{
"cells": [
{
"cell_type": "raw",
"id": "cf96e587",
"metadata": {},
"source": [
"---\n",
"title: \"Bayesian applications\"\n",
"description: |\n",
" A quick Bayesian refresher, an extention to regression models and other applications.\n",
"author: \"[Pat Reen](https://www.linkedin.com/in/patrick-reen/)\"\n",
"output: \n",
" self_contained: false\n",
"bibliography: ../_bibliography/references.bib\n",
"link-citations: yes"
]
},
{
"cell_type": "code",
"execution_count": 1,
"id": "6a85c462",
"metadata": {
"name": "setup",
"tags": [
"remove_cell"
]
},
"outputs": [],
"source": [
"knitr::opts_chunk$set(echo = FALSE)"
]
},
{
"cell_type": "markdown",
"id": "27b85f63-bb87-4f52-8f28-d1b3a92e1f3a",
"metadata": {},
"source": [
"# R: Bayesian Applications"
]
},
{
"cell_type": "markdown",
"id": "1d2c4207",
"metadata": {},
"source": [
"By Pat Reen - originally published on his GitHub site [here](https://pat-reen.github.io/More-Modelling-Recipes/), which has the [original code](https://github.com/Pat-Reen/More-Modelling-Recipes)."
]
},
{
"cell_type": "markdown",
"id": "6ab18002",
"metadata": {},
"source": [
"# Background\n",
"\n",
"Bayesian statistics reflects uncertainty about model parameters by assuming some prior probability distribution for those parameters. That prior uncertainty is adjusted for observed data to produce a posterior distribution.\n",
"\n",
"Under a frequentest approach, model parameters are fixed and the observations are assumed to be sampled from a probability distribution with those parameters.\n",
"\n",
"[Bayes theorem refresher](https://en.wikipedia.org/wiki/Bayes%27_theorem):\n",
"\n",
"$\\Huge {p}(\\theta,x) = \\frac{{p}(x,\\theta){p}(\\theta)}{{p}(x)}$\n",
"\n",
"Where \n",
"\n",
"* ${p}(\\theta,x)$ is the posterior, a combination of the likelihood, prior and evidence. Probability distribution of $\\theta$ given the observed data, $x$. \n",
"* ${p}(x,\\theta)$ is the likelihood which summarizes the likelihood of observing data $x$ under different values of the underlying support parameter $\\theta$. \n",
"* ${p}(\\theta)$ is the prior, the probability distribution of $\\theta$, independent of the observed data.\n",
"* ${p}(x)$ is the evidence (normalising term), the probability of the observed data $x$, independent of $\\theta$.\n",
"\n",
"The evidence term is proportional to the likelihood and therefore the theorem is often stated as\n",
"\n",
"$\\Huge p(\\theta | x) \\propto p(x | \\theta) p(\\theta)$\n",
"\n",
"A paper presented at the [2021 Actuaries (Institute) Summit](https://actuaries.logicaldoc.cloud/download-ticket?ticketId=4fda7653-5e3d-4514-a79f-ed0070a0f9be) (p2) sets out the 'tensions' that exist between Frequentest and Bayesian approaches and suggests that:\n",
"\n",
"> \"Despite actuaries being pioneers in early work on credibility theory, Bayesian approaches have largely given way to frequentist approaches. This is to our loss, since such methods have advanced substantially over the past couple of decades and they are well-suited to problems with latent variables or noise around underlying ‘true’ values.\"\n",
"\n",
"Here we'll look at a few simple applications of Bayesian techniques.\n",
"\n",
"# Applications\n",
"The sections below set out a simple example Bayesian refresher, regression models and other applications.\n",
"\n",
"## Libraries\n",
"A list of packages used in the recipes."
]
},
{
"cell_type": "code",
"execution_count": 2,
"id": "b9412743",
"metadata": {
"name": "Setup",
"tags": []
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Loading required package: MASS\n",
"\n",
"Loading required package: survival\n",
"\n",
"\n",
"Attaching package: 'lubridate'\n",
"\n",
"\n",
"The following objects are masked from 'package:base':\n",
"\n",
" date, intersect, setdiff, union\n",
"\n",
"\n",
"\n",
"Attaching package: 'dplyr'\n",
"\n",
"\n",
"The following object is masked from 'package:gridExtra':\n",
"\n",
" combine\n",
"\n",
"\n",
"The following object is masked from 'package:MASS':\n",
"\n",
" select\n",
"\n",
"\n",
"The following objects are masked from 'package:stats':\n",
"\n",
" filter, lag\n",
"\n",
"\n",
"The following objects are masked from 'package:base':\n",
"\n",
" intersect, setdiff, setequal, union\n",
"\n",
"\n",
"Loading required package: StanHeaders\n",
"\n",
"rstan (Version 2.21.2, GitRev: 2e1f913d3ca3)\n",
"\n",
"For execution on a local, multicore CPU with excess RAM we recommend calling\n",
"options(mc.cores = parallel::detectCores()).\n",
"To avoid recompilation of unchanged Stan programs, we recommend calling\n",
"rstan_options(auto_write = TRUE)\n",
"\n",
"Do not specify '-march=native' in 'LOCAL_CPPFLAGS' or a Makevars file\n",
"\n",
"\n",
"Attaching package: 'rstan'\n",
"\n",
"\n",
"The following object is masked from 'package:tidyr':\n",
"\n",
" extract\n",
"\n",
"\n",
"This is bayesplot version 1.8.0\n",
"\n",
"- Online documentation and vignettes at mc-stan.org/bayesplot\n",
"\n",
"- bayesplot theme set to bayesplot::theme_default()\n",
"\n",
" * Does _not_ affect other ggplot2 plots\n",
"\n",
" * See ?bayesplot_theme_set for details on theme setting\n",
"\n",
"Warning message:\n",
"\"package 'rjags' was built under R version 4.0.5\"\n",
"Loading required package: coda\n",
"\n",
"\n",
"Attaching package: 'coda'\n",
"\n",
"\n",
"The following object is masked from 'package:rstan':\n",
"\n",
" traceplot\n",
"\n",
"\n",
"Linked to JAGS 4.2.0\n",
"\n",
"Loaded modules: basemod,bugs\n",
"\n"
]
}
],
"source": [
"library(base) # Base r functions\n",
"library(fitdistrplus) # Fit of univariate distributions to non-censored data\n",
"library(lubridate) # tidyverse: dealing with dates\n",
"library(ggplot2) # tidyverse: graphs\n",
"library(gridExtra) # tidyverse: arranging graphs\n",
"library(ggthemes) # tidyverse: additional themes for ggplot, optional\n",
"library(dplyr) # tidyverse: data manipulation\n",
"library(tidyr) # tidyverse: tidy messy data\n",
"library(broom) # tidyverse: visualising statistical objects\n",
"library(DataExplorer) # package for exploratory data analysis\n",
"library(scales) # data formatting\n",
"library(stats) # statistical functions\n",
"library(rstan) # interface for stan platform\n",
"library(bayesplot) # Plotting bayesian models (ggplot extension)\n",
"library(rjags) # alternative interface for stan platform, regression applications\n",
"\n",
"# library(EpiNow2) # epidemiological model with stan backend; not called here as we'll use a pre-run model\n",
"# library(rstanarm) # interface for stan platform, regression applications; not called here"
]
},
{
"cell_type": "markdown",
"id": "7f09f7fb-4cc5-4988-ab68-2293265ff386",
"metadata": {},
"source": [
"## Mental health example\n",
"The [2017 Actuaries Institute Green Paper on Mental Health and Insurance](https://www.actuaries.asn.au/Library/Miscellaneous/2017/GPMENTALHEALTHWEBRCopy.pdf) talks about some of the challenges in obtaining reliable data and projections on mental health in insurance (p26):\n",
"\n",
">\"There are sources of data and research about the prevalence and profile of people with different mental health conditions, such as the 2007 National Survey of Mental Health and Wellbeing and many other epidemiological and clinical studies... [T]o have a complete and informed view of all this information is a difficult task for a full-time academic, let alone for an insurer. \n",
">\n",
">Even then, the nature and granularity of the data needed for insurance applications is different from that for population, public health or clinical purposes. Firstly, the ‘exposure’ (the number of insured people and their characteristics) needs to be recorded. There is probably a lot of relevant information that is not collected at the start of an insurance policy and can therefore never be analysed.\n",
">\n",
">Secondly, the claims information needs to be available at a detailed level regarding the nature and cause of the claim and other characteristics of the individual, their history and the cover provided. There is a clear need for consistency in definition, language and data standards to improve the quality of information available across the system. \n",
">\n",
">Naturally, when the insurance cover for mental health conditions is not provided (as in the case of most travel insurance products) there will not be relevant data from the insurance history. However, even when relevant data exists within insurers there are practical and commercial difficulties in turning it into a useful form.\"\n",
"\n",
"The paper goes on to talk about some of the insurance challenges in detail including\n",
"\n",
"* subjectivity in diagnosis\n",
"* reliance on self-reporting\n",
"* varying severity and prospects of recovery\n",
"* impact of co-morbidities\n",
"* correlation with financial incentive\n",
"\n",
"Based upon data from a single insurer ~19% of IP and TPD claims relate to mental health, with mental health claims contributing 26% to the total cost of claims (in 2015, p17). This is roughly consistent with the proportion of the general population that experiences an episode of mental illness in a 12 month period, from the [Productivity Commission](https://www.pc.gov.au/inquiries/completed/mental-health/report/mental-health-volume2.pdf), p110.\n",
"\n",
"In this simple example, we want to know what the rate of mental illness, $\\theta$ is in the insured population. Assume some true underlying $\\theta$, here a fixed value of 20%. Create a population, $X$ with $X \\sim B(N,\\theta)$ where N=100000. Pull a random sample from population."
]
},
{
"cell_type": "code",
"execution_count": 3,
"id": "5992b99c-40b7-44f6-97e8-6c15af911814",
"metadata": {
"name": "Generate Dataset 1"
},
"outputs": [],
"source": [
"theta_true <- 0.2 \n",
"pop <- rbinom(100000,1,theta_true)\n",
"sample_n = 500\n",
"sample <- sample(pop,sample_n)\n",
"sample_success <- sum(sample)\n",
"sample_p <- sample_success/sample_n"
]
},
{
"cell_type": "markdown",
"id": "685289b9",
"metadata": {},
"source": [
"### Choosing a prior\n",
"The posterior is proportional to the product of the prior and the likelihood. The beta distribution is a [conjugate prior](https://en.wikipedia.org/wiki/Conjugate_prior) for the binomial distribution (posterior is the same probability distribution family as prior). Assume $\\theta \\sim {\\sf Beta}(\\alpha, \\beta)$, then:\n",
"\n",
"$f(\\theta;\\alpha,\\beta) = \\theta^{\\alpha-1}(1-\\theta)^{\\beta-1}$ \n",
"\n",
"It represents the probabilities assigned to values of $\\theta$ in the domain (0,1) given values for the parameters $\\alpha$ and $\\beta$. The binomial posterior distribution represents the probability of values of $X$ given $\\theta$. Varying the values of $\\alpha$ and $\\beta$ can represent a wide range of different prior beliefs about the distribution of $\\theta$.\n",
" \n",
"Priors can be \"informative\" \"uninformative\" or \"weakly informative\", e.g. \n",
"\n",
"* non-informative - uniform dist => $\\theta$ could be anywhere in (0,1)\n",
"* weakly informative uniform prior => believe $\\theta$ more likely to be at either end of the ranges (less likely to be in the middle)\n",
"* strongly informative prior\n",
" + a and b both high (bimodial) => true theta likely to be at center of range\n",
" + a higher than b (strong \"success\") => success more likely than failure (where \"success\" is a mental health claim)\n",
" + b higher than a (strong \"failure\") => failure more likely than success\n",
" \n",
"Defining prior plots:"
]
},
{
"cell_type": "code",
"execution_count": 4,
"id": "1870ce55",
"metadata": {
"name": "Prior Plot"
},
"outputs": [],
"source": [
"plot_prior <- function(a,b){\n",
" theta = seq(0,1,0.005)\n",
" p_theta = dbeta(theta, a, b)\n",
" p <- qplot(theta, p_theta, geom='line')\n",
" p <- p + theme_bw()\n",
" p <- p + ylab(expression(paste('p(',theta,')', sep = '')))\n",
" p <- p + xlab(expression(theta))\n",
" return(p)}"
]
},
{
"cell_type": "markdown",
"id": "666b18dd",
"metadata": {},
"source": [
"#### Non-informative prior, uniform"
]
},
{
"cell_type": "code",
"execution_count": 5,
"id": "4dba757a",
"metadata": {
"name": "Prior example 1"
},
"outputs": [
{
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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot_prior(1,1) + labs(title=\"Uniform Prior, a= 1 and b = 1\") + theme(plot.title = element_text(hjust = 0.5))"
]
},
{
"cell_type": "markdown",
"id": "0b00ea21",
"metadata": {},
"source": [
"#### Weakly informative prior, bimodial"
]
},
{
"cell_type": "code",
"execution_count": 6,
"id": "eb79ac97",
"metadata": {
"name": "Prior example 2"
},
"outputs": [
{
"data": {
"image/png": 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sIFRVr+zgZEsgOnL1xSpLFbjwaRbMHp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\nAfkfHePp/v3mCO0AAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot_prior(0.5,0.5) + labs(title=\"Bimodial Prior, a= 0.5 and b = 0.5\") + theme(plot.title = element_text(hjust = 0.5))"
]
},
{
"cell_type": "markdown",
"id": "b3963338",
"metadata": {},
"source": [
"#### Informative prior, \"failure\" more likely\n",
"The higher the number of observations, the greater the influence on the posterior"
]
},
{
"cell_type": "code",
"execution_count": 7,
"id": "7eab7516",
"metadata": {
"name": "Prior example 3"
},
"outputs": [
{
"data": {
"image/png": 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BbAiCRzo7EDU1gAFxYpaJLdfEruMhUX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\npPcg0lbck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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
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S3lNRuXkEYZnYyQlF6zcQlpFEJazGs2LiGNoggpdXfNNk1IUi8hBaV2myYkqZeQ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",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot_prior(5,30) + labs(title=\"Uniform Prior, a= 5 and b = 30\") + theme(plot.title = element_text(hjust = 0.5))\n",
"plot_prior(20,120) + labs(title=\"Uniform Prior, a= 20 and b = 120\") + theme(plot.title = element_text(hjust = 0.5))"
]
},
{
"cell_type": "markdown",
"id": "3fd9f376",
"metadata": {},
"source": [
"### Deriving posterior\n",
"Prior plot values. Re-express binomial as beta dist."
]
},
{
"cell_type": "code",
"execution_count": 8,
"id": "e3c679dc",
"metadata": {
"name": "Prior"
},
"outputs": [],
"source": [
" prior_a = 50 #successes\n",
" prior_b = 250 #failures\n",
" prior_n = prior_a + prior_b #observations\n",
" prior_theta = prior_a/prior_n\n",
" prior <- data.frame('Dist'='Prior','x'=seq(0,1,0.005), 'y'=dbeta(seq(0,1,0.005),prior_a,prior_b))"
]
},
{
"cell_type": "markdown",
"id": "1e6ddd42",
"metadata": {},
"source": [
"Observations are taken from the earlier binomial sample."
]
},
{
"cell_type": "code",
"execution_count": 9,
"id": "2b2b749c",
"metadata": {
"name": "Observations"
},
"outputs": [],
"source": [
" obs_a <- sample_success + 1\n",
" obs_b <- sample_n - sample_success + 1\n",
" observations <- data.frame('Dist'='Observations',x=seq(0,1,0.005), y=dbeta(seq(0,1,0.005),obs_a,obs_b))"
]
},
{
"cell_type": "markdown",
"id": "ec388065",
"metadata": {},
"source": [
"In this example, the posterior is a simple combination of the prior and observations."
]
},
{
"cell_type": "code",
"execution_count": 10,
"id": "aecf637c",
"metadata": {
"name": "Posterior"
},
"outputs": [],
"source": [
" post_a <- sample_success + prior_a - 1 #combination of prior and observed successes\n",
" post_b <- sample_n - sample_success + prior_b - 1\n",
" post_theta <- post_a / (post_a + post_b)\n",
" posterior <- data.frame('Dist'='Posterior','x'=seq(0,1,0.005), 'y'=dbeta(seq(0,1,0.005),post_a,post_b))"
]
},
{
"cell_type": "markdown",
"id": "b1f71573",
"metadata": {},
"source": [
"This can be plotted as:"
]
},
{
"cell_type": "code",
"execution_count": 11,
"id": "321a7aaf",
"metadata": {
"name": "Plot"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message:\n",
"\"Ignoring unknown parameters: label\"\n"
]
},
{
"data": {
"image/png": 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1YkCyMHgkiKuWdEsjByIIikmHtGJAsj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\nkQgZIIhEyABBJEIGCCIRMkAQiZAB8v8BpuyZlLWjdkAAAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"model_plot <- rbind(prior,observations,posterior)\n",
"with(model_plot, Dist <- factor(Dist, levels = c('Prior', 'Observations','Posterior'), ordered = TRUE))\n",
"\n",
"qplot(model_plot$x, model_plot$y, geom='line',color = model_plot$Dist) +\n",
"ylab(expression(paste('p(',theta,')', sep = ''))) +\n",
"xlab(expression(theta)) +\n",
"geom_vline(xintercept = post_theta, linetype=\"dotted\", color = \"black\", label=\"blah\") +\n",
"scale_color_discrete(name = \"Dist\") + \n",
"annotate(\"text\",x=post_theta, y=0, label=label_percent()(post_theta)) +\n",
"labs(title=\"Informative prior\", subtitle=\"Low success\") + \n",
"theme(plot.title = element_text(hjust = 0.5)) +\n",
"theme(plot.subtitle = element_text(hjust = 0.5))"
]
},
{
"cell_type": "markdown",
"id": "90817fab",
"metadata": {},
"source": [
"## Regression - logistic\n",
"### Background\n",
"\n",
"RSTANARM is an interface in R for STAN where [Stan](https://mc-stan.org/) is a platform for Bayesian inference - it is a probabilistic programming framework where the guts of the inference method happens in the background, while the user focuses on parameterising the model in R. RJAGS is an interface in R for JAGS (Just Another Gibbs Sample) where [JAGS](https://mcmc-jags.sourceforge.io/) is similarly a platform for Bayesian modeling.\n",
"\n",
"Models in both STAN and JAGS can make use of Markov chains Monte Carlo (MCMC) methods. MCMC methods provide a way to take random samples approximately from a posterior distribution. Such samples can be used to summarize any aspect of the posterior distribution of a statistical model.\n",
"\n",
"RSTANARM and RJAGS have pre-written code for common models like regression. \n",
"\n",
"Under a Frequentest approach to linear regression, for a given set of response variables y, the relationship between y and a set of regressor variables x is assumed to be linear (informed by a set of parameters $\\beta$), with an error term, i.e. $y = X\\beta + \\epsilon$.\n",
"\n",
"The error term, $\\epsilon$ is assumed to be normally distributed and the regression co-efficients are estimated by minimising the error term commonly using ordinary least squares (OLS). We make some other assumptions about the error term - not correlated with X and i.i.d.; and define $Var(\\epsilon)=\\sigma^2$. The generalised form allows the response variable to have an error that is not normal - this is achieved by allowing the linear model to be related to the response variable via a link function and by allowing the magnitude of the variance of each measurement to be a function of its predicted value.\n",
"\n",
"With Bayesian inference we are interested in the posterior _distributions_ of the parameters $\\beta$ and $\\sigma$, rather than point estimates. We also want to influence those distributions with some prior knowledge of their behaviour:\n",
"\n",
"$p(\\beta,\\sigma|y,X) \\propto p(y|\\beta,\\sigma)p(\\beta,\\sigma)$ \n",
"\n",
"$p(\\beta,\\sigma|y,X)$ is not a normalised probability density function (i.e. is proportional to the likelihood and prior). However, we can sample from it and therefore estimate any quantity of interest e.g. mean or variance, [Numerical Recipes, p825](https://www.amazon.com.au/Numerical-Recipes-3rd-Scientific-Computing/dp/0521880688). For this we use MCMC:\n",
"\n",
">\"MCMC is a random sampling method... the goal is to visit a point $x$ with a probability proportional to some given distribution function $\\pi(x)$ [not necessarily a probability]. Why would we want to sample a distribution in this way? THe answer is that Bayesian methods, often implemented using MCMC, provide a powerful way of estimating the parameters of a model and their degree of uncertainty.\" \n",
"\n",
"### Heart disease data\n",
"\n",
"The Framingham Heart Study is a longitudinal study of cardiovastular disease in a sample population within Framingham, Massachusetts. A subset of data for teaching is available at request from the [U.S. National Heart, Lung and Blood Institute](https://biolincc.nhlbi.nih.gov/teaching/). This dataset is not appropriate for publication and has been anonymised, but is nevertheless useful for illustrative purposes here. The dataset:\n",
"\n",
">\"..is a subset of the data collected as part of the Framingham study and includes laboratory, clinic, questionnaire, and adjudicated event data on 4,434 participants. Participant clinic data was collected during three examination periods, approximately 6 years apart, from roughly 1956 to 1968. Each participant was followed for a total of 24 years for the outcome of the following events: Angina Pectoris, Myocardial Infarction, Atherothrombotic Infarction or Cerebral Hemorrhage (Stroke) or death.\"\n",
"\n",
"We'll look at a logistic regression model example using predefined Bayesian models in RSTANARM."
]
},
{
"cell_type": "code",
"execution_count": 12,
"id": "b3e12150",
"metadata": {
"name": "Heart data"
},
"outputs": [
{
"data": {
"text/html": [
"
\n",
"SEX | TOTCHOL | AGE | SYSBP | DIABP | CURSMOKE | CIGPDAY | BMI | DIABETES | BPMEDS | HEARTRTE | GLUCOSE | educ | PREVCHD | PREVSTRK | PREVHYP | HDLC | LDLC |
\n",
"\n",
"\t2 | 260 | 52 | 105 | 69.5 | 0 | 0 | 29.43 | 0 | 0 | 80 | 86 | 2 | 0 | 0 | 0 | NA | NA |
\n",
"\t1 | 283 | 54 | 141 | 89.0 | 1 | 30 | 25.34 | 0 | 0 | 75 | 87 | 1 | 0 | 0 | 0 | NA | NA |
\n",
"\t2 | 232 | 67 | 183 | 109.0 | 1 | 20 | 30.18 | 0 | 0 | 60 | 89 | 3 | 0 | 0 | 1 | NA | NA |
\n",
"\t2 | 343 | 51 | 109 | 77.0 | 1 | 30 | 23.48 | 0 | 0 | 90 | 72 | 3 | 0 | 0 | 0 | NA | NA |
\n",
"\t2 | 230 | 49 | 177 | 102.0 | 0 | 0 | 31.36 | 0 | 1 | 120 | 86 | 2 | 0 | 0 | 1 | NA | NA |
\n",
"\t2 | 220 | 70 | 149 | 81.0 | 0 | 0 | 36.76 | 0 | 0 | 80 | 98 | 1 | 1 | 0 | 1 | NA | NA |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|llllllllllllllllll}\n",
" SEX & TOTCHOL & AGE & SYSBP & DIABP & CURSMOKE & CIGPDAY & BMI & DIABETES & BPMEDS & HEARTRTE & GLUCOSE & educ & PREVCHD & PREVSTRK & PREVHYP & HDLC & LDLC\\\\\n",
"\\hline\n",
"\t 2 & 260 & 52 & 105 & 69.5 & 0 & 0 & 29.43 & 0 & 0 & 80 & 86 & 2 & 0 & 0 & 0 & NA & NA \\\\\n",
"\t 1 & 283 & 54 & 141 & 89.0 & 1 & 30 & 25.34 & 0 & 0 & 75 & 87 & 1 & 0 & 0 & 0 & NA & NA \\\\\n",
"\t 2 & 232 & 67 & 183 & 109.0 & 1 & 20 & 30.18 & 0 & 0 & 60 & 89 & 3 & 0 & 0 & 1 & NA & NA \\\\\n",
"\t 2 & 343 & 51 & 109 & 77.0 & 1 & 30 & 23.48 & 0 & 0 & 90 & 72 & 3 & 0 & 0 & 0 & NA & NA \\\\\n",
"\t 2 & 230 & 49 & 177 & 102.0 & 0 & 0 & 31.36 & 0 & 1 & 120 & 86 & 2 & 0 & 0 & 1 & NA & NA \\\\\n",
"\t 2 & 220 & 70 & 149 & 81.0 & 0 & 0 & 36.76 & 0 & 0 & 80 & 98 & 1 & 1 & 0 & 1 & NA & NA \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| SEX | TOTCHOL | AGE | SYSBP | DIABP | CURSMOKE | CIGPDAY | BMI | DIABETES | BPMEDS | HEARTRTE | GLUCOSE | educ | PREVCHD | PREVSTRK | PREVHYP | HDLC | LDLC |\n",
"|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|---|\n",
"| 2 | 260 | 52 | 105 | 69.5 | 0 | 0 | 29.43 | 0 | 0 | 80 | 86 | 2 | 0 | 0 | 0 | NA | NA |\n",
"| 1 | 283 | 54 | 141 | 89.0 | 1 | 30 | 25.34 | 0 | 0 | 75 | 87 | 1 | 0 | 0 | 0 | NA | NA |\n",
"| 2 | 232 | 67 | 183 | 109.0 | 1 | 20 | 30.18 | 0 | 0 | 60 | 89 | 3 | 0 | 0 | 1 | NA | NA |\n",
"| 2 | 343 | 51 | 109 | 77.0 | 1 | 30 | 23.48 | 0 | 0 | 90 | 72 | 3 | 0 | 0 | 0 | NA | NA |\n",
"| 2 | 230 | 49 | 177 | 102.0 | 0 | 0 | 31.36 | 0 | 1 | 120 | 86 | 2 | 0 | 0 | 1 | NA | NA |\n",
"| 2 | 220 | 70 | 149 | 81.0 | 0 | 0 | 36.76 | 0 | 0 | 80 | 98 | 1 | 1 | 0 | 1 | NA | NA |\n",
"\n"
],
"text/plain": [
" SEX TOTCHOL AGE SYSBP DIABP CURSMOKE CIGPDAY BMI DIABETES BPMEDS HEARTRTE\n",
"1 2 260 52 105 69.5 0 0 29.43 0 0 80 \n",
"2 1 283 54 141 89.0 1 30 25.34 0 0 75 \n",
"3 2 232 67 183 109.0 1 20 30.18 0 0 60 \n",
"4 2 343 51 109 77.0 1 30 23.48 0 0 90 \n",
"5 2 230 49 177 102.0 0 0 31.36 0 1 120 \n",
"6 2 220 70 149 81.0 0 0 36.76 0 0 80 \n",
" GLUCOSE educ PREVCHD PREVSTRK PREVHYP HDLC LDLC\n",
"1 86 2 0 0 0 NA NA \n",
"2 87 1 0 0 0 NA NA \n",
"3 89 3 0 0 1 NA NA \n",
"4 72 3 0 0 0 NA NA \n",
"5 86 2 0 0 1 NA NA \n",
"6 98 1 1 0 1 NA NA "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df_heart <- read.csv(file = '../_static/bayesian_applications/frmgham2.csv') \n",
"df_heart <- df_heart[c(1:23)] %>% filter(PERIOD==2) # ignoring health event data, only looking at observations at period == 2 (observations for participants are not independent over time; this does have limitations e.g. observations are truncated at death which could be due to heart disease)\n",
"ignore_cols <- names(df_heart) %in% c(\"PERIOD\",\"RANDID\",\"TIME\", \"PREVMI\", \"PREVAP\") #exclude identifier and time columns; exclude PREVMI and PREVAP as they are a subset of PREVCHD\n",
"df_heart <- df_heart[!ignore_cols]\n",
"head(df_heart)"
]
},
{
"cell_type": "markdown",
"id": "98ca72e3",
"metadata": {},
"source": [
"Data description (available at the NHLBI at the link above) highlights:\n",
"\n",
"* RANDIND: unique identifier.\n",
"* SEX: 1=male; 2=female (categorical, 1/2).\n",
"* TIME: number of days since baseline exam (continuous).\n",
"* PERIOD: examination cycle (categorical, 1,2 or 3). We'll focus on period 2 - observations for the same participant are not independent over time.\n",
"* TOTCHOL: total cholesterol level (continuous).\n",
"* AGE: Age of the patient rounded to nearest year (continuous).\n",
"* SYSBP: systolic blood pressure (continuous).\n",
"* DIABP: diastolic blood pressure (continuous).\n",
"* CURSMOKE: whether or not the patient is a current smoker (categorical, 0/1).\n",
"* CIGPDAY: the number of cigarettes smoked per day on average (continuous).\n",
"* BMI: Body Mass Index (continuous).\n",
"* DIABETES: whether or not the patient had diabetes (categorical, 0/1).\n",
"* BPMEDS: whether or not the patient was on blood pressure medication (categorical, 0/1).\n",
"* HEARTRTE: heart rate (continuous).\n",
"* GLUCOSE: glucose level (continuous).\n",
"* EDU: attained Education (categorical, 1=0-11 year; 2=High School Diploma, GED; 3=Some College, Vocational School; 4=College (BS, BA) degree or more).\n",
"* HDLC: High Density Lipoprotein Cholesterol - only available for period 3 (continuous).\n",
"* LDLC: Low Density Lipoprotein Cholesterol - only available for period 3 (continuous).\n",
"* PREVCHD: prevalence of Coronary Heart Disease (categorical, 0/1).\n",
"* PREVAP: prevalence of Angina Pectoris (categorical, 0/1). Excluded from model as it is a subset of PREVCHD.\n",
"* PREVMI: Prevalence of Myocardial Infarction (categorical, 0/1). Excluded from model as it is a subset of PREVCHD.\n",
"* PREVSTRK: whether or not the patient had previously had a stroke (categorical, 0/1).\n",
"* PREVHYP: whether or not the patient was hypertensive (categorical, 0/1).\n",
"\n",
"Using the [DataExplore package](https://cran.r-project.org/web/packages/DataExplorer/vignettes/dataexplorer-intro.html), we can see that the data is mostly complete apart from missing entries in 'glucose' and to a lesser extent 'education'."
]
},
{
"cell_type": "code",
"execution_count": 13,
"id": "59f5b93a",
"metadata": {
"name": "Heart explore 1"
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"rows | columns | discrete_columns | continuous_columns | all_missing_columns | total_missing_values | complete_rows | total_observations | memory_usage |
\n",
"\n",
"\t3930 | 18 | 0 | 16 | 2 | 8720 | 0 | 70740 | 334464 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lllllllll}\n",
" rows & columns & discrete\\_columns & continuous\\_columns & all\\_missing\\_columns & total\\_missing\\_values & complete\\_rows & total\\_observations & memory\\_usage\\\\\n",
"\\hline\n",
"\t 3930 & 18 & 0 & 16 & 2 & 8720 & 0 & 70740 & 334464\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| rows | columns | discrete_columns | continuous_columns | all_missing_columns | total_missing_values | complete_rows | total_observations | memory_usage |\n",
"|---|---|---|---|---|---|---|---|---|\n",
"| 3930 | 18 | 0 | 16 | 2 | 8720 | 0 | 70740 | 334464 |\n",
"\n"
],
"text/plain": [
" rows columns discrete_columns continuous_columns all_missing_columns\n",
"1 3930 18 0 16 2 \n",
" total_missing_values complete_rows total_observations memory_usage\n",
"1 8720 0 70740 334464 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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OTWq8stDESKlLdcitbjiKRBMJjW4yW3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\nKbkUrccRSYO/vxEp2zgiafD3NyJlG0ckDf7+RqRs44ikwd/fiJR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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
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CJB8uoIEBHBESAiQfLqCBARwREgIkHy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\nrkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"introduce(df_heart)\n",
"plot_intro(df_heart)\n",
"plot_missing(df_heart)"
]
},
{
"cell_type": "markdown",
"id": "7b0865c1",
"metadata": {},
"source": [
"Given around 12% of glucose records are missing as well as all of HDL and LDL (only available for period 3), drop the columns. Also drop rows with other missing data as these are small in number."
]
},
{
"cell_type": "code",
"execution_count": 14,
"id": "2f1ef3a8",
"metadata": {
"name": "Heart explore 2"
},
"outputs": [],
"source": [
"df_heart$GLUCOSE <- NULL\n",
"df_heart$HDLC <- NULL\n",
"df_heart$LDLC <- NULL\n",
"df_heart <- na.omit(df_heart)"
]
},
{
"cell_type": "markdown",
"id": "7ddb5561",
"metadata": {},
"source": [
"Plots of the data:"
]
},
{
"cell_type": "code",
"execution_count": 15,
"id": "d2852e30",
"metadata": {
"message": false,
"name": "Heart explore 3",
"warning": false
},
"outputs": [
{
"data": {
"image/png": 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TQRSKoG0kQgqRpIE4GkaiBNBJKqgTQRSKq2D6RtHIMkTbQHpC1I0kzzkLZekaS5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\nQJIGBJI0IJCkAYEkDQgkaUAgSQP6fxuMHn94SL1NAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot_bar(df_heart, title=\"Barplot\")"
]
},
{
"cell_type": "markdown",
"id": "03f79451",
"metadata": {},
"source": [
"Of the 3.6k remaining records, ~7% have a flag for heart disease:"
]
},
{
"cell_type": "code",
"execution_count": 16,
"id": "1561f0d0",
"metadata": {
"message": false,
"name": "Heart explore 4",
"warning": false
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
" 0 1 \n",
"3319 253 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"table(df_heart$PREVCHD)"
]
},
{
"cell_type": "markdown",
"id": "8b04d45b",
"metadata": {},
"source": [
"Further plots and checking distributions:"
]
},
{
"cell_type": "code",
"execution_count": 17,
"id": "54766439",
"metadata": {
"message": false,
"name": "Heart explore 5",
"warning": false
},
"outputs": [
{
"data": {
"image/png": 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OoWDpAyAVIKVA9lBWckhwutMCABUiyh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\nfXctEFkES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Bki8bkM52AEkTIPmyVZDs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\nDQRICDXQ/1JcPy3i5B1DAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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GhPLhL/euchRNp4RD66hZqohS/S8/nD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\nqGV5fl14OJFMSqQDj12bisFF2rRH8rbE1ERDRtwimZRIRx67NhV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QYZWsRHq1q8nftbv/e5Nid+1ur3xBpCagwipZifR+PaXw3/U8g3+y\n4Rp1Ee9kw/vzFMPH5QvHSG1AhVVirufqnEj3M9rmb3j6+xp1EZvy73lG/N3gGKkZqLBKfoci\n3T6Gffu4XIIPZC8XP+JS/r49/pdbCCI1ARUGQACIBIAAEAkAASASAAJAJAAEgEgACACRABAA\nIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJA\nJAAEgEgACACRABAAIgEgAEQCQACIBIAAEAkAASASAAJAJAAEgEgACACRABAAIgEgAEQCQACI\nBIAAEAkAASASAAL8H1JwviXeCftSAAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
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oklRapvlLA+emTEY1FNo5IlRcr5gB63\nbG44d2YgElmjEog0tUjugwKIRNaoBCLNLJJnlGpRkfweQaSyGXMOGYYtmyueUSqIRNaoZEWR\nso69hy2bL//XJhCJrFEJRJpXJJ9Hy4kkhDcVlb051hUiTSuSv3gWE0nwEmm7/fdDWqIgEnm/\n82KB0qESSZbCdq8LvTyYZETwEmlPlJa+QUWyEjq7SHSNOkriopSEUR5MMsJLpO0ym0iJjabT\nut95sVDh0Ii0XSBStkjbBSINJVKwbkhE2o5K0H5yF4m0NwQi/fdDRpUx4p5Q8nYD+T5dpNaf\nvxddpMch0uWilgeT+tA9araUpL/aLvNskewCm2+L1HxHRikHpSxYb5Ha7EHniSQTNIFIjgKb\nWSTS3rhKQp0CkWIibfeNN0QaQqSIRyQiPUoCImWI9EgURBpCpJhHVMPf2LWDSOmnnqXTtt8Z\nsZhHTURylAePjAiOIk1wZsP8IkU3SLQiqWc0cDyzgZ1ImaXDVCRXjc0lUtwjMpGGyAhEajGj\ns8gmFYm+N5T1cUpGhPKpApEIZ3R/Wlszqmc9DFQ2e98hkkRApEYzuovM+hxTY+OUzd73BI9W\nEUlApFYzuovMTL8WG6Zs7p1P8AgikfXmWNelRPIUmTajKdkwZXNFQCQFiNRqxgSRrNgwZXPl\nqJvGZTNERjSPIBLhjHGR7ItJhymbr+QHly8oEl2jRkyykki+vZ5jRsfFpMOUTfrjPBcTibZR\nIyZZSCTv4cNjRufFpMOUTfrjPBcRSUCkNjN6D8PvM7ov3RmlbM7dkRkhIxCpzYz+4ax9Rs+l\nOzbWvXNYlY2IP84TIpH15ljXZUTy7tg9BiI881lY987hVTYJj/NcSyTaRs2YZDmRPDN6L90x\nse+dw6JsBET6cmeEtFErJoFI+/GTdz4Dx71zOJSN6RFEEtgitWg0dAP1q2T+Rg0c98659L9n\njuJRx15YNHkn02YU2CKdL1Lw/E4d171z+peNtT1aeYskDEga9cYki4gUGGr4Cp5Oo6+w8945\nXcvmiqNq1hXJ9AgiUc4Y9Cijdpz3zulZNldcHi0rktcjiEQwY9ij3NphtmvnrBqIBJHOFSl2\nFoBjrc1753Qsm6+ix8RCJLLeHOu6gkh+j+JnATjW2rp3Tr+yKXu65UoikTQaiElWEskOJDTK\numz8V/JBpJO30SuLlHIWFu+y8V9avrhItI0GYpKFRLImJzU6QtlwFel8HtnosOSamUNvFh+R\nPKU2waMv/R7xEKlFH9IyQtpoKCZhdUpJE9wfUjM8aCzgEUQibDQUk0y/RXLX2gx3Wg15tLhI\ntI2GYpI1RQrfIFKLsS2boEeLihRICESqmzHBo+FFImx0bJF6ZmRykWRq1WDOCBfbsglvkJYU\nyb50gqBRiHRFuETKGuHiWjYRj9YUqWdGFhHpCGaOcDEtm5hHi4kkdGgaTYpJphZJyewjmHtg\nzrFsUu7xvZRIAiJlxgpFOoLZe88MyybpXvkriZTkEUQqn1FYIuV/VvErm6/qp1tCJLLeHOs6\nsUhaYm/BghTzK5u0h7dApMpGE2OSlUQqOZ7gVzZpD0FaSKQ0jyBS6Yx6Yi/OW+QnNMqtbBIf\nJrauSDSNpsYk84t0DxZ+ejMrG61kThqyUWKE9UEuEm2jqTHJtCIZn1Cln968ykZAJJ9IxI2m\nxiSzimR6dELtkPQ7GDT2YSDSFfNImKTR5JhkUpGMXebyomNVNsaxAET6co3NEjSaHpPMLtL+\nyym1Q9HvYNA8poZI5icmREqMpc6oe1TVGz5lY3oEkbKeCgWR8me0PZpAJMsjiASR2q6wlt2U\ne9eFYlzKxrSIpNHcGGF9QKTERHEQ6Svx3nWhGJOycXgEkazBWYiUGEua0eXRRCIRNpodI6wP\n2uEXykazYpKJRdIu4htcJNcGaWWRhA5NoyUxyXwiHdlNvfMzf5GcHi0skscjiJQaS5jR7dE0\nIhE2WhAzOJ7vfn8uh/EYthZ9uAaFCUWjZTHJbCK5P7sHF4l4naiSsVmPXDMe9N6iDxCJIpYj\nElFvGHCsU++eaGz2swshUhmhrvURyefRyFsk8nWiScZmP5ba8Og0kUgaLYtJEkVSd4LTEtVF\nJG/NQSSKGfWScIh0lMd/VzKSl4XhUavFZJHWi8e223j+cOjN6iGS36OBRXJ98lY3WhgzSsJ8\nvPtZj6f2vcn8t0hjiBTwaFyR/B51Fcl0RhnBa52RwqfysRDpkSHWIoU8mkEkwkZLY0oxbPpQ\nt+tV64xQNloakxSL1HIfuIju+8wt3iiuZbNj2nPOrh3PjKRW3f7pw3iLFNwejbtFarGVpRdp\nO36ou3st+jC6SBfmu3YRj0YVKbhWPER6jNbdLNIGdRuLRNpoaWw2kWIeQSSKGTOS0SwjxY+3\nZCES91G7qEeDihRerzVFYpqRyUSi703Psml03De0SGLoLRLzMxviHg0pUqvjvpFFKn+8JQ+R\n8hN1nkjx/bqa3vQrGwGRLMTgu3YFiTpNpGi91fWmW9nE12s5kYSIJAUiJcYcwTSPhhaJsNG6\nGSnro+6jhd9R40Qi9a4d2sUnfEAsJpKASGQxO6hktnftkC4+ZUMLkeobrZzxWNexRdIS27t2\nKBeftMMKkeobrZzxWNehRdLz2rt2CBcvUkb0lxaJqtHKGY91HVkkI6+9a4dq8QmfvPmNksxI\nWR81O7scxzEHFsnMa+/aIVq87tFJQzaJMcL6KN7ZZZqRcUWyPp961w7N4o3tEdOyOTMjN46d\nXaYZGVYkezvfu3ZIFi8gkit2nNHANSOjiuTYX+5dOxSLFxDJGVNOsWOakUFFch129q4dgsVb\nHnEtm9MysqOeYsc0I2OK5PKoe+0QLN7yiGvZnJaRG4pHEIkkdg86PepeO/WLz9xfXUUkzSOu\nGRlRJLdH3WunevEOj7iWzUkZuXF7YBxEIo1dg65yS5qxLHZe2ThXjGnZnJORHYhEH/sqvYPv\nWCJR9Lu2N84YYX0k92HPBvujxtFE8nvUvXZqFw+RXDHTI64ZGUykgEfda6dy8fkjKCuIdE8G\nRCKNiZBH3WunbvEFIyjsRapD2JzbgSxGEinsUffaqVq8b82GFqmqDw6P6jpf1RtfTDKQSBGP\nTqsd6xHEBGXjXTWmZVNfHxkZ0XPDNCPjiBTR6LTasR9BXF82/nVjWjb19QGREhNFvMKxzVGk\nUbracTyCuL5s/OvGtGzq6wMiJSaKdoUTPDqndhxPTq0vm8C6MS2b+vrAMVIP1Gz27YlbpLpH\nD3NZN3KqStfj0ZQihbpGucIJm6NIo1Qfwq5HENeWTXDlmJZNfX0k7toRdr6mN96YZASR1M1R\nYaNEteN/BHF52YQ/JZiWTX19QKTERNGtsFppvUXyPoK4uGwiR39My6a+PhKHXwg7X9Ebf0zC\nXiS90DjUjsejssVHPOJaNvX1kTb8Qtn58t4EYhLuIhl1xqF2zEcQV5VN7PCPadnU10dwOaGk\nMM0Ic5HMOuNQO9YjiCvKJuYR17Kprw+IlJgoihW293s4107B4mM7dmzLpllGbgTv2Mw0I5xF\ncpQZ59rJX3zcI65l0yojNwSOkUj69njhKjPOtZO9+ASPuJZNo4zcEMeuHWnny3ozvkjOMuNc\nO7mLF+GvYiv7ndubpBhhffiHX74gEk3f9h/uT2vOtZO5ePWDAiIdQCSqvl3/8xUZ59rJW3ya\nR1zLpkVGdm73NwmlhWlGeIrkLTLOtZO1+ESPuJZNg4zs3HIRzAvTjHAUKVBjnGsnZ/HqKrbp\nd5NGCevDHdTuGQSR6voW+qzmXDsZi1fHGSDSgX7PIIhU1bfgPg/n2slZvLqOEEkixj3Xg5tI\nkWMHzrWTvnh9HSHSgxSPuGaEmUixY3DOtZO8eOMMGIh0RySNwTDNCCuR4mnkXDupi9efUgKR\nHmg3y4dIFX1rmEU+ItkrCZFuWB5BpMK+xXPIu3aSFu+olHFFsm6VWXPLTHPHDsdIRX1LyiGD\n2inMxiPoWsthRbJulVlzp79Uj7hmhIlIiR51r53SbMwokn2rzAqR9B27Jp1v0qiEh0iJGnWv\nneJs3IPOz4tBRVLu8FcvknZmEEQq7JteXk1WmIdI7u3ulCLl3TLzXoWyBAaEgUhGdc0rkmf/\ndUyR1FtlVm+RjFPsRsxId5Gs6lpApDP63aTRA82ZWpHMU1VHzEhnkYTl0bwi+Q4BRiwb/VaZ\nlSJZp6qOmJFEkdxfFIS6ltQ3177OrCL5PBqybBSBqkV65GMFkTyZCnUtoW8nHnv3F8nr0ZBl\nQyiS7dGQGeknkmOvLjpf/9opFcmr0Zhlo5dF1ZkNxo7d3CI90kYokkejSUUSXzOKVJMRuXf/\n+LmqSFWP1jKf/V7REB8C+Rah++KMWDbVGXksRyZkHZHkFwcUWyTf5igyH+va8TcS2h6NWTa1\nGZGHyccEJUMjZqSPSAGPJhQpeCvrMcumMiOP5Wj5OBI0YkaSRdr0/6KJCizfe3gU7Tfr2gm0\nApHcyym45IhrRlJF2o7/a0UKajShSOYVsef0u0mjmcT6UHLJEdeMpH4hq/yoFEm16LRj79Nq\nx+aW4ZkGVdKJvCFFlxyNLZI8H6T+zIaYR+OK5G7gvtfv3R6NWTY1GXksx7h0QknQiBk5+1y7\nqEeTidTtAWlNGiWsj4vDo5Evvj9ZpLhHc4nU7wFpTRolrI+LfbOTNUbtchPlWn54uC6h36xr\nxzG3+nXjyf1u0ihhfTg3SBApYfl6vk6uqz4i6V/bn9vvJo3S1cd+ITREiibKWr6Wrkvh/U1Y\n1441r3n6y6n9btIoWX08roLFMVIkUdbyU7dHE4l0rCREMjiuOXLu7Y+YkZNEMjw6fYU7iOQ8\nHfO8fjdplKg+YiemjpiRM0Syd4RXEOlBzKMhy6auPiBSYqL05RsSdcni+SK5rrM5s99NGqWp\nj+gZ3iNmpL1IDo8WECl5x27Msqmpj2NkzpeYETNyrkhqFkv6zbp21NmsgQaI9OAYmfNmZsSM\nNBfJ5dH0IuV4NGTZlNfHMTInvLkZMSONRdI16nfGzLkiZXk0ZNmU1wdESkyUtnxjc5R0y60J\nRJLIVZ/t0Lo8I8dyIFIoUcoyjK2R+i0sRGre7yaNVteHetc1/9Z6xIy0EUkY3KYR9Jt17Tjm\nhkg66mdpYK93xIw0ESnm0TIiybNV1xTJRC22R23UtskFYpGuZWNqZHu0jkiP6yfWFMmcXy2C\n0CjMiBmhFclyyO3RQiJ163eTRuvqw775FkRyl45Xo5x71zEryPJs9O13k0ar6sPYKfF7NGRG\nWot0m0zWb9a1w6vfTRqtqQ9rp8Tr0ZAZIRJpz4nLIuddl9YQSXT84qx3MqyMdN8pGUKkhzaq\nQo9o7r3rphFJ3XWZrWzyMwKREhJ12HMftVOWn300OYtI2lZ5trLJzkjW2QsjZoRYJHP5BUeT\nEImk300aLawPidC+HTm5800albQVqeTqaohE0u8mjRbWxwP3MfRZnW/SqITmm+VbWhyTSRof\nBTPJOEYyZneP6Z7W+SaNSkhH7Yzll227Z9kiYdQOIhWXjraMwmvZ5hGpa7+bNFpXHxCppHSK\n713HrCBpsgGRruAYKb90RPG965gVJEk2INIORu1yS6fiEhxmBUmRDYjEofNNGpU0urCvpm+B\nGOva4dXvJo1S1UeXzjdpVNLmwr6qvgVi/WtHfWSh/vhCZv1u0ihRffTpfJNGJS1Eqrt3HbP0\n66gP0TUeqMus300apamPTp1v0qikgUiVX+YzS78ORKqvj16db9KohFyk6i/zmaXfAUSqqI9+\nnW/SqIRaJPV+S/T95lE7tkj/XanJ5JzweiebNCqhvvkJQd8CMQYiHQMM2+23NcumtD56dr5J\noxLim59Q9C0Q41E70qQfjSBSTn107XyTRiW092wg6VsgxqN2NvdrXv1u0mhlffTtfJNGJYQi\nGed8sFrhU0ftnKfCn93vJo2W1scCGaETieqi/OFFcp1HNlvZ5NXHChkhE4nsI4e1SPJshu3i\nO7PBe7nwuf1u0qgrE/eX2yMj9kfLEhmhEonu3nW8RYpnY4mysbfH+0fLuhk546nmdDGI1LdR\nBVMkS6zFMgKRqEVa4ojgjiGS4dFSGYFI5CKtMEZ1Z9NfKYdI+rkezlvjzAVEoheJRb+bNKqh\njSts+n/rZQQiQaT0mMkWfLVURiASREqPmWzWC4j04O3Xz/7sy0d16fBaYYhE0qiCvhu3Oaat\nlRFDpO/n2xbrnqkAABpsSURBVD1ThXiHSHsMIimxBJFWvfjeEOm3eP2x6PJXvECkPQaRlJhm\nknKOhzxrat27WBgiXYcpH/8g0hdE0mOZtOgD14xAJIiUHsukRR+4ZsS9a/cqftcmitcKQySS\nRjNp0QeuGTEHG7b9vKjtszZRvFYYIpE0mkmLPnDNiLUL9+dZiOfX7+pE8VphiETSaCYt+sA1\nI9OfAwXGo/iGTOfPKIFIgB2ji6Q9u6a6ZQAKgUgAEDC6SACAQiASAASYIn2/Pgvx8qdLXwAY\nFkOkz6wvZAEAO4ZIL+LlR6HPl7RThAAAO46TVn/4Thu1e5+fjFT27mp7MpKxHIYwv8R+clDa\n9Ui939gTyEhl7662JyMZVRiXNTWerWJGBXPL8/t6lfnny0vSMVLvN/YEMlLZu6vtyUhGDa57\nTbabrWJGFWvXLudL2d5v7AlkpLJ3V9uTWVulQKQJyUhl7662J7O2qjhRpMLl6VR9Idv7jT0B\nZEOhplZygUhzgWwo1NRKJgV1XSUS+WBDFr3f2BNANhRqaiWT0UX6/p1z9nfvN/YEMlLZu6vt\nyUhGGXIc+uwxg2qP7O+RIJJGRip7d7U9Gcmoo6iuK0Sq98getfubMXPvN/YEkA2FjGRUUWFD\nuYKVGCI9Zx0z9X5jTwDZUMipjQq2rexUg9ITFEqXp2Ge/Z16A6EbLd+0px+uPx6/HpNuP+9R\n+aoVGakkXe7Tk7JuxoobE+8zvKsT35vkJCMZy2Fugf4yOUaSNXLUhTHp+kMroiZkpJJ82Y+1\nezr+Nye+azlQ/hIinQzTwQa1Ot79+qwhUviHkSr9JS0ZyVgOpoMNT/pLvTTWEunJ9euT+VdK\nNvTXlGQkYzmsLVLOzC3erB31yOfp/UmfZOztQaT7D4jUEVOcX78zLjJv8WYdGOIck1YYbLiS\nKJJMAkTqiPfs75SZW7xZGo4RKNcxUkMyUkm+bGyRBgIihclIJfmyIdJAMD1p1ToaCo7aNaRn\nNjBqNxBcRZJfk8gfrm9O1hDp6fjfnPiu23P8JUQ6GVOkVy67dsogwpMxSRlsaNmDGxmpJF/2\nsaumjWEaE41Pm6fjBfkwTEYylsMQ5pXXMVJ/MlLZu6vtyUjGchjCbOLjRXx+v4ikpPV+Y08g\nI5W9u9qejGQsh32DyD/i3+Ub97W7k5HK3l1tT0YylsMW6Z94k3dcjdD7jT2BjFT27mp7MpKx\nHNYpQn8/xfPlHSLdyUhl7662JyMZy2EIczXo5TrWkHQT/d5v7AlkpLJ3V9uTkYzlMLc8/54v\nl99CvCbN3PuNPYGMVPbuansykrEcCbtwyoW4xkW5vd/YE8hIZe+utievtNYiRSTv718hQtHS\n2PkzZqSSV7+bNAq8mCK9bdcDpU199qUhkvJr6M3iVQIQiaRR4MUQ6U2I/fGXh0n+DRJE0uDV\n7yaNAi/W7bjef/69fYhDF+NeRY+X//3Qvnsj0aJ0IdIouL6Qfda+kDXuu6duoEJvFq8SwBaJ\npFHgxTrX7vO3+LgeJRnTHa8gkg6vfjdpFHgxRPrzc3i0XTdIxhdJm/XiSujN4lUCEImkUeDF\nvh5p+/eji+KRvmsHkbzw6neTRoGX+PdI28W3ZweRNHj1u0mjwEvimQ23n/K/B6E3i1cJQCSS\nRoGXqns2hN4sXiUAkUgaBV4gEkRKjwEvEMkRE0LIGE02BhapLBnLAZHs2O3mL48YTTbGFakw\nGcsBkazY/TZK9xhNNoYVqTQZywGRIFIoBpESgUgQKRSDSIlAJBwjBWM4RkoDImHULhzDqF0S\nEAnfI6XHgBeIBJHSY8ALRIJI6THgBSJBpPQY8AKRIFJ6DHiBSBApPQa8QCSIlB4DXiCSElO+\nMpExmmxApNmBSEdM/RJfxmiyAZFmByLJmHZamYzRZAMizQ5EgkjpMeAFIkGk9BjwApHSj5Hk\n7ZSMnwnZgEizA5GSR+0etyMzf6ZkAyLNDkRKrh2IVFMrswOR8kS6QCTgAiJliLQfEzlE+g9P\ni1qdKpHW4mERtkjABlskHCOlx4AXiASR0mPAC0SCSOkx4AUiQaT0GPACkdJrB2c2AC8Qiax2\nePW7SaPAC0SCSOkx4AUiQaT0GPACkfaY43zVPUaTDYg0OxDpFnNdQbHHaLIBkWYHIl1jzmv6\n9hhNNiDS7EAkiJQeA14gEkRKjwEvEAnHSOkx4AUiuUbtjtdE2YBIswOR7rt26gTlF6JsQKTZ\ngUg/MWPHTpWKKBsQaXYgkn1DO4jkiwEvEMkSSdvLI8oGRJodiCSELpI+eEeUDYg0O8uLFPYI\nImkx4GV1kSIeQSQtBrxApMAB0hdE0mPAC0QKbpAgkhYDXhYXKeYRRNJiwMvaIkU9gkhaDHiB\nSEGPIJIWA16WFim+QYJIWgx4gUhC3GO4jCIaA14SRNr0GyEm3luUVwkkiISbn8RjwEuKSPpv\n84j02LG7xdweQSQtBrzkirTNs0USqkgejyCSFgNe4iIZHkEkH2f1u2OjwEuCSOoh0iHS+A97\nfBwh3V4TtNeidCHSKCRukbbj9SxbpGPo++LdHmGLpMeAl8SP4u34fw6R1LO+L36PIJIWA17y\nRNr0ofDQm8WrBMygUEUKeASRtBjwkrdrZ7wMvVm8SsAIah5BpOQY8JIm0mb8fif0ZvEqAZ9I\nt1+IaueEfvduFHhJPLPh9vP+6xEJvVm8SsAj0u01Ve2c0O/ejQIvS55rZ+zXQaTUGPCyokjm\n8RFESo0BLwuKZA00QKTUGPCysEi319FGabIBkWZnPZHsb5AgUmoMeFlOJMc3sRApNQa8rCaS\n64wGiJQaA14WE8l5ahBEcsWE/QjDmlqZnbVEcp9iB5EcMTkeo8aAl0VF+tIebxmajyYbw4mk\njGwqMeBlKZE8p3xDJDsGkTJZSSTfpRMQyY5BpEwWEsl76QQGqhzcMtW7EwOxjkjugYZoozTZ\nGG6LhFG7TBYU6ct6vGVoPppsDCiSKwa8rCfSl/14y9B8NNmASLOzjEh+jyBScgx4gUgQKT0G\nvCwikv8AKdYoTTYg0uysIZI6Yud4vGWoUZpsQKTZWUIkoYjkerxlqFGabECk2VlMJPdT+UKN\n0mRjMJEc3yHdYsDLCiKFd+wgkhVznfl9iwEvS4nke7xlqFGabAwlkvM8u1sMeFlApJhHEMmI\nQaQC5hcp6hFEMmIQqYD5T/CVIrVe14rSpZ8Rx0gnM/0WKTJiF22UJhtjiYRRu3xmFynBI4iU\nHANelhEp9HjLUKM02YBIs7OKSMHHW4YapckGRJqdyUVK2B5BJCPmOUD6gkgh5hYpZccOIukx\n35DdF0QKsYhI4cdbhmI02RhHJO+XSF8QKcTUIilDdhApMQiRyphZJMUjiJQahEhlLCFSTW9o\nsjGOSDhGKmNikQREKpoRo3YlrCBSVW9osjGOSH6NIFKIeUXSPIJIacHAAdIXRAoxrUi6RxAp\nJWjkzJ4PeIFIEOmBgEjlzCqSWRMQKRoUEKmCSUWySgIiRYNRjyBSgDlFsmsCIkWDUY8gUoDJ\nRarvDU02RhApMmT3BZFCTCmS47MVIiUEReykROBlRpFc+ygQKR4U0ZMSgZcJRXIeNEOkaHBP\nGUQqYz6R3INPECkWvCcNIpUBkSDSDkSqYmKRaHpDkw2INDvTieT5NgQiRYM4RqphNpF83ypC\npHgQo3YVzCoSWW9osjGESPEY8DKZSN7TXCBSNCjilxIDLwkibVeO35RI6M3qIpL/dDGIFAve\n8waRykgRSfuFs0juke+63qRT3u8GM2Y3+kgcRCojU6SN9RbJ7xFEigUhUh1xkTb/r6E3q4NI\nAY8gUiwIkepIEEk7RJIi/fdDmy4V8/Co0+JzS7e45ts0imOkKhK3SCMMNoQ2SNgixYKPzEGk\nMhI/vkcSibY3jjw8NtH6pnpskWTuIFIZ84gU9IhIpJs4j020samGSEszza5dcMeOSKR9zBIi\nAZs0kRyDDVdCb9aEIm2XaUU6cmfF1Ov1gZfEMxtuPy/H/zuhN+tkkSIeNRbpP4ZjmFl4xzu7\njYGOxiTn2sU8ohBpu8y6RVKzp8eMi7qAlzlECpwbVNsbifRmOpG05Gkx86Iu4GUykeh7I9m2\n+1fTs4kkvCJZF3UBL1OIFPeI8nukyUQSXpHsa1GAlxlESvAIInmDxm7x5Zhuzwe8QKRskSY7\ns8HI3iPmPPMXeJlApBSPqEQqzQZfkczs3WPuExaBl/FFkpXQpiBpssFWJOtTaI95TlgEXoYX\nSUCkikbtrfnly3l4tMeAl9FFUg6VIVJ2o4694otvc/QFkUIMLpI65ASRcht1HV1e/B5BpABj\niyQgUkWjwilS6Ms44GUWkTJnTI/RZIO3SEoIT+wrZGiR9I9UiJTZqMsjqmQsx8giGbsmECmv\nUadHEKmQKUTKnTEnRpMNhiI5duxw85NyBhbJrASIlNOoxyOIVMi4IlmVAJFyGrU8SthBrqmV\n2RlWJHvsFiJlNGplL2W7XlMrszOqSI7vQCBSRqM+jyBSIRBpSZG8HkGkQgYVyeERREpv1Mhe\nahZramV2xhTJ5RFESm7USJ92MgNEKmNwkXJnzI/RZIOVSCGPIFIhQ4rk9AgiJcaCHkGkQkYU\nye0RREqLhT2CSIUMeEfaoxJ690QnUIGMRNI9ynz8O/Ay3hbJOdCQMmNZjCYbbEQyPMpsFHgZ\nTiSvRxApIRb1CCIVMq5IuTMWxmiywUSkuEcQqZDRRPJvkCBSNCbU7JU8IxR4GVak3BlLYzTZ\nYCGS7lFJo8DLYCIFPIJIkViSRxCpkLFECnkEkSIx5WuD0C23Qo0CL0OJFDhAijQKkdQPoeAt\nt0KNAi8jiRT2CCIFY/FhhoRGgZchRcpvdHmRlA+hyC23QjHgZSCRIhskiBSIaR5BpAaMI1LM\nI4jkj+keQaQGDCNS1COI5I0pA9/xW26FYsDLKCLFPYJI3piZPIhEzyAiJXgEkXwxK3kQiZ4x\nRBIQqTxm5w4i0TOESEkeQSRnzJU7iETPYCKdX5A02egmkvMzCCLRM4JISi1ApLyYe1sOkegZ\nQCS1FiBSVsyzTwyR6OEvklYLECkr5jm2hEj0sBdJrwWIlBPzjdFAJHq4i2TUAkTKiHnHOiES\nPcxFMmsBIqXH/N8ZQCR6INKsIvk9gkgN4C2SVQwQKTUW8AgiNYC1SHYxcBaJFUfqevdkETiL\n5PhQ5SxSi8UXzigcqSPoTU2tzE6aSJt88cMxOZBzApFcxQCRUmIRjyBSA5JEkvJs8r8bgZzX\ni+QsBoiUEIt5BJEakCLSdjlfJE8xQKR4LOoRRGpAgkjb5XyRBEQqnTHuEURqQLFI//3QqlMX\n1aNmC6EmUIEnipTgEURqQLxOt8vpgw2+7RG2SNFYikcQqQFRkbS9uXN27fweQaRILEUjiNSC\nuEg791/kfzdCbxaNSFSNLiKSskPcojd5pbUWed8jnSJSaO8EIoViSuJ6J2M5+IkU3DuBSIGY\nmrneyViODJFuow7NBxvCe/kQyR/TMtc7GcvB7Vy7yNEyRPLG9Mz1TsZyMBMpNuoEkTwx88Cy\ndzKWg5dI0dFbiOSOWQM0vZOxHKxECo3XFTdaNyNRNhr3205c72QsByeR4h5BJGfMkbjeyVgO\nRiIleASRXDFX4nonYzlYikTYaO2MRNlo2G/h/ADqnYzl4CNSikcQyYq5PeqejOVgI1KSRxDJ\njPn2h3snYzm4iHTUQ9/vY6wYTTZOEImwUW8MeGEiklIPECl9Rv/4TO9kLAcHkdTdfIiUMWNg\nnLN3MpaDgUi6RxApORjwqHsylqO/SIZHECkx6Bmuq2sUIpXCS6TYfBBJEvaoezKWo7tIVkFA\npJRgxKPuyViO3iLZBQGR4kFzd5ik0YQY8NJZJEdBQKRoMKpR/2QsR1+RlHpoe97yVCIleNQ9\nGcvRUyT3DgpECgfju3UFjSbGgJeOInkqAiIFg0ka9U/GcvQTyffJCpFCQTVpnJOxHN1E8u6h\nQKRAUEsa52QsRy+RtIqASIlB/bOHczKWo5NIWkWccCXNFCKZ23DOyViOPiIFPIJInqC9L8w5\nGcvRWyTLI4jkDjoOKTknYzk6PBBPG3jq0YFGtChdx1fXabfcgkgnc/4WySiJcy5JG32L5Bzi\n5JyM5ThdpJhHEMkRdHrEOhnLcbZIUY8gkhW0hxkIGi2KAS8nixT3CCIZQZ9GvJOxHP1E+nJ7\nBJH0oFcj3slYjnNFMooCIkX7HfCIdTKW40yRjpK4H0Jnv5Osa6fF4kMesU7GcpwokjBEKngo\nH+vaoV+8//CootGKGWtqZXbOE0kYIp16kfSQIkU8Yp2M5ThNJK0oxhTp8Uh382dCNkoWH9EI\nIrHiLJH0qrj4PeIr0nb/z/yZko38xUc1gkisOEkkoywufo8g0o0EjyASJ84RySyLS+FD+frX\nzkkipXjUPxng4GyR7r8XvpP9a8ct0n9XajKpoQ0ykLUKmnKKSNan67AibZf2WyTdI6JGSWas\nqZXZOUMkayfl/PvfDCSS5lF5v4l6o8eAlxNEcmyPRhVpU/9rI5LuEUQaheYi2UfNFeXRuXa2\n4/9GIhkaQaRhaC2S06NBRdqUH01EEpZHEGkUGovkGMUdVqRtu5/K0OrMBodHEGkUThPpMbnP\nHdnOqJ26xbssqul3XW88MeClrUgejyCSFfN4BJFGoalIPo8gkhnzeQSRRqGlSF6PIJIeE16P\nINIotBPJVRoQyRXzawSRhqGZSCGPIJJCSCOINAytRAp6BJEkgb26un4X9SYWA17aiOQsjZ73\nCGUqUkwjiDQMaSLJ7x037UtIX8JjHkGknbhHEGkUkkQ63Nm06e50e2oDIpkkeASRRiFFpO2S\nI1KCRxDpRtSimn5n9yYlBrwkiLQd/ugexapDm0zyTrKundzFp3gEkUYhU6TjEEm/uFrcr4lW\niyNzMcOTV7rxvbq6ms/rTWIMeIlXuLwo9GJdOSAz/KgGtTbUd6T77d/ZbZESPYJIoxAVybzq\nxiXSox600oBIgUVoW+4m/W7SKPASF2nbjOtuEkQy3pH+z1HgJJLQadTvJo0CL3nfI3l27QyR\nzHeEwXMUGIlkegSRpiBfJNfF1doxkvmOcHiOAhuRhOURRJqCDJHUq6x3jhQ//FGOnB9RFs9R\n4CKSwyOINAXtb8cFkY5FODSCSHPQ/nZclO8k69qJL97pEUSagua34yJ9J1nXTnzxTo8g0hS0\nvosQ7TvJunZii9ccSrxREEQahcZ3ESJ+J1nXTmTxukfN+92kUeAFIp0kkrZLl3wqPEQahba3\n46J+J1nXTnDx3u0RRJqDprfjIn8nWdeOvxFjjCHjRkEQaRQaitTg4gDWteNtQ/fIOtkbIs1A\nw/vaNXgnWdeOrwnDo5P63aRR4AUinSpS7omHEGkU2t0gklUJdBQp5hFEmoJmN4jkVQL9RHKf\nzdC+300aBV4aicTt6afdRAqM1rXtd5NGgZdGd1qtebcCMda145rd+y1s8343aRR4gUjtRFJ2\n6S6F307zymJNrcxOE5H4PY/7VJHux0LqoVHpt9O8slhTK7PTQiSGz+M+UyR5frd6eFT47TSv\nLNbUyuw0EInj87hPFOk4g0Hx6Px+N2kUeKEXqfapfNOJVPNdAK8s1tTK7ECkViIdt1Sq+C6A\nVxZramV2yEWqfrzl6CIpAt1vUdal300aBV6oRap/vOXwIqn3JKsdeeGVxZpamR1ikQgebzm+\nSCqVIy+8slhTK7NDKxLFU/mmEqn2gJFXFmtqZXYgUkOR0m65BZFmgFQkksdbziNSz8e4907G\nclA+Sm+Fx/JlgHSsBOEWKeOeHitskfo+fbp3MpaDTiSqp/JNIlLnp0/3TsZyQKQmIpknqUKk\n2SETiezxljOI1P9Zn72TsRztn49EGWNdO8dMDJ712TsZywGRmn4h26/fTRoFXiASREqPAS8Q\nCSKlx4AXiASR0mPAC0SCSOkx4AUiQaT0GPACkSBSegx4gUgQKT0GvEAkiJQeA14gEkRKjwEv\nEAkipceAF4gEkdJjwAtEgkjpMeAFIkGk9Bjw0ufGAv+NM2N7kIwZgEjdQTJmACJ1B8mYAYjU\nHSRjBiBSd5CMGcBdDAEgACIBQABEAoAAiAQAARAJAAL6iLT9cN5sFTOeAZIxA11E2uR/Z8xW\nMeMZIBlTAJF6g2RMQb9jpBNrp3B5J4JkjA5EYgGSMTrdRCp4K6tqh3XpIBnDA5E4gGQMz8ki\nyaHXsw+TOZYOkjERnbZIRW9lRe2wLh0kYwI6fSFbPld51XEFyZiBPt8jbWXfrpd+J1+6vFNA\nMqYA59oBQABEAoAAiAQAARAJAAIgEgAEQCQACIBIABAAkQAgACIBQABEAoAAiAQAARCJIW/X\nU+FE1lsTmiWvJVAEcsyQW+XnlX9oFoh0AsgxQ0pFKogBIpBjfghxLf2ff69ie71O+P4txO/v\n66vP66vP2998bC9HRM7y8ye/7nO9/xL7K4h0AsgxPx5W/Lq+uJqwXV88/7z4vr3abua8iN9H\n5BBp/5Nfl8s/Ie7zQ6QTQI4Zct+1e/m+/BHb5ee/Hxtexdv1v5+t0Msux9WwIyL3Bl9//Hq/\nvngWfy+XD7mhAm1Bjhlyt+Lz/vL59iZdtzLP12mf+yboGj0iUqRn8f1o5vPfnxeIdBLIMUOU\nwYZdhB192v5Ki+jWvOhzgaYgxwwhEem3eH779wmRTgI5Zogh0rN8k9Rdu/13axa5a3eb8g2R\nTgI5Zogh0ut1SOHvdZxBHWy4Ro+IMtjw+hhieL984xjpLJBjhojrWN0h0j6iLT704e9r9IjI\nWT4fI+KvAsdIJ4IcM+RNF+n2NezL++WifSF7uaiRY5aPl/uf3EIQ6SSQYwAIgEgAEACRACAA\nIgFAAEQCgACIBAABEAkAAiASAARAJAAIgEgAEACRACAAIgFAAEQCgACIBAABEAkAAiASAARA\nJAAIgEgAEACRACAAIgFAAEQCgACIBAABEAkAAiASAARAJAAIgEgAEACRACAAIgFAAEQCgACI\nBAABEAkAAiASAARAJAAIgEgAEACRACAAIgFAwP8pZYn6ByqgpgAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot_histogram(df_heart, title=\"Histogram for continuous\")\n",
"\n",
"qq_data <- df_heart[,c(\"BMI\", \"DIABP\", \"HEARTRTE\", \"SYSBP\", \"TOTCHOL\")]\n",
"plot_qq(qq_data, title=\"QQ plot\")\n",
"log_qq_data <- update_columns(qq_data, 2:4, function(x) log(x + 1))\n",
"plot_qq(log_qq_data, title=\"QQ plot, logged data\")"
]
},
{
"cell_type": "markdown",
"id": "c4c0ec42",
"metadata": {},
"source": [
"Most significantly correlated with heart disease are AGE, SYSBP, DIABETES, BPMEDS and PREVHYP."
]
},
{
"cell_type": "code",
"execution_count": 18,
"id": "6afa0cea",
"metadata": {
"message": false,
"name": "Heart explore 6",
"warning": false
},
"outputs": [
{
"data": {
"image/png": 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gW1mzTjZ54QL2KJlFiTne3Upp1hUt9ePTet8a9fz1bAkqpVhfLX1m7UmJ9/apLo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\naEMJ0cy1JYDwk8fYIUvU01kkVj5t23cCwC1Pz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CQALZp8wg7be3oAkOiN9R70bdiRY8nhx/WLVi2Yl6++UffddwE0/OhDAGFHjiozJj4e\nQItm2j/W7T//HIBYQF5afDYqCkDnDl9UtbYG0Pyzz/I12asCl8i0JPHeQwBN3tYGMzwdawG4\nlp0r59yfLsT1/+i9T2sW/t8aePDk4Zvq8F786IXJmYA7EXiyA1LRVpOQEB8LoGkzbVNs83k7\nAOkiXajS4vVrQwC4uGiDQCzBMmUSGxsLwLXgvmjX7gsAqSKdhtLi5b+ueJr34r26dQE0aNAQ\nwL69ew0bkHYNgGu9D7V1NmkMIEV9S1C84oeRz4+GsghcgzrvANh77jxXytK9WmvjyiwRHHbQ\noA0cl2LjALQoeIPt27UDINaFKi0O27cXQG8fH3bIEkHBwTItiU1JBeDaQBvf+qJZEwApGcK9\nsWGnzwLo1U4bmWOJ1bvCBMUzQtYN7+bVvP5HMi0BcOnKFQAtGjdmh+1bugFIuXFDTO89YlTY\n8RPJh/YZrNl/6bIRfXo1b9RQvjGMOCXtVlq8/NcVz5S320tx7NsveIS2/RyAWAerHPGCxT97\ndepk8LrC9ccnAGjRTBu8b/95GwApqenFF/vPmz9i8KDmn30m05L4W3cANHPWPkXb1H0HQNq9\nB4LiB0/+AeBUXSCYp8+8I+GDmjX+zMkEz+f/R8fuP0RERDgAruOVJaZOmWSE+Pq1awBee+21\nZb8EVn6t/A/fj8rIUBk04FRkFACu45UlJs4R6OBgfP1l19D1a5j3JkHc5SsAtq1YbtCAIsac\nPgOA60tliYnT/YwQJ125CuDd2rUVGcBx7vYdAFzHK0v8GBlj8MQ9aTeO3Mwc8FGRvqpuLrU3\ndGhVp5q1ccbIpz3eCEBNZ8gaW1kczpyOAMB1vLKE//QpRojnzFsIgBtXxxIsUyYREacAcB1Y\nLDFlskCsRZE4Pj4OwMbNhsdEhscnAuA6Xlli0mrD4er49OsAWFiOsWuO3/Oj/GEew7w6GKyK\n41REOACu45UlJk6ebIQ4dOfO/LxnvFNGDJMbmjp1KQ4A1/HKEr7LgwTFe36a9/Is/+/i8G4C\n/4V+P3J87+lzw79U9tf91PkLALiOV5aYuHCxmP5rr86hQSvqvlNbutrt+/aHHT85ok8vRcYw\nwoWa4mSRditfzNrtJhnt9lTEaQBcXypLTJw6zThx2P4DQWvWTps0UfB0w8acOQOA63hliYl+\n/sUUb/9rZ9iBgyMGD5JvyZnrKgBcxytL+O8/Jii+cT8bwGvlX/01Iqr61Pnjdx9QZ+cIKv+K\nu3zwSurgZp/It0QCqbEp/29wo+tYSE9inJx0qT5NmjTRPbx48SKXfvL0hcSJ+/cZ/l8lU5yb\nqwHQvNmn7HBNSPCakOAbNzNr2PKHN+miNKjWu6vhsFPA6pCJc+b97D9djriIMQcOmEo8d/Fi\nALY1agQs/3XidL8RQwaPGDy44cf1JU7R5chNxSPWAeTm5Y08dqb/R+999FZ13fyuLrWNqM0I\nvoDAEMCS4OABw5EMmeJRY8bWqmXX9JPCgZ5r1m3s/pWP/PrlBCeUipcGBk6Z7Ltw0WIfH8O/\n2bohN/kE7tg9afW6n4YP5uJz+jDP7yuPlmICfcL2KvhqFInj4uMB9OzR3aCSsff0OfmV86+V\nmg7gqzatePk5jx5/PXPu8G5eDd/jjyeWJuz4SUX63p0NR55ych/1Gec7ok+vhh+IDqSToITa\n7eTJvovktduw/fzRokaLVRkZ3l/1/HnB/OZN+eNl5dZ/QEFYWqY4R6PpM/jbEYMHyX/yAzh4\nRcEMIc2zZwDcl61lh+ujLq2PupQy/YcaRUdja54++3b77kHNGtevJTAAlEN6XJ0u5NjJQrrr\nVnBMnu6hricHJZMnTAgL3UVGRX/coAGAkydPdO74xd69YYMGDykdAzjs3357RP++LOw3YfjQ\nUr66Lv5z5jEPL2jtuqC165JjLtZ1cSm5y0XezgLQs66BcCbB4/btWxKHZsHO3m7osOEskjd2\nnNzROcouYfPmMK8OLLA3rueX+oKsh9kzN2yZ1teHm1phRrKysvxnzfKbOrVN0SH5JXKthw9n\nhKybPrBfm08b84oiYuMBDOgoMGuk9Am/cBHAN926mtuQQuzs7YYNGz65JNutIKPHTfDq1Onb\nQQNL7YpyCD97FsA3X/MnNpkQFsmL+H4I89jC0290XbP1wOXUAU0b6crOXlcB6POJgRtZ13OQ\ndvLIsdPCC8Lxgnb68TnpUiPgLT4iZ2aDIngVtmrVGsDoUSNK37Hr3dWrd1evb3r2cPXubv/2\n20rjdiak3ocf5GuyARw/Ff65l/embb/P8Z9ecpfbciUNgO7oOgvgTetKuocPNPy5dcVk559/\n+E+fsjvsoIdnKwDhp05+6dWhVi07waBdpQpFHmhP86TC4cXBx6eXj0+vfv37e7q3tLO3kxP/\nUEqv1h69WnsMaPd5y+997Wze5MXtsh5mD1/ya4N3a88e1M/kl1ZKVlbWtyNGNPy4wZzZs0r8\nWg8fDl3wc0OXOj8OG6xfGhK6F4Ci0XUlR8gfOwDIGV1XsWi7fVby7dajxNqtPiHrN4Tt3x8b\ndY4NaC47hGzYCED+6Doj0J0qAcCjTm0AP+zaz3PsfrsQC8Ako+sYNMauEO+imNscUTp17lJC\nYpl4tWtb/Eqaf/IJAMH5s8qM6djRCDFL9P5Ku4ACW+WERe+Mpp2z1G2Z+ejxkZuZP3yiIOZv\nYXToqGBCHCf+dvAAAMyr4xJ/7vi9mMZ07qLgvhATN2vWHMCAfgpmX3J0cZXVJ9Xso/cB9JtX\nZM0FVdZd03p1Xl0UfDU8sUqVYUKvrktLV4lS1Z07El6d6s6dvafPTR9oMk/Xq00ro89V3bod\ndvyk38jhpjKGYcJ229+odqto9gMTDxs1GkCjZq5siTtWpJs2Gq+OCkaX8sQqtTrswEE/XyPH\n/PHo8KHAEj8yUWfnHLySOrG1m0ksYZBjVwhvyZJSvrruKiRcdO3bocMAcLMcWMLdXXjMjbS4\n51fd9FckZqdIMKJ/XwCqTO2QMpbwbM5f8EkO3oO+tXKonZMra+qosDFDBgNQZai1xmSoAXi2\nFL4fpMViZ8mk/0fvAch89JgdsoSr5PCIGzm5ANzspDT/RdgqJNyLZQ4aMhSAumCGI0u4tXQX\nrEGRmCE2LI+tUcK9WObQYcMBZKgK7gsVuy88BWuQFvfo/mWlCq9qNMLDn8VgkxtUWdpVZljC\no4Gwi9/Nf275tt6ax0/Eaou6nFzn6yEeDeob59WxyQ2qgtV9WcJT5JFiUBwZFeXs4uLp7mGE\nV8emPqju3NFWfucOAM/GovGtyMTL73Tr49m4oaBXByBNfQtAK73+WTmw+Q2qW7e1xty6DcCz\nqfGxnLSbKgCtm8l6VLI1SrgXyxwm1BQ9RNqttLh79y8rKm+3I74dAkBVcGOyBG8dR+PERsDm\nN6jUBc9ztRqAp5vIw1+GOC39GoDWyi0c1KwxAG4OBEu4vSOwuCCAPht36C9Wx2rguHb/IQD3\nOs5KLZHg/9Gxk7MoMcrGqigt3T0AHD1yhB2yRIOGjYwQd+rUBcDJk9o1x1miW/evpA3wbN4c\nwKGCXRlYonF9Y1ZR//rLrgDCI7UDydnOE2xhPJmwO/PQMe38I5Zo3EB4XIK02K15MwDb//xL\na8ypcABsrTs5uNayBXAqQ/szwBL1bapLnMJWSKldtYrMS/yncXNzB3D8mLYpssTHDYTbrbSY\nTYC9cCGKHYafOglgoq/wBFtB3D08ABw5cpgdskSjRsLGSIt79e4DICIigh2ynSfYWncSMB/u\nyMVL2jovXgLQyEV4qGXvNh4AIuK1a26xnSfY0ncAUtSZLb/3ndbXR3DUnRw8PdwBHCp4SrBE\nY5HuQmlxSkqqq7uH39SpE8aNNcaSRg0BHI7Sjj9miUZCixsDSFFluA0bPX1gv/F9ROfNsPVT\nXBz4y+TKMqZpEwCHTmvXkmSJxh9+aERVDLZ+iouz8O+9HASbYkMl7ZYT9y7abtnOE6sMtVtP\nd3cAh44WPEKPHgPQuKFIUxEXs5XtuBcT6KblwP6KHzqmnRnNEo0b8BfPly9mS6K41FE84tnt\nHWcAx1O061CyRAORf+wdP3gPQHj6DXbIEl9+XKRdsfVT3n1L6udDKbTzhLfEHFix9YpRdOcJ\npeE9+ZMnBLeLuH3nvnXBYAUWhGMRPmnx3ayskSOH686c/XbosF+WFVkUW3/nCVVmpnMz/r+i\n7CsJVatoHRS2b5juDhNi+Tm5uf2/H6c7zdarXds1ixfaCg4CFdp5QpWhdq7Hj3Nkq1Xc0A0r\n62oA2LA5g2Ju5gTHnfRU2xoCmwHo7zyR+ehx0y381YyvDupZpUIFlma7TejuITEl4vymy6m6\nGn30z+Jf1xQ7TwBg+4mV3M4T6oyMBvX4v9A31Flcu2Uj81iET1osWMrbxEJ654kMleo9PS8q\n6959a2vtggVsZB6L8EmLNZqcQQO/0Z2B2LlLl1VBwbY6U8v1d55QZd2t8zV/JOv9PdutK7/O\n0uXbegNg65hoHj/5ZuES3Ym0XVybrh4/2rZ6NQAz12+ev+UP/feovwYKRHaeUKkynPVmCGXf\nu1t4E1WoCICtYyIt9p85a+4CgT9m+mugQGjnCdWdO+9068PLfHA4rGrBhEG2nwRb5WRG8Lp5\nGzbrV6u7BsrIxYGrd4Xp1iCI4M4Tqlu3nVvxR5hkR0dVrVLQdVi3HoruMCGd/93MH4O2/a5b\ngyASO09kqFQuek3xrk67ZSPznhW0WwmxRpMzUK/dBhVtt/o7T6gyMpzf57u22X/fKmwqr7+B\ngj0kDIo5dM8SRW/nCZVa7VyP/x8+O+NGoTFV3wSQn/NAjhjAd+MmBK1bz8vUR3/nCcHNJG7O\nnGBdqSJLsxAdG11399Hj73fu151IO6hZ4yVfFhk+NH73gfVRl3RrEIN2ntCivycEzwnj1jcR\nO91gJSXaaevo6BQbnzR5inYA5uQp02Ljk6xFGqK0uIat7cqVqxcs/Ikdbti4ec5cw9EyJ3v7\n5PDjfj9oR8L5/TAmOfw459UpomqVKmsWL+RCdME/LRD16sSMcXRIjrno56tdnMnP1zc55qLY\nbWlQPMd/+rZ1a9lgOz9f35tJiYJenSD2b1QO7+XFDZj74ZP64b28JDw2AJsupwKQ1lgMDo6O\n52MSuLjaRN8p52MSxNqttNjB0TE+KZVbuG7OvIViW5OJ4ejklJB4eUrBklpTpk5LSLzM/Toq\nEltbV10VFMyF6FauCuJ5dYI42dZI2rBqWl9tqGlaX5+kDas4r46HdeXXV48fzYXogsaP5rw6\nAIJenSKcnByTExP9pk5lh35TpyYnJoreRJJiQa9OgSU1a17Z/hs3JG76wH5Xtv8m5pMJenU8\n2HrF0l6dqDF2tZIP7eOGxPmNHJ58aJ+0TyZN0LbfARSnBkcnp8TEy1MLmuLUqdMSJduthNja\numpQUDAXolu1KihITrt1dEyOu+Q3WbsSqt/kSclxl8SftwrERuDk4JAcfZ4bEufnOzE5+ryo\nMTLEQevWAzDCQodqVS+MH84NiZvY2u3C+OFiPlmNNyov695pTqfP2eGa3l/O6sDf/m591CUA\nBr06RVh4xK5sYpblTuSgH7EzG0IRO3OhH7EzF6aK2JkEiYhdKSMdsStl9CN25kIwYmcu9CN2\n5kIwYmcuJCJ2pYx+xM6c6EXszIV+xM6MUMSOIAiCIAji/w5y7AiCIAiCICwEcuwIgiAIgiAs\nBHLsCIIgCIIgLARy7AiCIAiCICwEcuwIgiAIgiAsBHLsCIIgCIIgLARy7AiCIAiCICwEcuwI\ngiAIgiAsBHLsCIIgCIIgLARy7AiCIAiCICyEMrTH4v8nr7/8x9wm6PDyhbkt0JJ38oC5TSik\n7OzQaj/czdwmFPI076W5TdDy8t8ytOH1m1WEt2k3A3dvm9uCQl7mPDS3CVpeqWlnbhMKyXn8\n3NwmaKnx+J5hUalR6TVzW6Al714Z+ljkx+EoYkcQBEEQBGEhkGNHEARBEARhIZBjRxAEQRAE\nYSGQY0cQBEEQBGEhkGNHEARBEARhIZBjRxAEQRAEYSGQY0cQBEEQBGEhkGNHEARBEARhIZBj\nRxAEQRAEYSGQY0cQBEEQBGEhkGNHEARBEARhIZBjRxAEQRAEYSGQY0cQBEEQBGEhkGNHEARB\nEARhIZBjV0ZJSU3z/3GO1RvWVm9YByxbnpKaZrSY5eu+lFly7br/z4FWzi5Wzi4BIWtTrl2X\nc9b20L1Wzi5ipaxCRWYwUjNvz9r8R0XvPhW9+yzdvS8187aEOCo5dczKtRW9+4xZufZEfJJu\nEatB/2WESTI5jMdNcaOEKk/P1vx0Ic5+9Rb71VtWx11Jz9aIKZlG/6Wv3JN2QzBfrklpqT8t\n+NHOprKdTeWglcvS01LlnLV75w47m8q8zOiL56dM/MHOpvKUiT+cjjhptEm6ti2YN7tGtddq\nVHtt5a+/yLRt1187alR7zbgrpqgyZgStLdfMs1wzzyVbfk9RZUiIsx48XLNnLxPPCFqrLz5+\nMWbkoiXlmnmOXLTk+MUYxcakX/P/KcDKvraVfe2A1SEp6dfknLV9T5iVfW2+qffuhWzdxqry\n/ylAZlWFlqhvzdy4rULHHhU69gj8KzRFfUtCHHUlZfTy1RU69hi9fPWJ2AQxGatQkRlaY65f\n91/yi1WdD6zqfBCwZn3KdXkPur37rOp8oJ9//Fzkd/6zrOp88J3/rOPnIo2wB0B6WurCebNt\nq79mW/21VUoaqm110YYqXcoj5do1/8UBVg61rRxqB6wOSbkmu6k41OZlRsbEfDd1upVD7e+m\nTj9+5qxMA4oYk5buv2ChlU1NK5uaAStXpaSlGy1WqdWs1Ltv/+07d+VochVZkv4ge+GZCzUD\ngmsGBK+6GJ/+IFtaf1qVOeloRM2A4ElHI06rMhWVGodVfn6+SSoqO3h7e3Pp0NBQLpNL88S6\nGv0TefmCNUuUCnLv3j0ubfNaRX1BjkZTzc6Bl3nzSpKTo6NSsSojw/nDerzS/EciP/z3s/iV\n5+ZWq9+YX/nZcCd7O+EaAADbQ/f2GTMWQP5NAX/0+Nlzn/fpL1bKyIu7oJ+pefKkRu8hvMy0\ntcsda9joi6OSUz18Z+jmHJzr17qB9qMQ9OE6N/1kp5+vfn6c91QxO2VyGI/98D/2zjMuiqsL\n488mppjEkogaBYEYxRiN2AUsKBY0CkYTCyYmGhWxxYaxgRpLNFFERQUBjR2MsYENFBSwYKEs\nTXfpSzEiKiyW17R9P9xlWGdnZmcHEEPu/7cf7tx75s6z0/bsue0egOuwrEw9plN76meW/fHH\nR78cZmVe//Iz03fYHhIATl9toIXp7sF9dXNOZORMj7gMoGDql3xiZGv8+YrK1Oo2LZuxMm8k\n3jY147iBGY4fPTzddQKAwuLHTGbczetOg/vpmv167FSv3s+pfa2OEX9Q1Wr1h+ZNWZkJKUoz\nQW3Hjhx2nfQ1gHslT4Xrf09xnZVT+ujxe/0/ZWVmn/jV/H22DABFDx42G/IZK/PW4f1W5lp5\ngSdOTv1xvW7puW3eDl0761f1ipmFfmZpWVnDjz5hZeZev2xuaqpvzBB8ItRl+iwAmoKcCqnF\nxU2tu7IsFdGRVh+21K/hz6Q4Vo768ROTL8azMjP2+Jk3aay/+7Vbyt7znnsMw9au6NeR/UUu\nJCY7Ll4B4I8zR/i+y2tW7PchyGnp2I2VmRsTad5c8EV38pTL7PkANJm3dfMDDh12XeKpmxOx\nf7eDrY1+Dffe47hGBLVa3cqCfYfEJxu+UadO/hpA0UOOG1WgtPHju6yc0rKyhm31bpVrIm6V\nGbMAaPJzmMzY+Hhb55G6ZhGHDjr0tOOt5U2261mqLmvYkh0LyE2MMzdj//YZNFbl51t07KJb\n5OQ4KHCTdxOu35GitZ6snLJnf7TaupuVGTdlnFn9dzi/yv6kW/PPxejmHBk1tJe5qZhSFq8s\nWsOkTUw41FZYCpT9GyGOGgPjdemmWcbCOzK7s2B5gQKlEohLSAAQtHuX5pFa80jtv3ULAHlK\nigTjhyUluqXkY4SS5BQAQT6bNLkZmtwM/3VrAMhv3RbYJSDoEPHqOFEVFBKvTgJxGdkA9rnP\nehYS9CwkyHfmFABJ2SpO4/0R0QBSfDc+Cwm6sXkdAJ+Q00wpqYH5EIOFo9g/qFXCcZQRr66a\nSLr3AMD2/j0Lpn5ZMPXL9X16AEi7/5DTmNgwn3NffApgVqf2ujYHb2UQr04ycnk8gO3+uwuL\nHxcWP17vvRVAWipvlAXAgX2/EK+OxeHgAwBiYhMLix+fuxgLIMBvW6W0JcYD8N+5917J03sl\nTzdu3gYgNUVI2749u4hXJ4242woAB1ct+/ta1N/XonYsWQAgKZ073hASc1nX+OCqZQA2BWkd\nd9Xvd6f+uH7pxK8fRJz++1rU5Z3bAfwWcdEIMUnJAIK2+2gKcjQFOf7r1wKQpwk+0QeDiFfH\n4kT4Od2qgrb7APAO2ClWSXomgP2L5v5x5sgfZ474zp4GIDk7l9N43/kLAFICfP44c+TmNi8A\nPsdPsmxURfeIVyeBuJRUAEGbvTSZtzWZt/1/XAVAfkshsEvAocPEq2PLKCx0XeLpMWNaSeIN\nTebtq78FAzh8+qyxksiNuiNwb9HDp0UPtTdqmuCNun/vLuK3SSjVR3urbPPR5Odo8nP8fxZ3\nq8zguFX2HD4CQBEdqcnPSQw/A2BT4C7xSgDEyeUAgvz9NMV3NcV3/b29AMhT0yQYh124CCDi\n2BFSGnHsSGhYeGRMDGdV+sjv3gPgN9Th7nzXu/NdvQb2BpB27z6ncb760fxzMXNtOmXMnHB3\nvutpl+EAQpRZYkorQ61y7PTDcgK+nb5Xx7fjiydBngTArkcPsunYvz8AvtZYYeP7Dx4AsDTn\n/V9oQElqGgC7Ltp4gGOf3gAEGimcJ7mGno9QXDjHZ7B2u5/TAAdpYuRZOQBs21qRzYGdOgBI\nL+RujfWZPulZSFBr02YAOnxgAeDUdd5GqxUHfnUdPKBHm9bShAkwH3dj8OQwhP7jVpKU4ocA\nur6vjXPYt2gGIKtEVOPCzzfk4z9u3aVpxZ+/CWcvhufmR49xqpSk5CQA3bprQxR9+w0AkJnJ\nG6D95stR4WdPx8Qm6het27C5sPjxh61aA2jX/hMA58JO65uJJzlJDqBbD622fv0HAhBo5PrK\n5Yuws6djbyZJPmKiIh2AbQet9zyoRzcAfK2xoTGXAYwZ1J9sksSOoyfI5tWkFACf9rJp8M7b\nAGzat/v7WtT2hfPEi0lISQVgVx7hc7TvA0Cgic15wuTQ8AhFdCSH1PAIAGOHa28VkvDbJ7b5\nPjEzG4BN2zZkc2BnawB8rbFbZ03948wRK7PmADq0tARw8tpNls3Ph44O68GOIIokIfUWALvO\n2tYJx949ASizc/jsnV2nhUZEKs6f0S+6Ep8AYGg/+wb16gGw6dRRk3nbd9UKYyWlPH+j9nUw\ncKOOd/ki7Mzpqze4b1ThUk6MvlUmTg49x32r+K5do8nPsWrZEoD1x20BhJ47L14JgITkZAB2\n3bVRVcd+fQEoM7n/HQkbu86dD8Chdy+ySRKpCiEnXpfkovsAujV/n2z2tWwBIPNhKafxjcLf\nAQz8wLzeG68D6NK86d35rj8P6C2mtDLUKseOE+FW0erYsfJEXboEgGl4JQn3JUslGGdmZwOo\nW/dNry0+snfqT5s9V5Un1L+HmVLZqQAAIABJREFUXXnsNQBMwytJuK9ey2c/brhzyE5/q5Yf\ncJaGno/0239wyYxp4gXoEp2SBoBpeCWJhbv2G9wxKTsXwD53jr+SAH6NvnLqevyUIQOkqRLG\nEe94oakFXquOyglX79wFwDS8ksTKWMNdr05k5JzLLfj64+fc2RGtLHcP7vthQ+M6YrIlXY4B\nwDS8ksTKZbwt2iM+H73nwGHivQlA4mrb/XdXRtuVyzEAmPYskljusYjP/vMvxuwP+s2gNgGi\nEhIBMA2vJLFgy3ZO4xMb1v59LYqVOXXkcJJIzcoB0FKwfdCAmKvkidb+0yAJ95Vr+OzHjRge\nsjuQs3U1ZHegbssswW08b9s9i5jkVABMwytJLAzcY3DHpKwcAPsXzdXNPHXtpv/p8IVjpPSu\nAxB1/ToApuGVJNzX/sRnP855WIi/r9UHHC+6VGUGgJbmQg2mYuC+UT15b9SRX4zZx3+jCpdy\nUv7yf/5WWcV/q3w2POSXQOK9CSBPuwUgaJuPeCUAoi5fAcA0vJKE+7IVlTcmrPbyFqnkSt4d\nAEzDK0msiOLuRqm4/xCABc/rVLi0MtQ2x865HM5SJg6nH6IT3lH/KEa5fV2fx0QHTvvQ0xx/\nBPkQNlarywB0tO1JXD2/nTst2rYruie2ZTD0PMffLwHGOg/jK1IVFDpPct3gsdimM7vTnkgE\nQm4CbDp+qtvsRT99+9XoPhxdOtRPnozf4OM6eACJ6lU5g8DR0a1qOZcrpb9t2R9/TI+4PP7j\n1h83elc3f3gryyqQZGRQ7bORowza+G3fMrCvzbKVa8UYCxB25pRR9iM+r9ThAJyMkdJVnCBP\nzwDwRf++ZHPNL3sBNHnv3Y0HDpHBE3LBYVX6GBspYQJyBiE/2KOchoq01w+5icH7SEjXGfN/\nmvzNaPteTKaq6N6IFWt/mvxNj/JwvrGERlwwyn7sMN6vuXqbL4AmjRp5Bf5CBk8I913hI+xs\nVd6oEm7j6rhVvHYEdBw0ZIPnUvH3lVZMWHhVGXvMnwsgMuYS2Qw+eswoJeFZ3L0FOPGOTQBg\n8lZd35tJZHhEatF9kaX6GPQcGOqIl/jywznigbONVT9TeEdhh0+/lFX/zZvPvcIMDp6oQog/\nl3j1svUnnwCIjIrqP9TpxKlTUyZMqNbj6jNz2QqnAQ6Tx45+wcdt/t67roMHkMDenM/Yr+OY\nlNsAvurf5wWrqnFi7xQBGGVl4O/1y8P77zf7esJkEvZzm/5dTct5ERQ9eLhsx86lE79mjY1Y\n5reTeHg7jp7YcfSE7tCKmqKouNjzZy+P2bOEesRXBaYm77l+OogE9uZ+rn3xztkeOKxH10mD\nqyXoLg3PjZuJh+d3MNjvYLDi/BnO8N5/DdP333cb/yUJ+82fOqVGNIwfNWq1l3f/EdrgLvHz\nqpV1l28QH26P/NYe+a0rE0d/+F5DkaW6POc5CPp2tcqx08XgeFijdtSvQbj05YE1VMLB3h6A\n68zvXrBjFxB0KPR8ZOKZUNLv5EUyuo/d6D52X/Xv02fBsubvvcuK2+0MjwBQHb3rXnIO3MoA\noNu7Thqs2Ul0B7RWLZ+NHPXZyFGjxn7pNLjf++83ExO3Y81OYnBA60tF0YOHU3782bpVq5Vu\n7JHg7VpakubayJvxA2fM3X86XN/mRVJUXDzZfZH1x21Xfc8xmKBqGW3fa7R9r/ED+vWet9jU\n5L3R9r12nj1/8trNm9u86r/9VnUfXTztrFqRobKRV2P7fzVh37GQVfNm8xmz5h/hHNBaOxg7\n3GnscKdvRn1u6zzS9P33jY3bVQlWrT5MvBjpt3uP3+49G1aumPzVV+LbYaXRptG7d+e7Arik\nKvj88KnDt9IX9ewmslQata0pthbj9OmQajI2Wonxox9cFy0F0HGIE5kPj2TqpiUztDvHRA/6\nENdt/IbnOnbk3Ss+dT1+8egRldTwEjLQQmi4RsGjx+dyC2Z3bi9gU+UMdGRP+SGBLl27A+Ac\nP1sZHIeIbUCsKob1FopsqX6/y+nVkb2YoRUkkkeid5XBaaD0WJeqoKAKvTqRox9Ik+tX67wB\nTNvsC6DrjPlkPjxioJuWjFP/foaNePZi2mrJLCckeld5HAe/6BuVRWVuFQabzp0BcI6fNU6M\n4yBpxtbt2/lu+FlTfHf+9GnPnj1DpeN2g1py9+Qh+SM+0v7MkXlMSHzOYGllqFWOneRxrDU4\nAJYTt0mTADCjHEjCvlcvCcbOo8foz0hMdhGl5KtxAFQF2qFqJGFv00Pk7lWL6+ABAPLuacPR\nJNGn/cecxiNXr3/D2UX95IlAhRl37gKw78Axr9W/iPEftwZQ8EgbKiMJ22Ycc6Qx5JSWAejZ\nXMhGJGRCE+ZDMr+eMBlAQb72niQJ255SRnt98+Wo5iZvl6mNmKOHgUxownxI5oRvpwDIL9dG\nEnaStImEDH1Q/a6dJ4wk7Dt15LOPTUn9YPho+04d9eNwAnuJhAxuUBVo+2WShL2txCc6Ni7e\nontPe9seErw6108HAVAVafv7kkTvT7gfxpEr1r4+5HP1Y6HHuTK4jRsLQFVY/qIrLARg3727\nhKok7EUmNGE+JPObiS/6RmXBfatIevk7T5wsM7MsLTNuHuDnxEz4BoAqP18rJj8fgD1Pu79R\nxiWlpQDatWkjUsk31m0B5KsfkU2SsGvBnraTwJcvprQy1CrHDnoumvh2WMk7Vgf2vXsCCIuI\nIJsk0cm6gwRjErqLjNKOsyOJUSPFTthm36M7gLBo7Rw/JNGpHbcvJQCZBo/56GaKr6R3+7YA\nziVoR+yThHVLS07jsX16orwLHQCy8gSZ+o6BzJ/SStAHevmxbdYEQFSedtoXkmhv8q7ALmSG\nFMsG1dUsbmPXC8DFC9rO1yTR/hPuG1iYEZ+PBhB7VdvTmaw8QSbGkwb5abwQoZ2RhyQ+6WAt\nuUKD2HeyBhB+TTvnNkl05Gn9V6ryek6avnTi1/O+HKNfamfdHsChcO3DTpadIBPjiRVjawMg\nLCqabJJEp/ZS/tsoM7NsnUd6zJ4lrbNUnw7tAJyLl5NNkuj4IXdHtLH9egOISdFORUZWniBT\n35Fp8JgPMdBNi8G+RzcAYTHa6RtJolO7tsZ+KQA9u3QCEHxSO/SBLDtBJsYzCnKjXozU3qgk\n0b46b1QW9jZVdquM+2w4gOhY7dzdZOUJMjGeWDF2tiifgo5JdPqEPX+yGONp7t/LTJrKU1IB\nlKrLQsPDoTM3ikFszZoBuJijdbhJ4pMmjTiNuzdvCuDYbe3PHFlYgkx9Z7C0MvxXVp5gGfDl\nc+5ocOUJY11Ag4MnOJeLKCnMb1BfG3sjQTjSf07YuOjevckzZuqOnHWbNMl3M0+XAr2VJ1QF\nhRZ27IEFJSkJTFc50paq75/x5YspBc/KE3n3iltNYkfv7wXvrP+Wtm8NWU/iWUgQAPWTJxM2\nbtMdSDu0e2e/ma5NGjZgcmZt3+l/9rxuDZxUfuUJAGQ9sepYeaLg0ePuB46zMm9PHFXv9de1\ne+04gOfXkFgUc31fWrquDcex9PZiIbDyREF+XreO7HWWFFl36pXfwKRnnn6HPP38MrV65rRJ\nusNsBzp+6rVpu0njivUJjFp5Ij8/r1N79tjJTNXd+uXaSM88/Q55fPks9FeeUP1+94Ph7DFD\nDyJONyifoebVHvYASLc5ZmAEC2YOFH2DO2eON3mPw4/nXHlCVVBg0Z19F5XcTq54ok0t8fwK\nE3z5nj97rd7MMWmF/r7gWnlCVXSv1TdurMzi3/YxXeVIWyrxz9SPn0xYv1l3IO2wHl395kzX\nfZz19+KEc+UJVWGhRW92D5OSxBsVp+XDj6C3wgRfPjNyguHu9ctNGnH89gusPJGfn9f5E/aN\nmpFbcaOSnnn6HfL48oVL9VeeUBUUWPTQu1Vu6dwqZpZ4foUJvvzSsrLx383VHWbrNHBA4Pp1\nTfhGAOitPKG/XASAkqyMBvXLxZg0BaApvmvQODLmEjNyghDk7zd2JHeHHP2VJ/LVj7oEHGRl\nZsycQOaiA9DUyx8A6TYHnbERDKnTxpu8VVdMKYv/7soTeH4dCD4Do3bUX1hC16A6AnvmLVoo\nEuI9vtf+Eff4foEiIZ7x6owybtK4ceC2rRt+1N4QQbt3rVv1gxFKTJsrLpzzmDVDW/msGYoL\n5178AAhCi8YmKb4bmS5xi0ePSPHdyOeT1X/rLb+ZrkyIznfmFJZXB8D/7HliWZ2qqx3Td96O\nHuPEdJib3bl99BgnAY8NwL60dADCNpWSZNYiJjZxzvyFZHPO/IUxsYn1eG5gYerVr++1aTsT\nolvvvZXl1RmLmVmL2JtJ8xZo5wObt2BR7M2k+pK0icT8/aa3Du9fOlE76f/SiV/fOry/AdeC\nbxDRYW6l26SDq5aRznZLJ36dfeJXTq+OV4ypqSI60mO29g+Sx+xZiuhIaU80p1dnhJImjVMC\nfBa7fEE2F7t8kRLgwzcAov7bb/nNmU5CdAB8Z0/j9Oqki2neXHH+jEf5FJseM6Ypzp+R/KJb\nNW920GYv0tnOY8a03JhITq9OGDOzFldvJM1zL79R3RddvVG9NyqLKrxVGtSrF7h+HROi8/95\nrZBXxynGzEwRe4XpCecxf64i9grj1Rll7NC7V8SxI6S51m3CNxHHjvB5dZyY1X/nysTRc220\nk3bNtel0ZeJoxqvTZ1HPbn5DHUh3urk2neKmjNP124RLJVMLI3YvPy9yuhPj0IvY1RScEbua\nokoidlUCZ8SuphCI2L1gjIrYVTf6EbuagjNiV1PoR+xqCs6IXU0hELF7wehH7GoSvYhdTaEf\nsatB/tMROwqFQqFQKJT/JtSxo1AoFAqFQqklUMeOQqFQKBQKpZZAHTsKhUKhUCiUWgJ17CgU\nCoVCoVBqCdSxo1AoFAqFQqklUMeOQqFQKBQKpZZAHTsKhUKhUCiUWgJ17CgUCoVCoVBqCdSx\no1AoFAqFQqklUMeOQqFQKBQKpZZAHTsKhUKhUCiUWkKdmhbwn+fVl+kSaDQ1rUCL3HlxTUuo\nwDpkbU1L0PJ63yE1LaGCpKL/1bQELZqX5r4FYNLWuqYllPO4rKYVVPBaq49qWkI5LdvUtIIK\nnvz+qKYlaNGoS2paQgWyt9+paQlaGjmNqGkJFTwUbUkjdhQKhUKhUCi1BOrYUSgUCoVCodQS\nqGNHoVAoFAqFUkugjh2FQqFQKBRKLYE6dhQKhUKhUCi1BOrYUSgUCoVCodQSqGNHoVAoFAqF\nUkugjh2FQqFQKBRKLYE6dhQKhUKhUCi1BOrYUSgUCoVCodQSqGNHoVAoFAqFUkugjh2FQqFQ\nKBRKLYE6dhQKhUKhUCi1BOrYUSgUCoVCodQSqGP3kqJMT/f84QdZ3bdkdd/y2rxZmZ5eeWNi\nY7SSrGxPL2+ZZWuZZWuvgJ3KrGwxewWHnpRZtmZlkkp0P8aKMZZwPO6OnOqoOb3gzor9v77h\n7PKGs8um46fSC+4IGF9TpM/avvMNZ5dZ23deSErVLSI16H+MEqPMyPBctUZWv6GsfkMvn63K\njIzKGEdGRU+bO09Wv+G0ufMio6KNUsKQk52x1ftH61aNrFs12rtzW062kKQH9+8dObSXGG/1\n/pFlnJRwc/Uyd+tWjVYvc79+NUaCmNzsjG3eazu2NunY2mTvzu25hsQcPbSPGG/zXstnTCoU\nKeClukDKzCzPn9bLmrWQNWvh5eevzMwSs1fw8RBZsxbSSnmVZOd4em+RtW4na93Oa+duZXaO\nKCUnT8tat9PNITXof4zVI0qzUunp6SmTyWQymZeXl1KprI6jELIy071+WmXZrJ5ls3oBfj5Z\nmUK/Agyhx3+zbFZPP//KpailC+dYNqu3dOGcK5eixFSlzMn13LLtlY87vvJxx4279ypzcsXs\nFXz67Csfd2Rlqu7cIVUNnzE7+PTZ0kePxFT1nJiMDM81a2XvmsjeNfHaut3wQ8RvrFvquWat\ncFWGheXlL9u5t07fIXX6DvE+dESZly9gHJt6a8ZGnzp9h8zY6HMhPrEyxxVAptFoqqnqfyPO\nzs4hISGc+bqbujasIk4bFsXFxUza5J239Q1K1eqGTd9nZeYqFeYtOF6dIo0jL17sP+RTAJqn\nT/iE4W4Bu/KysoafdGZXfjnK3LQ5byVAcOhJl1lzAWhyKt5EqoJCi572LEtdA11uWA4UqF8k\n4XjsgXsArsOyMvVYh6xl5aifPGk8dhIrM2OnT4vGHL/01xTpfRYs0805u9qjXwftrw6nDze0\ne+ejHgv081/vO0Q/s1StbmhmzsrMTU0xb2EmwThg9x7X72brlkaEhjjY99GvKqnob/1MwqMy\ndc9OH7Ayz0bLmzXnkPTg/r1+PT5iZZ44d83yg1YAkhJujh/lqFsUsO94d9veujnCL7FHZepe\nnVuyMs9EJfKJcbBpyxYTHmvxQSvdnOtXY1y/HgEgMb2YZWzdtA4rp6YuEB6XcdRfVtbQ6mN2\n/TdjzU1NOWooJ/h4iMu0GQA0d/KMLdXySK2n5FHDzj3YSqLOmzdvJqTk5GmXuQsAaNIr/iBx\n+nBODn1DdmzjqKIV++uLp7S0tGHDhqzM3Nxcc3P2JRNJ7u+8/k1ZmfoTK/ZFuXwzzdRUyIEO\nPf7brGkTAeTcee7qBx3Yvdh9lm7OwcMn7XpVvJDNH2ayqip99Ojd7r1YmTkRZ8ybCV6g02fH\nuS8C8E9ahdeiunPHsv9z7y6nfvYBK5c3afQeZyWyZuxHo1StbmjBfopzkxPNzXgeIn5jeUpK\nx959WaWJMRet27fXr+pv+Q1OhRXHevy40dAvWJlZh/aYN22ibxybeqvXjHm6Oec2ru3Xme0E\n8/GwXVcmbWIi9K+SRuwqIF6dvqNG8nXR9/P0qYySuPh4AEF792iePtE8feK/bRsAeXKyZGNV\nXh7x6oxWkpwCIMjHW5OTrslJ91+7GoD89m2BXQKCDhGvjsVDdaluVeQjQZJIjqOMeHXVQVxG\nNoB97rOehQQ9CwnynTkFQFK2itN4f0Q0gBTfjc9Cgm5sXgfAJ+Q0U0pqYD7EYOGoz4wQk5AI\nIGjXTo26RKMu8d+yGYA8JUWCsSov3/W72R4LFpTkqzTqkqsR5wAcPn5cvBhCWoocwE+bAuQZ\n9+UZ95et8QagvJ3KaXzh/Bld4582BQDY/4sfKQ05FgzgxLlr8oz7v4ZG6RYZJWadt39ienFi\nevGy1UJiLp4/q2u8zttf/4h3CvOJVyeSl+oCxcmTAAT5btPcydPcyfPf8BMAedotgV0CDhwk\nfpuEUiElKakAgrzXa9JTNemp/qt/ACC/rRBScug34tWxIDUwn8SQowCWTHOVoMqA5rg4AEFB\nQRqNRqPR+Pv7A5DL5VV+IADJ8gQAPr6/5Nwpy7lTtnaDD4Dbady3DSHowG7i1bEoKMhb7D5r\n1pzvk5UFOXfKjp6MAHAq9JiwgLiUNAAHN6z7Jy3xn7RE/x+WAUhSCEUoAw8fJV4di/BLVwGc\n3+VPqjq/yz/0QlTktevCAp4TkygHEBTor3lYrHlY7L/ZG4A8hfspFjb227UbgOJGLClV3Ihl\nMiUQr0gHcGDZor8unvnr4hk/99kAkjK527X2hZ0HkLYv4K+LZ+ICtwHY/JvRb1cxUMfOAJwx\nPE7/rwpJkMsB2NnYkE3HgQMA8DWwijFeu36901Apjl1CahoAu87aoJ1jn94ABFpjnSdPDY2I\nVESG6xfdf1gCwNKU4w9WlTMfd2Pw5DCEghCVQZ6VA8C2rRXZHNipA4D0Qu7WWJ/pk56FBLU2\nbQagwwcWAE5dj+erecWBX10HD+jRxohG6oSkJAB2PbTBD8f+/QHwNS4IG1+5dg3A0MGDGtSv\nD8CmWzeNusTXe6N4MYTbaUkArDt3J5t2vR0A8LVpRkWEARg8bCTZJInDB38hmx4rN8gz7pPo\nXZu27QFERZ41Ukyyrhjb3v0A5Gaz4xNaMZFnOcQE7da12eW3yd7BUW9XXl6qC5SQkgrArlsX\nbf197QEItMY6f/NtaPh5BU/LnXCpASVptwDYde6kVdK7JwCB1ljnqTNCIy8owk8ZrNlz0xY3\nlzE2Ha0lqBImISEBgJ2dHdl0dHQEUE2tsakpSQA6d9PeCX369geQlcnbaDj5m9ER4acjL3G8\nW+JvXAPQb4BjvXr1AXTu0j3nTtmanzYJC0i8fRuAXSftaRzUyxaAQGvs8BmzQy9G3T59Qr/I\ndflKAA422meQJFIzuJ9BThKSkgHY9dDW4OjQD4CSpwZhY79fdgOwaqWNwZMEyZRAYnomANt2\n2jD/oG6dAaTztMZumzfrr4tnrFqYAbBu1RLAySvXpB1XGOrYSaSSMTlhomJiADBtqSThvmix\nNOPQ06f9AgKXLPheipJr1wEwDa8k4b5mHZ/9uOFOIYE7rFqym+EAZOaqANSt+4ZXwE6ZZetp\nS5epCgolSBKDI97xQlMLvFZN9UenpAFgGl5JYuGu/QZ3TMrOBbDv+TYRhl+jr5y6Hj9lyACj\nxERdugyAaaojCfelHhKMU2/dBtDS0tIoAfrcvHYFANPWSRJea5dxGm/xPyDPuM/KHDWOI/Cg\nuJUCgIT0xBN3/bK+mI3ruMVs3nFAv3V1lMsEJh0VGXY4aPekaRwxaT5eqgsUdTUWANPwShLu\nP6zisx834rOQPbusPmQ3bIkpNaDk+g0ATMMrSbivW8+rxGloyI5tVh9YClcbfPJ0aORFN5cx\nEiQZJCoqCgDT8EoS7u7u1XGsa1djADANrySx5oclfPbDR4wO3PNryw85/hMqFbcAmFtwvJYF\niLoRB4BpeCUJ9595/0W4DB1yYttmK0sLkfWv8TPiQY66fBkA0/BKEu6e3E+xsPGGVSuh82eJ\nJEimBKLkyQCYhleSWOAbaHBHeUYWgAPLOAKclYc6dlqYyFx1ROO6Po+JDpz2oadOc+ZLMFbl\n5Tl//sWGdWttyv++GEXo+Uij7Mc6DeMrUj96BKDjEGfiF/odCLLoaV9UzP5FrxIGgaPnYhUi\nEHITYNPxU91mL/rp269G97HTL1U/eTJ+g4/r4AEkqiee0DNnqsp49fr1AJo0buzls5X0zZcn\nCzX98GFsUE0X4r0NGjKclb9357bRTvbzF69kwmmixYRJFqO8lQJgYLmYO4X5s6d+OW/Ryg4d\nuwru9xwv1QUKDT9nlP3Yz4RehsKlBpREXjROyTDDbQ6lZY9c5i5wcxlj3baNRFmChIaGVke1\nnJwPN+K2AeD0GbunF4PPpp8BmJg0DvDzIYMnbqVyd+zRJfSCcYHYsZ8O5ita6jYFQGSstu01\n+LTR74fQs0Y8xcLG82dODwr0b9PNhgyeaNPNJijQf/7M6cZKIkgLuXkfOtJl8oz10yaPcWD3\nOxfAoOfAwO7nSxFG1+djgnacjqBuSO/mzZu6RQYHT1QhM+fOdRr66eSJHPGPFwzx5xLPhFi3\nbQsg8srV/uO+PnHu/JTq+W/9EtL8vXddBw8ggb05nw1llcak3AbwVX+uXvAvFs9Va4gD4bdz\nl9/OXYr4m0yzRXXz4P69bd5rp8yYzxoeAaBJ02ajxk0kYb+vJ0np1CVFzKa1U6ZXiFn3w0J7\nB8eRo796AUcXoAYv0EtO9I2bAL4Zyf5XQAHg9dMq4uEd2LvzwN6dkZfiOcN71cF452Fr/AIG\nfKvt9Uj8vBqk4M7vApsvgOaNTaY6f0oCe3PHfC5yr+c8B0Hfjjp2gF5HOhK042xs5XTmqrVZ\ntjIE7Pol9NTpxGvXSI+cmoU1VMLBzhaA62KP/45jN7qP3eg+dl/179NnwbLm773LitvtDI8A\nYFTvumqiXduPNOoSAJFR0f2dnPcFHVrluZTP2LpVI91N/UZV8Ty4f2/F4jlWbdvNnMvR3jR4\n2MjBw0Y6jxg7fpRjk6bNOON2rPlH9BtVjRLzw5I5Vh+1nzFX26vh6KF9UZFhv4ZcfKdeDT9N\nRl2g/xQBhw4DqI7eddUKa3YS1oDWqsKqTVtS85VLUeNGDTv2W/D8hZ7VcSCOQ1taJBz9dceh\nw36HDm/4ft6kL0Ya1Q5btQQfOeruuSzixDGHPr0BREbH9B8+wrTZ+2M/N64poDKMcbAf42A/\n3nFArxnzmjc2MSpuJwbaFKvF+XlqWg4HRo1+IMauM2YA6NijB5nijhTppiUqGeBQmd1rK0O7\ns+eF4YS4buM3+Ohm5t0rPnU9fvFoI8ZaCuM0hGNiFIPGJDH2C+0/SDKJBgkOVR57B96WGgB3\nCvMFvDqGDp26Alg4p7L/+IVHP9wpzGd5dQBWeswFMNq5L5nijmTqpo3ipbpAToOqYHahKsHJ\noa/kfVWFd0IjL3pMn1plasTh5OT0wo41YJARtw1rL6atlsxyQqJ3xuLUT6ILYv2R1fblS/9J\nS5w34etnz/5AVcTtnAYbMYaJMXaZ7AqAeHVM4uBvRyopRpdhdux5fDixadcWwJcrefusS4Y6\ndlqqcLKSyuM2ZTIAVZ52UiiSsO/NbpySYGy0ki9dADCjHEjCXlJ3PefJU/VnJCb1/+twHTwA\nQN49bUCIJPq0554fa+Tq9W84u6if8E8fCGTcuQvAvoOUKVXdJn0LQFU+Dosk7Hv1lGDMt5cA\nZI4S5kMyydCHO4Xao5BE1x4cPQsJSQk3B/ex7trDTt+r+871S+tWjR6VsWdB44TMUcJ8tGJc\nJuiL6dKd95smJd4cYt+xS/eeul5dZajZC8Su/+uvAKgKtDNWkoS9rU0lq5WixGUMAFX5WHKS\nsO/eTXKFGbkqAP1sRP2mSsPNzQ2ASqWd2Igk7O0rG24hE5owH5L55deTABQUaF/sJNFDr4uC\nGKTt5TZmFADVnfILdOcOAPvy8dSVoaSsDEC7Vh8aIWbiBACq/PLnIj8fgH1PnofIGGOCUX34\ndJnq/CkA1d0i7bHuFgGwt/6E0/izJSvq9B1S+vixtGOJhzp2BiY0EZjZrvokEbcs7Nx5skkS\nnay52xcEjMnMdsyHGOjElhP0AAAgAElEQVSmDSux6Q4gLFo73T9JdGonZYZPp/4OACKvXCWb\nJDFqqJQ/oDVO7/ZtAZxLSCKbJGHd0pLTeGyfnijvQgeArDxBpr5jIPOntGrWVIIY8sIKi4gg\nmyTRqUMHCcY9bXoACC7/80pWNSBTqRlF1+52AK7EaEfekMRHH3NLysnOGD/KccqM+Zw95z51\n/hxA3A3tbUNWniAT44mkS3c7AFdjLpBNkvjoY+43b252xtejBk+ZPv/rSezO1Jxeo26aj5fq\nAtnb2gIIu6jtF08SndpXyyINBpR07wogLOayVknMZQCdPmbPDi0eMn9KKwuJcwWLgfhwYWFa\nJ4AkOnXqVB3HsrHtBSD6ovZOIIl27blvG2G6dOsBIPT4b2STLDux9vlGA336dOuC8inomETH\nj9hziYth+g9rXvm4o/y2EkDpo0cnL0ZBZyIVMdj3tAMQFql9ikmiUwfup1jYmAyAjb2h7fge\nGR0DwMN9vpHfSUufjh0AhN/QDqcjiY6tuX1WlwH9AMTItQOeyMoTZOq7qoWuPCG02gTf8Ijq\nXnlClZdnYcUe1VVy93emqxxpSyX+mUFjBt29uNFbeYJzuYiS5PgG9bSdQkgQTn+qYf38ouL7\nkxct0R1m6/ali+8a7kHmVbLyBACynliVrzyRd6+41ST2lCX3gnfWf0vbxk3Wk3gWEgRA/eTJ\nhI3bdAfSDu3e2W+ma5OGDZicWdt3+p89r1sDJ5wrT6jy8i3asedML8lXVdwt9RsCIL2yDBoz\nHfMZ7mamN2ncWP+4AitP3CnMH9yH/da+nJDN9E4jPfNIhG+r948B27z0KyGlj8rUS+ZP0x1m\na+8weMXaTe81qpAk/BK7U5g/xJ49t/ul+CxGDGlLJf7ZNu+1Ads5xOh7b7p76aK/8kRNXSDO\nlSdUBQUWXdnxuRJlWsUT3awFuNaQ4MsXUwpwrDyhKrxjYc+e2ack/lqDeu9o62zdDs+vMCGc\nP23ZSr+gQ7o1cFOJlSdUKpWFBXvQeklJSYMGDTjtDSKw8kRBQV7PrmypycqCeuX3LemZp98h\njzOfGTnBcDM5y8Sk4rbRX3lCf7kIAA+vX2rwjvb0knXDdFeY4MuPjL3OjJwgHNywTmAUrf7K\nE6r8fItP2E9xSW5WxUP0rgkAzcNig8acpXyLWBhceUJ1t6jlmG9YmfdP/dbgbe0ve52+QwD8\ndfEMgNLHj79Zs153IO0wux7+C+Y0eZe9nAkndOUJI+DzwFjDKfgaajmXnahkPM+8RQtFktxj\n0UKy6bFooSJJzjcAwihjo5WYNldEhnvM0kYvPGZNV0SGM78BRtHEpFHguh83LNVO2xPk471u\nEcck8v8KWjQ2SfHdyHSJWzx6RIrvRj6frP5bb/nNdGVCdL4zp7C8OgD+Z88TSwlizFuYKeJv\neizQnkyPBQsU8Tf57xYDxqs8lwbt2kn6cnksWJCbmsLtNAjSrLnZiXPXpszQ/gmeMmP+iXPX\n+MYccHp1DO/Uq79i7SYmRLdsjTfLqxMlJjx2yvRyMdPnnwiP5RXD5dVVkpfqApmbmiouRXnM\n+U5b/5zvFJeipD3RlcS8eTNF+CmmS5zH9KmK8FMGfDJB/IIOAahMDQYxNzdXKBQeHtppBT08\nPBQKhWSvThhT0xaRl+JnzdHOPzprzveRl+LrSR24M3+hp4/vL6Sz3aw531++mabr1XFi3qzZ\n7dMnmJ5wS92m3D59gvHqjMLBpvv5Xf6kbddtzKjzu/wFvDpuMWZmihuxTFzNw32+4kYs70Mk\naGxuZpabnMhMXLdh1Uo+r06UsKZN0vYFLBmv7VO0ZLxL2r4Axqtj0eDtt/0XzGFCdH7us8V7\ndUZBI3Y1wIuc7sQ49CJ2NUVVReyqBP2IXU3BGbGrKQQidi+Yl+olph+xqzG4InY1hl7Ersao\nRMSuyhGI2L1g9CN2NYh+xK6mMBixe5HQiB2FQqFQKBTKfw7q2FEoFAqFQqHUEqhjR6FQKBQK\nhVJLoI4dhUKhUCgUSi2BOnYUCoVCoVAotQTq2FEoFAqFQqHUEqhjR6FQKBQKhVJLoI4dhUKh\nUCgUSi2BOnYUCoVCoVAotQTq2FEoFAqFQqHUEqhjR6FQKBQKhVJLoGvF1gDPrRVb9qAGlbC4\n0dKxpiVo6ZZzrqYl6CCT1bSCcl59adYhBZ41eVnWc3yp3mFvPi2taQnlNHivphXo8ORlWRQV\nf78saxwD+Ptt7mXsXzyv/vmspiXoUOeledEV3alpBRUUv1aXSdO1YikUCoVCoVD+E1DHjkKh\nUCgUCqWWQB07CoVCoVAolFoCdewoFAqFQqFQagnUsaNQKBQKhUKpJVDHjkKhUCgUCqWWQB07\nCoVCoVAolFoCdewoFAqFQqFQagnUsaNQKBQKhUKpJVDHjkKhUCgUCqWWQB07CoVCoVAolFoC\ndewoFAqFQqFQagnUsaNQKBQKhUKpJVDHjkKhUCgUCqWWQB27lxRldrbnxk2ylm1kLdt4Be5S\nZmeL2Ss49JSsZRv9/MgrsdM8lstatpnmsTzySmxVi32OcDzujpxqqlyZle3p5S2zbC2zbO0V\nsFOZJfK0nJRZtmZlkkp0P0Yr2eAts2gls2hlhJKQkzKLVnylpEKjZJSLyfJc7yUzs5SZWXrt\nCFBmZYkScyJUZmbJyoyNj5+2eKnMzHLa4qWRl69IEENIVypXLF/25ut13ny9ziZv73SlsvLG\nxEaKmHTlDyuW1X2jTt036mze5J2eLihGnDGxESlAmZHhueZHWcNGsoaNvLZuU2ZkSDMmmfof\nkTKMQqlUenp6ymQymUzm5eWlFLyCEg+Rnu65cpXs7Xqyt+t5bfFRpqdLNib5uh+jxWRkeK5a\nI6vfUFa/oZfPVsPXSNA4Mip62tx5svoNp82dFxkVbawY7VGUymXLPOu8+kqdV1/x3rhR+BII\nGxcVFQUGBpLSZcs8RV5NZXq654ofZG/Wlb1Z12vTZsMXiN849tq1abO+k71Zd9qs7yIvXhRz\ndHb9SqXnsuWyOq/J6rzm5e1t8GwIGBcVFQUE7iSlnsuWG3tvKzOzPH/eIGtuLmtu7uXnr8wU\n9749HiJrbs7KLCouDjgQRKry/HmDyKoMItNoNFVSUSVxdnbmKwoJCeE048uXtrvuJl8m3+58\nNfBRXFzMpE3KHugblJaVNbTuysrMvXTBvHlzgWqDQ0+5zJ4HQJOl0M0PCP7VdYmnbk7E/j0O\ndjb6Ndxo6WhIuwHC8dgD9wBch2Vl6umWc04/s7SsrOEnnVmZuZejzE2FT8tJl1lzAWhyKl40\nqoJCi572LEtdg+eQyTiUtO/EVnIl2oCSkJMus+YA0ORy/GZEXrna32U8X6mWVzk8idKysoZt\nP2GLuXbZ3NRUSMyJUJcZswBo8nOYzNj4eFvnkbpmEYcOOvS046zhWRMzvsrV6tImJmxvIz0j\nq4U5+70m3vjihQuDHQcC+N8ff7GMhd9hanVp08bs+pUZWS1acIsRY3zxwoUhgwcCePqMLebN\np6WsnFK1uqH5B6zM3BS5uRnHCRQ25vThnIYMDgk6oJ+PBu9xZIqjtLS0YcOGbBm5ueZcV1AU\nTx6xD6FWN2zGvkVzb6eZt2jBoUfQWJWXZ/HRx6xSzeMybiV//81dvxn7q+Wmppi34LlGgsYB\nu/e4fjdbtzQiNMTBvg+Hlrfrc4sESktLG733LiszKzuH8xIIGxcVFTVv9j6rNO3WbSsrK2bz\n1T+fsetUqxs2acrKzE1X8l4gfuPYa9ds7fvqFkWcPePQty/4qMN+0ZWWqhs2Yt/8uVmZPGdD\nyLioqKhpc/a9pEhL1T0bFRTdYVdeVtawTTt25TeuGnjfHg9xmT4TgKZQVVF3cXHTDuxfNEXM\nRasPW3JWUvxaXSZtYmIicLiXJWIXooP+JgBnZ2fiPDGQnMrsLl6e8NGrnLjkVABBmzdqshSa\nLIX/j6sAyG8pBHYJCP6VeHUsVIWFrks8PWZOK5Hf1GQprh45BODw6TPVIfs4yohXV03EJacA\nCPLx1uSka3LS/deuBiC/fVtgl4CgQ8SrY/FQXapbFfkYr2STJjdDk5vhv24NAPktg0rm8JWq\nCgqJVyeBuKRkAEHbfDT5OZr8HP+f1wKQpwmKORhEvDoWew4fAaCIjtTk5ySGnwGwKXCXBEnx\ncfEA9u4/8L8//vrfH39t9/UDkJScJNk4T6UiXp10MfsOPH3219Nnf23z9QOQnCQoRtA4L09F\nvDqRxCXKAQTtDNCU3NeU3Pff7A1AnpIqwZhkMp/ES1EAlszjuMMrSVxcHICgoCCNRqPRaPz9\n/QHI5fKqPER8AoCg3b9oHpdpHpf5b/UBIE9OkWD8sKREt5R8jBOTkAggaNdOjbpEoy7x37IZ\ngDyFR4ygsSov3/W72R4LFpTkqzTqkqsR5wAcPn7cKD0A4uPiABw4ePCvv//56+9//Hb4A0ji\nvW+FjMnvIFN64OBBAJs3bRIWEBcfDyBo717N/55q/vfUf/s2APKkZAnGe/YfAKBITtL872ni\n9WsANvlsNeZkIC4+DkDQgf2av/7U/PWnv5+foBgh4xMhobqlQQf2A/DevFmsEnkSgKDtWzWF\nKk2hyn/9TwDkabcEdgk4EES8OhYnws7pVhW0fSsA74BAkUoEeFkcOzGwQmLiI2R8uxvlmVXy\n6EaRkJYGwK6LNibk2KcXAIHWWOcp00IjLigizuoXXYlLADC0X98G9eoBsOnUUZOl8F39Q5Vr\nno+7MXhyGEL/WipJQmoaALvO2r84jn16AxBoA3WePDU0IlIRGa5fdP9hCQBLU96YkyglXZ5X\nInCBJrmGno9QXOAIQxLWbvdzGuAgUUxKKgC7ruVi7PsAEGiNdZ44OfRchCI6Ur/Id+0aTX6O\nVcuWAKw/bgsg9Nx5CZISExMB2NrYks2BAwcBSFdyu85ijH/++aehw4ZJUAJALk8EYGP7fP08\njUpijNf//NPQoUaISUhKAmDXozvZdOzvAICvpc8oY881a92+nWjTjR3drzwJCQkA7Oy0wVpH\nR0cAVdsaq/2mNj20hxjQHwZPC4/x/fsPAFhaSI0mVpz28vr7ixDDY3zl2jUAQwcPalC/PgCb\nbt006hJf743GStI+F7baSzBoEHkuuC+BsPHJ0FAAY8aMJZsksWOHn7CAhEQ5ADtbbduO48CB\nAPhaY4WNfX22aP731Kp1awDWHToACD11SvjoevUnArArfzAdB5H6uc+GsHHoyZMAxo4ZQzZJ\ngrjCopSQ9223LtrK+/YBINCE6vzNt6Hh5xQxF/WLQsPPARj7mdYPIQm/vftFKhHg3+HY8TV0\ninTOBHZ/AUeXQNS1GwCYhleScP/xJz77cc7DQgJ8rT5gt+AASE1PB9DSnCN4XrU44h0vNLXA\na9V3iKhr1wEwzZ0k4b5mHZ/9uOFOIYE7rFpynJbMXBWAunXf8ArYKbNsPW3pMlVBoRFKYq9x\nKFm9ll+Jc8hOf04lAELPR/rtP7hkxjTxArjEmJaLMQXgvmoNr5jPhof8Eki8NwHIf9CgbT4S\nJMXERAFg2lJJYtHCBdKMT506GeC/4/uFiyQoARATHQWAaUslCV4xhoxPnzoZ4L9jgTFioi5f\nAcA0vJKEu8eyShoHHzkaeuas27cTxCsRT1RUFACmnYsk3N3dq/IQMTEAmHY9knBfvESCcWZ2\nNoC6det6bfGRvV1v2uw5qrw848RcugyAaUslCfelHhKMU2/dBtDS0tIoARxH4boECxZwXwJh\n4+MnTvz19z+sXaZOdTMggPOcL+K+88Uby5OSAATt3St8dHb9UdHQvyEXfC/BOOT4Mc1ff7J2\ncZvqKlbJ1Vjov29XruazHzfis5A9uzhbV0P27NJtmdUq+forkUoE+Hc4dv92uj6PiQ6c9qER\nHNEUAcY6DeUrWr3VF0CTRo28AneRwRPCLYaSGYS3q6NaXULPG3taeMMq6kePAHQc4kz8Qr8D\nQRY97YuK71eXEmdeJaqCQudJrhs8Ftt0ZnfaEyvGyKDa2OFOBm28dgR0HDRkg+dSMcb6nDp5\nsqqM81Sqz0d8tu6n9T16cPQKFVX/KWPECBrn5ak+H2m0mNAzHKH0ShqXqtUuk6a4fTvRun17\n8ZUbISM0tDqqfe4QxnQIETZWl5UB6GhjR1w9v8CdFh99XHTPiG4hoWeMESNovHr9egBNGjf2\n8tlKBk/wtS8Lc/KkEZfAKGPSpP7FF18ImxkVVBNp7LVpc8fuPTasWzd29CjxlaM8zFYdxnJ5\nEoBRhs5GReXGvm8/Exv9kaemARg1jPfX3KDnwCBliFmtpPo6zAG4efOm7uZzgyeq76g6eG7c\nRDw8v4PBfgeDFRFnOcN7/x2IP5d4JsS6bVuQgQvjvj5x7vwUlzEvWMnMZSucBjhMHjv6BR9X\nGNP333cb/yUJ+82fOqUGlcyZ893QYcO+nfRtDWpgmDv7u6FDh038tubFRF+5CuAbl7E1LeSl\ngPhzibFXrD/5BEDkxaj+Q4edOHlqysQJNSXJc9Ua4uH57dzlt3OXIv6mVSspA96rnKKiouXL\nli1ZurSfg8S+H5XBtHlztylTSCRv/pzZBu2rm6KiIs/lyz2WLHHo16+GlRQXe/68wWPOdw69\nevLZPOc5CPp21LHTwjkqtkaUVAftWrcmQ2Ujr8T2/+qbfcdOrJrH25H/vwBrqISDnS0A18Ue\nL9ixCwg6FHo+MvFMKOkB+fIwdrjT2OFO34z63NZ5pOn77wvE7Vjzj+gPWa0Mu3YGnjp58vrN\nuPr1G4ixZ80/oj9ktVJidgWeOnXy2g2xYqqVgD17AVRH77p/I6yhEg597QG4zpxVg45du7Yf\nadQlACKjovs7Oe8LOrTKcymfcZ1Xn2s60282rSqKiopcp0zpYN1h5cpV1XQIYcaOHjV29Khv\nvvrS1r6vafPmxsbtqpaioqLJrlOtO3RYtbLqO50bp6S4ePL8763bfbzq+6rp7UCbYv81OPWX\n8geL7MW01ZJZTkj0rnYgecxBlSNBieuipQA6DnEi8+GRTN20dDEDB1SyBgA2nTsD4Bw/KwGj\nRj8Q4+nT3AB079qFTHFHinTT0sUYM/qBGM+Y5gagR7cuZIo7UqSbNgqnIYMlG6vy80PPnPVY\nMF/CcSuDk5OUdnnjDvHpkGoyloDTEGPElBuTxNgvPiebZJYTEr2rPMOGGXEJWMYqlaryXp3T\nUN6GQvHGNj16AHD5+mvJMrT1G/NKYRmrVKoq9Ooq875VFRRUrVeHf4tjxzdMQeTscQK7v4Cj\nS8Bt3FgAqkJtd36SsO/RTUJV0vZ6OXH70gUAM8qBJOzLxw8ahfPkqfozEpP6RSn5ahyHkvIh\ney8Yt/FfAlAVFJSLKZAsxnniZJmZZWmZEVNFkDlKmA/JnOI6FUCeStsvmCR692ZPHCjBWBgy\nRwnzea7+vPL681QAevcRFCPOWCRu304EoMrPJ5skYc8zO6AY44ysbAD9eveujCph3NzcAKjK\nLwpJ2NtX6jywDzF5EgBmlANJ2PN8KWFj51Gj9WckJruIFTPpWwCqvPLTnpcPwJ6nUUzYmG8v\nAcgsJMyHZJLBDSIvgUHj2NjYlh9Y2tvbi/fq3KZMgfgLJGjs/PkXsjfrlqrVIg/NUf9UV3B8\nQY6pAcUYx8Zes2j5ob19HwleHRncwH7f2krsARwbF2/Rzdbe1qYKvTr8Wxw7Asu7MrapVH93\no9yySh7dKIizEhZ9iWySRKeP2TNwiqFnl84AgkO1PVvJshNkYrx/HfY25LTEkE2S6NROymkh\ngczIK1fJJkmMGir2D3r5BaqsEjINHvPRzRRfib2NDYCw8tntSaJTe/YUmmIY99lwANGx18km\nWXmCTIxnFL379AFw7px2ohmS6Nixo7HGnF6jblqUmN4c9Vtb84jhN+b0GnXTfBC3LKx8RBRJ\ndOrQQbIxmW6jFc8g6yqB+ARhYWFaGWFhADp1kji+h/sQvXoBCDsfoT3E+QgInBZBY6dPPwUQ\neTGKbJLEqBEjjBDTsyeAsIjy+iMExQga97TpASD4tyNaMVHRAMhcd0bRx74PgPBw7a1IEnwP\nkbCxUqns1dNuydKlc+dxzHXKB3HLws5pJ2kiiU4drSUYjxszBkB0jPYXjaw8Qea6EyumTx8A\nYeHl9YeT+rnPhrCxUqm07dXLY8mS+XOlTACpfd9eLH/fXpT+vlVmZtk6feYx57v5bmLH5Irk\nZVl5QhcBl0tg7YfK7F4lK0/oH45PhsGVJ1SFhRa92H05S+Q3mZ5YZN0w1goTfPnMyAmGuzeu\nNNGbmBtVsfIEALKeWHWsPMG5XERJcnzFabFsDa4FJPTzi4rvT160RHdwq9uXLr5rVnKr0Vt5\nQlVQaGHH/rNYkpJQocSiFbjWkODLF1MKcK88oSoosOjBDhKU3EquEGNmiedXmODLLy0rG//d\nXN1hX04DBwSuX9eEq6OuwMoTeSpV61bs4f1FxfeZ3mmkLZX4ZwaNGXT30kX4HZaXp7LSq//u\nvYr6SVsq8c8MGjPo7vWcSL2VJ1T5+Rbt2T+HJapsMs8ZyteT0JTcF2MMYNo8d79dv7AyOajE\nyhMqlcrCwoIto6SkQQOp/Qv1Vp7gXC6i5E5BxWl5ux7K+88JGxfduzd5+gzdkbNukyf5buaZ\ngJdr5QlVXr5FO/b44pJ8VYWY+g0BkG5zBo2ZkRMMdzPTmzRuzKGFf+UJlUrV8gNLVub9Bw+Z\nS0B65pEIn7DxsmWeP67hmP9ItzOf/soTqrw8i9bsxRhKiu5WnJM36wLQ/O+pQeNStXr8xG91\nR846DR0a6Lu9SZMm+qoAjpUnVCqVRcsP2fXfv9+gQbmYOq8BIPOYCBt7Llu++scf9Y+pPwcK\nwLHyhKqgwKKbLbtyRWrF+7a5OZ5fYYIv3/PnDas3beFQorcv4d+38oQuAoE0/SUlqmR3kbPc\nCRw9hAs+GQYxb95cEXHWY6Z2YjOPmdMUEWcl969fNW9O0OaNJEblMXNa7qULnF7dy4+5aXNF\nZLjHrOlk02PWdEVkuLTT0sSkUeC6Hzcs1U6zFOTjvW4R98RmvEounPOYNaNcyQzFhXM1NQDC\n3NRUER3pMVvbE85j9ixFdKQ0MQ3q1Qtcv44J0fn/vJbPqxOmhbl5ckraovJpxhYtXpKcksY3\n5sAoYwm0aGGe9Hz9SQJijDEWibmZmeLmNaZLnMeC+Yqb1/h8MjHGfrt+AWDAq6sc5ubmCoXC\nw0M7N5uHh4dCoZDu1XEeokULRWK8x0Lt7GIeC79XJMbznhZB4yaNGwdu37ZhrfbXOmj3L+tW\n8fxJ4xVjpoi/6bFA+xLwWLBAEX+TX4wB41WeS4N27SSd7TwWLMhNTeH06gxIMjdPu3V7yVLt\nkIslS5em3brNdwmEjTm9OsMCWrRQJCd5lM9F57FokSI5SegC8Rs3qF8/0Hc7E6Lz375NyKvj\nrN/cXJGW6rFE+2B6LFmiSEtlvDqjjDm9OiOUmJoqYi56zPlOW/mc7xQxF6W9bzm9uirhZYzY\n1XoMRuxqiiqJ2FUJnBG7GkMvYldjcEXsagqBiN0L5qV6h+lH7GqMSkTsqh69iF2NwRWxqykE\nInYvGP2IXU2iF7GrMfQidjXIvztiR6FQKBQKhUKRAHXsKBQKhUKhUGoJ1LGjUCgUCoVCqSVQ\nx45CoVAoFAqllkAdOwqFQqFQKJRaAnXsKBQKhUKhUGoJ1LGjUCgUCoVCqSVQx45CoVAoFAql\nlkAdOwqFQqFQKJRaAnXsKBQKhUKhUGoJ1LGjUCgUCoVCqSVQx45CoVAoFAqllvDSLLX7X+VG\nS8eallBBt6ywmpZQTlPTmlagw99/1bQCLU9erWvY6EVR/PBpTUvQUlz6v5qWUEGr5i/Lsu51\n//qnpiVU8NojdU1LKOfVl+hXT/ZOTSso597L8jQDQOO3X5ZbV/N+i5qWoMP9YpGGNGJHoVAo\nFAqFUkugjh2FQqFQKBRKLYE6dhQKhUKhUCi1BOrYUSgUCoVCodQSqGNHoVAoFAqFUkugjh2F\nQqFQKBRKLYE6dhQKhUKhUCi1BOrYUSgUCoVCodQSqGNHoVAoFAqFUkugjh2FQqFQKBRKLYE6\ndhQKhUKhUCi1BOrYUSgUCoVCodQSqGNHoVAoFAqFUkugjh2FQqFQKBRKLYE6drWEcDzujpzq\nqFmZne25cZOsZRtZyzZegbuU2dli9goOPSVr2UY/P/JK7DSP5bKWbaZ5LI+8Emu0mPR0zx9+\nkNV9S1b3La/Nm5Xp6ZU3JjbGK8nwXLlK9k592Tv1vbb4KNMzJBuTfN2PsWIY0tOVK39Y/nbd\n196u+9qWzd7p6UrJxiRf92OUkqzM9A3rVlk0rWfRtF6Ar09WptCVYgg59ptF03qsTFKJ7sco\nJQByszO3b1rbxapxF6vG+3dtz83OFDB+cP/esV/3EePtm9ayjEm+7scoJRnp6atXrmjwzhsN\n3nnDZ8umDMEbWMCYZOp/jBKjVCqXL1/2+muvvv7aq97eG5VKobtF2LioqGjnzkBSunz5MuGq\nKurMzPRc97OsqamsqamX7w5lptB1YQg+dkLW1FRaqZCYjEzPtetkJk1lJk29tvsqM4TECBur\n8vNJqfOX44OPHitVl0nQA0CpVC7z9Hz1lVdefeWVjRsNXyAxxoeCg199pbK/+5kZ6evW/NDk\n3bpN3q3ru3VzZoaop/vYkcNN3q0r+aBKZbrn8hWy19+Qvf6Gl/cmpVLw5S9oXFRUFLBzFyn1\nXL5CuCrBoyg9PT1feUX2yiuyjRu9DF4gMcbBwcGvvCKTpodBptFoKllFbcLZ2ZlJh4SEcObr\nEhIS4uzsrGupuwtnPoDi4mImnd24m0StOoTjsQfuAbgOy8rU0y0rjJVTWlbW0LorKzP30gXz\n5s0F6gkOPeUyex4ATZZCNz8g+FfXJZ66ORH79zjY2XBU0ayFfl6pWt2w6ftsMUqFeQvpxpEX\nL/Yf8ikAzdMnPAPwPr8AACAASURBVN8G+Psvjsqbm7Erv5XKq4TfWJWXZ9G2HatU80jNKeTJ\nq0KvRbVa3axpI1bmbWVmixbmxhrn5ak+svqQVfr46Z+6m8Xq//EpKStTt2/F/nG9EpdmasZx\nfhhCjv02y20igNy7FT+EBfl5dl0+ZlnqGgAoLuVVAuBRmdq+C/u7nLqY8L7eRQHw4P69gbbs\nwx0Ni7X44EMAvxfmD+3biVUap7ynu9mqOa9frlarWzRnO4KptzLMuG4bYWNOH27Ip0ODfz3K\nbNZ9ow6fEgBqdalJo/dYmRmZ2ebmnHeLkHFRUZGZaTNWaUrqLSsrK2bztQe/swxKy8oatvqI\nlZkbd93cTMgtCz52wsVtOgDN3QJjS7W8ynFaStVlDVu2YotJjDM347hJhI1V+fkWHbvoFjk5\nDgrc5N2ksYl+Vf+8x/vHoLS09L1332VlZufkcF4gkcaHgoPHjRsH4O9//mEZ3y99xqeEhVqt\nbmXRlJUZn6w0E3y6jx05PHXy1wCKHj41eIjGb7Ndz1K1uqEJ+1zlZmSYm/O8cvmNi4qKmupJ\nVaSkWFm11q9KU+d1PpGlpaXvvtuQlZmTk8t3gcQYBwcHjxvnAuCffzgcs/v3KzwHExOO24mB\nRuwqIK4YA8uZC+EC5b4dZ1UvRvZxlBGvrjqIS04FELR5oyZLoclS+P+4CoD8lkJgl4DgX4lX\nx0JVWOi6xNNj5rQS+U1NluLqkUMADp8+Y4SY+HgAQXv3aJ4+0Tx94r9tGwB5crJkY1VeHvHq\njCUuIQFA0O5dmkdqzSO1/9YtAOQpKRKMH5aU6JaSjwRJAOLj4wDs3rv/8dM/Hz/9c+s2PwDJ\nPOdH2LjkYYluKfmIV5IsTwDg4/dL7t2y3Ltl67x8ANxK4z4/hKD9u4lXx6K0tES3KvIRrwTA\nrRQ5gB+9/eOU9+KU9zxWbwSgvJ3KaRwVcVbX+EdvfwAHdvuRUrW6VLeUfMQrSUiIA7Br977S\nR89KHz3bstUXQEpKkgRjksl8Ll29AWC++0LxYuLi4gDs33/wjz///uPPv339dgBITuYWI2wc\nGhqiW7p//0EAWzZvMiBAngQgyG+75m6B5m6Bv9d6APK0NIFdAvYfJH6bhFJDYuQAgvz9NMV3\nNcV3/b29AMhTucUIG4dduAgg4tgRUhpx7EhoWHhkTIzRkuLiABw8ePDvf/75+59/dvj7A0hK\nErpAwsaBgYHEq6sk8sR4ADsC9xY9fFr08OnGzdsApKVwv2cI+/fuIl6dZMgXDNq/T/PHM80f\nz/x9fQHIBW9XPuMToSd1S4P27wPgvWWLNEkHDwb984/mn380/tpzLpdsHBgYQLy6ykMdOy36\nrhinx8YJy/JFenXzcTcGTw5DStODGBLS0gDYddFGKRz79AIg0BrrPGVaaMQFRcRZ/aIrcQkA\nhvbr26BePQA2nTpqshS+q38wQoxcDsDORhvhcxw4AABfA6sY47Xr1zsNleLYJciTANj16KGt\nvH9/AHytscLG9x88AGBpbiFBBoskeSIAGxtbsjlg4EAAGTytscLG9x/cB2BhbilNSWpyEoAu\n3bRfuU/f/gCyM3lbqyeNH30+7PSFK/H6RSUPHwAw4/oTLBLFrWQA1p20oXHbXv0AqHK4G9qi\nI8MAOA4dQTZJ4kjQbrJZ+vABgOamQpEJAZLkcgA9emjPef/+AwGk89zARhmvWbXi20mu3br3\nEC8mMTERgI2ttv6BAwcB4GseEjY+dTIUwOgxY8gmSfj77xAWkJCcAsCum7ZBwLGvPQBlZhaf\nvfP4CaFh4Yor0RJKDZKQnAzArrv2JnHs1xcAX9OwsLHr3PkAHHr3IpskkaoQ+jPMCTnntnZ2\nZHPQIMMXSMB4+PDhoaGht27fNlaGPilJcgDdemhfrX0dBgIQaI0d7/JF2JnTV29wO2EiSUgk\n73PtHeg4cCAAviZUYePQUycBjB09mmyShJ+/v7GSEhMTANhVnHNHCF0gA8bDhzuHhobevm30\nfcIJdeyEeGH+mWQc8Y4XmlrAuP5P4om6dgMA0/BKEu4//sRnP855WEiAr9UHH+gXpaanA2jJ\nFTkXKyYmBgDT3EkS7osWSzMOPX3aLyBwyYLvpSi5dImj8iVLJRhnZmcDqFv3Ta8tPrJ36k+b\nPVeVlydBEoCYmGgATMMrSSxexP0FhY2zs7IA1K1bd8tm77frvjb7uxl5eSrxSmKvxABgGl5J\nYvWKJXz2w0eO3rnv15YfcjSF5OZkA3jzzboBvj4WTest/X5OQb5x5yfu+hUATMMrSXivW85p\n7O23Xz8I97nLBJLIz8sB8Mabdffv2t7FqvGPyxf8XpgvXsnlS9EAmIZXkvBYwh1mE2985Ldf\nz5w+9e3kKeKVAIiJjgLAtASRxMLvF0gwPnrsxB9//s3axdV1qrCAqCtXATANryThvmIln/24\nkSNC9u22+pDdqi6m1CBRl68AYBpeScJ92YrKGxNWe3kbLSmK45wvcHeXZjzOxeXEiRO6jeOS\nuXI5BgDT8EoSyz0X8dmP/GLMvqDfPmzF8XSLJyomGgDT8EoS7gu5nx1h45CjRzV/sNud3Vxd\njZbEdc7djblAusYuLuNOnAipkgsE2seOga93HVNq0MkjNpyWXbs+103t5s2bTPqGjMMHkgAZ\nOVHlfezIAAjdrnL6OZwI7OgVuMv9x5/cxo11+9LFui27k40Wrj52ZIiDbmc4/RyRxqq8PAur\nNhvWrZ0/e7ZAJVr0+tiR8Q26bab6OSKNvbb46HuEd7MzmzTm6Hwj3MeOjG/QbTPVzxFpvGWz\nt75HmJNb0LhJE2ZToI8dGd+g22aqnyNyxwBfH32PMC41y0SnD41wHzsyvkHXXdPP4UN5O9XF\nua/fnqPdbHsD2L9ru75HeO5q2nuNKsQI9LEjHeNKHz0TyDHWmHTF+3aSq/dmH1YNwn3sXn/t\nVQC6Dpl+jjTjpCR51y6dw8LP9evnwGTq97EjQxx0O8Pp53AibGa4Eq4+djKTpgA0xXcFckQa\ne65dt9rLO+LYERKrCz56zMXVja8qgT52ZIiDbmc4/RwJxnz54vvYkQEQul3l9HNE7siHfh87\n2etvANB1yPRzpBnLk5I6du0WEXbWoV8//VKBPnZkiINuZzj9HAnGApXIRI+pEHry/1NwDpUw\nOH5C10BgIIWuJ4fnB0/81/DcuGn1Vl/8v727j46jvA89/szKhD/S4rSA06RYocQxpY6RaTi8\n+UWJ3YbGsDqXpOTavfaBxLKRATexcYiNVw1cK7hJ7YbUN1hXIoTeew/yP20O2mDeImGnxBYH\nEkvUnFi60HskXG61kMS6Sf+g2dHcPx5pPJ6ZHc1qd2d+evb7OT4+M7OPZp553d8+b6NU55OH\nO588PNz3bGjxXq3du3179pa1rV8IadSVMB3VDZ74cdPSpUqp/mPH1tySferppzffeWeKudJR\n3cDLP1l69dVKqaNHX7zlM5/+wQ/yX/jipoRzoqO6Z/qP/9GSpUqp4y8dW/+5W1949un1G+6s\n9aZ/8fN3Dj2yb9PdO3RUp6bL+Xp6jy7+wyVKqVdO/FPbHZ891vfsbZ/fWOvMlKKLT/7iv2xI\nKwM+hULhwa/91e4H9nijurqy8fbbOw58a81tn9Ozufu2p5sfRCgUCu0PPpjbvTs0qpPGGzlE\nd54gsAvhBmfeQK2SEju4lnzsY7oYr//4wJoNd/zP7z+1d8eXE85D9+Pfyz99ZPDll+dfNPuB\nRarFV8i3urlZKbXl3r+MDux8g4+U1bMhDt8KP/nJTyml7r2nLRjY+QYfKbdnw4x8K7xpRbNS\natd920IDO9/gI2X1bPD5xc/f2btn+8f+cMndXz5Xfe9boQ74OnI7goGdr9dqaJlcVTzxve8q\npaJb1+nSNVdoMVtVFAqFtrs2L7266aGHStaoGm/xoo8OHu3vfOLvO5/4+/3/9cHWDRtmrIf1\njT8SWiaXCt/oJHEK2+aQQqHQ2tbWtPTqvQ89GJ3SN/5IaHGaKLSxqw43novf5WLuyq6ZzW9x\n/VfrsrfoWT3KiS69qygz5fR+0Im33HOPUmrZ9dfrIe70R97pWeZk7WdqlLgSa2+5tUaJy/Un\nn05ol+NYtfrmiE//7e0zwaiuRj6z9pZZJz7z1lvPHHn6K/dXLZO33lrGBeBLPDY2VnlUl/30\nn876b6sue/OnZ5e46eNLDu3/pvPu+H13b33vvfdU9crtbs1ma5S4Qjf/WRmXcbVkby1jo77E\nY2NvxYzqystSOce8rMRlIbCbYnw0Njttf7FOKTX29tt6Vk80Xz+bsfdm91fnZWZzq1LK7Vug\nJ5pXrqw8cdk52bQpZOUrVswiccvn/3NwRGL9JxG8o5C4pWutm7copdxeDnpi5cpVoWuITnz7\nn98WHJFY/4mPdxQSt3Rtwx2blFJuLwc9ccNNszn4mzZ+PjgisV5/kHcUErd0TXd9cHs56IlP\nXHdTqS3+8+Crt3zymk9cd1MwqtvetiE4IrHbtcLLNxyJXvjFTVuUUmemrwQ9sXxF+AmKk/jN\nf3lDKbWyubnUvmh6FBL3n16oOzeMjU1dAHpi5arwVc2Y+OWXBxZ99A9WrmqOH9W13bFRKTV2\nZqoxnJ5ovunGmH9eXW133qGUGjtzZjozZ5RSzcvDL5KyEp+dmFBKLbkyZLR2lx6jxP2nF97V\n1qYCx7y5xLkuK3F8ekAT959eeMcXNiulzkzf3XripuXVebSWojs3jI1NP0XH9PM8/N6ZMfHA\nyy9/ZNGi5pWrYkZ1eowS99/UVso55mUlrhyB3Tm+2C5+paovpUmFds3XX6eUeu5HL+lZPXHN\nH/lHcI1j+Sf+WCl1OP+0ntWvndAD48XNzMqVSqnnXvjhVGZe+KFS6pqmpnIT65Ht3H86gXc6\nRk6WK6We6+ubWnlfn1LqmqarZ5FYF931HzumZ/XE7Z/9TzFz4rVi5Sql1A9feEHP6omrm5bN\nIvHatbcqpY4efVHP6onbPvvnMXNy/Y0rlFI/Ojq1y3piydLw4xPtT25eq5Q6/tLU8dETt7Tc\nFn8NOoY78dLUvuiJK69aGpp49P+8eefnP7Pp7h0bvhgyIpou53vlxNSYZHriT/8s7s2+YuVK\npVRf39Qx1xNXl7iA4yTWQ6J8NDBYbhyrVjUrpV544Xk9qyeWLQu/WqITj4yMrFyxfPcDe7Zv\nDxnAspTmG29USj13dOrM6olrln687D2pBh1Q6iHo3IlrloZfJNGJt+6837rkg0OnXldKTfy/\nX+Wff155xkYpI0urVimlnn9+6pjriVInqKzEFdIx3NH+qStTT3z86vDLuFqaV+nn+dRG9cQ1\ny0o8/CMTj4z87xtXrsrt3n3f9opaAemb4vnnp3oc6olly/wDmM8iceXoFXueOfrmCVWzXrFj\nb7/9kRX+VqVnh17VY9Gp0p1kQ5e7PSdc468cX3Cx//0HSoX3itVdWf2ZGf83t6lcsN9rROJz\nWS2/V2zo6yLOvn3mXE48/V6jExfeeaf1nnvznoGa2zZtOvTt8EY50b1iQ18X8X/Hf37RdK68\n/V6jE79TKNx9911Hnv6B+1Hr5i3f/rvveBNH9IoNfV3EqTf+9bd/eyonpTrJBpe/++47X91+\nzw+fP3d8Ntyx6evfPG/w2+hesaGvizj2kzd/azoz3k6yjz6y77uP/m1wJfpT3fBOj3WnfW79\nnQ889DfelBG9Ys+89daSq/xB2Ftvv+OeIG+/1xkTK6W2f2nb49/t8i10RfeKHRsbW/RRf7+l\nd3/+i4sumq+nvf1eoxN/7Wt/te/hrwc34W3MF+wVO3bmXz/yiet8C8++cfrcs6VE/9Za9IoN\nvi5CKXX2X96Yf9F0Zjz9XqMT9//TS27PCa2nq3PdZ8N/ikT0ih0bG/uDyy/3LfzFL385f/7U\nCfL2b50xsavyXrFnzrz1x0v9o3K8MTruXoSler9W0it2bOytjyzy3w5n333n3CPX0+81OnH7\n1x7s2LcvuNHQPrMRvWLHxsYuv9w//ugvf3nWPebe/q0zJnZF9IrlzROz5HurROjy4JsnSq0q\niRzXWOOHPzzc92zu3q16Nnfv1uG+Z90nb7n27vhyz7f/Vje2y927dfSlF8OjulKZWbhw+LWh\n3K6p4Yhyu746/NpQqQ4QZSUuV+PChcMnf5qbHscrd/9Xhk/+NConpRMvuPTSx77z3/ZPfy/2\nPPH4X+8tY9Bmr4ULGwdfe/2ru6YGB/nqrgcGX3s99Ct/xsSXLljw6KP/fd9ff1PPPvE//tfe\njpBHYSm/f9nCF4//dNv2qQFTtm2//8XjP3WjurJccsml3/jWd3IPPqxnD3Z+b1d7eU24fu/D\nl/3jcwOb7p4qTNp0945/fG7gt0pkJjSqc/3uxZe2f/1b23dNnaCHv9X1lzvbI9L7XLZw4U9O\nnnKbxH3l/t0/OXmq1AmKk/jx73YppUqtIVpjY+Op13+2e3qond0P7Dn1+s/cqK6sxKFR3cwZ\nuOz3h4//KLf9S3o2t/1Lw8d/NOtnS4UaL7tseOC42xIud9/24YHjblRXVuLVK1f0ff8fdHVt\n25139H3/H0pFdTNkqbHxZ6dP79kzdcz37Nnzs9Ong3HALBJX6LLLFp545bUdO6cGrtuxc9eJ\nV16b3UUYX2PjwuFTp3K7p26H3O7dw6dOlXzkRiYOjepmlaXG06eH9+zJ6dk9e3KnTw9HnKD4\niStHiV0KalFiVxXBErvUhJXYpSZQYpeW6BK7hEWU2CUsusQuYREldgmLLrFLWLDELjVhJXZp\niSixS1j8ErsEBEvs0hJRYpc8SuwAAADqDoEdAACAIQjsAAAADEFgBwAAYAgCOwAAAEMQ2AEA\nABiCwA4AAMAQBHYAAACGILADAAAwBIEdAACAIQjsAAAADMG7YlPgfVdstVxyySW1WO0syMmJ\nkpQZOTlRkjIjJydKUmbk5ERJyoycnChJmSEnoeRkphY54V2xAAAAdYHADgAAwBAEdgAAAIag\njZ0hrr322ldffTXtXCglKSdKUmbk5ERJyoycnChJmZGTEyUpM3JyoiRlhpyEkpOZ5HNCiR0A\nAIAhCOwAAAAMQWAHAABgCAI7AAAAQ9B5AgAAwBCU2AEAABiCwA4AAMAQBHYAUtbS0hJ/FgAQ\ngcAOAADAEAR2AAAAhiCwAwAAdcfUZh4EdgAAzAbNQ4WLOAUtLS29vb1JZiYxBHYAAMBAvb29\nobGdwVGdIrADAACm8sV2LS0tZkd1Sql5aWcA9cj4+wrlog5rTvDeue454l5GUOgtnNalomM7\n9/9U8pAkAjsAKauHR60BfFFd6DSgSl8SKV4qEqI6b7Bb05xQFQtANErvJIj4UizVjAn1Seyl\nku7W9WFx1TQnBHYAUiaq5xoxCmCqOvkRQlUsgJSVqiVJpepEQpWNcBwfL5qHSlaqS6w7beSV\nTGAHIH2+cEo/edNtjpNiBjAjId04uEKEq88TRGCHmuBnK8olqueazoCEnAgRcV5SqS4X0o2D\nKwQCEdihJnjYYRaERHWu0BY5crKXsNCjkfxPuBnb5tftCUKoiIpXU68WAjsAgoj6bpaTEyGC\nR4PjgyA5NTa+Wzj18t2I2SpmhsAOtVW7axemkhDb0cZuTkj9OkGQ/DOSyt2d5OYI7FAroTcP\n35cIktZzjXAhKKLkIzhbV6JLp+r2sIhVD99BBHaoodCKGzml9BBC1EO2nmOUOUFUNw4l7OrF\njNI6X0lenAR2qAkaOJdi/BBKcx0nRT4h3TgQasYTUZ+3WJJffAR2QHKowIomvEVmPVTizBV0\n4xCrTnqezkJiA2QS2AFIn+QWmSmOfwvAJMkMkElgB9QvUfXCAltkupElpQ7ShF4YNLBDUGKD\njMRX6wEyCexQE9IaOCNITr2wtBaZFNEJJ+rZUofj384hMo8/JXaYw4KXLw2cIRxfxqUIedu9\nqJ8Bosa/RZC0s0AbO8xtbmOC4EJALG8tCZeri0MRn5C2oZCGXrEwBE83H4ENPuDjLXRRnBSl\nlLySD7G4ZmYciaY+Dw7j2AFmqs8n2ozEtsj0ljoT2SAOLhKOQCheKQZUE29DmhPEtsikAA9z\nC484rzp85xuBnVGib+Akb28GHy/F134r3QFH5NQLz4kWmdLyAwQFn/NpdS0X0kdYyG2b5Hci\ngZ1R5FRpCbmlpfF1mlPnH6h0z5EEcrIkZJg0UeSUfAgpykUpoY+yOh8PMsnvRAI70wRfWkL9\nkUypj76LUoT8OpJGyL4LyYZLTrG3EKLGo6lPBHYG8r60hLsIEUTVCwsh52uJ9gzycQogEIGd\nsYjqEE1UvTCCOP6hRPWFEnib1Pp1VXNLfe44gZ2xKLFDfOnWC1M0BVQR94tP8EesMvooEdgZ\nyFv6EmxyV5+EvA0JobhK5ePUICY5ffiCG62Td74R2JkmtK976PJaZyN6Sd12/yTEDOVr5Cfq\nlEEJqwBFhFKPFAnDnSSZgVLZcKXeZLZ234kEdkaRcxHzlA/FYYlWV9UlM6KGek6QMwpMqS0m\nH3bPiWEpE8abJzBL0ZdOnd9XmEPSHaxHSDEqNdRzgvyzk1Zja2lHpn7KlQnsjCKtukTO4OPe\nTac+qIeclrxi64VTPCyiHv3UUANmSPJHGoEdakXU4OO+jabYflZOS16BUQIRTCghPwPkEPuD\nBErYkPhyenJ4f6TVersEdqgJOa39RGVGTk6kEfVlkHqZbinp1lALUZ97HV/qb8NLMoKJI3Qs\np7R+DCRTBk9gB8Av4Yey+5iT0KEv9QYMESixk0bgiRCSJVGtCELrjlLJiW/rNXrSEtih7gh5\n8ImKGLS0nsLSjoM0Qr4dqQANFVG+K/AeTxhlzNFqVLpJYAfg3JOFryJR5HwdSsiDQBHlu6kP\nHeojoYwq+etZzh0UihI7zCVymqyKIu2wCCkK0uR0FhZCVA21HMIjGJVSMCFqPISgtAIsaQ3+\nNNrYoTyiqkuEDD4uKpyS05JXwuPeJaezsBzSdtz3bZRWFxPhw/ulnrfgLZNiSbyQX2hyGvzR\nKxZlE/WkCz79VXo5DA2nVEr5EdKS13tMUm+8RWdh4YLlqSmWCcn5ng4SlZkUpR7gBqXb4I9x\n7GAOOTe2nJzIQdPmUNHF3qk0nEq3kMyn1M+k5LOhJ2RGeHVL/sMklfrZJA8IgZ2BJLRVopQl\nlNjD4n3SpZvJ1A+RnBMkqpBMMn6feIWG3cmXp0qWVoldYu0gCexMQ1ulsiT/o03yieALUiwh\nhWQyUWLnI6plhZyeHPVznRDYGYW2SjGleIcLb/qtpdKhREjvFswVQr6n5VTcoxT5j9zqIrBD\nfZEwYJtb71k/D5oZyeks7G5aVLM2eMn5npaQh6Bg00yZ+UyAnEslSQR2xkr9Zo7+Vk6lR1Ly\n242QelMYaeOBCeksrAL3Du0ZNCFDKTG8X7Tgb5J6rq6pz70msEOtyLmjZD7UUs+VwGMiAe0Z\nQsnZazk5iVafZUXSiG3wV1MEdkahrVIoOQO2aTzxgyJqPOv50hVSSIb4RD1qUJ8I7Ewjra2S\nEHL6e0oLUySM2xzxMzr1w5XucHFpbbosyd9TMhs+Smi/C8kS+51GYGcgOW2VBEp3wDZpT3zJ\n5buph+CIJmSMzNSvVWlFdN7f9imeo4jZ+sQAxZjzhDzjSkmrAE/UYZHcmIyoTjKKplwyj0Dd\nFnJDI7BDbQkf1SmV/Eh4NYhw6VaASi7ITBHXapC09ruQLLGWxAR2qJXQQhdKYng1iHyhDVUV\n120d734EOe135aAvVFCSLYkJ7FBDoa396rm9heTaT3hxInwomppRuu135ZDWF0pyg78a/Rgg\nsENNEMEAhqFoKg6OUqi0jobk41+7Y0JgB6SD6NaLF27OIakXTc2Jq0VINiQgxg1VuwNCYAfU\nLyG1EqKe+NLetCYWXctVvb7YoFxCxqMJ5sTUE0RgByRHVI9LI59oleOwlIsjBrGkNfhLBoEd\nakJUBCMKrwYBKuTrxiHzRRQQy/iqYQI71FAwhiOCUbwaJCDiqkjryIReuvV8muTUUAeHgaT2\nE/GlGNUl1jaUwA61Evwxreo+gkGoiKsirbb5pUbqqdsLWOaO1/nwSWJJ7t2S1tZ5pRjMIfP7\nAHNF8uEUI/UAleAGSR2BHWqC7z/APLyQA5i1xBqDEtgBAGZGd6hQkl9skBa6swQlORQOgR0A\nYAbUUIeqz72OJm0wP8kN/mqEwA6AXKkM70fRlHAUkiGm+rxhCexQK9FP2/q83xBqrgx3kkpO\n4MOjA4hGYIda4fmLmKRdKozUg5jkDO+HUuqwwR+BHQCEqJPvAFSCUayFk9bgLxkEdgBE4GUP\nAAzGmycA1BFe9iAfrQwRUx12RJ0Rb57AnFefty5mh6E05OMUICYuldRl0s4AAAAAqoPADgAA\nwBBUxQIAMBvBdoe0J5OmDhv8WY7jpJ0HAPWOlz0AQFVQFQtAhBkLPwAAM6LEDoAU9VBLAgA1\nRWAHAABgCKpiAQAADEFgBwAAYAgCOwAAAEMQ2AEAABiCwA4AAMAQBHYAEItVWuUr7+/vZ9w+\nAJVjuBMAiCUigKv8QapXzgMZQIV4VywAlIHYC4BkVMUCQNVMTEx0d3fr+tnu7u6JiQnvpyMj\nIwcOHNCftrS0HD58WC93ywK9E74CQu8SPT02NtbS0tLe3h5n0/l8vqWlxbKsrVu39vf3V3u/\nAYjhAABiiPPMzGaz3gdsW1ub+9Hg4GDwCdzT0+OcXwRYalvBT3O5nFKqq6trxk339PT4ttvX\n11fx8QAgESV2AFCGiJ4T+Xw+n8/rWM1xnJ6ens7OTrd4rLOzUyl14sQJ/eno6KhSav369cpT\nveuUU8+7ZMkSx3E2b94846b1VsbHxx3HGR4eVko98sgjFR8JABIR2AFAdRw5ckQptW7dOj2r\nJ06ePKlnDx065DjOFVdcMTQ0lM/nu7u7K9zc6tWrY25aF+Y99dRTQ0NDixcvdhynt7e3wq0D\nkIlesQAQbhnhaAAACs1JREFUy4wdV0t1m3X/pL29vaOjI/RT38qD2/IuKfVpqU0PDQ21t7fn\n83mlVFtb20MPPbRgwYLSOwpgDiOwA4BYKgzsuru7t2zZ0tbWdvvtt1988cUf+tCHPvjBD6pE\nAjttbGxs3759nZ2d2Wx2//79ixcvjrPXAOYWAjsAiGXGwG7r1q2dnZ2lEvj+fGJi4gMf+ICK\nF9gVCoWIKHDGTXv19/evWbMmekcAzF20sQOA6mhublZKuYOYDAwMWJblDkeijYyMKKUmJib2\n798fsSrdKm5gYEAnPnjwYCWb1gOd6E0vWrTIXT8A81BiBwCxzFhiNzExsXHjRt2UzTU6OtrY\n2KiUOnz4sO6d6uMthMtms7pbgy9xb2+vfuFYqRK7cjfd29tLbAcYiRI7AKiO+fPnP/bYY11d\nXXo2l8sNDw/r0EoptW7dOt9H3r/t6+vzzq5bt66np0fHXnGCsBk37a5Nx45EdYCpKLEDAAAw\nBCV2AAAAhiCwAwAAMASBHQAAgCEI7AAAAAxBYAcAAGAIAjsAAABDENgBAAAYgsAOAADAEAR2\nAAAAhiCwAwAAMASBHQAAgCEI7AAAAAxBYAcAAGAIAjsAAABDENgBAAAYgsAOAADAEAR2AAAA\nhiCwAwAAMASBHQAAgCEI7AAAAAxBYAcAAGAIAjsAAABDENgBAAAYgsAOAADAEAR2AAAAhiCw\nAwAAMASBHQAAgCEI7AAAAAxBYAcAAGCIeWlnAAAQ4nd29r7fsi7MWO/LWBdmrAss64KMNS9j\nXZDJzMtY8yxrXoPVkLH0dEPGashk5mWshozVYFlTExmrocFqyGQarOnZ4D/Laste9fizI5mM\nNS9jZTwfZTxpGhoyweW+xPMaMpnzVz49mzk33WAp21Z20f//pD09XVS2rYq2Mzn1qWPrj2xn\nOrFj22qy6BT1hO0Ui8q2nUmdwHZs27GLyrbff9fOXx182PEscWzbsSenlhSL09NFx7Yn7UnP\nEluv3CnaTnFy0rYni0WnOOkUbec39mTRdoqTzm/syf+wnfcmnffsyX+3r/31m2lfL8AUSuwA\nAAAMQWAHAABgCAI7AAAAQxDYAQAAGILADgDEed+OpxLbVveR4cS2pZzkNvXrR7+R3MYAMQjs\nAAAADEFgBwAAYAgCOwAAAEMQ2AEAABiCwA4AAMAQBHYAAACGILADAAAwBIEdAACAIQjsAAAA\nDEFgBwAAYAgCOwAAAEMQ2AEAABiCwA4AAMAQBHYAAACGILADAAAwBIEdAACAIQjsgDrS39/f\n3t5uWZZlWe3t7QMDA0luXW83Tsr+/v6WlpZZ/GFZWlpaDhw40N/fXygUfB8VCoX+/v4DBw54\nsxHBl2EASIvlOE7aeQBQc4VCobW1NZ/P+5bncrm9e/cmkwcdnMV55vhSxv/DWeRHKdXV1bV5\n82bvR93d3Vu2bNHTs8hwVfzOzt73W9aFGet9GevCjHWBZV2QseZlrAsymXkZa55lzWuwGjKW\nnm7IWA2ZzLyM1ZCxGixraiJjNTRYDZlMgzU9G/xnWW3Zqx5/diSTseZlrIzno4wnTUNDJrjc\nl3heQyZz/sqnZzPnphssZdvKLvr/n7Snp4vKtlXRdianPnVs/ZHtTCd2bFtNFp2inrCdYlHZ\ntjOpE9iObTt2Udn2++/a+auDDzueJY5tO/bk1JJicXq66Nj2pD3pWWLrlTtF2ylOTtr2ZLHo\nFCedou38xp4s2k5x0vmNPfkftvPepPOePfnv9rW/frOKpx6oBCV2QF3QUV1XV9f4+LjjOI7j\nDA4OZrPZjo6O/v7+tHM3A53hGq28ra0tGO/m8/m2trYabREAaofADjDfwMBAPp/fv3//5s2b\nFyxYoBc2NTXpsrpHHnnETVkoFLq7u3XVZ3d3t7eOUi8cGxtraWlpb28PXaKUmpiY8K5hYmKi\nVK5GRkYOHDigU7a0tBw+fNjdUHDCWxU7YyYLhYJes3e1paxduzafz4+MjHgzls/n165d60tZ\nateCGY4+DqHHDQCqgsAOMN+Pf/xjpVQ2m/Utb2pqGh0d7e3t1bMTExOtra1uFeSWLVtaW1t9\nkVl3d3c+n29sbCy1ZOPGjd417Nq1KzRLQ0NDV1555c6dO/VsPp9fv379jEFYzEy2trbqNcdZ\n7ZVXXqmUGh4edpfoab3cK+auxUwcPJIAUDkCO8B8OspZvHhx8CNvYPHMM8/k8/lcLqerPnO5\nXD6ff+aZZ7zplyxZ4jiOt0Wad0k+n8/n8z09PXoNPT09nZ2doVW9nZ2dSqkTJ07olKOjo0qp\n9evXK09LtdDq1ziZbGpqOnv2rOM4fX19Sqknn3wy4uAsXrw4m80eOXLEXaKnfYcrYteCGY5z\nHIJHEgAqR2AHYMqxY8eUUtu2bdOzekIvdK1evdr3V94lOiRat26dntUTJ0+eDG7r0KFDjuNc\nccUVQ0ND+Xy+u7u7ipnctm3b/Pnz3bwFm9D5ZLPZzs5OXaVbKBQ6Ozu7urp8aeLvWszEwSPp\n9b4dT0XnuYq6jwzPnKhaEuyt9+tHv5HcxgAx6BULmC9mn81gMu+S6E+9S4JC19De3t7R0REn\nZfxsxMlk8KOhoaFly5b19fWtXr26v79/zZo1J06cuOGGG4JrjrlrZSUGgCqixA4w3/79+5VS\n3v4BXqWW11R3d3dHR0dbW1tfX9/g4OD4+HjyeXBdfvnlSqkXX3zR/f+qq65KMT8AMGsEdoD5\nli9frsJqJEdGRlpaWtx6TD3Ah9vJVE+UNeqHTuwEBFPqjgWHDh1avXp1U1PThRdeWNYmKslk\n0Pz583O5XEdHx8TEREdHRy6X0zW5we3G2bVyEwNAFRHYAea74YYbstnszp07vYODDA0N7dy5\nM5/P33zzzXpJc3OzUurgwYN6Vk/ohTHpxG4v1IGBAf2Ki1LpdWHhxMSELlOMv4lKMhnqU5/6\nlFLqscceU0pdd911pbYbc9fKPQ4AUDXB35QAzDM+Ph5arOX23HQc5+zZs74hUbLZrO5e6ng6\nfrqCS4JrUEqNjo4G0/f09EQ8kdytB/+w8kyGfuStCw7NcJxdczMc/zgAQHXxcAHqyODgYFdX\nl445crmcO9qIa3x83O0Q6n1NhRM7ZvKuIZfLDQ8Pl0rvS+b9VA9TEhrYVSWToR/pw+JuNHq7\nvl3zZbis4wAAVUSvWAAAAEPQxg4AAMAQBHYAAACGILADAAAwBIEdAACAIealnQEAgFJKWVZU\nbzbva8oq6fQWZz2+V6LNYnPlbkX+HvnWlsCZAmaHwA4A0lfq9bLup94QITqwqMp6Koy0ZtzK\n3Noj3xarkh+gRqiKBYCU8fU/V3CmIB+BHQCkTFSsYF7sUsU9MuzIwEhUxQIAzmNeKzHz9ggo\nhcAOAHAe81qJmbdHQClUxQIAzjEv6DFvj4AIlNgBQHKSrBOk/hGoQwR2AJCcJAOsqgwgYgDz\n9giIQFUsACCceSGReXsE+HCJA4AIwZjDu6TW72mo7raS2Ury2wquudbbAspFYAcAAGAIqmIB\nAAAMQWAHAABgCAI7AAAAQxDYAQAAGILADgAAwBAEdgAAAIYgsAMAADAEgR0AAIAhCOwAAAAM\nQWAHAABgCAI7AAAAQxDYAQAAGILADgAAwBAEdgAAAIYgsAMAADAEgR0AAIAhCOwAAAAMQWAH\nAABgCAI7AAAAQxDYAQAAGILADgAAwBD/H7pY3P10Kn8+AAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot_correlation(na.omit(df_heart))"
]
},
{
"cell_type": "markdown",
"id": "c6acee62",
"metadata": {},
"source": [
"Split data into training and testing data sets."
]
},
{
"cell_type": "code",
"execution_count": 19,
"id": "6db10752",
"metadata": {
"name": "Split data",
"tags": [
"remove_output"
]
},
"outputs": [],
"source": [
"# Create a random sample of row IDs\n",
"sample_rows <- sample(nrow(df_heart),0.75*nrow(df_heart))\n",
"# Create the training dataset\n",
"df_heart_train <- df_heart[sample_rows,]\n",
"# Create the test dataset\n",
"df_heart_test <- df_heart[-sample_rows,]"
]
},
{
"cell_type": "markdown",
"id": "4deaa64e",
"metadata": {},
"source": [
"Fit a simple GLM using all data:"
]
},
{
"cell_type": "code",
"execution_count": 20,
"id": "adce718a",
"metadata": {
"name": "Heart glm"
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = PREVCHD ~ ., family = \"binomial\", data = df_heart_train)\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-1.3274 -0.4061 -0.2666 -0.1721 3.0678 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error z value Pr(>|z|) \n",
"(Intercept) -7.771752 1.252690 -6.204 5.50e-10 ***\n",
"SEX -1.163457 0.179755 -6.472 9.64e-11 ***\n",
"TOTCHOL 0.002251 0.001766 1.274 0.20250 \n",
"AGE 0.086854 0.011635 7.465 8.34e-14 ***\n",
"SYSBP 0.010511 0.005092 2.064 0.03900 * \n",
"DIABP -0.014227 0.009529 -1.493 0.13544 \n",
"CURSMOKE 0.340968 0.255911 1.332 0.18274 \n",
"CIGPDAY -0.006939 0.010363 -0.670 0.50315 \n",
"BMI 0.053302 0.020091 2.653 0.00798 ** \n",
"DIABETES 0.392274 0.291334 1.346 0.17815 \n",
"BPMEDS 0.531433 0.222946 2.384 0.01714 * \n",
"HEARTRTE -0.013636 0.006523 -2.090 0.03659 * \n",
"educ 0.099809 0.076119 1.311 0.18978 \n",
"PREVSTRK 0.218284 0.490566 0.445 0.65635 \n",
"PREVHYP 0.374206 0.221446 1.690 0.09106 . \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"(Dispersion parameter for binomial family taken to be 1)\n",
"\n",
" Null deviance: 1366.6 on 2678 degrees of freedom\n",
"Residual deviance: 1174.0 on 2664 degrees of freedom\n",
"AIC: 1204\n",
"\n",
"Number of Fisher Scoring iterations: 6\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"full_model_glm <- glm(PREVCHD~.,data=df_heart_train, family = \"binomial\")\n",
"summary(full_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "c85c4a84",
"metadata": {},
"source": [
"Use stepwise regression to reduce the explanatory variables:"
]
},
{
"cell_type": "code",
"execution_count": 21,
"id": "67239a8f",
"metadata": {
"message": false,
"name": "Heart stepwise regression",
"tags": [
"remove_output"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Start: AIC=1368.59\n",
"PREVCHD ~ 1\n",
"\n",
" Df Deviance AIC\n",
"+ AGE 1 1257.1 1261.1\n",
"+ SYSBP 1 1325.2 1329.2\n",
"+ PREVHYP 1 1327.7 1331.7\n",
"+ SEX 1 1337.6 1341.6\n",
"+ BPMEDS 1 1345.2 1349.2\n",
"+ BMI 1 1354.7 1358.7\n",
"+ DIABETES 1 1355.7 1359.7\n",
"+ DIABP 1 1361.9 1365.9\n",
"+ HEARTRTE 1 1362.1 1366.1\n",
"+ PREVSTRK 1 1363.0 1367.0\n",
"+ CIGPDAY 1 1363.7 1367.7\n",
" 1366.6 1368.6\n",
"+ TOTCHOL 1 1364.8 1368.8\n",
"+ CURSMOKE 1 1364.9 1368.9\n",
"+ educ 1 1365.6 1369.6\n",
"\n",
"Step: AIC=1261.14\n",
"PREVCHD ~ AGE\n",
"\n",
" Df Deviance AIC\n",
"+ SEX 1 1217.7 1223.7\n",
"+ PREVHYP 1 1246.1 1252.1\n",
"+ SYSBP 1 1248.2 1254.2\n",
"+ BMI 1 1248.4 1254.4\n",
"+ BPMEDS 1 1249.1 1255.1\n",
"+ HEARTRTE 1 1252.0 1258.0\n",
"+ DIABETES 1 1252.8 1258.8\n",
"+ DIABP 1 1253.6 1259.6\n",
" 1257.1 1261.1\n",
"+ CURSMOKE 1 1255.2 1261.2\n",
"+ CIGPDAY 1 1255.6 1261.6\n",
"+ PREVSTRK 1 1255.9 1261.9\n",
"+ educ 1 1256.7 1262.7\n",
"+ TOTCHOL 1 1257.1 1263.1\n",
"\n",
"Step: AIC=1223.74\n",
"PREVCHD ~ AGE + SEX\n",
"\n",
" Df Deviance AIC\n",
"+ SYSBP 1 1202.3 1210.3\n",
"+ PREVHYP 1 1203.6 1211.6\n",
"+ BPMEDS 1 1204.5 1212.5\n",
"+ BMI 1 1207.8 1215.8\n",
"+ DIABP 1 1213.4 1221.4\n",
"+ DIABETES 1 1214.0 1222.0\n",
"+ HEARTRTE 1 1215.3 1223.3\n",
"+ TOTCHOL 1 1215.6 1223.6\n",
" 1217.7 1223.7\n",
"+ PREVSTRK 1 1216.4 1224.4\n",
"+ educ 1 1217.3 1225.3\n",
"+ CURSMOKE 1 1217.6 1225.6\n",
"+ CIGPDAY 1 1217.7 1225.7\n",
"\n",
"Step: AIC=1210.28\n",
"PREVCHD ~ AGE + SEX + SYSBP\n",
"\n",
" Df Deviance AIC\n",
"+ BPMEDS 1 1195.5 1205.5\n",
"+ BMI 1 1196.7 1206.7\n",
"+ HEARTRTE 1 1198.0 1208.0\n",
"+ PREVHYP 1 1198.8 1208.8\n",
"+ DIABETES 1 1199.7 1209.7\n",
" 1202.3 1210.3\n",
"+ TOTCHOL 1 1200.9 1210.9\n",
"+ DIABP 1 1201.4 1211.4\n",
"+ educ 1 1201.5 1211.5\n",
"+ PREVSTRK 1 1201.6 1211.6\n",
"+ CURSMOKE 1 1202.0 1212.0\n",
"+ CIGPDAY 1 1202.2 1212.2\n",
"\n",
"Step: AIC=1205.54\n",
"PREVCHD ~ AGE + SEX + SYSBP + BPMEDS\n",
"\n",
" Df Deviance AIC\n",
"+ BMI 1 1190.0 1202.0\n",
"+ HEARTRTE 1 1191.5 1203.5\n",
"+ DIABETES 1 1193.1 1205.1\n",
"+ PREVHYP 1 1193.2 1205.2\n",
" 1195.5 1205.5\n",
"+ TOTCHOL 1 1194.2 1206.2\n",
"+ DIABP 1 1194.2 1206.2\n",
"+ educ 1 1194.7 1206.7\n",
"+ CURSMOKE 1 1195.1 1207.1\n",
"+ PREVSTRK 1 1195.4 1207.4\n",
"+ CIGPDAY 1 1195.5 1207.5\n",
"\n",
"Step: AIC=1201.97\n",
"PREVCHD ~ AGE + SEX + SYSBP + BPMEDS + BMI\n",
"\n",
" Df Deviance AIC\n",
"+ HEARTRTE 1 1185.6 1199.6\n",
"+ DIABP 1 1187.8 1201.8\n",
" 1190.0 1202.0\n",
"+ educ 1 1188.3 1202.3\n",
"+ DIABETES 1 1188.3 1202.3\n",
"+ PREVHYP 1 1188.4 1202.4\n",
"+ TOTCHOL 1 1188.5 1202.5\n",
"+ CURSMOKE 1 1188.9 1202.9\n",
"+ PREVSTRK 1 1189.9 1203.9\n",
"+ CIGPDAY 1 1190.0 1204.0\n",
"\n",
"Step: AIC=1199.6\n",
"PREVCHD ~ AGE + SEX + SYSBP + BPMEDS + BMI + HEARTRTE\n",
"\n",
" Df Deviance AIC\n",
"+ PREVHYP 1 1183.5 1199.5\n",
"+ DIABETES 1 1183.5 1199.5\n",
" 1185.6 1199.6\n",
"+ CURSMOKE 1 1184.0 1200.0\n",
"+ DIABP 1 1184.1 1200.1\n",
"+ TOTCHOL 1 1184.1 1200.1\n",
"+ educ 1 1184.2 1200.2\n",
"+ CIGPDAY 1 1185.4 1201.4\n",
"+ PREVSTRK 1 1185.5 1201.5\n",
"\n",
"Step: AIC=1199.51\n",
"PREVCHD ~ AGE + SEX + SYSBP + BPMEDS + BMI + HEARTRTE + PREVHYP\n",
"\n",
" Df Deviance AIC\n",
"+ DIABP 1 1181.3 1199.3\n",
"+ DIABETES 1 1181.3 1199.3\n",
" 1183.5 1199.5\n",
"+ CURSMOKE 1 1181.8 1199.8\n",
"+ TOTCHOL 1 1182.1 1200.1\n",
"+ educ 1 1182.1 1200.1\n",
"+ CIGPDAY 1 1183.3 1201.3\n",
"+ PREVSTRK 1 1183.4 1201.4\n",
"\n",
"Step: AIC=1199.28\n",
"PREVCHD ~ AGE + SEX + SYSBP + BPMEDS + BMI + HEARTRTE + PREVHYP + \n",
" DIABP\n",
"\n",
" Df Deviance AIC\n",
" 1181.3 1199.3\n",
"+ DIABETES 1 1179.5 1199.5\n",
"+ educ 1 1179.5 1199.5\n",
"+ TOTCHOL 1 1179.7 1199.7\n",
"+ CURSMOKE 1 1179.8 1199.8\n",
"+ CIGPDAY 1 1181.1 1201.1\n",
"+ PREVSTRK 1 1181.2 1201.2\n"
]
}
],
"source": [
"# specify a null model with no predictors\n",
"null_model_glm <- glm(PREVCHD ~ 1, data = df_heart_train, family = \"binomial\")\n",
"# use a forward stepwise algorithm to build a parsimonious model\n",
"step_model_glm <- step(null_model_glm, scope = list(lower = null_model_glm, upper = full_model_glm), direction = \"forward\")"
]
},
{
"cell_type": "markdown",
"id": "c79bd620",
"metadata": {},
"source": [
"Summary of the model:"
]
},
{
"cell_type": "code",
"execution_count": 22,
"id": "2a1068eb",
"metadata": {
"name": "Heart stepwise regression - summary"
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = PREVCHD ~ AGE + SEX + SYSBP + BPMEDS + BMI + HEARTRTE + \n",
" PREVHYP + DIABP, family = \"binomial\", data = df_heart_train)\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-1.2381 -0.4063 -0.2700 -0.1729 3.0992 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error z value Pr(>|z|) \n",
"(Intercept) -6.776549 1.106023 -6.127 8.96e-10 ***\n",
"AGE 0.084172 0.011073 7.601 2.93e-14 ***\n",
"SEX -1.134134 0.170509 -6.651 2.90e-11 ***\n",
"SYSBP 0.011127 0.005026 2.214 0.0268 * \n",
"BPMEDS 0.538117 0.218937 2.458 0.0140 * \n",
"BMI 0.047248 0.019361 2.440 0.0147 * \n",
"HEARTRTE -0.012867 0.006413 -2.006 0.0448 * \n",
"PREVHYP 0.367789 0.220910 1.665 0.0959 . \n",
"DIABP -0.014075 0.009425 -1.493 0.1353 \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"(Dispersion parameter for binomial family taken to be 1)\n",
"\n",
" Null deviance: 1366.6 on 2678 degrees of freedom\n",
"Residual deviance: 1181.3 on 2670 degrees of freedom\n",
"AIC: 1199.3\n",
"\n",
"Number of Fisher Scoring iterations: 6\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(step_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "c66c5fb5",
"metadata": {},
"source": [
"Dropping BPMEDS, HEARTRTE and BMI as little impact on AIC:"
]
},
{
"cell_type": "code",
"execution_count": 23,
"id": "549b53ff",
"metadata": {
"name": "Heart final regression - summary",
"tags": []
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = PREVCHD ~ AGE + SEX + PREVHYP + DIABETES + TOTCHOL, \n",
" family = \"binomial\", data = df_heart_train)\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-1.1702 -0.4182 -0.2772 -0.1830 3.0145 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error z value Pr(>|z|) \n",
"(Intercept) -7.371509 0.734203 -10.040 < 2e-16 ***\n",
"AGE 0.091994 0.010190 9.028 < 2e-16 ***\n",
"SEX -1.084013 0.168352 -6.439 1.2e-10 ***\n",
"PREVHYP 0.622003 0.176473 3.525 0.000424 ***\n",
"DIABETES 0.543020 0.282690 1.921 0.054744 . \n",
"TOTCHOL 0.002377 0.001755 1.354 0.175643 \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"(Dispersion parameter for binomial family taken to be 1)\n",
"\n",
" Null deviance: 1366.6 on 2678 degrees of freedom\n",
"Residual deviance: 1198.5 on 2673 degrees of freedom\n",
"AIC: 1210.5\n",
"\n",
"Number of Fisher Scoring iterations: 6\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"final_model_glm <- glm(PREVCHD ~ AGE + SEX + PREVHYP + DIABETES + TOTCHOL, family = \"binomial\",data = df_heart_train)\n",
"summary(final_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "ba864202",
"metadata": {},
"source": [
"Fit a Bayes glm using the same explanatory variables. Here parameter estimates no longer have test statistics and p-values as in the frequentist regression. This is because Bayesian estimation samples from the posterior distribution. This means that instead of a point estimate and a test statistic, we get a distribution of plausible values for the parameters, and the estimates section of the summary summarizes those distributions.\n",
"\n",
"Further documentation on Bayesian generalised linear models via Stan [is here](https://mc-stan.org/rstanarm/reference/stan_glm.html). Documentation on choice of priors [is here](http://mc-stan.org/rstanarm/articles/priors.html). If priors are not specified, default weekly informative priors are used - you can call a summary of the modeled priors (see below). Default priors are autoscaled to make them less informative (see below for notes on scaling)."
]
},
{
"cell_type": "code",
"execution_count": 24,
"id": "c4678d8e",
"metadata": {},
"outputs": [],
"source": [
"not_run_sample_only <- function(){model_bayes_glm_heart <- stan_glm(PREVCHD ~ AGE + SEX + PREVHYP + DIABETES + TOTCHOL, family = \"binomial\",data=df_heart_train, iter=2000, warmup=500)}\n",
"# chains is number of sample paths from posterior; iter is number of samples within a chain; warmup is number of iterations to discard"
]
},
{
"cell_type": "markdown",
"id": "a252a238",
"metadata": {},
"source": [
"A summary of the model below. \"Sigma\" is the standard deviation of the errors; \"mean_PPD\" is the mean of the posterior predictive samples.MCMC diagnostics - \"RHat\" is a measure of within chain variance compared to across chain variance (<1.1 implies convergence); \"log-posterior\" is similar to likelihood."
]
},
{
"cell_type": "code",
"execution_count": 25,
"id": "e0aa0efc",
"metadata": {
"name": "Heart rstanarm glm - summary"
},
"outputs": [],
"source": [
"not_run_sample_only <- function(){print(summary(model_bayes_glm),digits=4)}"
]
},
{
"cell_type": "markdown",
"id": "067f59d9",
"metadata": {},
"source": [
"The stan model used default normal priors for intercepts and coefficients. Default priors are automatically scaled to limit how informative they are - below we can see the adjusted (scaled) prior for the coefficients differs from the default 2.5:"
]
},
{
"cell_type": "code",
"execution_count": 26,
"id": "8dd6a518",
"metadata": {
"name": "Heart rstanarm glm - priors"
},
"outputs": [],
"source": [
"# summary of priors\n",
"not_run_sample_only <- function(){print(prior_summary(model_bayes_glm),digits=4)}"
]
},
{
"cell_type": "markdown",
"id": "a1986024",
"metadata": {},
"source": [
"Credible intervals express the probability that a parameter falls within a given range (vs a confidence interval which is the probability that a range contains the true value of the parameter). These credible intervals are computed by finding the relevant quantiles of the draws from the posterior distribution. They produce similar ranges to the confidence intervals from the frequentist approach."
]
},
{
"cell_type": "code",
"execution_count": 27,
"id": "6b743fe0",
"metadata": {
"name": "Heart rstanarm glm - cred"
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Waiting for profiling to be done...\n",
"\n"
]
},
{
"data": {
"text/html": [
"\n",
" | 2.5 % | 97.5 % |
\n",
"\n",
"\t(Intercept) | -8.83403551 | -5.95320077 |
\n",
"\tAGE | 0.07229529 | 0.11228084 |
\n",
"\tSEX | -1.41856263 | -0.75773533 |
\n",
"\tPREVHYP | 0.28161591 | 0.97470859 |
\n",
"\tDIABETES | -0.03837607 | 1.07525870 |
\n",
"\tTOTCHOL | -0.00110349 | 0.00577671 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|ll}\n",
" & 2.5 \\% & 97.5 \\%\\\\\n",
"\\hline\n",
"\t(Intercept) & -8.83403551 & -5.95320077\\\\\n",
"\tAGE & 0.07229529 & 0.11228084\\\\\n",
"\tSEX & -1.41856263 & -0.75773533\\\\\n",
"\tPREVHYP & 0.28161591 & 0.97470859\\\\\n",
"\tDIABETES & -0.03837607 & 1.07525870\\\\\n",
"\tTOTCHOL & -0.00110349 & 0.00577671\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | 2.5 % | 97.5 % |\n",
"|---|---|---|\n",
"| (Intercept) | -8.83403551 | -5.95320077 |\n",
"| AGE | 0.07229529 | 0.11228084 |\n",
"| SEX | -1.41856263 | -0.75773533 |\n",
"| PREVHYP | 0.28161591 | 0.97470859 |\n",
"| DIABETES | -0.03837607 | 1.07525870 |\n",
"| TOTCHOL | -0.00110349 | 0.00577671 |\n",
"\n"
],
"text/plain": [
" 2.5 % 97.5 % \n",
"(Intercept) -8.83403551 -5.95320077\n",
"AGE 0.07229529 0.11228084\n",
"SEX -1.41856263 -0.75773533\n",
"PREVHYP 0.28161591 0.97470859\n",
"DIABETES -0.03837607 1.07525870\n",
"TOTCHOL -0.00110349 0.00577671"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"confint(final_model_glm, level=0.95)\n",
"not_run_sample_only <- function(){posterior_interval(model_bayes_glm, prob=0.95)}"
]
},
{
"cell_type": "markdown",
"id": "75f3ad32",
"metadata": {},
"source": [
"### Adjusting scales and changing priors\n",
"\n",
"stan_glm allows a selection of prior distributions for the coefficients, intercept, and auxiliary parameters. The prior distributions can be altered by specifying different locations/scales/dfs, but all the prior take the form of a single chosen probability distribution. \n",
"\n",
"Some drivers for wanting to specify a prior:\n",
"* Available information/ research might suggest a base value for our parameters. Particularly valuable if our own observed data is sparse.\n",
"* We may not have a good idea of the value, but know that it is constrained in some way e.g. is positive.\n",
"\n",
"The scale is the standard deviation of the prior. As noted earlier, the model autoscales to ensure priors are not too informative. We can turn this off when we specify our own priors. Documentation on choice of priors [is here](http://mc-stan.org/rstanarm/articles/priors.html).\n",
"\n",
"To allow for varying distributions across the priors, we need to define the model in STAN or JAGS. See the linear regression example below for an example of this in JAGS.\n",
"\n",
"Specifying our own priors below. Little impact on the posterior estimates."
]
},
{
"cell_type": "code",
"execution_count": 28,
"id": "7c1dc098",
"metadata": {
"message": false,
"name": "Heart rstanarm glm - adj"
},
"outputs": [],
"source": [
"not_run_sample_only <- function(){model_bayes_glm_scale <- stan_glm(PREVCHD ~ AGE + SEX + PREVHYP + DIABETES + TOTCHOL, family = \"binomial\",data=df_heart_train, iter=2000, warmup=500,\n",
" prior_intercept = normal(location = 0, scale = 10, autoscale = FALSE),\n",
" prior = normal(location = 0, scale = 5, autoscale = FALSE),\n",
" prior_aux = exponential(rate = 1, autoscale = FALSE)\n",
" )\n",
"print(summary(model_bayes_glm_scale),digits=4)}"
]
},
{
"cell_type": "markdown",
"id": "7f12f84c",
"metadata": {},
"source": [
"### Model fit\n",
"\n",
"We are able to extract predictions from each iteration of the posterior sampling. We can extract predictions for new data. Could be tested against the observations for goodness of fit. The follwing from the [rstanarm manual, p43](https://cran.r-project.org/web/packages/rstanarm/rstanarm.pdf):\n",
"\n",
">\"The posterior predictive distribution (posterior_predict) is the distribution of the outcome implied by the model after using the observed data to update our beliefs about the unknown parameters in the model. Simulating data from the posterior predictive distribution using the observed predictors is useful for checking the fit of the model. Drawing from the posterior predictive distribution at interesting values of the predictors also lets us visualize how a manipulation of a predictor affects (a function of)the outcome(s). With new observations of predictor variables we can use the posterior predictive distribution to generate predicted outcomes.\" "
]
},
{
"cell_type": "code",
"execution_count": 29,
"id": "02ef18ab",
"metadata": {
"name": "Heart rstanarm glm - posteriors"
},
"outputs": [],
"source": [
"not_run_sample_only <- function(){posteriors <- posterior_predict(model_bayes_glm,newdata=df_heart_test)\n",
"posterior <- as.data.frame(posteriors) # each column is a data point from the dataset and each row is a prediction\n",
"# Print 10 predictions for 5 lives\n",
"print(\"10 predictions for 5 lives\")\n",
"posteriors[1:10, 1:5]}"
]
},
{
"cell_type": "markdown",
"id": "e774ed70",
"metadata": {},
"source": [
"We can plot the posterior distributions for the model parameters from the samples:"
]
},
{
"cell_type": "code",
"execution_count": 30,
"id": "dd0622b2",
"metadata": {
"name": "Heart rstanarm glm - plot posteriors"
},
"outputs": [],
"source": [
"not_run_sample_only <- function(){posterior <- as.matrix(model_bayes_glm)\n",
"\n",
"plot1<- mcmc_areas(posterior, pars = c(\"AGE\"), prob = 0.80)\n",
"plot2<- mcmc_areas(posterior, pars = c(\"SEX\"), prob = 0.80)\n",
"plot3<- mcmc_areas(posterior, pars = c(\"PREVHYP\"), prob = 0.80)\n",
"plot4<- mcmc_areas(posterior, pars = c(\"DIABETES\"), prob = 0.80)\n",
"plot5<- mcmc_areas(posterior, pars = c(\"TOTCHOL\"), prob = 0.80)\n",
"\n",
"grid.arrange(plot1,plot2, plot3, plot4, plot5, top=\"Posterior distributions (median + 80% intervals)\")}"
]
},
{
"cell_type": "markdown",
"id": "ab7a2025",
"metadata": {},
"source": [
"We can extract the $R^2$ from the posterior distribution and plot:"
]
},
{
"cell_type": "code",
"execution_count": 31,
"id": "ad8f4bd9",
"metadata": {
"name": "Heart rstanarm glm - r2"
},
"outputs": [],
"source": [
"not_run_sample_only <- function(){r2_posterior <- bayes_R2(model_bayes_glm)\n",
"summary(r2_posterior)\n",
"hist(r2_posterior)} #expect normal"
]
},
{
"cell_type": "markdown",
"id": "9b8fb6ef",
"metadata": {},
"source": [
"Posterior predictive checks can be extracted using \"pp_check\"\n",
"\n",
"* \"dens_overlay\" - each light blue line represents the distribution of predicted scores from a single replication, and the dark blue line represents the observed data. If the model fits, the dark blue line should align closely with the light blue lines.\n",
"* \"stat\" in the \"pp_check\" function, we can get a distribution of the mean of the dependent variable from all replications. These are the light blue bars: the means from each replication plotted as a histogram. The mean from the observed data is then plotted on top as a dark blue bar. \n",
"\n",
"Here the outcome is binary so the density overlay outcomes are concentrated at one or zero."
]
},
{
"cell_type": "code",
"execution_count": 32,
"id": "9e899a42",
"metadata": {
"name": "Heart rstanarm glm - prediction"
},
"outputs": [],
"source": [
"not_run_sample_only <- function(){pp_check(model_bayes_glm, \"stat\")\n",
"pp_check(model_bayes_glm, \"dens_overlay\")}"
]
},
{
"cell_type": "markdown",
"id": "0b348804",
"metadata": {},
"source": [
"Further considerations: The [loo package](https://mc-stan.org/users/interfaces/loo) provides \"efficient approximate leave-one-out cross-validation (LOO), approximate standard errors for estimated predictive errors (including comparisons), and the widely applicable information criterion (WAIC).The loo package can be used to estimate predictive error of any MCMC item-level log likelihood output\".\n",
"\n",
"## Regression - linear\n",
"\n",
"The above example looked at a binary response. In this example we'll look at predicting a continuous variable using data on my household electricity consumption over 2016-2021. The above example used stan_glm in RSTANARM. Here we will use a model defined in RJAGS with additional flexibility around the choice of priors, which is also possible in a paramaterised model for STAN. RJAGS combines the power of R with the \"Just Another Gibbs Sampler\" or \"JAGS\" engine. To get started, first download the \"JAGS\" program, then set up the packages as above.\n",
"\n",
"Both JAGS and STAN allow for the parameterisation of a range of different models. The example below was chosen for comparison with a conventional GLM approach.\n",
"\n",
"Data prep:\n",
"\n",
"* Daily electricity usage for a household in Sydney over 2019-21. Rows represent half hourly readings/ estimates.\n",
"* Data are grouped into daily usage.\n",
"* Also includes are temperatures, sunlight and rainfall data for the area taken from BOM.\n",
"* Calculated fields for weekdays vs weekends, seasons and a post-covid working from home indicator.\n"
]
},
{
"cell_type": "code",
"execution_count": 33,
"id": "5387102b",
"metadata": {
"name": "Elec data"
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"Date | Usage | MaxTemp | MinTemp | Rain_mm | Solar_Exposure | Season | Covid_Ind | Weekend |
\n",
"\n",
"\t2019-12-21 | 21.064 | 26.7 | 21.0 | 0.0 | 27.1 | Summer | 0 | 1 |
\n",
"\t2019-12-22 | 9.529 | 19.9 | 18.6 | 0.0 | 11.9 | Summer | 0 | 1 |
\n",
"\t2019-12-23 | 15.739 | 22.1 | 17.2 | 0.0 | 14.4 | Summer | 0 | 0 |
\n",
"\t2019-12-24 | 18.652 | 24.0 | 18.6 | 1.8 | 18.3 | Summer | 0 | 0 |
\n",
"\t2019-12-25 | 18.924 | 23.2 | 21.6 | 0.2 | 27.8 | Summer | 0 | 0 |
\n",
"\t2019-12-26 | 14.584 | 23.6 | 21.4 | 0.0 | 30.8 | Summer | 0 | 0 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lllllllll}\n",
" Date & Usage & MaxTemp & MinTemp & Rain\\_mm & Solar\\_Exposure & Season & Covid\\_Ind & Weekend\\\\\n",
"\\hline\n",
"\t 2019-12-21 & 21.064 & 26.7 & 21.0 & 0.0 & 27.1 & Summer & 0 & 1 \\\\\n",
"\t 2019-12-22 & 9.529 & 19.9 & 18.6 & 0.0 & 11.9 & Summer & 0 & 1 \\\\\n",
"\t 2019-12-23 & 15.739 & 22.1 & 17.2 & 0.0 & 14.4 & Summer & 0 & 0 \\\\\n",
"\t 2019-12-24 & 18.652 & 24.0 & 18.6 & 1.8 & 18.3 & Summer & 0 & 0 \\\\\n",
"\t 2019-12-25 & 18.924 & 23.2 & 21.6 & 0.2 & 27.8 & Summer & 0 & 0 \\\\\n",
"\t 2019-12-26 & 14.584 & 23.6 & 21.4 & 0.0 & 30.8 & Summer & 0 & 0 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| Date | Usage | MaxTemp | MinTemp | Rain_mm | Solar_Exposure | Season | Covid_Ind | Weekend |\n",
"|---|---|---|---|---|---|---|---|---|\n",
"| 2019-12-21 | 21.064 | 26.7 | 21.0 | 0.0 | 27.1 | Summer | 0 | 1 |\n",
"| 2019-12-22 | 9.529 | 19.9 | 18.6 | 0.0 | 11.9 | Summer | 0 | 1 |\n",
"| 2019-12-23 | 15.739 | 22.1 | 17.2 | 0.0 | 14.4 | Summer | 0 | 0 |\n",
"| 2019-12-24 | 18.652 | 24.0 | 18.6 | 1.8 | 18.3 | Summer | 0 | 0 |\n",
"| 2019-12-25 | 18.924 | 23.2 | 21.6 | 0.2 | 27.8 | Summer | 0 | 0 |\n",
"| 2019-12-26 | 14.584 | 23.6 | 21.4 | 0.0 | 30.8 | Summer | 0 | 0 |\n",
"\n"
],
"text/plain": [
" Date Usage MaxTemp MinTemp Rain_mm Solar_Exposure Season Covid_Ind\n",
"1 2019-12-21 21.064 26.7 21.0 0.0 27.1 Summer 0 \n",
"2 2019-12-22 9.529 19.9 18.6 0.0 11.9 Summer 0 \n",
"3 2019-12-23 15.739 22.1 17.2 0.0 14.4 Summer 0 \n",
"4 2019-12-24 18.652 24.0 18.6 1.8 18.3 Summer 0 \n",
"5 2019-12-25 18.924 23.2 21.6 0.2 27.8 Summer 0 \n",
"6 2019-12-26 14.584 23.6 21.4 0.0 30.8 Summer 0 \n",
" Weekend\n",
"1 1 \n",
"2 1 \n",
"3 0 \n",
"4 0 \n",
"5 0 \n",
"6 0 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df_usage <- read.csv(file = '../_static/bayesian_applications/elec_usage.csv')\n",
"df_usage <- df_usage %>% mutate(Date = as.Date(Date, format=\"%Y-%m-%d\"), EndDate = parse_date_time(EndDate, '%Y-%m-%d %H:%M:%S'), StartDate = parse_date_time(StartDate, '%Y-%m-%d %H:%M:%S'))\n",
"df_usage <- df_usage[c(-2,-3,-4,-6)] %>% # drop start and end dates, rate type, duration\n",
"group_by(Date) %>% summarise(Usage = sum(Usage), MaxTemp = max(MaxTemp), MinTemp = min(MinTemp), Rain_mm = max(Rain_mm), Solar_Exposure = max(Solar_Exposure)) %>%\n",
"# Add in fields to identify seasons, weekend/ weekday and an indicator for the post-covid/ work from home period\n",
"mutate(Season=\n",
" if_else(month(Date)>= 3 & month(Date) < 6,\"Autumn\", \n",
" if_else(month(Date)>= 6 & month(Date) < 9,\"Winter\", \n",
" if_else(month(Date)>= 9 & month(Date) < 12,\"Spring\",\"Summer\"))),\n",
"Covid_Ind=if_else(Date>= \"2020-03-15\",1,0),\n",
"Weekend=\n",
" if_else(wday(Date)==7 | wday(Date)==1,1,0))\n",
"\n",
"df_usage$Season <- factor(df_usage$Season, levels = c(\"Summer\",\"Autumn\",\"Winter\",\"Spring\")) # change season levels\n",
"\n",
"head(df_usage)"
]
},
{
"cell_type": "markdown",
"id": "3b777963",
"metadata": {},
"source": [
"Data is mostly complete:"
]
},
{
"cell_type": "code",
"execution_count": 34,
"id": "b973bc81",
"metadata": {
"name": "Usage explore 1"
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"rows | columns | discrete_columns | continuous_columns | all_missing_columns | total_missing_values | complete_rows | total_observations | memory_usage |
\n",
"\n",
"\t732 | 9 | 2 | 7 | 0 | 23 | 709 | 6588 | 53464 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lllllllll}\n",
" rows & columns & discrete\\_columns & continuous\\_columns & all\\_missing\\_columns & total\\_missing\\_values & complete\\_rows & total\\_observations & memory\\_usage\\\\\n",
"\\hline\n",
"\t 732 & 9 & 2 & 7 & 0 & 23 & 709 & 6588 & 53464\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| rows | columns | discrete_columns | continuous_columns | all_missing_columns | total_missing_values | complete_rows | total_observations | memory_usage |\n",
"|---|---|---|---|---|---|---|---|---|\n",
"| 732 | 9 | 2 | 7 | 0 | 23 | 709 | 6588 | 53464 |\n",
"\n"
],
"text/plain": [
" rows columns discrete_columns continuous_columns all_missing_columns\n",
"1 732 9 2 7 0 \n",
" total_missing_values complete_rows total_observations memory_usage\n",
"1 23 709 6588 53464 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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UAkGAoiBUAkGAoiBUAkGAoiBUAkGAoi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\n+6qASPsw1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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
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Dgm4LDgKqBDQ1/ai/1PHqxppxyKdKP5YvG1L9Bs9RHNxgckioSjzmHB1bva03Yl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\nqh4A4BxQ9QAA58D/B8wU4adQ0yc8AAAAAElFTkSuQmCC",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"introduce(df_usage)\n",
"plot_intro(df_usage)\n",
"plot_missing(df_usage)"
]
},
{
"cell_type": "markdown",
"id": "7f216c0e",
"metadata": {},
"source": [
"Drop records with NAs as they are few, also only include non-zero usage, review explanatory variables; Gamma dist potentially a better fit than normal for Usage given the skewness in the tail; alternatively use normal with a log link."
]
},
{
"cell_type": "code",
"execution_count": 35,
"id": "623056ec",
"metadata": {
"message": false,
"name": "Usage explore 2",
"warning": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"1 columns ignored with more than 50 categories.\n",
"Date: 707 categories\n",
"\n",
"\n"
]
},
{
"data": {
"image/png": 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uYBaYEACfOAtECAhHlAWiBAwjwgLRAg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\ngNS4EJAWPu7KzwlIjQsBaeHjrvycgNS4EJAWPu7KzwlIjQtvCRJ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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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XrzvAPZkkiiMyRESgmQeNSHSAKPjiKS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",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
"text/plain": [
"Fitting of the distribution ' gamma ' by matching moments \n",
"Parameters : \n",
" estimate\n",
"shape 2.9114935\n",
"rate 0.1164095\n",
"Loglikelihood: -2813.89 AIC: 5631.78 BIC: 5640.902 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"image/png": 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KSxoKBIZS+HQaQsVSCSO6KgSIUvh2lapH5u0uyPiEsDx0hHRSp9Fr9lkTq6SbM/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\niGSCPEIkaJRGHpMy06h2YwCiaWNEChuOQhbCiARVaEKkYI8QCRq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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
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Org7fCc1zE2bVSg5PHcIpL70+6jTpf0lfn9+ng7P+sdd511uAk0l+tlPv3iFGB+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\nBEAkAAiASAAQ8D/0U/rQ68ICagAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"P-P plot\""
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"df_usage <- na.omit(df_usage)\n",
"df_usage <- df_usage %>% filter(Usage>0)\n",
"\n",
"plot_bar(df_usage, title=\"Barplot\")\n",
"plot_histogram(df_usage, title=\"Histogram for continuous\")\n",
"\n",
"qq_data <- df_usage[,c(\"MaxTemp\", \"MinTemp\", \"Solar_Exposure\", \"Usage\")]\n",
"plot_qq(qq_data, title=\"QQ plot\")\n",
"log_qq_data <- update_columns(qq_data, 2:4, function(x) log(x + 1))\n",
"plot_qq(log_qq_data, title=\"QQ plot, logged data\")\n",
"\n",
"usage_fit_gamma <- fitdist(df_usage$Usage, distr = \"gamma\", method = \"mme\")\n",
"summary(usage_fit_gamma)\n",
"plot(usage_fit_gamma)"
]
},
{
"cell_type": "markdown",
"id": "72ba76fd",
"metadata": {},
"source": [
"Usage correlated with season, max/min temp and covid wfh indicator. Max and Min Temps are not surprisingly highly correlated with one another, with the seasons and with solar exposure."
]
},
{
"cell_type": "code",
"execution_count": 36,
"id": "9cd71a99",
"metadata": {
"message": false,
"name": "Usage explore 3",
"warning": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"1 features with more than 20 categories ignored!\n",
"Date: 707 categories\n",
"\n",
"\n"
]
},
{
"data": {
"image/png": 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n+P7BUzcC0b1gew78w57ahoD3VzES9FIzjsF0ukrSg18RqAhm+2ES+bte0CQN/V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Qjx0hhBBCiIWgwo4QQgghxEJQYUcIIYQQ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\nAFBcXFz7nXd4jTdv3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LXm0C+n70ibC3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\nAAAASUVORK5CYII=",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"plot_correlation(na.omit(df_usage))"
]
},
{
"cell_type": "markdown",
"id": "556df649",
"metadata": {},
"source": [
"Split data into training and testing data sets:"
]
},
{
"cell_type": "code",
"execution_count": 37,
"id": "5500b858",
"metadata": {
"name": "Split data - usage",
"tags": [
"remove_output"
]
},
"outputs": [],
"source": [
"# Create a random sample of row IDs\n",
"sample_rows <- sample(nrow(df_usage),0.75*nrow(df_usage))\n",
"# Create the training dataset\n",
"df_usage_train <- df_usage[sample_rows,]\n",
"# Create the test dataset\n",
"df_usage_test <- df_usage[-sample_rows,]"
]
},
{
"cell_type": "markdown",
"id": "1bbcb8e7",
"metadata": {},
"source": [
"Fit a simple GLM using all variables:"
]
},
{
"cell_type": "code",
"execution_count": 38,
"id": "6162df3b",
"metadata": {
"name": "Usage glm"
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = Usage ~ ., family = gaussian(link = \"log\"), data = df_usage_train[-1])\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-46.096 -4.220 0.013 4.539 50.118 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 5.398e+00 2.017e-01 26.766 < 2e-16 ***\n",
"MaxTemp -2.440e-02 8.537e-03 -2.858 0.00444 ** \n",
"MinTemp -9.728e-02 9.487e-03 -10.254 < 2e-16 ***\n",
"Rain_mm -2.596e-06 1.343e-03 -0.002 0.99846 \n",
"Solar_Exposure -1.989e-02 3.765e-03 -5.283 1.87e-07 ***\n",
"SeasonAutumn 7.897e-02 8.573e-02 0.921 0.35740 \n",
"SeasonWinter 4.277e-02 9.590e-02 0.446 0.65579 \n",
"SeasonSpring 8.101e-02 8.540e-02 0.949 0.34326 \n",
"Covid_Ind -2.651e-02 1.103e-01 -0.240 0.81007 \n",
"Weekend -4.936e-02 3.338e-02 -1.479 0.13983 \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"(Dispersion parameter for gaussian family taken to be 86.41346)\n",
"\n",
" Null deviance: 118331 on 529 degrees of freedom\n",
"Residual deviance: 44933 on 520 degrees of freedom\n",
"AIC: 3879.3\n",
"\n",
"Number of Fisher Scoring iterations: 8\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"full_model_glm <- glm(Usage~.,data=df_usage_train[-1], gaussian(link=\"log\"))\n",
"summary(full_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "be0bf55d",
"metadata": {},
"source": [
"Use stepwise regression to reduce the explanatory variables:"
]
},
{
"cell_type": "code",
"execution_count": 39,
"id": "266e57b3",
"metadata": {
"message": false,
"name": "Usage stepwise regression",
"tags": [
"remove_output"
]
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Start: AIC=4374.51\n",
"Usage ~ 1\n",
"\n",
" Df Deviance AIC\n",
"+ MinTemp 1 50908 3929.5\n",
"+ MaxTemp 1 62836 4041.0\n",
"+ Season 3 68921 4094.0\n",
"+ Solar_Exposure 1 103729 4306.7\n",
"+ Covid_Ind 1 110444 4339.9\n",
" 118331 4374.5\n",
"+ Rain_mm 1 117996 4375.0\n",
"+ Weekend 1 118331 4376.5\n",
"\n",
"Step: AIC=3929.47\n",
"Usage ~ MinTemp\n",
"\n",
" Df Deviance AIC\n",
"+ Solar_Exposure 1 46018 3877.9\n",
"+ MaxTemp 1 48534 3906.2\n",
"+ Rain_mm 1 50478 3927.0\n",
" 50908 3929.5\n",
"+ Season 3 50372 3929.9\n",
"+ Weekend 1 50785 3930.2\n",
"+ Covid_Ind 1 50893 3931.3\n",
"\n",
"Step: AIC=3877.94\n",
"Usage ~ MinTemp + Solar_Exposure\n",
"\n",
" Df Deviance AIC\n",
"+ MaxTemp 1 45300 3871.6\n",
"+ Weekend 1 45829 3877.8\n",
" 46018 3877.9\n",
"+ Rain_mm 1 46010 3879.9\n",
"+ Covid_Ind 1 46014 3879.9\n",
"+ Season 3 45804 3881.5\n",
"\n",
"Step: AIC=3871.61\n",
"Usage ~ MinTemp + Solar_Exposure + MaxTemp\n",
"\n",
" Df Deviance AIC\n",
"+ Weekend 1 45101 3871.3\n",
" 45300 3871.6\n",
"+ Covid_Ind 1 45298 3873.6\n",
"+ Rain_mm 1 45300 3873.6\n",
"+ Season 3 45131 3875.6\n",
"\n",
"Step: AIC=3871.28\n",
"Usage ~ MinTemp + Solar_Exposure + MaxTemp + Weekend\n",
"\n",
" Df Deviance AIC\n",
" 45101 3871.3\n",
"+ Covid_Ind 1 45100 3873.3\n",
"+ Rain_mm 1 45101 3873.3\n",
"+ Season 3 44938 3875.4\n"
]
}
],
"source": [
"# specify a null model with no predictors\n",
"null_model_glm <- glm(Usage ~ 1, data = df_usage_train, gaussian(link=\"log\"))\n",
"# use a forward stepwise algorithm to build a parsimonious model\n",
"step_model_glm <- step(null_model_glm, scope = list(lower = null_model_glm, upper = full_model_glm), direction = \"forward\")"
]
},
{
"cell_type": "markdown",
"id": "e3a95db9",
"metadata": {},
"source": [
"Summary of the model:"
]
},
{
"cell_type": "code",
"execution_count": 40,
"id": "fe19d99f",
"metadata": {
"name": "Usage stepwise regression - summary"
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = Usage ~ MinTemp + Solar_Exposure + MaxTemp + Weekend, \n",
" family = gaussian(link = \"log\"), data = df_usage_train)\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-46.465 -4.196 0.078 4.629 49.779 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 5.396219 0.096133 56.133 < 2e-16 ***\n",
"MinTemp -0.095761 0.007011 -13.659 < 2e-16 ***\n",
"Solar_Exposure -0.019246 0.003249 -5.923 5.73e-09 ***\n",
"MaxTemp -0.024253 0.008169 -2.969 0.00313 ** \n",
"Weekend -0.049882 0.033198 -1.503 0.13355 \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"(Dispersion parameter for gaussian family taken to be 85.9083)\n",
"\n",
" Null deviance: 118331 on 529 degrees of freedom\n",
"Residual deviance: 45101 on 525 degrees of freedom\n",
"AIC: 3871.3\n",
"\n",
"Number of Fisher Scoring iterations: 7\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"summary(step_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "ac61f5a7",
"metadata": {},
"source": [
"For simplicity, we'll assume a model defined by MaxTemp and MinTemp only, noting the significant correlation with other explanatory variables."
]
},
{
"cell_type": "code",
"execution_count": 41,
"id": "a5be9b3e",
"metadata": {
"name": "Usage final regression - gamma"
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = PREVCHD ~ AGE + SEX + PREVHYP + DIABETES + TOTCHOL, \n",
" family = \"binomial\", data = df_heart_train)\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-1.1702 -0.4182 -0.2772 -0.1830 3.0145 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error z value Pr(>|z|) \n",
"(Intercept) -7.371509 0.734203 -10.040 < 2e-16 ***\n",
"AGE 0.091994 0.010190 9.028 < 2e-16 ***\n",
"SEX -1.084013 0.168352 -6.439 1.2e-10 ***\n",
"PREVHYP 0.622003 0.176473 3.525 0.000424 ***\n",
"DIABETES 0.543020 0.282690 1.921 0.054744 . \n",
"TOTCHOL 0.002377 0.001755 1.354 0.175643 \n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"(Dispersion parameter for binomial family taken to be 1)\n",
"\n",
" Null deviance: 1366.6 on 2678 degrees of freedom\n",
"Residual deviance: 1198.5 on 2673 degrees of freedom\n",
"AIC: 1210.5\n",
"\n",
"Number of Fisher Scoring iterations: 6\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"gamma_model_glm <- glm(Usage ~ MaxTemp + MinTemp, family = Gamma(link=\"inverse\"), data = df_usage_train)\n",
"summary(final_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "adf84d4c",
"metadata": {},
"source": [
"Changing the family to gaussian with log link (later graph shows little change in predictions, although AIC is higher). Select gaussian for ease of comparison with the Bayes model."
]
},
{
"cell_type": "code",
"execution_count": 42,
"id": "2aeffae8",
"metadata": {
"name": "Usage final regression - gaussian"
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Call:\n",
"glm(formula = Usage ~ MaxTemp + MinTemp, family = gaussian(link = \"log\"), \n",
" data = df_usage_train)\n",
"\n",
"Deviance Residuals: \n",
" Min 1Q Median 3Q Max \n",
"-51.898 -4.306 -0.382 5.030 48.100 \n",
"\n",
"Coefficients:\n",
" Estimate Std. Error t value Pr(>|t|) \n",
"(Intercept) 5.414631 0.099962 54.167 < 2e-16 ***\n",
"MaxTemp -0.041520 0.007992 -5.195 2.93e-07 ***\n",
"MinTemp -0.092090 0.007316 -12.587 < 2e-16 ***\n",
"---\n",
"Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1\n",
"\n",
"(Dispersion parameter for gaussian family taken to be 92.09666)\n",
"\n",
" Null deviance: 118331 on 529 degrees of freedom\n",
"Residual deviance: 48534 on 527 degrees of freedom\n",
"AIC: 3906.2\n",
"\n",
"Number of Fisher Scoring iterations: 6\n"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"final_model_glm <- glm(Usage ~ MaxTemp + MinTemp, family = gaussian(link=\"log\"), data = df_usage_train)\n",
"summary(final_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "ba85fbc2",
"metadata": {},
"source": [
"Extract coefficients:"
]
},
{
"cell_type": "code",
"execution_count": 43,
"id": "f21683ab",
"metadata": {
"name": "Usage final regression - coeff"
},
"outputs": [
{
"data": {
"text/html": [
"\n",
" | coef(final_model_glm) |
\n",
"\n",
"\t(Intercept) | 5.41463097 |
\n",
"\tMaxTemp | -0.04152022 |
\n",
"\tMinTemp | -0.09209007 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|l}\n",
" & coef(final\\_model\\_glm)\\\\\n",
"\\hline\n",
"\t(Intercept) & 5.41463097\\\\\n",
"\tMaxTemp & -0.04152022\\\\\n",
"\tMinTemp & -0.09209007\\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| | coef(final_model_glm) |\n",
"|---|---|\n",
"| (Intercept) | 5.41463097 |\n",
"| MaxTemp | -0.04152022 |\n",
"| MinTemp | -0.09209007 |\n",
"\n"
],
"text/plain": [
" coef(final_model_glm)\n",
"(Intercept) 5.41463097 \n",
"MaxTemp -0.04152022 \n",
"MinTemp -0.09209007 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"final_model_glm_coeff <- as.data.frame(coef(final_model_glm))\n",
"final_model_glm_coeff"
]
},
{
"cell_type": "markdown",
"id": "b5b564cd",
"metadata": {},
"source": [
"Project the result for a dummy record showing the link:"
]
},
{
"cell_type": "code",
"execution_count": 44,
"id": "96f9804b",
"metadata": {
"name": "Usage final regression - sample proj"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"[1] \"Dummy prediction with min of 10 and max of 20:\"\n"
]
},
{
"data": {
"text/html": [
"1: 38.9908026539508"
],
"text/latex": [
"\\textbf{1:} 38.9908026539508"
],
"text/markdown": [
"**1:** 38.9908026539508"
],
"text/plain": [
" 1 \n",
"38.9908 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"38.9908026539508"
],
"text/latex": [
"38.9908026539508"
],
"text/markdown": [
"38.9908026539508"
],
"text/plain": [
"[1] 38.9908"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"print(\"Dummy prediction with min of 10 and max of 20:\")\n",
"predict(final_model_glm, newdata= as.data.frame(cbind(MaxTemp=20,MinTemp=10)), # model and data\n",
" type=\"response\", # or terms for coefficients\n",
" se.fit = FALSE)\n",
"# replicate\n",
"exp(final_model_glm_coeff[1,] + final_model_glm_coeff[2,]*20+final_model_glm_coeff[3,]*10)\n"
]
},
{
"cell_type": "markdown",
"id": "8a37e974",
"metadata": {},
"source": [
"Adding the predictions to the test data:"
]
},
{
"cell_type": "code",
"execution_count": 45,
"id": "101ad33c",
"metadata": {
"name": "Usage GLM predictions"
},
"outputs": [],
"source": [
"# predictions, normal\n",
"pred_usage <- as.data.frame(\n",
" predict(final_model_glm, newdata= df_usage_test, # model and data\n",
" type=\"response\", # or terms for coefficients\n",
" se.fit = TRUE, # default is false\n",
" interval = \"confidence\", #default \"none\", also \"prediction\"\n",
" level = 0.95\n",
" )\n",
")\n",
"\n",
"# predictions, gamma\n",
"usage_pred_gamma <- \n",
" predict(gamma_model_glm, newdata= df_usage_test, # model and data\n",
" type=\"response\", # or terms for coefficients\n",
" se.fit = FALSE, # default is false\n",
" )\n",
"\n",
"# rename\n",
"pred_usage <- rename(pred_usage,usage_pred=fit,se_usage_pred=se.fit)\n",
"\n",
"# add back to data\n",
"df_usage_test_pred <- cbind(df_usage_test,pred_usage, usage_pred_gamma)"
]
},
{
"cell_type": "markdown",
"id": "93e87026",
"metadata": {},
"source": [
"Plotting the results shows a poorer fit for winter when the usage spikes and in instances with outlier temperatures. Predictions for the test data are not hugely different to the gamma family model."
]
},
{
"cell_type": "code",
"execution_count": 46,
"id": "5f66cc2f",
"metadata": {
"name": "Usage GLM predictions - graph"
},
"outputs": [
{
"data": {
"image/png": 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B7AKtCABKgHsAokGwQ4jlQ4UJORKgKR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\nPlIsf39/K6YOi7S2XLs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"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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K2Z9QYau/++RcpJ8jIWEoSqNSwsLCwXCTxJU6TddgtE0krg8ncwj/baL5at+s/i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\nNBWcfhcMAQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"df_usage_test_pred %>%\n",
"ggplot() +\n",
"geom_point(aes(x=Date,y=Usage,color=Season)) +\n",
"# add a modeled line\n",
"geom_line(aes(x=Date,y=usage_pred)) +\n",
"geom_line(aes(x=Date,y=usage_pred_gamma), linetype = \"dashed\") +\n",
"labs(x=\"Date\", y=\"Usage\", title = \"Actual vs predicted usage by date and season\",subtitle=\"Dashed=Gamma Pred; Solid=Normal Pred\") +\n",
"theme_pander() + scale_color_gdocs()\n",
"\n",
"# plot temperatures\n",
"df_usage_test_pred %>%\n",
"ggplot() +\n",
"geom_point(aes(x=Date,y=MaxTemp,color=Season)) + \n",
"labs(x=\"Date\", y=\"Usage\", title = \"MaxTemp by date and season\") +\n",
"theme_pander() + scale_color_gdocs()"
]
},
{
"cell_type": "markdown",
"id": "168cc43f",
"metadata": {},
"source": [
"Plots show slightly higher residuals at higher predicted values for the step regression model and final selected. QQ plot suggests skewness in the data, which we could see earlier in the histogram of usage. "
]
},
{
"cell_type": "code",
"execution_count": 47,
"id": "65de2d6b",
"metadata": {
"name": "Usage GLM evaluation - traditional plots linear reg"
},
"outputs": [
{
"data": {
"image/png": 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FYfNd9HAOlgMY4Gdu1ExD79hOxGwhrpYM138aJP1O8PpEX0HiA1SOkyIGqnpA5B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\ndZV3FbKpNR3d5mbnLZK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"text/plain": [
"Plot with title \"\""
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
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3k8elyQVle1IOXdBZC6yf9VqjWMbPifewNINxNA6ij/1Izw5up3FONG7WhVuP1g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\nBkju422H7ZBlAkgTaByQbhO121AbTACpvw5PvjFAutF9pB213LX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WncmvEbUT/ogjwLePzQ6XQtoxNtqcpngWr9VYNrXKG1t/fVoqASni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\nYQAAAABJRU5ErkJggg==",
"text/plain": [
"Plot with title \"\""
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"par(mfrow = c(2, 2))\n",
"plot(final_model_glm)\n",
"plot(step_model_glm)"
]
},
{
"cell_type": "markdown",
"id": "c185df98",
"metadata": {},
"source": [
"Define a regression model in RJAGS. The structure here is more flexible than stan_glm which is predefined. This allows for a wider selection of prior distributions and a mixture of modeling choices. Also possible to specify model forms in this way for STAN.\n",
"\n",
"$Y_i \\propto N(m_i,s^2)$\n",
"\n",
"Where \n",
"\n",
"* $m_i = a + bX_1i +cX_2i$ \n",
"* $a, b, c and s$ have some assumed prior distributions.\n",
"\n",
"Note that the distribution syntax is slightly different to R, for example in R a normal distribution is specified using the mean and standard deviation, but in JAGS the second parameter of the dnorm command is the distribution’s precision (1 / variance)."
]
},
{
"cell_type": "code",
"execution_count": 48,
"id": "4e3425aa",
"metadata": {
"message": false,
"name": "Usage rjags regression - define",
"tags": [
"remove_output"
]
},
"outputs": [],
"source": [
"usage_model <- \"model{\n",
" #Likelihood model for Y[i]\n",
" for (i in 1:length(Y)) {\n",
" Y[i] ~ dnorm(m[i], s^(-2)) # link=log\n",
" log(m[i]) <- a + b*X_1[i] + c*X_2[i]\n",
" }\n",
"\n",
" # Prior models for a, b, c, s\n",
" a ~ dnorm(0, 0.001) # Intercept\n",
" b ~ dnorm(0, 0.001) # MaxTemp\n",
" c ~ dnorm(0, 0.001) # MinTemp\n",
" s ~ dunif(0, 10) # Error\n",
"\n",
"}\""
]
},
{
"cell_type": "markdown",
"id": "f08b86ba",
"metadata": {},
"source": [
"Simulate from the model:\n",
"\n",
"* burn-in period of 2k iterations aims for convergence and throws away these earlier test samples.\n",
"* 10k iterations for 3 chains.\n",
"* saving every 10th sample only in order to save space."
]
},
{
"cell_type": "code",
"execution_count": 49,
"id": "4c8d978a",
"metadata": {
"message": false,
"name": "Usage rjags regression - simulate"
},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"Compiling model graph\n",
" Resolving undeclared variables\n",
" Allocating nodes\n",
"Graph information:\n",
" Observed stochastic nodes: 530\n",
" Unobserved stochastic nodes: 4\n",
" Total graph size: 3458\n",
"\n",
"Initializing model\n",
"\n"
]
}
],
"source": [
"usage_sim <- jags.model(textConnection(usage_model),\n",
" data=list(Y = df_usage_train$Usage, X_1 = df_usage_train$MaxTemp, X_2 = df_usage_train$MinTemp),\n",
"\t\t\t n.chains = 3)\n",
"\n",
"\n",
"usage_posterior <- coda.samples(usage_sim, \n",
" variable.names = c(\"a\",\"b\",\"c\",\"s\"), \n",
" n.iter = 10000, n.burnin = 2000, n.thin = 10, DIC = F)"
]
},
{
"cell_type": "markdown",
"id": "883780d3",
"metadata": {},
"source": [
"Summary of the results below:\n",
"\n",
"* The mean of the `b` chain value was -0.040. This is an *estimate* of the posterior mean of `b`. This is consistent with the GLM above\n",
"* The corresponding *naive standard error*, 0.000253, measures the potential *error* in this estimate. This error is calculated by dividing the standard deviation of the `b` chain values by the square root of the number of iterations (or sample size). This is a *naive* approach to calculating error in a setting with dependent samples.\n",
"\n",
"Also showing the density plots for the posteriors as well as the trace plots for each of the chains."
]
},
{
"cell_type": "code",
"execution_count": 50,
"id": "9be78550",
"metadata": {
"message": false,
"name": "Usage rjags regression - summary"
},
"outputs": [
{
"data": {
"text/plain": [
"\n",
"Iterations = 1001:11000\n",
"Thinning interval = 1 \n",
"Number of chains = 3 \n",
"Sample size per chain = 10000 \n",
"\n",
"1. Empirical mean and standard deviation for each variable,\n",
" plus standard error of the mean:\n",
"\n",
" Mean SD Naive SE Time-series SE\n",
"a 5.42368 0.107372 6.199e-04 0.0073562\n",
"b -0.04263 0.008776 5.067e-05 0.0009216\n",
"c -0.09124 0.007518 4.341e-05 0.0004607\n",
"s 9.55992 0.244700 1.413e-03 0.0018704\n",
"\n",
"2. Quantiles for each variable:\n",
"\n",
" 2.5% 25% 50% 75% 97.5%\n",
"a 5.21873 5.34977 5.42454 5.49497 5.63821\n",
"b -0.06033 -0.04832 -0.04240 -0.03661 -0.02634\n",
"c -0.10548 -0.09641 -0.09151 -0.08617 -0.07628\n",
"s 9.04907 9.39190 9.57360 9.74782 9.96562\n"
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
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KQorUCkYLH3srum3CLFaUWtp0CKqeM0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\nFCGFAAAAAElFTkSuQmCC",
"text/plain": [
"Plot with title \"Density of s\""
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
},
{
"data": {
"image/png": 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avhKYeQe44akIJFoivHSA1IPu1SqoJkhNoEyTry7SDis8nuTdVLPUqMZPnzTYsk\nmXfQzowNSGDRM9vHDbN1wsJAkvGy3ByhFoktJGyE+hBzb6PrgcS2nt2Hjc61qyDFGIkcJGmo\nBiRdWIBUYySNGFkduAoSdyDZiLgJEkfXrgyOnnPXzFwEyZqyLBAs3zzivCJa4l9du+uCRPIl\nBMqQjQeRJp0QIs2C6+10PsPjIGEFSR4T7o/Dk8YJMVI5QrRItAkSa/YdqceH0Z4cFj0ynVfc\nlmYPQTbWMZkDSBsVdbxK16hrpAgSHwGpziOpYSgVKMasZu1shg7t1iQEjCBZ60kLeIwkI2IL\nEtuTz9hAYk9emEVyRCRxQlRjJAcJzKDpfX0NSNeNkdyNkzSxgVQypSFwksEcWUHiaisEJGan\nkaUxIDgKofMrSBj8k5oUtbLEnFSb0Rifg/IYyS0SiPHDChLbFHIE6YIWydaZdDESeIxEzD6g\nNa5dqWtyi1I8OvYJhQKS5Fd9QhbEaZvGSBhMRSk5guRPPpOJrKlrR56t8Jbk4NqJRTKQJAtC\natJkm8vGSPJdkyiGIIAE0uH0ydC1SweLhDrrejuMjju6iqCsSQCpArMjlv5+RLoWTjqJHk1b\nn5CrRdK7CSnESDiARBEksnGu4M/1UoaKOl6li9TMUdhCKEuNBJBoG6Syp87TaPKhgoTqYoPN\ncfhrxj5G8jVUlnSTGEm8Mh05q2u3CxJVkLABCUeQpEg0iwQeI9H1QJI8ls6imGtHrMk3M85m\nkQpMBhL1IKEtdiipBTBrwg1I0SLV8JOi/XH63OMrQ6SBRA5S8Q906boZNgdJ2m8LJF04IyCh\nLhhkv5RJRR2v0jXqQEIDCXuQ0NJwbEOJgiQuobp2NmEmICmTNUZC/yI5neaRZz/bFA95j9YY\nCeXrYNiqz0BCAwnrIhJuQZJRm+YggR5Cm9BQlBDu2iABy2q1OUiSZ3DXLtxuMYBkMRJJihXC\n9F6paSJ7smlBkR2k6sBZ1kyPaUOTgiRbszaqxMv65A5JWKhFQoog8QwkDks5bRm7oXRJkFrX\nThM1oDFSXSOItijOyKMaI6F0YQVJ5/180Qcw+LBilcb2TT4OkhkUB4kqSDSAxFsgsWXt0EFi\nB8kfD9eCJOcmTUQbFfVqNROygBUkaECyXlunFiRskikNB6AchtnWgZN5tTFGknqFECNBRUh6\nCkWQNOVmUXMBSR9eXUHCCBJFkOy8KkgoIHHr2tVOWWZ+dYppWlHHq3SRRotkIJUlJEQ1Rgog\nmW+n25N8b43N6clwISChgITqcuhjotVL09HHv+DHY6To2gnCdotsB5L6ZhPXjnXtGOmk8cwi\nkcVIJCfIF6IAACAASURBVCvfK0jSFV9hkeS40/zGpGgHCUeQyqivz09gCxJ9cKQ+8O9Bqp6d\n+HY+j1SDLmZz7eyoASTLPQTXzkCixrVjt0i1LAWJO5C6ZIO0prSyxUix3i4Ckq7WkogHRpAo\ngMQ6QGkjaWpV/2YDSTbQelGLxGbuIkghUJEXNf2N+rUJlnAQ145jjFQtEsxiJJzESAR2xtqQ\nPhhqMZJCemrVh+PWH5ubiGSpIW+AxA1IbCbZsPCRH6PP5yBhde1sMFPJY4L8W2IDSIJecO2s\nLQwk+UA8vpK77107G4oVJNKAu7p20ovUixOQimvHF05/Sz8lsmUYESScJBvcIvm8qLgWxZ8z\nkEKMRAEkD0r8sTfsk+tyE6T5++oGNjGSgWQxEleLRNqHSEoiTdGH77VrQLJAwk/nB0CC/SLa\nGAnRXLuCDQtIYBaJ1LUzayHV04PE1kZubnSwaydBLUbiGCNJY5OCxD1IwpZkcVnz5NJOBSRN\nFDUgcWuRxPUAB6l17ST159VyQZBCjGQP7RtAwhojaV6HG5BQm9FAKjhWk1NA6mMkA5KxrjOw\nyXMFyVxDsBipgsR9jKRZpZLXAOxiJHKQ7OlpklRSkDC4dvSaGOkcSOggFVgKSCwWiWUeooIk\nZr0BCTZAavCRcqyxBSTp7Mw2Oeggja7dDCQ0kECfEVSzdgaSoKHtKYm5If2tnRJRY6Ty3ryi\nDtT6Ws1jJBuXS1wU55GklWzElvo0r87GdQyuHSqB7raxpmlGkCzWmVkkS8bKuiWE6mlvZO1q\ncr63SNRYJOsQ0IEkX4l2PYukFtVmaUDuS2J75EIxG8EiMdeRCbVbs3V8dpBYCTTXjq2emPUL\nkNBycg4SboHkbSHl2fgcQaIJSHKhqAk5tK8MLjZvBtKVVzbI5VKNkaiLkWTAMdfOyAMDaStG\nck5sRaVJs3ZmCisUHiOxPVOXyMyY5AeJ2xiJtNG5Dq8VJGpAYskiGvw6dRFA0kjxRSDBmcdK\nS8bGujxEkFBBCq4dV3ugt8KVX9EimQlqQAIFSebMFSR2kDimMBrXjucgqdtuIA0xkqaHWL+6\nr7SxPoBLQisDiQJI35o0fz5IMlDPXDvxcCtI3IDENo9EfYxkz8qtBsk7K5T1Q6yGgd0ikS3+\nRVv/V96SXWXdK9mMsMZI5I1Hmk+st1l2Fok1azcBifzmmJeBxKxd5lDWjg2kEiNByTwMyQbL\nfsuvFiTuQAIHSSpZCkRA8z4MJA4WiRAtSYNeR2qyjEbJrMaUFMoKmA4kbkDiEaTGIvE7uHZo\nSf8CkgT2BSSoIGmsYm2FdncJhnmIIUaqiyE9+lXjIiBZSiC6djq6yWS3dHqNoRqLFKwYB5Ak\nu1MX4fauHUB9IikISFI8SFYPXgrSPXUWSb6byLKUMk9eY6Q6OcHBa9ChhS2ZV45VdhdHq1gh\ne2wnyxPdtU65gkQBpCZGklPTFGgESfw4GelI7gSoIIk96y1SjZEqSDohIc+MBLV91wXJqkez\nJkhzkKyp2G/kK67TCBJ4erwRopkLIJ8XdZDUO0T7ennU+UQ229K6ds5RDxJPLZImG8CyEHK1\nHUh4bZAmrl0ESVvAQEJvAp2/cIvEESR7PrsUiApSsUjlHlibd2MPLN2Xa0GC2hYOEqnLQNDG\nSHK7WQOS3KoG9eu5SCf8Nd5zkCxG2qio41W6SHE6yxaMoMZIWvcDSKgNQRUkiZHKJ2NqFQwd\niZEaqnSJl0WkbpEqSGBmRaFAmTv1GMneZ7a7CTTCBVu7ZzGSMWrZD88IqUtX2suSIq8DCWwZ\n9uYG9aVZc7LkSgWpeK3V2WosklUy966d9GAFibdBgppsYJ04twy7g1Q2gDCoaUuwxci39KI+\nzknWJghI1IGE0SL1IOkis2qRNirqXp0f3vKBI6KuvpKHRUvn1xhJnYUQQpRqEF9ZGknTY2he\nQDU/GsbaI5rQxXWj2xG4B6mPkVQgd9maa6d5HzH9crhyMfVkzSI5SDgHqexD1ug+9f6squ8P\nfCTZoO4u25o5BwkCSDVG8uwzNyBxAxLZzUfVIkXXzkBS+6NV564HeqavxkgVLHft5iAxe9NZ\njKTRQAQJFSRNyb8BSNrx9Z4XrulvXaodHpM0gmQDn4z/IEvsSq3oL0vQSPCon4RF/yFOIr01\n0EAia8Uyp49QO42npVAmwhSkWYwkZyleKNkoXRqJ9HJRg2wCBQmnFfWsBjg0IavJN+uFvWtH\n4S7+ECMFkLiJkQgOgsQWEZG0vI0zqE6IhatQSY6uXTnhFiRdikkRJPV4uHHtAkhIbwESWm/2\nR5uDWSR37dBiJLS0ZGt/mC1pDRxAshV1rMA2IKFNQzlQApLESIDmn4vVk5ySzrGzJj8kaJqC\nZBZJ4iSyewtjjATBtdO+el2Q0LLYWyCJDCRCHQbrGq8QI+m7AhL0rh07SGCpBc801POJIIHF\nSNWFLwkDwhEkkuebcAMSKkhQQWJz7RqQJrV1EZDYRm9LNtQvzWlBUphitCNdnK0axP/SWLc+\nFkAddI9DWpDsg2rXih23GMnS3xLHsK5hsCyiOtp6MgqSxUjq2rHapxAjSbLVQAoZxtfNI90v\nIm5iZ1e/gK0HyRxSBUkdK4kauU02cA8SVZDsOys7kEii4g2QeAskPesbSLpgpJywZGJ1VBTX\nTraMIPkdHSyuvPgjFwapVLh+fRGEdYrgPFXXzjot2rO8ySbLPLGEemurPJK2Rq8OkqRg5CiT\nZEOjNkZykBBjjCQnouHWkCzclVkvnf0VkJoEwDViJNChKlqk8r4tFABbxuUgYQsSeYwkWzUg\ncXXt6iQH6FsytHkzhRjJfLwRJJ9Q1XeB/XmH7JPuBpI+Ik+WKkeQ7FEUZEmonwJpZ7cRJHXt\nJJIpZ6zTsMqT+1+sW1rMrj1QqqEFCWuP1/0OymKkh6STk2KRBMfi2qHPgkiQBduH+HbVH2md\nE1k7yXuCg4QOEthUtCPCDhJHkPSfb1WzdtUi2aAViy/DKlozGwTS7ZltgLyNwBakWRXKbITY\ntwYkRgcJ1FkTx2YTJAlxLw8S6EOYJWvSglR7szZ7A5IMOhY82Y0SQA1I9r7LLZJ26j7ZMIcL\n9GjFf6sxEtUYiSQn1bh2thYwPMioi5FkNLCHuEu26dtVv0IdSJIDkopuQOIpSGoriDyRpxZD\nDxnS3/bArToJEBRBUteuAwksRtLtHSSLkeRSbHjyiNqwEJCkI/UgscVIrCDNBp6ngQRBB46I\nCoWCVIYokmS4WSG5SrsprOQkokUykKS/azIWIJggthFNDY27dg4SRpA02aDLl49JXbsBJE2l\nWDJ2SDaQJSwRXxgjHVAEiRSkso5ebtaS9ytIc9eODSTcBIkCSDKLF9VMzE1Bkv5tAE5BKgVa\nskE70wwkWVAr22njlz3LRyVQeilItv0Ji0QaI0nFgD+ondkzzdrTZU2U9Dx37WpdSGfEdpfG\ntaO5RVLT0KS/LWMkuQJJKrG5LcUbsAzDntvoIJFNU+oBPQgEN4oScP2kRZoOgmKJwNyqBiSb\npN6IkdhBivNjYqo82SDfzaIVuw2SNICxdC9G4g2QBESBd7RIDUjGHP8QSHoyp0AKMZK6cvUb\nyGqn1OQcAnhuDyXZIO0bpFOhFaSSE6Q5SGwTswKSTZSSkqRPb9AwOIBJlron0kVMljAhNM/6\njH4CpANeg+QuK0i2Blq/KgRmIBE3IOmCYD+gOnwNSJpnbWT50QASNiCRxkjuW1aQaMsiVZBA\nQaIeJLwESPUM7x9RF7XJuEIOkT4zDatF0rjEQaKyCB+GrurzSLXmteMDwaZFGkAC9M8FzA4k\nVLetZhC4jZHQZmFL/pD8CYPszpzbIp1HqpfwnapfpRlI3IFkD3xqZ7+EHLRlQAZSg4hl7Vge\npiqZPV3OFRVBEh9rDhL69g5SWLlkZ8XeoC1IUkIASebASlPoqZd7Bl8PkmRKDh2xedqM9U4F\nidTvkvpFHegGhXmn6trp8p9CqoFU3gacxEgk35U+BUkCGq1+m+FFrhEP1kw76ENEHSS7ONSR\nUJOQml+ofqWf+xVjJAPJUsWDRepAkkFQk3Oa/h5ActcugsQDSN7glidoQdKEoh0dNfWtZYwg\nKTNTkGqMxBYj6T2FLHcx/gRI0wTH5IhYQbIYqUymFGeANpLWNdlQhiRxc5WmCpL4wmrGWFc5\nsIIk6UG1J6w5mplrJ96mZ+108t1cO72taQskTzYA1hOUPSNIxuvVQUL3COR9m+3ZBIkdJBxB\nInnQdwSp24rdK1FfZBYjwQmQdLHd4NppN5uBhA7Sz1iko0c0Q6SerjpKM3q0rxlI4AO5zZ1D\ntE3gFknTPCCP4NoEaR4jsXsPpVxrWa3guUUCDSV0PTjVlU9hZEVLTLpFei1Ip+aR7oAEHUgS\nETUgDTGSsNSBxH3STmYbQgcYQJIHszRH3gcJZzHSAJL4dO4EvQFIY4QglyRfLGGJY+1sJLjI\nAwTtMzaQdESzOSdvS0s26NfK1hjJQZIbhsR8KEgcLRIaSGAgCaOyFkIjsWqR/EyYlCHyh4N5\nHrJx7cA8jleBBMOLzS36ZAPfB4ltHOe5a7cJEsxAkqpR66AUGUisINUYiQNI1JQp7zmR3Lt2\ncl0RJFSz+uMgtXtOU6t1qGFZcComXx6MW4ej4h7ZPKiCxI1FsiOVuqrGyUwUg92soATJk8M3\nQJKnPIKDZM9VAP0KngCSWRnqXTuoDFnmu6ZLGAJIemeweYlLqv5wwxzK2rHGSDsWKWw+Awm5\n79RlfY48VH3bIiE5StZNUI2Sg8QDSCGz0F2VdinqLZI0KoMH9zYfaUcuj9y4tEUqT9UsL6gB\nieLNQmoUpK6pTvSop8YOJNrqb7QUKDK3UImTNVgk0AXfwbUzkKqvqeamunb6P9haO3HtLBpi\nSSqgDwnSNKV9W4uEmjiUgPqJVT8c9xBIOAXJ5jk6i6Qr2mwpwSRG8nxe8YIdJJqBhF5tfghJ\nkNoWjUWiziKNIFlm3i7S3ZnitgSQ2OZGPEa6Nkia/jaQZCosgGTPlwsgsS2jdM+2unZuvUkc\nLylDLRLZKtdAVASJGpAYgmsnzRlB4hAjQYiRxK2UVrebMprJMPlMt2tiJLouSBLU6aV7f9pz\n7SJI3E6P6dqhAyDZLYLa8GqRMIKETYy06drZ59W0cQWJLJA2kEJHcpA2YsqLgMQGks0/6KzL\naJEEqbKSZObaeWSiqYEWJBaQ3LWT25UqTvq5TMF2WTswm1FjGU1h6Ar/AlJ1W8Ez8WqRQvp7\nDpJz9iqQzsVIGhixDTAtSDAHyVxU8CAkHjBk7cL3VU1AcrcLW5A4gMTbFqk/mrsrfv6lQMID\nIL3aIqn/fDAjJKdYLoTYF+/a0yq0f5VuL1/EohYJDJkKkg34ZrfIQWKzSGggsTzNQXN3Hkg5\nSGDJhtvelrPD3iIxy32USqO7dtLhbNkDg61/sBPsQNJ7lDRGws2KWqoxWu03iH/cLncfJG5B\nogEknoIkj0Jh/XZ6Hu5Ara0cQWJuQIquHVeQeAaS7DAHiRuQLP1tl/ozINUfd49ojx+tIKFa\npACS44QVpGmMxBUktoUhASSwEUzsiN1DxNazHCT0pxjqw5jUtQNzLKQ1lUB7Jhs1FslBssfd\nefhqIKnrUkHyZcwPVf1K9TESA2yC1J7m1CLFEYICSBhAmsVI2srBtbPkYdiiB4lPg9S7dpps\nCA7Cz4AE9eXdI3qMBAISCkhM1eMBj5HIQILqEXUgEWkOjG0qQ20z6E0NsjIFEVqQMAZP8jaY\nRTJTIk/qEteuBlmeLCAHqbSAzg3arJcv6aoguWsXZ9Aer/qVOgtSn2xoQSIPS1iXNcjPChLM\nYySz4ept6XsDSKHo+yDZ+FpB4kmMRO7ayaZvAlK1SCFG0jFBZ/4t2QAKkufuGtfOssxya34E\nye8OQpsAlicbmkUSCoktX2APHIgg1a5UR1r0H1BdO39wh3x/sTzUtwOJe5BeFyPdP3wDUnkD\nwB5vcB4kjNe1BdIs/c218rG+FcpDmd4L++yCJHOWWyDxGCP5pu8Fkq4vsSVChoatt0cdfwA8\n8C8gAXMNZOrTJN2EI+s6MfMikewuLtQHY8jjtty1CzGExUgcJ6f05Ls8wQCSGDE1tAqSNHQF\nSZ/ObzHSK+aRDhx+apEGkORyu+MEp3ofJPk0gDSNkdQHQG/L4yCNl0VT124Kkq1E0U1fDxKc\neUC7g2TJBl1WY1k7jcFl1U8LkjaqgKT+FXiMVCrAY6QAUrBIesttde0qSHorOAxCxLr0pJkH\nwhojsQY7mrXzGVkbMPR86mNh3wQk7dP3QTKn2g40gKRLtANIsvZ1jJGcHK+Z3rUbQbJyNi3S\nABK3IJXrncRIQzU9ESRmXUrxWNZOZmdAE2jBIvkDScGSDSAggeWTpNpJh7YhRiptIV8YZdaj\nfnWIgwQsDzoB8JGzehfgBcm5+zwSiuvZgKST9w6SLi9y124ESW70+FbVn9JBkDzIXAgSDyDx\nBkg2bm0kG6DOD9firZw5SEwnQGpdu/54/FyQTh0RtDvVZEO51UinBHQAIYuRAkhKky5+R5fd\nVDmCRHYvhWaqZT1PHyOV4EkWELUgQY2R6rwFNiVXkCTxw2zfPuvriWYgyaWjPV72iVW/3Q57\nnxlIfAKkxq/qQZJfVEGC8P313X42A9ukv+vhBovUl9O9heoV6EWGc+9AIorTEW8CEhlIZWTW\n7zfwWFNBUgepAwkNJHP37HmLNw0xEmjdUARJTqMBiQwkoiZG0hUp7qHHNQtoj2MrFkliJLbH\nkUuMxCNIrCBZ+vu5VX9YQ9EVJLgPUt+LK0j6sCweQKJ2Nsp3rOTYU1WYHwdJzmUKUm+RZunv\nSSnXAgk9a6dPOWEbhurSmR4k7EGyf+jZhuALVNdOP1aQQJJ3rEFNtUhUQSLcBslduwgS6Df/\nOEjqJpAOqA4SeGZIn1txRZBq1g6PgjRaJBpA4lMguWuHbRU9BlK9yAEkeFeQeARJbguikGzQ\n7FbprVsgaYwEE5B4GyQcQCoOmTxpU5rdatSMYLjPpTFIE5A4gFTMF1uMxAoSVJA0O/nUqj+s\n1SDZdTlI5X8ByULi8YIRG36qaxezDVvrM2ZZO9lzTH/7EVuQKGTKaX7X94VBkqlQzeC5T6cx\nEmxZJH/cDMI9kKgDyZINdgJMASR2i6QxEvUgOUwRJLZwmvWxVcT2RUgRJDCnh8ge1fXUqj+s\nASReDRIZSEy+jGQGkrl2aO7FN2Ikjbrvg8RDjKTLbwddCyTuLJIuYbD5WH3autiladaONQpG\ntIqeuXZgILFO+ahnyQZSWRdB2rIgR7DbNrZiJN4AyVw7ljWyHGa4IkjagprYe0uQul2nMRL5\n9I6vKdVS7oBkMVJtzA4keACkaYzkl8SzZMM7gOQB4ACSSL4wbwZStUgypWZf43IPJDSQOovE\nspxB11fIEVqQcBYjzUDCCUh6LhsWidD8vOdV/WFtgMQTkKb7b4Fkz/iJOWi984u3QFKPLoLE\nj4FUotRqLu+CVJ/X+UYgsV5nB5JOyNoX28GBGInvuXY4AUlwk6hXkvACUkkukZxNAAn006Mg\nlSuzCfQQI1EFCeGaINk79mTgYyA1fx0AaWqRao5tH6T5KZwDqV6SHFW+I+GdQSKNvFlWcmqu\ngSYgcR8jsYZIx0GCDiRZMEtNskGSa2ZAqAdJ7CTqFG8TIylI0nJ1zUUACd8MpMMWqfnrUZBw\nBlL9WV6dBYlqtmEXJDnjNwNJwZcBQ5+/5OnvChI5SOwWySdkyxEOxUiMbYwknro8ts5cO2mG\n0uylv4PEYw1I6kiSn4scSdIYknYMIMVVgFxBqjGSunah+a8FEus8UmAHxlTDVFRBMmaIj4Hk\nrh0vAgl3QeIOpHqMtwBJxh2agyTJUdwAqYmRWNg6nmzAASRf7+fNroZDAqsRpMa1YwcpunYa\n5FozNhaJ7UztrpArg9R/eBQkqU6r0fJWBIm2QCr5P09SyBsLXLtwHRsgsYJEbw2SLryhANIY\nI5k31YLECpJWdAsSwdy1U5DstvA5SKTmbhsk2AdJF6P3rt1bgYTdh4dBChaJe4sEeyBxXLen\nx5J37c9tkObvUTUz2yDdDqqn67u+JUj6UDosj0Mo3V/vMo0gMdf0N4NaJLPNE4vE4QFz8kSs\nGCOBgsQtSBLzCEgQQRJaLC6j0bXDGUidawegvn+ICJ9Z9Yc1A4kfBkmehtKC5DGSL2s8BNLE\ntdsocwOkcMBTIG2Ucy2QJB7hAFIhq3ROJANJ1u8YNPXxcWaRWFg6AFLJb2p45ckGkJvwGpBu\n/yzgqRapQlCINJPEFSSWmKiJkWgG0jvFSI+DJAG+9UwFyY9B+yD1mfT6s7w6RrKdSDmXnazd\nm4OENo9kMZKCRHI7A/gNcCi9WGIhNSwVpBojTV07AYnFSzsGUrmzAtiNpcRIgPdBsqCqXK4m\nG+qJSSWAPGalnCmZa/fUqj+sxSCxtUVNNrQg0UapA0j2rr84AxKdBqn/YNCVQQIHSfL5Mtsi\nqxtsda7ESAzuSUk7o434cYrOM00hRuI7IMmeDlJnkQJIxdHUBGILEh4Aieyp2AoSfShIGEHS\nF36McyB1Fmmrg8/Pg4JzWfz5OyANHwy6GEianelBQu3dkmxoQZI83ACSHr2f694HCYTIGCOV\nvTTZoOnbPZB0pok7185AKqe0CxJ/Nkg1RrJe/D2Q6p8PWKSwWOPDQKKa5izZr0JEBElueyOd\n/GGxYYgdSIqSvAjCCBLrfUEOEkxAoh4keQoiDDESVItkrh0bSNiApN5iPDGbrGAFCfg9XLv6\n3ulkQ5NR1oPUPNphkB517fgESNMPBl0HJK4WSdLDWEGi0i/F7bn9ChZpBtKGaxdBAtRJHaNo\nCyR3uOTuTUWjzEVNQYIOJNRsfQUJ5yBZNPcOMdLw3lGQfEVD5cgv9A5II3k3BZAOlW/HkoJ/\nHZDQLFIBSZMNXYzEkxipZsX6Mg0kzTPzDCTQlXbbIMUVEVsxkoHUuXaHQPIv+Z5V1PMFVeNn\n/A2LxHwHpG3X7g5IpyrJl6vorp8JEqlr545SBGkSI/EsRhpMvxVSLZJarTlIsAGSMm73Mc1A\nQpuz62Ik3geJwxYMPwvSXtEzkKZdcUNPAukRixRAGjb5SJD0Xu3yFXstSOdiJO5Biq6dPAxq\nHyTeAgmaGAmsrCZG4iZGak/KYyS5pquDNL75OEj1GNcCySYmhg/eGCQJGIpDVlIQwSJxBxKY\nRboHkuRtbJHPANLo2nG0SLxrkSAUhgNI44QIAASQJKb6ZJBCGiceo44m02M91bUbNvkAkHgC\nUvHBBCTGAaSydwNSM8PQFBJAMt9uChLMQYox0gZI0IPECVKUJO4esEizgz0Ikp5HTb0Pm7w3\nSDyAJB8pSDcCsANJfzUgRYvfl1lBkozfFkgbFklPzUCyUg0koN4ija7d2CUGkD7ctdsBabuM\ny4A0P+T1QOLWIpWPBpCgtUgTkO67dhojPQYSNCB5+vsXAGm+2ckYKUFaqQ2Q7PKmIMkKvDuu\n3TGQ7I6LEyDVRXuNRYIAEjwMkku/zmKzol6pp4C0ESNBvH9ust+dUzhYvh8rHG968u8NEnP0\nnyYg8YEYSfbfLjPESFsgedbOTqkFqXXtAKJF4h6kNkaadIkeJPx4kKZZOzf5GzvO3py38v1z\n4E8HKWbtZiCNMZKt++pBan61hRyIkVqQuLdIWyDxDCREy80etEjI7wfS4ZPcsUivBakperKR\n5pKGt+eHvCxITbZhFiPJRp1Fgt4iTStavkBbOWKrryMg2bE14d6UugES+71Rh0HqG/AXAYle\nBpIdaydGUpDGy3o7kDhapPK5unYaI8k2D4HEChJ3IBkQQ4x0FyRZIoFQn9sk52QbN5d6H6Q3\ndO3OgjRyEdLfzxZ9PkjMXsWySk3f4yFGkm08FnJPi23vnZLlYXWNa1dBYjFI3uJlh5eC9I4x\n0gmQeJ5UeAikB1277vcHghSeFhPnkcrnbYwk22yCxLbBdtk9SBBBIunwU5B4AyTuQPJSOpCG\nk3n/GOn4Sdos0l76+7i+59p50dsgjW/Pj3g9kHgCkm9SHmvfx0jykfZr3/aua9eubDgDktiY\nCUh8DKQPjJGOH5GaO73iMV7n2v0CIHHoZzVG8k2mMZJ8dA4k/Qwfskhbrh0fA2kYdztD+oau\n3QntgnTeJD14El3RJ0Da0BNB8s6wtecdkPAQSKG0GUhzeV5w07Vjg0hB4tG14wCS7MYrQQrv\nfBZIvAESy8Ohf0KXBgnYTvAcSDVrN3HtZFHbCZB2LdIJkNoYiU+AxPdB6qcrEqQX68ogBWv0\nIEg8GCQFKXSz74JU/cIWJPYbketihMYiQYL0oPp1buGTHwNpqmuBtJfPuQ9Sn8SW7oWwyrXj\nTZCotUjcg9RaJD3I/AofAIlfA9KB4z4rRpqBNLULPyeYPaVre+snbNluvj3DcM+1G0HiHqS4\n96Mxkh12FyQ+CtKk2MtaJLjfUZ5QdIJ08jz8xUGQVDtJO7Ybf6Yg8VmQ+AhIoYQRJLNk4fOx\n2NEiDfopkO533mfFSFOQlpf1LV0FpGiTTh3Ra7g82mqyz/SLBx4DyV07DiDxAZDgFEj3Ku/n\nQOI+ZTjbZKkSpEdO5pEjVpBG124pSDFG4nMgsVkk7kEa9QBIr46Rtll6StHvA9KJrZ+w5TeP\nGFy7EyBxD9KebEK2ksQdSGWrTZAYN0GaxkhXtkjf3uQRvW4Nw+N6d5B2YyTv8fPjnXTtKkiy\n/wmQ4DhIBywSJ0jX0/VAaveEqunW1Lh2s2Mds0jHkg39memL7kziu7LnJkijrgvSAT0PpOcc\neKGuB9K5IzYgTffZel76cZDmx29A2o2R5I+DIB1w7X4xkN4Bow8CaeLY7YO0FzR3ZUgBW7v/\nNEj8MpB2fYOnFf0OGP0KIO3MTJ2MkTZ2n4PEmyDVt6Z6wCLxa0CC4cXmFiuVIJ05DT2Z06Pd\nQuueuQAAIABJREFU467dUpD4PEhbpR0AiX8EpANF/NIgnVlq8VyQ6o/jR7wOSMNdK82mCdLD\nepcY6TIg3elhzwVpTy8H6a5+KZDewyZ9PkgviZEmm22BNPm40WVB+rEY6fqTSPwBIPmr2Vfe\nwP4RE6Rz+qGsXYJ06jTu9PqngHTs5C4OEr8MpLtKkI5u/YQtw5ns7vcISPvn8jqQGHzzJ1gk\n/nSQnnHU1boOSI8dMcRIVweJj4F0RCNIWx++QveWcX1T7wHS4dSVbPyELb93xO+AdPQktxrS\nQLqzmW7zSSC9NGuXIK3V9UDi4yDVDdeDxD9tkZ5cdIK0Vo/HSCcPuVPGdP/D5SZIjylBWqrL\ngrS6uAeO9NEgpUVaq3tHfCDSTZBOFvtD80jPOOpyvTlIr7BIq/Z/d5BgeLG5xUolSGuVIO0c\n+RUgHZiqSpCObvyELb93RLq3wflDPm3/BOkhJUhrdfeICdJzi/kpkDJrt1ZPaKQX57eeCNJL\nivmhGOlNQDqV7UqQ3qC4T8vaJUhrlSBdq5iXFf0mMVKC9DIlSA/pbUB6yrYJ0o8V9+Ri9g6f\nIC3fNkH6seI+DaS3iZGesm2C9GPFJUg/owTpVUqQHlOCtFQJ0jWKSZA2lCC9Sp8B0uuLTpCW\nKkG6VjGvK/pNQDqjBOkNikuQrq8E6Q2KS5CurwTpDZQgXV8J0hsoQbq+EqQ3UIJ0fX0YSJ+p\njwPpA5UgvYESpOsrQXoDJUjXV4L0BkqQrq8E6Q2UIF1fCdIbKEG6vhKkN1CCdH0lSG+gBOn6\n+lGQUge1vOqzjZbreJU+sbmeUPCDp/sWu11P2UY/eMDnFvwWtZ0gfexuLzzgcwt+i9pOkD52\ntxce8LkFv0VtJ0gfu9sLD/jcgt+ithOkj93thQd8bsFvUdsJ0sfu9sIDPrfgt6jtBOljd3vh\nAZ9b8FvUdoL0sbu98IDPLfgtajtB+tjdXnjA5xb8FrWdIH3sbi88YCr1KypBSqUWKEFKpRYo\nQUqlFihBSqUWKEFKpRYoQUqlFihBSqUWKEFKpRYoQUqlFihBSqUWKEFKpRYoQUqlFihBSqUW\n6HUg+eP2/LF744vpflsb7+21s/Xq3e7vceY5gz+rbKOH9bImBits58V0P7i3+1Zh8NhuJ0u7\nf367l3cpZRs9rle1sF/Kzov5flA/PbrXg4U9stv989u9vEsp2+gbem0Dv7SRHtzt1DnaRx8B\nkijb6CFdHKQDlTDdS13e0z2i/ju82y8PUrbRt3d+pLCXNNJDtV12PF/ah4GUbfSYrg2S73C6\nabe2fsvR7pXKNnpMr2zg09UND+31cJU9tttngZRt9KBe2MDQ/jzSSP5tT792I71O2UaP6nUN\nDPHXiavI0e51yjZ6WC9rYIgvYP5iZ8dze+1svXy3u+e3f3lXUrbR43pVC4ev5MzlJxdVttE3\n9B5NnEpdXAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlS\nKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJ\nUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QJ8B0r0vE3ifL4T4XH14G73xqQcd\naaTUz+rD2+jNT1/14Y30EfrwNnrz01eBfLkP+/fc2JfP65cy3n7ql02Fz+2bgD6jDq6uD2+j\ny5/gIQ3fvAb1O9pKC84/h/Bu6sn68Da6+vkdE4R/te7bP+eff8b1v4M+vI3e4iTvaqMRyh/w\n/o30EfrwNnqLk7yr6g00X1XvLbQzGr6D//0R+vA2uvwJHlLbCBwb4V4jxd+pJ+rD2+jq53dM\nj/vfze/UE/XhbXT18zsmb4ChNZij/73RWp9RCRfXh7fR1c/vmNSR9p/B/y6TE5M5irDbZ9TB\n1fXhbXT5E0yl3kEJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIq\ntUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlS\nKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJ\nUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVA\nCVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1\nQAlSKrVACVIqtUAJUiq1QAlSKrVACVIqtUAJUiq1QG8KElR970D//A3gzzXnlGr1a7XRLw7S\nn7cjXL6R3lO/Vhv94iB97f9/i04p1enXaqM3Bemmb7sMi46R2tav00bvcI4b8gr+evHX7/AH\n8/9uXsAff5U3//uPL3/gf+Xll4/92z//Dnv+9Ydu1o+XYafUCq1vo7/+AZdsow8B6Ssc/Qf/\npY7Erfr/KS9vFf5befVbbSX97F9DI4WdUku0vI3+E/a/lD4EpK+h7m/+Hf5Tavrrj/9+/fz7\nqzW+Xv7rVuv/Lm0i+t/ts7//KC3Y2qO6U2qNlrfRb7eA6YvG3199Jff0ISD91b39j9IEf//j\n68cfZTOoePxZNv+rZIKaRgo7pdZoeRt9/fHvF537OX0ISPrW3//+84/yV6j8IXX0m7z88iTG\nRnrBaf9SWt5GtwgJ/vjvC079pN6464yN9A9vjr1GAmskSJCereVtxP/+HQAu6H2/cdcZGukr\nQP3jP39PGqndLy3S67S8jb70f/8qaYuL6Y27ztBIoJ62+N9/Vf+7nc/bi5H+yhhpqZa3UdH/\nXXDIu9wJHdfQSL/dav+f5S/LCP1eMkJ/3prEx7C/7mXtLpcRel8tb6Pfb/v/L7N2KzU00r+K\nm10SpDYPcRvyfpe365Cnn/2T+9Gu7pRao+Vt9D+4aBt9Ekj879/g93//LSsc//uHT4D/66uZ\n/oyuw+0zyfx0PkLYKbVC69vo//787ZJt9MYgpVLXUYKUSi1QgpRKLVCClEotUIKUSi1QgpRK\nLVCClEotUIKUSi1QgpRKLVCClEotUIKUSi1QgpRKLVCClEotUIKUSi1QgpRKLVCClEotUIKU\nSi1QgpRKLVCClEotUIKUSi1QgpRKLVCClEotUIKUSi1QgpRKLVCClEotUIKUSi1QgvSB6r9t\nKPV8ZWV/nmB4kXq6sq4/TjB9mXqusqo/TgnSTyir+uOUIP2Esqo/Txkj/YDW1zWkDmp51fdN\nkG30bR2v8xUN9+Qjfqh+sKKyjQ4qQXoDJUjXV4L0BkqQrq8E6Q30goraKiLb6KASpDdQWqTr\nK0F6AyVI11eC9AZKkK6vBOkN9JPzSE8r+sP0eSDRU476o3pab95a2bAxz4gs1UtU9pD/CcIh\nbPP2I5JdywuK7369QtmPyjbbbVdOBL62i2/YH0h3lzuRXgDULbDZPBRtFwTyJlolIKBvidwp\nQXoDPQukA2vt4vulH9Gtf1Hp/1CYuP0D7cm3dwllt6/fpN2tggSItx+G5FfH/uqdtxeEiAIS\nRiShUPdV3NeHX4eD2/5Ytrp1b9KO/bU3I8peqGg2ImUfC4hUOC/l3i4J5GzAwZIL1C0KSF+H\nLMwjEcpogH03S5DeQFcB6dYFb8NyBAlvXR1JhmsDiQwkaYxb17t19Fs//PpHt45fuuJXH72x\nBVRA+jJLdNtNQLr1axSQyqe3j4AKSLe9b+WWF19nI/vf+Pj6DWggCjQ3Im4gFVRvR6XbDl/j\nwe08yo6300aS6xIDdAPTULsNHeWgVE5QQKp29V4F7lfpGiVIB3UVkNBBunUoLN3RoFCQbm9K\nVy+dv/T7mxko9qZ03NKlAUrPL4M9FlywjPckfdgMxI2c20sS2ErnVyhJQCr4lU9vRd0wLX1e\nvEY9zdvpOEi3kvzM5WTKaQhItxMBKa+8JxbOQUISW1SuY7uiDtf6IiVIB/XyGGledAFJO1zp\ntqU7cgEJZLi+dTZUV6v03PIHsPTxAheS9Xwqrh5of5dPbhYGxcqUIknM1W3r0vFvzqBsfuML\nDKTCCAq6N0rZOCkgoZqecn4s24JiVEqrIGHhRUi6baQgoYMk11FOBWijog5W+jIlSAd1kaxd\nGaJLN4sg3V4WBw07kEQ3Fkisg3T40hkFJDUSaCAVnxHFrJkzZUCWQyt4aCAViwS+AWoZt1+g\nnBTIxRTKVqzc3XZ21w4dJD03o02sUwuS/oeAGxV1p87PN9PLj3hTgvSkouEW0FSQoIKkfY20\ng7F2RfW3GM3eoPVyqj3burn0cWJjrYKExpJGUgYSuWuntNk/AUlJBdmxos1+RIogCcdlQACl\nUi6wHEPPhm0fEts4r6jjVbpIOUdxUNcA6daxQM2AjfyADlLtYuJGeYzEoBaD0Zw02RNt4Ddb\nxdX7MxtAWKVJhWqiFFcyv872JCPT7ZkbJKy20t+0d0DPCsxkFbDs6CynylZuWqT303VAsh5r\nxgWMDaj9HP2X9D+w3cyrsj6OZmHc6bNuXYgECaUgFtsZKKMmwIZo0VoFFDVkU/vj/BpIBoZa\nsnqNkSwFCauTmiC9my4DEvcg+ZBfI3q3GE3fxzqQm63SH1B38B2p+lbxWApe82cDEtW3WpDq\nocCwEVgVEdTILMZIFSTDDfy86QIgPXJ37hklSMePe78tIkgSw4cuD5sgVQct9PJoThoafIeG\nkND7B9JQu/ZkLz2vDiTqjkHhbQ4btTGSklSYY/Qg0NN6D7VRWqQf0/PT30e2UNcOJh1c+1pj\nkSggFanpiQgRTu33YB27332MkSYlRJAqkziqjZGG8/eECKL7daHEBOnd9MT094kNoPbd9peC\nRbUjts6dgwLNuxWOBi+1B1hTFqG8mYGiERHqPxlBgrpByMsP5rKCM+CVIL2dnhgj3Tv0fZCC\n/ZnFSLVPNp2z6aD2EbR7ALZZuz2r0m7R8deecv+ifj4WFkGKp6y/TlTkI1v+3BFv6tdufICu\nkWwAakZ461yNlzYLRO6IJn1YBKH3t7/9841SLJibgDQpfu9PMgPpVjK6s/OKOl6li5QgHdQ1\nQLL4uzcctQtSS9VOt223m/hm0ovHtycFTIzW7KPd89k60O4OCdK76UIgTZ2raoEmLtX2Ttvy\nGKl/f9bXZzFSv/mGzRt2O2RD6+bzijpepYuUIB3UZUDqe+qZjtjGSMc66v13Ns9l66PNcxzs\nbA0A5c/h+hOkd9NFQJp2y/nfp0b2HT0YI00t45kCN95o2frwrN1b6NylXwSkR/rhxudTIh7U\nTmhz95QzRtrWWxikdwRpyINN+tfpaGj7cAfcuHsxUnAnz5/DfVG83zxB+hG9I0j3O+PBYP3x\nGOnsZmdipLvgTmKkzwbpHUh6S5AO5b3WajdGOr7f989g48NpRR2v0kVKkJ6y9VKFor/d7Q58\n/mqdi6jG3acVdbxKFylBesrWS9WD9ECM9DxtxkgbW64/gWlFHa/SRXpS/0iQFuonY6QnKWOk\nY0qLtFLRIv18jHR2v3VnsPHhtKKOV+kiZdbuKVsv1ckY6Vvd8gf0zfP5ZJDewiC9L0hn/KKn\ni8LPI1uuP4FpRR2v0kVKkJ6y9VKdjJGOdb9vdt8XajdG+nSQ3oGkdwTplR141nnPbPwiVl8B\n0oHNf2WQTl3754B0NWP0BjHSgYcEJUhHt37WaZwqekXPC31w1YF+Ui+ySPd6S4J0dOtnncap\noj+i6y/SC2Oksvn+w+sSpKNbP+s0ThX9gx32Zfud1bSijlfpqc0PPXxwnd6Co18WpE+zatOK\nOl6lizZPkI5u/azTOFX02i74EUh9dtbuGUddrXcE6SO6/mJNK+p4lS7SC2Okq93V/o4g/XSn\nvaKmFXW8ShfpCf2Dyn8vKepb+lVB+jSrNq2o41V6cIczX6u4SJQWaa3SIu3pJUuEYHjx3SMe\nUIK0WBkj7WpaUcer9OTmL0x/J0iLlRZpV9OKOl6lJzdPkAb9qiB9mlWbVtTxKj25eYI06FcF\n6cP0wTESPZS1e/nc0zuC9GnWZIWmFXW8Sg/u8BNZuwRprdIi7WpaUcerdJF+BqRZqc8EaXqV\nCdJnaFpRx6t0kZ4D0r0Y6QIgnf1G9wTpovrRW83vfyX9N5QgLVaCtKtpRR2v0scbY9ERt5Ug\nrVWCtKtpRR2v0kX6RWKkscAE6VM0rajjVbpIrwMJ7oD0TG2AdOY0EqSL6nMfx7Vxo/k9kHQn\nnHz0bSVIH6xpRR2v0oM7/NA80vRUqp1qS5WqSJAOFP3TnfaKmlbU8So9t/1rVzbMSzoG0lOU\nIL2J4AFNK+p4lZ7c/LVZu40Yyd9P16477lGv4ac7+jE9goPogcJe/MyGK4P0S7t20P64U/RL\nuuab6ZE2em+Q6C1A2qiRZ4IE+0V8zyLRAS3v3CtP7t6JP9JGbxIjKTAtTQdBeoo+BqQzHewX\nULnWR9robbJ2GyDRDkj6+uct0rxKrgHST/fcC+oj55GEn8dAko+eAtIMmcuA9FUe7JeQIO3q\nkTb6EJDavopPj5GuDBLb6X1Q1u61eqSNHmvNvb02PnswYFGQpvvfsnYwBcn2vb345SzSASVI\nu5pW1PEqfawhDn726DOHyfaeWqQNkHzfAtJjBe8rQfpkTSvqeJU+1hAHP3scJBpcOztUBanv\nwT8XI0FD+w7lCdJ1Na2o41X6WEMc/Oz7IBGPIFmMBPMYicrvF4EEGyDBD4LUFhEmVeubP91p\nr6hH2uhlMdKD/fk+SKWzzmMkemWMdEWQtpQg7WpaUcerdJG2kg2vB4nXghSPMweJE6SP0LSi\njlfpIq0GiTVrV0HykjZBOhYjnbz2oyBBPfME6Yq6u0pjWlHHq3SRFsdIpI9ZPWWRDKT9GOnc\nteNJi/SDIJ1ZffKKnvtueqSNXgcSPlTcPkiwkWzQfe+kvz8VJLAfubLhMT3SRtcHCcujv0/H\nSHjjbz9GOpcWOQ6Su6M/AxLUX1tFJEi7eqSNXgQSfguks8mGGwpfu2ExSatAOpVsqPNekCBd\nTe8cI6H5YGePpm5dBIkOxUgFJNz17Z5okRKkd9YjbfQy145XWCR9y0q649pJnZyPkU6DBP7W\nFUAKMdIvB9Ka26YeaaMruXaT5XTfBYkH1+5OLVHcAeIJtfepWIH1qnqQ1IJ+neSPZO12C/hY\nkG76PkyPtNErQIIRpNiS/moG0u2yhBayrQNIW1k7jBbpuSAh9yCBnOwPgnRXHw3SXb1tjHR7\nXoam0M6AVLa5dd+YbIgg0T5IeC9Gmn1A8f1HLBImSG+vaUUdr9JFmoJ0c9FakHyzDqT6roKE\nzTxSC9LXJ7UTNztzrZOWJmw360WGoV+Kn9UUpLpdgvQxmlbU8SpdpC2LVLpnB1Iz/t8FiWzl\nnZYiIN3eu/XfducKErbLG0I1fQckvxKn1EHqY6StJQYXAumjHm3ywTESYIlYIkjSu7ZB4g2Q\nUDdTkGAOEvYg0YAP2asWJwGJwhnYQgWcgoS7IKFapGktXwikZ2jsz+tw/d6R3jlGKh0xfDgH\nKaxLNWAkRuIpSLc+Kvf87YOEeyC1uQjt/jRYJOIpSOGOpw8C6VIG6gdOZlpRx6t0kTYsEm9Z\npCoD5qYKEtqaG8NO0wtqkaYg8TZI2IM0nAJWkMDPh+auHXWuHX8ESMdFG68PbH5hTSvqeJUu\nUn9EmMZItXOh/44gab+Vy2rTeTpzdBwk3gIJeLRItAAkaueRNrIN1wCp9O0XdvBHiqLJqyUl\nzDeFaUUdr9JF2gQpWCSauHbYLADCABIpYWaRKkjlWavME9fOqkkt0phi2ACJKcZIAaR5jES4\nBRJXi3RpkI73upO6GyN9g971MVLz3rSijlfpIt0BSaAYQcIeJKogSa6u9E8LmcwiMUn37Wdd\ntUYakJrkQg+S8SIu32CRbiv3zoBE1bXbyn9fF6RLeWAZI/nf5QsMKkhoIIWvN5qAhDVrtweS\ndt++1Fon2II0uHbsf/OeaxcXKfWuXZjLKvNIBhJ+vEXKGOn8lneOM3tCjZagIPEMpHrWQ4wk\n9qIDiQaQ5lm7Wie3H0jbIA0WyUGCFqSjMRLY2RpIl042vFmMNN2ddv46ezJ08RipWqTbzwhS\nde24ydoFkDxGEotUjtqDFIvtQdJiOpBwAlKcRwK4HyNhXTtRQYJ3skhrGaLpS1X3zUoZIx0+\nos74jCBxcO22QNIgo2btSgA/gCRZu2YYuZ1CqQ80kKR2epDKMbYtUpOiJ0mG1CzENki3ZYWC\nXQVpVs3XBemxfvoks5YxUguSdOsIEjSunQEj4z5p1k4SbwYSjfNIBlK79g1t5YscOX57VGeR\nPC++BZKnv2kGUnTtWA3c+4N0XD8aI20c7fvJwWlFHa/SRdoCqZyhxEgCEk1jJLQJGE9/UwSJ\nunmkKUgYQJLfVFNxLUhWbThm7aJFopK2m1gkrhapAYneCqRvT71sfkL9BwtjJBo/P1nCu8RI\nNsfjrh0qSBRACunvOl1EYR6J7Gki2skHkLh37TBk7aRyeHTtqAXJ3lWQsLVI5SvrCKeuHUSQ\nWteO3gSkI13wbv/smDkRI52BK4A/Mz10AKt73uw1QQIFCQ+BRGqRQoxEHu6Xb2CUrB3sx0h6\nM1JJ11ktuY3TcyN17QaLhBUkcyTNysxAQphZJAGJrw/S7LuVz683hQPbPKgBmg1DNH5+8NCD\nrgdS+fMmO2uWqOQGEvUgcQsSWNbOHpQvqbB7IEm4UrN2ZExZLDNYJN3Ps9wSI1WQ3CKFVEgF\nqRyljZFAvnLVXDu6Pkj3XaOtzvnsGOkRGzkaqpOu32VBQgcpWCSyZINnAWSOyBYQwMy183tl\n1etSkMLVo/5oak1SFgqNFvhV0u0gE5CYK0gQXTszk+xPNBGXGqpFogISxxiJbBnHnYp6pXqL\ndMht2+qmG55W/ZzaP047crYH/bIxEqODJPOiDUiDa+fzrrcOuQGSph4iSNCApHsJSSGW1oy4\nF+ggda5dOWvioyChuDUcQOqydpe3SLU3bUM1DOsbvZI2ibsdnmqcRDtwdu9PMOk+oOaTNrdx\nP0Ya0i3XA4mQxxjpNmbDDCSU2VADydbaUQWJt0AKMdJt7V2NkeR+Qo+RStLBQLqRtDmPVM6c\nG5DkgUZyjTsgyeMpymWUZANtmaSrgDT2sDFLNn7S/n0sRjriIG58CP0b4eQmqB2zSm8TI2mX\nr/NIESShADdBUttCASTyaZ/eItnKhq+9wCdko09QiiGb4WWNkSau3QwkUJCaGAkkWa8DbY2R\nxK3rLdKlQfIOOQzOd7rc8RiJ6vGPHX3HXRx223XtBmMK45bdBtOKOl6lizS1SNo7O5BARnDZ\nuAz3OICEdR7JQGpiJGhcOyj5DM81FE59hZB4Z3diJAcJepCws0gbILF2F7KI6fogNQPOfp/t\nOy3VrnkmRmoxGfbsnTYv4OEYaf7m3O+bV9TxKl2kFiRUkPScFSRSkKiCVK6LLSKimrXDwSJV\nkKCApLauFI7VHJVDYzF0OI2RsMZIFEFSAm5JA3ne1yZIck3YWyS3gG8BUu2P52MkNWFku8O9\nGCmw870YiQaQzsdI7X7+a15Rx6t0kcIR0UHyuqzJhg2QaoxU+2XZQJMN2GXtyuNPqmsn/1uM\nJAihPgW8qaYOpDFGKmcXQbKyuYmRWEGSjDj5qGlzVtcHqcrcvNqr1BZ8O0bactTG94d3/I3h\nHHZipGPrYzfOZ15Rx6t0kRqQbp01zCOBzyORgFQ+sG0bkOrabL+1zkGiBiRCv3vJYiTz7aRe\n1KdjW8XKBRwJrMw+haXd0kJTkLAFSQ4N0IIEhPoUP3wLixRwiINz073qwL7tRs2mdtuhHmj6\n2dQ2baE3K5xmv8JptVZsL0a6KEjCDgTjKVHRF0hIoCBpBCSmBwNINf2tR5N+OgFJjlwKLyB5\ncWQkIlsCHvUd0kp2187z3/o0y3J2jWvHLUiksVhjkW4XrH2A9ZYRmt2l9ZSqP6whRiL06uj7\nVufvtdZjEiONpDUm5KEYyU8PaHuryV99UT3I1G50K4KuCFI5tQISq7MVQGpcO1KkMMRILUg2\nXyv3+ZXZXFCQpBak8AYkjY40ZvH6uweSBEojSFL1pRgFydo3gKQZFLRkAzUgPdZIy3UiRuo9\nq4YMGyKdRqDJRqZi4uuOFFyzmeWBaRKjtS5ordJ8Ek91EiT1mIb3LmqRrDrq6Abq/FiMhHri\nClKZkhGQyKdW1fVrQcICEhtI3IAEOnckHpy+ZqtgNpAI64RsTQ2y1OfctUPuQZrGSNoeKA8u\nvzZIoaPVGMk6F9QORrMuT92e+w5e36kpItD06GhVbMgb7Ne9GGkH6ojoYOTmFXW8ShdpCyTp\nnHL7glsk1K45goQerleQSqb79qk8pEFBwmLxWtdOJ1892RBB6ixSuUsdcAYSjiC1FkmukCpI\nYR5JM4S3znJ1185xcFio7cs6OFDtvO2vrbe6d0eQ4ofYeG7RadwQdaz0J8B2oNaK9TEShdHh\n4iA1a+2wgmQOnYJEE5BkZrPIQPIYyUFCv/ya/iZZ7i3YWAtqnDQDiezJEJpC6EBibag2RkI5\nCKF9m9jNtWvnkVqQLmiRQg+vflftWxR6YdNNsVoUjnuP5qExIediJLUcbkAgsuj8za3kUNTg\nQTYxUrWH84o6XqUHd5g/4mR6xLIoqHQ01nEeZG7pBlJwlwwkFpBoK0YieYo4tRbJFiCVwrGY\nK1bToaQ2NahW7vYetDGSrlzQKdzCkYBEFUWy5eWTGIkVJD8h0m9Jq4+UuCJIteOBD9vUdfIW\npM5n0o1L9hLcs4qjvNRIcefRK60s0tLxbEAJNUYKJir8onhGOMRIMVLbjZHifsWPIGvhsaKO\nV+nx7WFvx5lrBzqao4Q5gPrIKutxrPm6ABLWGEkfAUTSDg4SRddOu6qCBCH9Zqk6b3huhG5p\nAAAgAElEQVS9Xb3UuJdfQJJ1DBjcDLCbDatNK+tZC0i68qkDya5WF/eVGbErgxQ6Gshl3/L3\nmhyi2iehBaztk8KQtGzbWet2NPRq9UkaW1bBVT+GvKNrSbXjkx+3LadJm4wmy0ukkN8NpzCv\nqONVemLzPZI6kFC6VhGrv1Pes87JA0jcxEjYg8QtSHJktZHFRQPZSyeEHCSpKK7gBtfOQNLJ\npilIdrYVpHK6dR6JBSTWgdRiJAFprK6LgBT6GcgYHntp7apyVW6ZR16kMvtACHzzkrpBs+Pa\nHypIXufWPyC+Ubt6tUa2zFLyhdq4wVaRdo3WioUpaAWpjH4vdu0eBEl7MuvKaAwxkicTWpBI\nQCpLqPUZJjYhW0DiFiTLNhhIqKuvqcky6B3ntqpPat9AQpbl6C1INwOn+UKpaTlZaCxSGyP5\nKek9gmVGWkG6oEUKWEBreeSCrZeDoxL6ti74aEAaOLJ+ryBF57DJ2oWjmlWx0QzVf6gRqIFE\n9fTjWemLAFCwah1IiD5suK8/VtTxKj2x+WmQdPWpggSoIHmPq8kGKgcoEQzLLXpqkVDXCMla\nO7dIOmtT1pc6SKCmRJ5C1Fafg+TDGMuqQAGJWPuRgVQcPmIfsvSRDgUk3geJ3gKk6hd1MVLr\nakk3ruEPGBA2OyTZS3el6mFJoChzHmBrSjDESNTgaeVtxEhuImsPGuaRKjbuSrQHd5DqZRZj\n6R1irKjjVXp8+8LRAZBspPIYqawMYsQtkGRJAYV5pNtRBCSwqKqNkdiqZARJV+lQqD+lzpLc\n0lIcYiTWpXmsPj9bxsH9hnsgVUdWXbtiNq8LUuhmIOMHVdfO5lAlMQMYQGr6ZI2RbDo69PrB\nIjkTBLX395M/pCCZ9xd20rbTGf0+RjK3MDh4FGxpTHb7yhQMFgnmFXW8Sg/uoA9CPHREu3br\nWi1IPpBUkNBBwgCSHOrW01uQeAsk1PVGFSQOtp071069P0lzo1skcy0sdadXU2Mk/bMMyepa\nRpAKeSUXIiDhTkW9WJsxEqldCjGSjv7Wq0nJiLw4TJMYiXRzMfIlW+srIWvWTg4FBlmhGRCi\nNaFwimYKmbxIQnN8POFR55GqgxnGb6wxEkeQLjqPFKu7iZHUvkhSbgCJHCR7ErfswZq1E09s\n4trpIlmqMZIbd69ADo0dQCKoq/IcpOKakSQc0apZYiRvLfEK5P4LwGppKYIkQdNTq/6w9mIk\nc+0qSFjd4Dg1g76VjkpSZ9EBsJ7cWSQ1gw1IdTetQQJDotqgGiOBgeQdx8sre+nKlQoQurNX\nXVZguybLtF4aJHMIsPhnIUaK6W91/ZDMIkEFSX00ualWPMCSBu9AQgGpTH+iLtkz18Lr2OaR\nKkjq2hWmJPMu45OnsMQiiZeGqLNMApJ2IiggEXauXdn5+iDVHt8kGyJIlhaDABJZJGVDvmQv\n3UmLh5UlLPoYdJmswDiP1CfnQI4ZsLTT9MRDsY7abtIhKvEQsKE+AAsJdX1Kjf4lMRK9KEY6\nNSFrJkkftSpdcu7aSTxRVi6UeJRqjCQJcvGwyOstunZWBwaSDGo2jxRcDTAnWEv2RLUMw2J5\nBCQG70FEOk9rTUEaI4HHSPpocJ+QbRK6JDmIi4IULAiIIZZ5JKEEbBqBFSTwPqq/bSSXlSBm\n7Ws6rcxHV4ukIEk9goFUE4JO7zxGKjBqS+riyzg/RWLRpjESWeM5d8TVQMkhGF8VI8HwYu+I\n1vEsnjOQJP0tp96AhAqSuHYYnrKvHVquuUwVSVSjs0QOkix/EJCkEdi9Z8QOJN8i9BodZnuQ\nwgSIgYRW9QoSyv3r3jdbkPBNYiTwqYnqf2mVE5DdrlUTY+4ShUkdrEk9xjKyaYxU0jKlUKlR\nvbsZ1If2OR+Nkbg9NftNwbWTIJXqPBJ0IJU+gZaZLw3rk2KsGHqMxNKZZhV1vErPtsCBI/o4\nUT3vksUy/0FBMufO+n0DEtpNedqhIYLE0bWT9dZUHuwobS52bcyAxxjJOoTFSOL1e2aWxHba\nogzNjIQYCTqQsIIENSd8YdfOhpPo2kH1eXQdLpcQiJAdFRl5BBYBiWUJV6zYspU9tLpaJJ8J\ndYukcJjbjyFGEshK0TFG4lmMRGq0JDJWV55CM1vmhAwkCTasN8KFQfIYyUGiYLR1CsdsDeik\nKclkqMdIUp9gdyxZjOSFtCCV1Ch7EqGlqIKkaxA8IQs288raxrLIhzxGcrg0/U12jMKu5jXK\nc1+1w2mMhB4j4byiXqxZjERW7ROQQK8KSBNG8l4JWaWboyYbNMHTgWTzSDCNkexJUwqSEdfG\nSBAsUhcjsdpLA6lkB93L4y5iiylIrpGeBLqsE/STijpepWdb4MAR7ewthe9Ogkd5pK6dObCg\n0xFqkTxG0oFGcZNsnPl8NiiS3mhbhjIgA6nhSLIeNqUNblEcJBSQZB6JNcTeiJEKlLJFBYna\nGAkNpOvGSDaWky6sL5dANo90w8tAUg/BYhLJ/Ui1AoCOJ2RjpjmBwo3Ej22MRAaSzfVqksOz\ndqiJjAiSxUj2PDchwpqGWpCsZ5jBUxeDg2snne3aMZJ1Je1XoI9qQGhB8hQ1iWV3T7jGSKAW\nCc2uSZaMDVa1SAqSufMBJDf+iGr3a4ykrh3HGMkn3RUknQa31nLXjmRY6ECyIhUkcXrwVSCd\nSQiFlJauKJaUp6fEymJ9HfPZHWWptwiSp78JQ+as8CmcEPqzazVGKpUMFSTQFS0+jyReMqAZ\nwxgj6TS5mH5ZolAi5VKGRkwSc4vvYDESyR0IIUaCH4iRTmbtvA+jZeyru0vWeBOQSAxwjZFo\nUzoH564dilGzrJ3eC2tQoHnXtfcgoiEC9tQIaWM2kMBBKjFX8fR5CyQf+jRTIabVQHqFa3dq\nsAP04bgDqbp2xeMGiiDptTObOwAWI8UHD+kRPEYSkEqM5KMVSBDlFqkcxyySxkgwxkikIJGd\nv/U1+6KTYJHMdVN/W1qKdB5JVuyBjqX0MpBOHdHdb9DuaiDVC7cYCbdZsQRfaUprb0RZlBc3\ncZBC+puCKXGQFC4ZVdsYaQCpxkioMakUpTHSFkgyuJLmxvGFIJ1zv33hs82RDyCxgmQWSdcm\nkMZIZdATb5qbGIkrSPV7BjxGIouRZKlPA5ItE2ecWySpWY+RiOI8EphrR22MZHwTuquijlFh\nqg69L1oidOaImuiRzlu6m7p2U2rKVdqju0hHCfYYybqxuXbIbYzkx7F5JGCuoaQbHQcJtdOA\ntzg22V3HvXCkIGlbUAtSjZHKYCG+a3TtdLayteQXAcm/haCAVPo6kS53REt+RpBkqeLg2kGx\nSLwRI5W+CwweI4kTLtC0MRKQ5TrF7EMDkkRtDpLGSGoG9eZPsAkiUAevXJnHSHZfp61sEM/B\nh7+fBQmq6pvBDsSeLtg0rh3bqmF3i6yldBCHMI+kvhhPYiSslk0CX4+G/P8KktZrfa29po+R\n3CKRg0SNa0dukawE7EDSmnnQbTjZFPeLmFkkMfVQLZIObcqag2SuUQCJxbcmt0iaC9BbZwQf\nBwk8RirzSMG1Axk1yRKAPImRdEFJtUjsgU9pPRxAKu6gpYBIFjp3IIlv+kMgHRrtrFtHpNRF\nUyNgGcwQI6G3LdV5JO30Yhk06VYKsY7rMdJg8ixGmsrIlRNjd+0YdAmGgaTZKzsPjXo6kFhz\nq2hPiiAfX5SuFVV/tGWOxUg2Jt9SIgYSe9SqIMnyp9sOOmPh41wPErubbO3UWCRuYiS2GEnn\nRAQkbixSNWSoDzuTZ4w280jgwW6JkeT8yUBCfU3srp3HSMWfB01MMLe3YF7EtSuGQSM9Fhu7\n0aXJXIFqkZyVASTSP6Uk239fZgMNVOFj2Mo8RQWJA0gaI2GMkRqQZP6YqtETgF4eI53M2pE/\n55I3QSrfXWjpb+nTZPNIJQsXLRJoVXEFiUD4YHvUrrlUrFk7qCCR3DKDjUVisJWO5i2GGEny\ngKQOvlski5FkpYvnQEgnJtsYiXXasqwGfKSNnh4jmYNTqtpjJNTIwSzStO8bSGgtomlqtKR1\nI7CPZOyRZ4erFzmkMtjg0+Ve/Ul4jKRJLQPJoWR76orcjOiuHYsf4kaIdNYKzGA+s+oPqwPJ\nYyQoMRJVkGACksRIbOMOyUJH9hhJq6X4bvK0zWqRyipjlplEFIdsDpLNFRBqlTpIoOvH9SkA\ngqRaxiFGKptKzr2Nkbi6dqUHsMdIlwTJHmrHDpLlE9oYCRt7gZOevSH29XzuEuo8EgeQ1I+Q\n1MBGqqMN4CJS9V2fSNQkuFkkDiCZL+fnJQ4fv9C1u68BJHKQqkXiaJEk+6Dzeh4jRZCKY6wW\nCe0pT/JxiYw6kIqX1YFUTktBIgcJK0haMOmCTDkndAta9pQnzaClGWzq3GMkc2RkLZ/NEvLL\nY6RTboPen1JSLxzvmLNkA7QgzWIk9qAI/BYF7+nMmjcinTz3GIklayfWRK2SoSrj3Bg9SUhm\nds3S7FbUNnUWI7kdQl9vqWVQeJDDw1W/Tj1I4qxWkHgWI0GYR9IYiaVRK0gcQcIIkq5EAf1f\ns3ZMspyrsUgSIwWQqMZILH5YedSopRaDRZJkAsgF8BAjMbtFYrFIcte23z3wOpDOBbKgoU+Z\nigsgmTcFESQInmwTI6GBJBvZChWqFqmkhNBiH4lLAkg6aSHhi5kG4C2QSEGyD/toyqasYMxF\nOluaz1LPA8Ntsw9X/QNqi5hmVt0icW+RUBbWOUisIAFbclMskqzbsMKkiTqQ2O8PVpA0RhIz\nNYAkt60pSDzESHraZMkGsZNEBpLGZ7J0ro2RKkgoboUNqBYj8YvmkR6YoxBoSi60VD7GGAl8\nMNRkJWggYlaLO5AiZljz5u7aeYw0A0miFxSTVKIzaBihLv3tIJljBthI3FW/J1c6IM5dxyvH\nSGr0WWMk1uhD7Lalvx0ktBCjde3EDrCYgXKzBOr07cQiiZdClreQL4yT5aKki4P7GInVM5Z1\njwaSNjbbErEOpFJoiJECSNog+qRP/b6rq4JkvUwMpqy3cpCEDbUu9pQm8D5a3i5XV0w5Vn8Q\n6yIVnsdIZRisIJl/hbp+qCZSdfnIHkhye46mvz3caubIbBkSky/mCEkU+dD0cNWv1A5I1SLJ\n1QtIXEGqyclNkGKMFOeROILESlsASfYXkHgGktyEzITBIrG4mMXznFgkmzqXGIllHklYLCBJ\n/IeMlwbJ/bpWM5DMLQtYKElukdT/m4BEMUaStY9qkTiCVLqJWi6orl0LEnqCVW4vEpDQU91U\n54ZwCKOwgmQ5v5pmxMYgXQkkZlCHSRcUe4wkz1jX7+qQeSSIFokHkBg4xEhsIE1iJCB92Vsk\n4UdAYn0Kk1gkCCD5AgUxUjrWGSis7GsOXRZjhBipsCbpcjlNrRPil4B0MkbSbirJFLZof5TH\nSGauEGwRdwBJrZlPK2m/VAJA7Zg8pMmydgqSeFfi2+mufYxEmv2pIBkVBhKHvDYLJjJwM2N4\n9IEOyGjn08L6eNUf15mEkHhA0SIFkFhBAumVgpCGGCCum88jVZA8RmKzSAx6t7NbJLAZCtRv\nuwogMfqdaOqahRhJ5r3LMNeBVGMkrhYJNNmuq5sVJBb7JrkFsBhJr+2KWTvrQiR3dBlI0j0Z\n9SEOM7TsqS4OkiwzMENlI734FuozopWkMRKYRZI1IhST7+p8eR5BswKta2cgQcUfzYqRhsZE\nup2D2EvtJPa3Xz4NJLAfRwY77Tk1RmINkTRG2gLJZ8ZHi9TESDJbygaGg8RqkSQFN4BkFsmq\nrYJk80j2PTxIASTuQJIYD/2h7g1I5tqBXehLQTpzRLuLNIBEY4zkCUzPNCBO3UGoIFVPSY6O\nNvVr47+BBA1IVEHSGMlRRzuLHiQ/Aa6LLf0ENkCyieYuOfEaiwT11wH3WxNq1SIJADaPJJND\nEGMk3o+RuE1/G0jcg8QjSHZwNAh7kMQ+sa47ZZvbKvUOipOcRGORipcvc5keAynbpDfJvDpG\nOndEkAdsFZvRWyTuQFLvTVf8oK6lNIvUUdWEHApSqVP0JHcDUoGC9CF10IFkQXUxM2zJAVk4\nqaXJGetkYMzn6bJYN1M6Zwt9jHR5kDRG4gAS9skG6byS6PYYiacxEtcYaWqR2EGax0iam5Oz\na2MkPRgoSGwWiXUYlGOwxUjl/CUvzB4jiTSA01y71clLQdrbq0t/m+Wxp+uA3pylo30ASXqr\nx0glcHKQ3FBNzdWmHKRioSRtZ5aGKcwQCUggN9iw5RPY7J/GSGLsLNMHOhCIDZPoSi/LVp+U\nQSG6e9+u+sONc9Ii6esWJHaQynjdgESaDCdZqlAPqvcumEUy39FLNpAsRuIBJKwgscdIlv72\npEAAic3jdJMZ5pEYdIIFI0iaclCQqkW6Mkikrh2osbBJflt9p2MbNiCh5h4MJPCfzfhe+rlM\nwFqnR1nuUkqckCUYkN5wHkAisUjy9BTQ4LUeUzuNWCSBQ59shDYWNCCRYd8MBd+u+gOqMdIx\nkDRG8teiGCNRGyOpRVKQqLNI6oG5e7Zvke6CFNLfVjhjMFy7IEm8h5LI60HSMaOdR7ouSOIF\nNxapYgBkT0+V+U5qQKquncVP7cIHS4v7HX/ucnUxUplSlAd9tnGXPQWiNXJl/nwCklLk5ZTz\n5xoxGUgSIphr93KQzj2ffdO1o5r+jskG3Z3qigL1mhwkpuja8SRGEs50HslAYouRzPmyvdp5\nJOAYIxGxRW6bFok1RpLzZj+4Zvm4mUfyDYaK2tcrLJJY8ejaGQL+UBhsXTt7doOCxN4RDcKQ\nbOAAUnjm7giSPIUN3DHr7JXHSJZsYGS7t0nTbRoj6eI9LEuR3bVrQAKPkaCJkb5f9Us0guSu\nVx8jQU02VOetWiTpy0LhHKRZjCSH0GflkoMUYqR6Sqh4a8K6gqSFq0WiFiQOMRI3MRJ7I1SQ\nYoy0WVHHq/S4ToIkIYeBZF94WDrWHCR/qFljkdSaRfeuZu102HekOpDslmqy9X/lUyvdXDvw\nhxB4LAUWI7HFSJYXlBiOdIJdefJEX5hHsgTKpUGyv/oYKYAULRLKKG9BfjuWG0hsIHEXIwkO\n3MwjMYf0dxH6OSnqqLZKJ2PZ/UAeQHJ0tkCyGEkzkNUibVbU8Spdow4k0rvAJEARkLRToaWP\n0e/kwYlrV2eQQoxk6edivaEur7ZIqQdJLFJJegi4oDGS3jFuIOnUUj+PpMzKJ5YujyChsCXL\n/MW1KmdvF4q6ROWpVX9YY4wUZfNIFpJMQeLBtQsgscdI0SLFwt0iBZA4gETUgKTxkYHkrp0l\nwLdA4gAS9yChlM7NPNJ2RR2v0jVqGqkDSS2SmRMFiStIpdYACWcxkv20uEadPlmUiuZyNSCV\n5HXn2v1/e2eCXSkIRFHYAbX/zfZpa2BWNGjEvHdOd5KvDIr31wCqTiQJSFIX35vChTeEQgTJ\njF/wiVFiixlB4nrEH+IvgBSkNSySRuA2gyn77MRIW6GmRdKLtvEF0gQp6UO+KNGra1eCJOsb\nyEBySRXRIjnFKj9OASmbR+qfqH09AlLYB0mvSZeBRE2QMr/Oy6mIjxfyal8OQPIZSF5BIi+u\nHd+6zIvtvGa/1bWzeSQKqWvn1bUjx2tiPM8m0UquXQKSL0GizLWzGIn0AtwFqbZIsoqrARKV\nIGmMlHTSKT7RIsU+JB0rXTvKamEbmM0jdU/Uvp6xSFSApEkvZkwubANpc46CgUSGkBNrlLK0\nDUSQpVSKUg8kr7eWW4ykj/8SkJxaJJ7u5tucgktiJOlDkIlme3SVxUhBLBLDKtP/rwYp60gG\nUhLZUC9GClosqgKJ+iBtGYgji+T081hLqEEqXLsYuLVA8hH898dIlWsX0hgps0heHw/idLKz\nDZIq1uAlEEo/3+6MZpBCGyRekJJbJF32Hzjlun2deZe5dhw9eV5lm8RIThlmkPha2571JssE\nZcHFvad+WPsxEiskX96tZEOMkf5/lIOk+2jxpmt3BiQft+gOZ0CyxEgGklmkbB6pe6L29QBI\ncaGAgZS7diSunYG05exI098RJNVmN5ymlUPQ+2ztog8JSNszObaObAk7ZxaQSpB8DVIoQZJM\nt6w148ci8u1IdkACkk9BinNKd576YQ1YJFkvrftUMRLtgcRf8G4/RgoSKdUgUT6b4+zi34mR\nqEp/x04dxUi0QIxEwdLfXZD4V54JJZklbVokb0YpmM2SRXQZSNvCwyDrGGqQXA1SMJDUtdNH\nHju9RW/bXZYOajsbKjYnq2s0t4vICUjxAFYDqRUjWXHL2mW2QzSWbEhjpLqKvICCZPUbMUXW\nri5NEaQiRgoG0gIxEmdEFCS3C5JXkHoxUmaY+MJkL0A9O5dYJMpA4mUNvrBI6SxWGSNtfoHG\nSGws5VHe0o7cAEISI3nJ4wfPX7JqkUICkuudqIfldv5KQLKLrpX+dtnXf+naxXmkdnOJazcC\nkn6aZjWa80hZ6dIitWKkIK7d2y1SKGMkbyBRHSMR8Sp570rXzlUxUpC8soAUM9AFSCGxSCVI\nMo/kAl8XjHTl2pEaJKd5EjFMYpGINPvgvTwARx6ZyO8L4AN4a4zU6IiBtBMjkVqrfowUlzo0\nLRKdAEnbKkGiMkbKSucgVTGS5fZWiJFSkMhAypMNGm7I5So35yUWib/MswWrIWhe2YLOuBwn\nJCDx0mVeohRjpMDP3+UYx8vyZm8guRQksSjcM31wbBIjKUgSPMnaNbFI9jIRJwbrzlM/rAOL\ntP2/XXn7MZLt17ZIFiO1QVLXrtGDLkjpj2D/KpCyA7EOl9uiRXp/jMRrMFKQnLeEN2dVokXi\n5b+eHcEOSI4Xt26ZaamFk7Wy/iE0QJK1xbpuTi55tkiOLZI+h4Nth9veCmwxkoIkCcdgLmQZ\nI/2HRi4OAymk6W/3SpBKxYh+Zx7JAp86RLoBpJbyrF23tNWgiTxf7sVG6fUxUmKRKLp2Mplq\nUYrFSJLichRB2iZp4wd8WaojZl8siWuXg+TkfgoDyZIHFDKQ5EnqAlKMkfQB67yY3SlI21p1\nzdrpfKyOjrp2cvvlUiCx0hiJlbt2th9vy4qWINWN3wFS17VrgeTXBonXmFrUQSQTmeSja0cl\nSD4FSV07ijHSNiZBjYSXrF0J0pYLtwngICCF0iKR3YRo80gWI3HOT0Eitkik6e9g9pESkDiJ\nEbx/r2vXVhojUSNGMnerHSPRYYw0DFKvg3QOpLwzJUjte7feBFLM2ilImmNjiyQ3KKYxEh9W\nTDZUIMki1Rwkr6FLBhJlINk9sZJ5DfzMrS5IjRiJCY4xkoHkC5C8geS3DnJsduepH9YQSCG6\ndharJzHSDkjyd8e10ypClk8vW2/3Kf2Rx0h0CFLVidUsUuA74w0k83bUtdM1OxGkzCK5HCRz\n7TT/HYgsY1FbpAgSGUghsUgkSewqRspBcpL+dtEUKkh8xemcbAKSNMtf33JX4K2nflhDTVcg\npcUTW9W85odAOm2RWsTsWKS0tdiJNlALgOSbIFECUihAUm6cgeQaMZK+AG8DSXMPHI64GCNx\ny3xF/6fA6WqFrSin3NgiyRudDSTvkxiJp7hctEheD4u/rEMDJE8SIwlIlBmkFUDK/0gtUssC\nNVppfazbfgqSunZtvrJOfQekUIBE+m0XnLzbox0jUW6RXAoSU+cNpBBBCvsgeZ0alad6koHk\nXXTtfBojbS5mBVJmkazDxI0rSD6C5FcCiaoY6SxI7Rgp9uBqjBTSXS7GSFWH1gNJ7k2WrJ3r\nWiR9ekwDJHnYSQ4S85WBRA2QXAYSFSDx63SyZIO5dpyFE9cuxkjm2jVB4qekED/5ZaUY6b/6\nIPX3TFqZ7tplG2OIU4FUdmr/eJtB3kjBa3teqdHJotQ+SPylHWQaKcZI1LNIJK+PkhtmshjJ\ny614JUgUQbKHesROFiDx/a3i2llPOEZyZYxEKUiUgRRjJFmnF7Rjt536YV0DiXYsUrOVu0DK\ndxmYR8rUce2a+74KpMIi6dMy1LUT78flFokykMgpSGQ5NMkqxawd55mJ12iTXPdNkEIO0pY+\naoBEpWuXgMTAskewOesaI+mRb2FVDhKtBVLrajzr2k2OkZq79EFqt/5ukFxUVnvTtdu2dUGi\nEiSdkHU5SF4qSeeR1CLFLmUgOcu390GSUkKF5NupARKJRaLMtUvOh1f+BaSwlmsXuhnjOTHS\nLJAaO18AqX1KXmORtvxy17WjAiS5o1gdKo6RXAOk/5stRqIUpO2SPgmSa4NEAhL5hkXakgsC\nErFpPAYpfAekUpdipNPzSJ1dzoHUrugtFqldo80jGUiuCRKnF5zPQeJbtmVDApK+7TMukAh2\nO4aSSjsgUQ0SGUhaSmr2/PAF77RCi5GIQRLPzpN+Kkce284sUudEPazLIFnxKTHSTj8GQNrZ\n+VTphUBiXgQkCnn62yySLIP0doa3KIMvyQwk/mGrv4m9Oy/XaQ4SlSBxItGdASlaJK6BHUvP\nz7tl15BniwZcu86JelgPxUhH80h3g/Qhi0Q1SL4EiSJIXkrxNRxB8l2QKAOptkgVSBvabggk\nL52JMRJxyoKXCKUgcUfaIMnRsGeXtPt2kOjHrt1hD94B0k5XlgBp2yMDSWIk2geJomtHESRK\nZj5bIPEnpI8OGgBJYiSmJAXJHg4Uc8JeXLt45ClIYpGc9qw+UQ/rGZD6Hx9bpFPqUfcdkKgB\nEmUg8URMHiPpNo2RDCTlwZINiWunIEkSnEhWJTVBGomRQuXauQgSL/uJIIUWSEWMRItl7egM\nSKMVJD24H6QzWg0kKixSDlJeUydG0nuFCpDoDEhFkp4EJKpjJDKQnO+AxPvlIFEVI7kFQRov\nDot0oq0rNQ6B5FwWI0WL1HHtLEZKXLsQQaJ9kKiwSAKSS19iZjGSZjQqkEIOUjLHrMeVx0i8\nimn1GKlb/Mw1K1UApDM18qs9E5CK6X2O1kMSI/1XGySqXDsFiRKQ+A9KQIoFaVeHzG8AAAkA\nSURBVBekyFEGEjUtUg1SPmx1jMTGsHeiHtVjIMG1u64jkIolHQKSG7BIpK/DakzIUghdi0QN\nkKoeO3veVx4jqWvnatculCAVFkksYRYjfRWkcxUApNM18q1BOUhdi2SnPUk2uBgjRZCia5eA\nRAVIKUMpSCE41wYpTTYEfwhSNiu0B9K2eUWQxov/qkWaoQVAqixSKHY3kIrzLss+a4vUjJGC\nPNH2Okipb2dr7WSOqAIpDINEf8EinY2RzvXj17QeSC4DKXHtcpCyGIlKkMyIZCAlBUlBqg+b\nW2mBtIEwBFJRXwZSIMRIl/vxa1oLJHcIkszg5DHStkvML3RdO/tN9qsskuxrIG2NxhcacNau\nAIk8EVUg7cVI9GmLdK6C8xX9kt4KEn/UB0l1ECMlHKQgOVlrdx0kn4BUpL9TkLSVz4M0Xvya\nRXq9XgUS/4gguQokF1wOEmvz2xQk3rkEKfpTIciD79sgUbIfdUByPZDKGInYrRsAiRAjLa33\ngCR/ngTJy6YKJP4/BSmzSP0YyapmkHoxEl//239WWRkjUQck2gVJHmz8x0Bana+vgEQKkksr\nSzgoQOKPYvByHiSzSES7IFHl2sV7rLQ+aT2ZR/ouSOcqWEafA2nMIlU3ljRAIn7NS91tyTZE\ni2Q9aVqkgRgp2bAoSOPFYZGeaTvNOA/HSLz9FpDa7fRAoh+BRJZsoNVAQox0w54/qvEkSIWL\nVLl2naxd9fTcFki0A9KJGOkYpGQT6bpagLSW3ghS3KEEiU6DlOxZgXRgkcKeRUpBymOkzMKQ\nTMZWa7zaIP0Fi/RR3QaSS3SmxpMg1S2mdaf7zQXJpxap2q6fDKa/4xb5zz0Dkn3b9Bt4LEZa\nXfdZpOP9j0Gqdv8JSNbCoGvXA4nYmxsGyZcG6cC1exikyqGtdxkQXLsb9hwt0N7hwCI1E2lS\ncNAiUQMk2zsHqdlHZ9NW5MhipLQf6Z91jFSlv7MtvNb5kbdR2LdHvwmANKg7Y6SjEocgUQ2S\nmwBSyyI1+jMMEs0DSbY6Sg3SCiDdU3whvS7ZcB9IVukMkHxqkap+pH/WMVIFHpVbvwwSLNJD\nbe/mJn4AkqkLUrXfMUg0AJK4a+lHb7FIFm7+OEYaLw6QHmp7J4X0oxgpahSk3p2Zwk4E6dC1\nOwVSeAwksoPob/9h9fVHAOmhto9A6u7QyLX/zCKNgnQcI+0+K6BpkeghkI6EGGlQXwJpf0bE\nNB2kA4tUT8gOxEjfBQkW6WTFFydkD0ByT4JE00DKVezf3AqQ1tJ9Ful4/z8LUlFdq92nQcqb\nOP4SvFTtJoA0veoOSLtFJoF0vNceSHQqRjoL0sct0kd1Z4x0VGJxkKwjky3Sx0GCRXqo7csg\n0ThIQzoEicZAOmqnDdLeHg8KIA3qD4J06rm1IyDVM7LpX6dBurLHVYl32m8AIA3qD4I0apG6\nvXHlLz8DqdSDFmlLs7u9FhAjDep5kH6UEQJIM+Vi5b0mYJEG9QRIEwfpnSANlDkhgLSi3ufa\n7Rdxe8V6t/zlut8inai/IYC0ogDSQYN7n60OEmKkeVoQpN0aR0A61eDeZ6u7dsjazdONIB2m\nFOaDNP+a288hPtMHzCMtoPtAOvreXgOkK40BpL3iAOlyxZOzdqPN/poA0qziCwkgzRdA2isO\ni3S54r8G0nQBpPcLMdICAkjv12pZux/vsKI+BdJHtdo80vROrCCA9H4BpAUEkN6vu0HaKwWQ\nBgWQ3q/FQPqbWhekvyOAtIAA0vsFkBYQQHq/ANICAkjv12JZu78pgPR+AaQFBJDeL4C0gADS\n+wWQFhBAer9+FSRoUNNPPcZousZP6Y3DdUPDF7u7RLH3CWP0ixXe2/ASZxsgfbbYgxXe2/AS\nZxsgfbbYgxXe2/ASZxsgfbbYgxXe2/ASZxsgfbbYgxXe2/ASZxsgfbbYgxXe2/ASZxsgfbbY\ngxXe2/ASZxsgfbbYgxXe2/ASZxsgfbbYgxXe2/ASZxsgfbbYgxVC0F8UQIKgCQJIEDRBAAmC\nJgggQdAEASQImiCABEETBJAgaIIAEgRNEECCoAkCSBA0QQAJgiYIIEHQBAEkCJqg50Cyx+3Z\nY/fqX5rlejvvldrZe3ax4xJnnjP4u8IYXdZjQ+y0sZ1fmuXcUfFeY+5asZOtHfdv9/BeJYzR\ndT01wnYoO7+0y7m4dbTUxcauFDvu3+7hvUoYox/o2QF+dJAuFjvVR930CZBYGKNLejlIAyeh\nWUpc3tNXRPw3XOzPg4Qx+nHhK409MkiXzvZW8HxrHwMJY3RN7wbJCpwe2t7eS37bPSmM0TU9\nOcCnT7e7VOryKbtW7FsgYYwu6sEBdvn/I4Nkb3v624P0nDBGV/XcALv0x4mjwLfdc8IYXdZj\nA+zSX1z7l52C50rt7D292GH/9g/vTcIYXddTI5y8khPLT14qjNEPtMYQQ9DLBZAgaIIAEgRN\nEECCoAkCSBA0QQAJgiYIIEHQBAEkCJoggARBEwSQIGiCABIETRBAgqAJAkgQNEEACYImCCBB\n0AQBJAiaIIAEQRMEkCBoggASBE0QQIKgCQJIEDRBAAmCJgggQdAEASQImiCABEETBJAgaIIA\nEgRNEECCoAn6BkhHLxNY54UQ39XHx2jhricaGSTod/XxMVq8+6KPD9In9PExWrz7Iscv9yF7\nz42+fF5eyvj/f3nZVLJd3wT0jXPwdn18jF7fwSFVb15z8R1t2wi2t7vkU+hmfXyM3t6/Mbnk\nXzz3+Z/t7d84/hX08TFaopOH6gzC9odbf5A+oY+P0RKdPFT0BrJX1dsI7XwbruB/f0IfH6PX\nd3BI+SBQOghHg5T+hG7Ux8fo7f0b03X/O/sJ3aiPj9Hb+zcmG4BqNIhS/7szWt84CS/Xx8fo\n7f0bkzjS9n/if2+TE405iqTYN87B2/XxMXp9ByFoBQEkCJoggARBEwSQIGiCABIETRBAgqAJ\nAkgQNEEACYImCCBB0AQBJAiaIIAEQRMEkCBoggASBE0QQIKgCQJIEDRBAAmCJgggQdAEASQI\nmiCABEETBJAgaIIAEgRNEECCoAkCSBA0QQAJgiYIIEHQBP0D9BHHd1i+YVoAAAAASUVORK5C\nYII=",
"text/plain": [
"Plot with title \"Trace of s\""
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"summary(usage_posterior)\n",
"plot(usage_posterior,trace=FALSE)\n",
"par(mfrow = c(2, 2))\n",
"plot(usage_posterior,density=FALSE)"
]
},
{
"cell_type": "markdown",
"id": "e8997a9d",
"metadata": {},
"source": [
"We can plot the posterior distributions for the model parameters from the samples:"
]
},
{
"cell_type": "code",
"execution_count": 51,
"id": "7e5ef094",
"metadata": {
"name": "Usage rstanarm glm - plot posteriors"
},
"outputs": [
{
"data": {
"image/png": 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lE00YsLiqROrEcJImGUXgOQjKKxEQkh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",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"posterior <- as.matrix(usage_posterior)\n",
"\n",
"plot1<- mcmc_areas(posterior, pars = c(\"a\"), prob = 0.80)\n",
"plot2<- mcmc_areas(posterior, pars = c(\"b\"), prob = 0.80)\n",
"plot3<- mcmc_areas(posterior, pars = c(\"c\"), prob = 0.80)\n",
"plot4<- mcmc_areas(posterior, pars = c(\"s\"), prob = 0.80)\n",
"\n",
"grid.arrange(plot1,plot2, plot3, plot4, top=\"Posterior distributions (median + 80% intervals)\")"
]
},
{
"cell_type": "markdown",
"id": "1996fc9f",
"metadata": {},
"source": [
"Similar to the earlier example, we could extract the $R^2$ from the posterior distribution as well as run posterior predictive checks.\n",
"\n",
"Further considerations: extracting the mean of the parameter projections, we could produce predictions for the test data. We could also produce predictions for test data point based upon each of the samples from the posterior, so above we would produce 2400 predictions for each data point (3x10k, discarding the first 2k from each chain and only saving 1/10 of the samples).\n",
"\n",
"## Estimating COVID 19 infections in NSW, Australia\n",
"\n",
"[This paper](https://actuaries.logicaldoc.cloud/download-ticket?ticketId=4fda7653-5e3d-4514-a79f-ed0070a0f9be) presented at the 2021 Actuaries (Institute) Summit discusses a method of forecasting COVID infections using the package [\"epinow2\"](https://epiforecasts.io/EpiNow2/index.html). The package makes use of STAN. \n",
"\n",
">\"[Epinow2] estimates the time-varying reproduction number on cases by date of infection... Imputed infections are then mapped to observed data (for example cases by date of report) via a series of uncertain delay distributions...\"\n",
"\n",
"That is to say, the model makes some assumptions about lags in symptoms and in reporting (assuming some distribution for those delays) in order to estimate the true underlying number of infections (backwards). Using that backcast it projects out how those infections might be reported over time. The model also estimates the effective reproduction number in order to predict future infections.\n",
"\n",
"Covid case and test data sourced from the department of [NSW Website](https://data.nsw.gov.au/) on 17/01/2022. \n",
"\n",
"We should be careful in placing too heavy a reliance on any models of incidence which are based upon case data (particularly where case rates are expected to be under reported or where testing is incomplete). The example is purely illustrative and does not attempt to correct for gaps in the data.\n",
"\n",
"Case data:"
]
},
{
"cell_type": "code",
"execution_count": 52,
"id": "0f6466dc",
"metadata": {
"name": "Case data"
},
"outputs": [
{
"data": {
"text/html": [
"\n",
"notification_date | postcode | lhd_2010_code | lhd_2010_name | lga_code19 | lga_name19 |
\n",
"\n",
"\t2020-01-25 | 2134 | X700 | Sydney | 11300 | Burwood (A) |
\n",
"\t2020-01-25 | 2121 | X760 | Northern Sydney | 16260 | Parramatta (C) |
\n",
"\t2020-01-25 | 2071 | X760 | Northern Sydney | 14500 | Ku-ring-gai (A) |
\n",
"\t2020-01-27 | 2033 | X720 | South Eastern Sydney | 16550 | Randwick (C) |
\n",
"\t2020-03-01 | 2077 | X760 | Northern Sydney | 14000 | Hornsby (A) |
\n",
"\t2020-03-01 | 2163 | X710 | South Western Sydney | 12850 | Fairfield (C) |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|llllll}\n",
" notification\\_date & postcode & lhd\\_2010\\_code & lhd\\_2010\\_name & lga\\_code19 & lga\\_name19\\\\\n",
"\\hline\n",
"\t 2020-01-25 & 2134 & X700 & Sydney & 11300 & Burwood (A) \\\\\n",
"\t 2020-01-25 & 2121 & X760 & Northern Sydney & 16260 & Parramatta (C) \\\\\n",
"\t 2020-01-25 & 2071 & X760 & Northern Sydney & 14500 & Ku-ring-gai (A) \\\\\n",
"\t 2020-01-27 & 2033 & X720 & South Eastern Sydney & 16550 & Randwick (C) \\\\\n",
"\t 2020-03-01 & 2077 & X760 & Northern Sydney & 14000 & Hornsby (A) \\\\\n",
"\t 2020-03-01 & 2163 & X710 & South Western Sydney & 12850 & Fairfield (C) \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| notification_date | postcode | lhd_2010_code | lhd_2010_name | lga_code19 | lga_name19 |\n",
"|---|---|---|---|---|---|\n",
"| 2020-01-25 | 2134 | X700 | Sydney | 11300 | Burwood (A) |\n",
"| 2020-01-25 | 2121 | X760 | Northern Sydney | 16260 | Parramatta (C) |\n",
"| 2020-01-25 | 2071 | X760 | Northern Sydney | 14500 | Ku-ring-gai (A) |\n",
"| 2020-01-27 | 2033 | X720 | South Eastern Sydney | 16550 | Randwick (C) |\n",
"| 2020-03-01 | 2077 | X760 | Northern Sydney | 14000 | Hornsby (A) |\n",
"| 2020-03-01 | 2163 | X710 | South Western Sydney | 12850 | Fairfield (C) |\n",
"\n"
],
"text/plain": [
" notification_date postcode lhd_2010_code lhd_2010_name lga_code19\n",
"1 2020-01-25 2134 X700 Sydney 11300 \n",
"2 2020-01-25 2121 X760 Northern Sydney 16260 \n",
"3 2020-01-25 2071 X760 Northern Sydney 14500 \n",
"4 2020-01-27 2033 X720 South Eastern Sydney 16550 \n",
"5 2020-03-01 2077 X760 Northern Sydney 14000 \n",
"6 2020-03-01 2163 X710 South Western Sydney 12850 \n",
" lga_name19 \n",
"1 Burwood (A) \n",
"2 Parramatta (C) \n",
"3 Ku-ring-gai (A)\n",
"4 Randwick (C) \n",
"5 Hornsby (A) \n",
"6 Fairfield (C) "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"data": {
"text/html": [
"\n",
"test_date | postcode | lhd_2010_code | lhd_2010_name | lga_code19 | lga_name19 | test_count |
\n",
"\n",
"\t2020-01-01 | 2038 | X700 | Sydney | 14170 | Inner West (A) | 1 |
\n",
"\t2020-01-01 | 2039 | X700 | Sydney | 14170 | Inner West (A) | 1 |
\n",
"\t2020-01-01 | 2040 | X700 | Sydney | 14170 | Inner West (A) | 2 |
\n",
"\t2020-01-01 | 2041 | X700 | Sydney | 14170 | Inner West (A) | 1 |
\n",
"\t2020-01-01 | 2069 | X760 | Northern Sydney | 14500 | Ku-ring-gai (A) | 1 |
\n",
"\t2020-01-01 | 2074 | X760 | Northern Sydney | 14500 | Ku-ring-gai (A) | 1 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lllllll}\n",
" test\\_date & postcode & lhd\\_2010\\_code & lhd\\_2010\\_name & lga\\_code19 & lga\\_name19 & test\\_count\\\\\n",
"\\hline\n",
"\t 2020-01-01 & 2038 & X700 & Sydney & 14170 & Inner West (A) & 1 \\\\\n",
"\t 2020-01-01 & 2039 & X700 & Sydney & 14170 & Inner West (A) & 1 \\\\\n",
"\t 2020-01-01 & 2040 & X700 & Sydney & 14170 & Inner West (A) & 2 \\\\\n",
"\t 2020-01-01 & 2041 & X700 & Sydney & 14170 & Inner West (A) & 1 \\\\\n",
"\t 2020-01-01 & 2069 & X760 & Northern Sydney & 14500 & Ku-ring-gai (A) & 1 \\\\\n",
"\t 2020-01-01 & 2074 & X760 & Northern Sydney & 14500 & Ku-ring-gai (A) & 1 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| test_date | postcode | lhd_2010_code | lhd_2010_name | lga_code19 | lga_name19 | test_count |\n",
"|---|---|---|---|---|---|---|\n",
"| 2020-01-01 | 2038 | X700 | Sydney | 14170 | Inner West (A) | 1 |\n",
"| 2020-01-01 | 2039 | X700 | Sydney | 14170 | Inner West (A) | 1 |\n",
"| 2020-01-01 | 2040 | X700 | Sydney | 14170 | Inner West (A) | 2 |\n",
"| 2020-01-01 | 2041 | X700 | Sydney | 14170 | Inner West (A) | 1 |\n",
"| 2020-01-01 | 2069 | X760 | Northern Sydney | 14500 | Ku-ring-gai (A) | 1 |\n",
"| 2020-01-01 | 2074 | X760 | Northern Sydney | 14500 | Ku-ring-gai (A) | 1 |\n",
"\n"
],
"text/plain": [
" test_date postcode lhd_2010_code lhd_2010_name lga_code19 lga_name19 \n",
"1 2020-01-01 2038 X700 Sydney 14170 Inner West (A) \n",
"2 2020-01-01 2039 X700 Sydney 14170 Inner West (A) \n",
"3 2020-01-01 2040 X700 Sydney 14170 Inner West (A) \n",
"4 2020-01-01 2041 X700 Sydney 14170 Inner West (A) \n",
"5 2020-01-01 2069 X760 Northern Sydney 14500 Ku-ring-gai (A)\n",
"6 2020-01-01 2074 X760 Northern Sydney 14500 Ku-ring-gai (A)\n",
" test_count\n",
"1 1 \n",
"2 1 \n",
"3 2 \n",
"4 1 \n",
"5 1 \n",
"6 1 "
]
},
"metadata": {},
"output_type": "display_data"
},
{
"name": "stderr",
"output_type": "stream",
"text": [
"`summarise()` has grouped output by 'date'. You can override using the `.groups` argument.\n",
"\n"
]
},
{
"data": {
"text/html": [
"\n",
"date | descr | confirm |
\n",
"\n",
"\t2021-05-01 | cases | 2 |
\n",
"\t2021-05-02 | cases | 8 |
\n",
"\t2021-05-03 | cases | 9 |
\n",
"\t2021-05-04 | cases | 7 |
\n",
"\t2021-05-05 | cases | 9 |
\n",
"\t2021-05-06 | cases | 4 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" date & descr & confirm\\\\\n",
"\\hline\n",
"\t 2021-05-01 & cases & 2 \\\\\n",
"\t 2021-05-02 & cases & 8 \\\\\n",
"\t 2021-05-03 & cases & 9 \\\\\n",
"\t 2021-05-04 & cases & 7 \\\\\n",
"\t 2021-05-05 & cases & 9 \\\\\n",
"\t 2021-05-06 & cases & 4 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| date | descr | confirm |\n",
"|---|---|---|\n",
"| 2021-05-01 | cases | 2 |\n",
"| 2021-05-02 | cases | 8 |\n",
"| 2021-05-03 | cases | 9 |\n",
"| 2021-05-04 | cases | 7 |\n",
"| 2021-05-05 | cases | 9 |\n",
"| 2021-05-06 | cases | 4 |\n",
"\n"
],
"text/plain": [
" date descr confirm\n",
"1 2021-05-01 cases 2 \n",
"2 2021-05-02 cases 8 \n",
"3 2021-05-03 cases 9 \n",
"4 2021-05-04 cases 7 \n",
"5 2021-05-05 cases 9 \n",
"6 2021-05-06 cases 4 "
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df_cases <- read.csv(file = '../_static/bayesian_applications/confirmed_cases_table1_location.csv') \n",
"head(df_cases)\n",
"df_tests <- read.csv(file = '../_static/bayesian_applications/pcr_testing_table1_location_agg.csv') \n",
"head(df_tests)\n",
"\n",
"# cases\n",
"df_cases <- df_cases %>% mutate(descr=\"cases\",date=as.Date(notification_date),cases=1) %>%\n",
"filter(date > \"2021-04-30\",date <= \"2021-12-31\") %>% \n",
"group_by(date, descr) %>% \n",
"summarise(confirm=sum(cases)) \n",
"head(df_cases)"
]
},
{
"cell_type": "markdown",
"id": "8a351b69",
"metadata": {},
"source": [
"Plotting recorded cases by date (PCR test outcomes only and only to 31 December 2021):"
]
},
{
"cell_type": "code",
"execution_count": 53,
"id": "d3baa594",
"metadata": {
"name": "Case plot",
"warning": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message:\n",
"\"Removed 1 rows containing missing values (geom_col).\"\n"
]
},
{
"data": {
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ST5iE49iGTT8xzJRSSATpbdtev6HJYP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\n/wGCewRjhWYkcQAAAABJRU5ErkJggg==",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"df_cases %>% mutate(omicron=ifelse(date > \"2021-11-26\",\"first case+\",\"pre\")) %>%\n",
"ggplot(data=., mapping = aes(x=date, y=confirm)) + \n",
"geom_col(aes(fill=omicron)) +\n",
"scale_x_date(date_breaks = \"months\" , date_labels = \"%b-%y\", limits = c(as.Date(\"2021-04-30\"), as.Date(\"2021-12-31\"))) +\n",
"labs(x=\"Date\", y=\"Cases\", title = \"Covid cases by date, NSW\") +\n",
"theme_pander() + scale_color_gdocs()"
]
},
{
"cell_type": "markdown",
"id": "89bbc4ac",
"metadata": {},
"source": [
"Test data:"
]
},
{
"cell_type": "code",
"execution_count": 54,
"id": "03b4e2fe",
"metadata": {
"name": "Test data",
"warning": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"`summarise()` has grouped output by 'date'. You can override using the `.groups` argument.\n",
"\n"
]
},
{
"data": {
"text/html": [
"\n",
"date | descr | tests |
\n",
"\n",
"\t2021-05-01 | tests | 4514 |
\n",
"\t2021-05-02 | tests | 4775 |
\n",
"\t2021-05-03 | tests | 14877 |
\n",
"\t2021-05-04 | tests | 10868 |
\n",
"\t2021-05-05 | tests | 13126 |
\n",
"\t2021-05-06 | tests | 24029 |
\n",
"\n",
"
\n"
],
"text/latex": [
"\\begin{tabular}{r|lll}\n",
" date & descr & tests\\\\\n",
"\\hline\n",
"\t 2021-05-01 & tests & 4514 \\\\\n",
"\t 2021-05-02 & tests & 4775 \\\\\n",
"\t 2021-05-03 & tests & 14877 \\\\\n",
"\t 2021-05-04 & tests & 10868 \\\\\n",
"\t 2021-05-05 & tests & 13126 \\\\\n",
"\t 2021-05-06 & tests & 24029 \\\\\n",
"\\end{tabular}\n"
],
"text/markdown": [
"\n",
"| date | descr | tests |\n",
"|---|---|---|\n",
"| 2021-05-01 | tests | 4514 |\n",
"| 2021-05-02 | tests | 4775 |\n",
"| 2021-05-03 | tests | 14877 |\n",
"| 2021-05-04 | tests | 10868 |\n",
"| 2021-05-05 | tests | 13126 |\n",
"| 2021-05-06 | tests | 24029 |\n",
"\n"
],
"text/plain": [
" date descr tests\n",
"1 2021-05-01 tests 4514\n",
"2 2021-05-02 tests 4775\n",
"3 2021-05-03 tests 14877\n",
"4 2021-05-04 tests 10868\n",
"5 2021-05-05 tests 13126\n",
"6 2021-05-06 tests 24029"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"df_tests <- df_tests %>% mutate(descr=\"tests\",date=as.Date(test_date)) %>%\n",
"filter(date > \"2021-04-30\",date <= \"2021-12-31\") %>% \n",
"group_by(date, descr) %>% \n",
"summarise(tests=sum(test_count)) \n",
"head(df_tests)"
]
},
{
"cell_type": "markdown",
"id": "f8eab568",
"metadata": {},
"source": [
"Plotting tests by date (PCR tests only; to 31 December 2021):"
]
},
{
"cell_type": "code",
"execution_count": 55,
"id": "5867e653",
"metadata": {
"name": "Test plot",
"warning": false
},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"Warning message:\n",
"\"Removed 1 rows containing missing values (geom_bar).\"\n"
]
},
{
"data": {
"image/png": 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MZOkfwgUmEg0qEg0llApENBpLOASIfS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\n",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"ggplot(data=df_tests, mapping = aes(x=date, y=tests))+ \n",
"geom_bar(stat=\"identity\") +\n",
"scale_x_date(date_breaks = \"months\" , date_labels = \"%b-%y\", limits = c(as.Date(\"2021-04-30\"), as.Date(\"2021-12-31\"))) +\n",
"labs(x=\"Date\", y=\"Tests\", title = \"PCR tests by date, NSW\") +\n",
"theme_pander() + scale_color_gdocs()"
]
},
{
"cell_type": "markdown",
"id": "754b9911",
"metadata": {},
"source": [
"Merged to get positive test rate:"
]
},
{
"cell_type": "code",
"execution_count": 56,
"id": "22b4245a",
"metadata": {
"name": "Merged data",
"warning": false
},
"outputs": [],
"source": [
"# merge\n",
"df <- merge(x = df_cases, y = df_tests, by = \"date\", all.x = TRUE) %>%\n",
"mutate(pos_rate=pmin(1, confirm/tests)) %>%\n",
"fill(pos_rate, .direction = \"downup\") %>%\n",
"# add smoothed positive rate\n",
"mutate(pos_rate_sm = fitted(loess(pos_rate~as.numeric(date),span=0.1))) # loess - Local Polynomial Regression Fitting; span - the parameter which controls the degree of smoothing\n",
"# drop descriptions\n",
"df$descr.x <- NULL\n",
"df$descr.y <- NULL"
]
},
{
"cell_type": "markdown",
"id": "9d6b1cb0",
"metadata": {},
"source": [
"Plot of positive rate shows that the proportion of tests returning a positive increases to above 5% from 25th December 2021, suggesting that the case data beyond this point is less complete. "
]
},
{
"cell_type": "code",
"execution_count": 57,
"id": "0bcf6918",
"metadata": {
"name": "Merged plot"
},
"outputs": [
{
"data": {
"image/png": 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iVRsVZWRFNiY33YgEju6X9veAeweWSG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",
"text/plain": [
"plot without title"
]
},
"metadata": {
"image/png": {
"height": 420,
"width": 420
}
},
"output_type": "display_data"
}
],
"source": [
"# positive rate\n",
"ggplot(data=df, mapping = aes(x=date))+ \n",
"geom_point(aes(y=(pos_rate))) +\n",
"geom_line(aes(y=pos_rate_sm)) +\n",
"scale_x_date(date_breaks = \"months\" , date_labels = \"%b-%y\", limits = c(as.Date(\"2021-04-30\"), as.Date(\"2021-12-31\"))) +\n",
"scale_y_continuous(labels = scales::percent_format(accuracy = 1)) +\n",
"labs(x=\"Date\", y=\"Positive test rate\", title = \"Positive PCR test rate by date, NSW\") +\n",
"theme_pander() + scale_color_gdocs()\n"
]
},
{
"cell_type": "markdown",
"id": "78257973",
"metadata": {},
"source": [
"There are some pragmatic methods for adjusting the case numbers for [increasing test positivity rates](http://freerangestats.info/blog/2020/05/09/covid-population-incidence). For our purposes we will focus the model on case data before 23 December 2021 in order to exclude the period where the test data became less reliable/ complete, noting that underlying data completeness issues are likely present."
]
},
{
"cell_type": "code",
"execution_count": 58,
"id": "41b78b3a",
"metadata": {
"eval": false,
"name": "Epinow2 - inputs"
},
"outputs": [],
"source": [
"\n",
"not_run_sample_only <- function(){# Reporting delays (delay from symptom onset to reporting/ testing positive)\n",
"reporting_delay <- estimate_delay(rlnorm(100, log(6), 1), max_value = 15)\n",
"cat(\"Mean reporting delay = \",reporting_delay$mean, \"; \")\n",
"\n",
"# Symptom generation time (time between infection events in an infector-infectee pair) and incubation period (time between moment of infection and symptom onset)\n",
"generation_time <- get_generation_time(disease = \"SARS-CoV-2\", source = \"ganyani\")\n",
"cat(\"Mean generation time =\",generation_time$mean, \"; \")\n",
"incubation_period <- get_incubation_period(disease = \"SARS-CoV-2\", source = \"lauer\")\n",
"cat(\"Mean incubation period =\",incubation_period$mean, \"; \")}\n"
]
},
{
"cell_type": "code",
"execution_count": 59,
"id": "c710616c",
"metadata": {
"eval": false,
"name": "Epinow2 - projection"
},
"outputs": [],
"source": [
"not_run_sample_only <- function(){\n",
"df_cases_fit <- df_cases %>% filter(date <= \"2021-12-22\") # exclude data before 23 December 2021\n",
"\n",
"estimates <- epinow(reported_cases = df_cases_fit[c(\"date\",\"confirm\")], # case data from NSW\n",
" generation_time = generation_time,\n",
" delays = delay_opts(incubation_period, reporting_delay),\n",
" rt = rt_opts(prior = list(mean = 2, sd = 0.2)),\n",
" stan = stan_opts(cores = 6, samples = 3000, warmup = 500, chains = 6, control = list(adapt_delta = 0.95)))}\n"
]
},
{
"cell_type": "markdown",
"id": "56863560",
"metadata": {},
"source": [
"Importing a previous run of the above:"
]
},
{
"cell_type": "code",
"execution_count": 60,
"id": "5b6c38b4",
"metadata": {
"name": "Epinow2 - Import run"
},
"outputs": [],
"source": [
"load(\"../_static/bayesian_applications/covid_estimates_summary.RData\")"
]
},
{
"cell_type": "markdown",
"id": "4d490ded",
"metadata": {},
"source": [
"plot(estimates) produces predefined plots of cases by date reported and date of infection as well as the effective reproduction number. Given the dramatic increase in reported cases towards the end of the period, it is not surprising that the range of forecast cases is wide. Interestingly, the forecast/ partial forecast reproduction number reduces; presumably this is influenced by the earlier observations where case numbers were low. This issue has not been investigated further, however there are articles that discuss the [impact of changes to the testing procedures](https://epiforecasts.io/covid/methods.html) and other limitations.\n",
"\n",
"![](../_static/bayesian_applications/covid_estimates.jpg){width=100%}\n",
"Merging forecast reported cases with the actual case data:"
]
},
{
"cell_type": "code",
"execution_count": 61,
"id": "8f8dd829",
"metadata": {
"name": "Epinow2 - Testing forecast"
},
"outputs": [],
"source": [
"df <- merge(x = df, y = df_reported, by = \"date\", all.x = TRUE) %>% filter(date < \"2021-12-30\")"
]
},
{
"cell_type": "markdown",
"id": "63592dab",
"metadata": {},
"source": [
"Plotting forecast vs actuals below - the week to 29 December is fully forecast from the model. Actual cases fall within the projected 90% confidence interval range, noting that the test positivity rate increased materially from 25th December so it is likely that the actual cases are under reported. "
]
},
{
"cell_type": "code",
"execution_count": 62,
"id": "a7b1bce9",
"metadata": {
"name": "Epinow2 - Plotting forecast and actual"
},
"outputs": [
{
"data": {
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"text/plain": [
"plot without title"
]
},
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"source": [
"\n",
"colours <- c(\"actual\" = \"#3366cc\",\"modelled\" = \"#dc3912\")\n",
"\n",
"ggplot(data=df %>% filter(date >= \"2021-12-01\"), aes(x=date)) +\n",
"geom_line(aes(y=confirm, color=\"actual\")) +\n",
"geom_line(aes(y=mean,color=\"modelled\")) +\n",
"geom_ribbon(aes(ymin=lower_90, ymax=upper_90), fill=\"#dc3912\", alpha=0.2) +\n",
"labs(x=\"Date\", y=\"Reported cases\", title = \"Reported cases by date\",color=\"Legend\") +\n",
"scale_color_manual(values = colours) +\n",
"theme_pander()"
]
},
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"cell_type": "markdown",
"id": "2f25a76c",
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"source": [
"# Common issues in MCMC projections\n",
"\n",
"* Divergent transitions: Common fix is changing the step size using the adapt_delta argument in STAN.\n",
"* Exceeding maximum tree depth: the is a point of efficiency. See notes [here](https://mc-stan.org/misc/warnings.html) for assistance in STAN and other potential warnings.\n",
"\n",
"# Further reading\n",
"A few books and articles of interest on STAN: \n",
"\n",
"* [STAN documentation](https://mc-stan.org/users/documentation/)\n",
"* [STAN linear regression model](https://m-clark.github.io/bayesian-basics/models.html)\n",
"* [Applied Bayesian Inference in r using STAN](https://www.r-bloggers.com/2020/01/applied-bayesian-statistics-using-stan-and-r/)\n",
"* [Prior selections - STAN package](https://github.com/stan-dev/stan/wiki/Prior-Choice-Recommendations)\n",
"* [JAGS user manual](https://people.stat.sc.edu/hansont/stat740/jags_user_manual.pdf)"
]
}
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