; // development period\n", | |
| "}\n", | |
| "\n", | |
| "transformed data{\n", | |
| " int n_origin = max(origin);\n", | |
| " int n_dev = max(dev);\n", | |
| " int len_total = len_data + len_pred;\n", | |
| "}\n", | |
| "\n", | |
| "parameters{\n", | |
| " real r_alpha[n_origin - 1];\n", | |
| " real r_beta[n_dev - 1];\n", | |
| " real log_elr;\n", | |
| " real<lower=0, upper=100000> a_ig[n_dev];\n", | |
| " real<lower=0, upper=1> r_rho;\n", | |
| " real logloss_pred[len_pred];\n", | |
| "}\n", | |
| "\n", | |
| "transformed parameters{\n", | |
| " real alpha[n_origin];\n", | |
| " real beta[n_dev];\n", | |
| " real sig2[n_dev];\n", | |
| " real sig[n_dev];\n", | |
| " real mu[len_data];\n", | |
| " real mu_pred[len_pred];\n", | |
| " real <lower=-1, upper=1> rho;\n", | |
| " rho = -2*r_rho + 1;\n", | |
| " alpha[1] = 0;\n", | |
| "\n", | |
| " for (i in 2:n_origin){\n", | |
| " alpha[i] = r_alpha[i-1];\n", | |
| " }\n", | |
| " \n", | |
| " for (i in 1:(n_dev - 1)){\n", | |
| " beta[i] = r_beta[i];\n", | |
| " }\n", | |
| "\n", | |
| " beta[n_dev] = 0;\n", | |
| " \n", | |
| " // Create ascending set of sig2\n", | |
| " sig2[n_dev] = gamma_cdf(1/a_ig[n_dev],1,1); // map into [0,1]\n", | |
| "\n", | |
| " for (i in 1:(n_dev-1)){ \n", | |
| " sig2[n_dev - i] = sig2[n_dev + 1 - i] + gamma_cdf(1/a_ig[i],1,1);\n", | |
| " }\n", | |
| "\n", | |
| " for (i in 1:n_dev){ \n", | |
| " sig[i] = sqrt(sig2[i]);\n", | |
| " }\n", | |
| "\n", | |
| " // first origin and dev period (top left corner of triangle)\n", | |
| " mu[1] = logprem[1] + log_elr + beta[dev[1]];\n", | |
| " \n", | |
| " for (i in 2:len_data){\n", | |
| " mu[i] = logprem[i] + log_elr + alpha[origin[i]] + beta[dev[i]] +\n", | |
| " rho * (logloss[i-1] - mu[i-1]) * origin1id[i];\n", | |
| " }\n", | |
| " \n", | |
| " mu_pred[1] = logprem[(len_data) + 1] + alpha[origin[len_data + 1]] + \n", | |
| " log_elr + beta[dev[len_data + 1]] +\n", | |
| " rho*(logloss[len_data] - mu[len_data]) * origin1id[len_data + 1];\n", | |
| " \n", | |
| " for (i in 2:len_pred){\n", | |
| " mu_pred[i] = logprem[len_data + i] + alpha[origin[len_data + i]] + \n", | |
| " log_elr + beta[dev[len_data + i]] +\n", | |
| " rho * (logloss_pred[i-1] - mu_pred[i-1]) * origin1id[len_data + i];\n", | |
| " }\n", | |
| "}\n", | |
| "\n", | |
| "model {\n", | |
| " log_elr ~ normal(0, 1);\n", | |
| " r_alpha ~ normal(0, sqrt(10/1.0));\n", | |
| " r_beta ~ normal(0, sqrt(10/1.0));\n", | |
| " a_ig ~ inv_gamma(1,1); // inverse gamma for numerical resaons\n", | |
| " r_rho ~ beta(2,2);\n", | |
| "\n", | |
| " // model where we have data\n", | |
| " for (i in 1:(len_data)){\n", | |
| " logloss[i] ~ normal(mu[i], sig[dev[i]]);\n", | |
| " }\n", | |
| "\n", | |
| " // model where data is missing, the prediction period\n", | |
| " for (i in 1:(len_pred)){\n", | |
| " logloss_pred[i] ~ normal(mu_pred[i], sig[dev[len_data + i]]);\n", | |
| " }\n", | |
| "}\n", | |
| "\n", | |
| "generated quantities{\n", | |
| " vector[len_data] log_lik;\n", | |
| " vector[len_total] ppc_loss;\n", | |
| " for (i in 1:len_data) { \n", | |
| " log_lik[i] = normal_lpdf(logloss[i] | mu[i], sig[dev[i]]);\n", | |
| " }\n", | |
| "\n", | |
| " // simulate posterior predicted losses\n", | |
| " for (i in 1:len_data) { \n", | |
| " ppc_loss[i] = exp(normal_rng(mu[i], sig[dev[i]]));\n", | |
| " }\n", | |
| " for (i in 1:len_pred) { \n", | |
| " ppc_loss[len_data + i] = exp(normal_rng(mu_pred[i], sig[dev[len_data + i]]));\n", | |
| " }\n", | |
| "}\n", | |
| "\"\n" | |
| ] | |
| } | |
| ], | |
| "metadata": { | |
| "kernelspec": { | |
| "display_name": "R", | |
| "language": "R", | |
| "name": "ir" | |
| }, | |
| "language_info": { | |
| "codemirror_mode": "r", | |
| "file_extension": ".r", | |
| "mimetype": "text/x-r-source", | |
| "name": "R", | |
| "pygments_lexer": "r", | |
| "version": "4.3.3" | |
| } | |
| }, | |
| "nbformat": 4, | |
| "nbformat_minor": 4 | |
| } |
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