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02-bayes-theorem-rpubs.html
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02-bayes-theorem-rpubs.html
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<!DOCTYPE html>
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<title>Bayesian Regression Models with RStanARM</title>
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0;transform-origin:0 0;-webkit-transform:translate3d(0,100%,0) rotateX(-90deg);-moz-transform:translate3d(0,100%,0) rotateX(-90deg);-ms-transform:translate3d(0,100%,0) rotateX(-90deg);transform:translate3d(0,100%,0) rotateX(-90deg)}.reveal.page .slides{-webkit-perspective-origin:0 50%;-moz-perspective-origin:0 50%;-ms-perspective-origin:0 50%;perspective-origin:0 50%;-webkit-perspective:3000px;-moz-perspective:3000px;-ms-perspective:3000px;perspective:3000px}.reveal.page .slides section{padding:30px;min-height:700px;-webkit-box-sizing:border-box;-moz-box-sizing:border-box;box-sizing:border-box}.reveal.page .slides section.past{z-index:12}.reveal.page .slides section:not(.stack):before{content:'';position:absolute;display:block;width:100%;height:100%;left:0;top:0;background:rgba(0,0,0,.1);-webkit-transform:translateZ(-20px);-moz-transform:translateZ(-20px);-ms-transform:translateZ(-20px);-o-transform:translateZ(-20px);transform:translateZ(-20px)}.reveal.page .slides section:not(.stack):after{content:'';position:absolute;display:block;width:90%;height:30px;left:5%;bottom:0;background:0;z-index:1;border-radius:4px;box-shadow:0 95px 25px rgba(0,0,0,.2);-webkit-transform:translateZ(-90px) rotateX(65deg)}.reveal.page .slides>section.stack{padding:0;background:0}.reveal.page .slides>section.past{-webkit-transform-origin:0 0;-moz-transform-origin:0 0;-ms-transform-origin:0 0;transform-origin:0 0;-webkit-transform:translate3d(-40%,0,0) rotateY(-80deg);-moz-transform:translate3d(-40%,0,0) rotateY(-80deg);-ms-transform:translate3d(-40%,0,0) rotateY(-80deg);transform:translate3d(-40%,0,0) rotateY(-80deg)}.reveal.page .slides>section.future{-webkit-transform-origin:100% 0;-moz-transform-origin:100% 0;-ms-transform-origin:100% 0;transform-origin:100% 0;-webkit-transform:translate3d(0,0,0);-moz-transform:translate3d(0,0,0);-ms-transform:translate3d(0,0,0);transform:translate3d(0,0,0)}.reveal.page .slides>section>section.past{-webkit-transform-origin:0 0;-moz-transform-origin:0 0;-ms-transform-origin:0 0;transform-origin:0 0;-webkit-transform:translate3d(0,-40%,0) rotateX(80deg);-moz-transform:translate3d(0,-40%,0) rotateX(80deg);-ms-transform:translate3d(0,-40%,0) rotateX(80deg);transform:translate3d(0,-40%,0) rotateX(80deg)}.reveal.page .slides>section>section.future{-webkit-transform-origin:0 100%;-moz-transform-origin:0 100%;-ms-transform-origin:0 100%;transform-origin:0 100%;-webkit-transform:translate3d(0,0,0);-moz-transform:translate3d(0,0,0);-ms-transform:translate3d(0,0,0);transform:translate3d(0,0,0)}.reveal .slides section[data-transition=fade],.reveal.fade .slides section,.reveal.fade .slides>section>section{-webkit-transform:none;-moz-transform:none;-ms-transform:none;-o-transform:none;transform:none;-webkit-transition:opacity .5s;-moz-transition:opacity .5s;-ms-transition:opacity .5s;-o-transition:opacity .5s;transition:opacity .5s}.reveal.fade.overview .slides section,.reveal.fade.overview 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section:before{display:none!important}.reveal.overview .slides section>section{opacity:1;cursor:pointer}.reveal.overview .slides section:hover{background:rgba(0,0,0,.3)}.reveal.overview .slides section.present{background:rgba(0,0,0,.3)}.reveal.overview .slides>section.stack{padding:0;background:0;overflow:visible}.reveal .pause-overlay{position:absolute;top:0;left:0;width:100%;height:100%;background:#000;visibility:hidden;opacity:0;z-index:100;-webkit-transition:all 1s ease;-moz-transition:all 1s ease;-ms-transition:all 1s ease;-o-transition:all 1s ease;transition:all 1s ease}.reveal.paused .pause-overlay{visibility:visible;opacity:1}.no-transforms{overflow-y:auto}.no-transforms .reveal .slides{position:relative;width:80%;height:auto!important;top:0;left:50%;margin:0;text-align:center}.no-transforms .reveal .controls,.no-transforms .reveal .progress{display:none!important}.no-transforms .reveal .slides section{display:block!important;opacity:1!important;position:relative!important;height:auto;min-height:auto;top:0;left:-50%;margin:70px 0;-webkit-transform:none;-moz-transform:none;-ms-transform:none;-o-transform:none;transform:none}.no-transforms .reveal .slides section section{left:0}.no-transition{-webkit-transition:none;-moz-transition:none;-ms-transition:none;-o-transition:none;transition:none}.reveal .state-background{position:absolute;width:100%;height:100%;background:rgba(0,0,0,0);-webkit-transition:background 800ms ease;-moz-transition:background 800ms ease;-ms-transition:background 800ms ease;-o-transition:background 800ms ease;transition:background 800ms ease}.alert .reveal .state-background{background:rgba(200,50,30,.6)}.soothe .reveal .state-background{background:rgba(50,200,90,.4)}.blackout .reveal .state-background{background:rgba(0,0,0,.6)}.whiteout .reveal .state-background{background:rgba(255,255,255,.6)}.cobalt .reveal .state-background{background:rgba(22,152,213,.6)}.mint .reveal .state-background{background:rgba(22,213,75,.6)}.submerge .reveal .state-background{background:rgba(12,25,77,.6)}.lila .reveal .state-background{background:rgba(180,50,140,.6)}.sunset .reveal .state-background{background:rgba(255,122,0,.6)}.reveal.rtl .slides,.reveal.rtl .slides h1,.reveal.rtl .slides h2,.reveal.rtl .slides h3,.reveal.rtl .slides h4,.reveal.rtl .slides h5,.reveal.rtl .slides h6{direction:rtl;font-family:sans-serif}.reveal.rtl pre,.reveal.rtl code{direction:ltr}.reveal.rtl ol,.reveal.rtl ul{text-align:right}.reveal.rtl .progress span{float:right}.reveal aside.notes{display:none}.zoomed .reveal *,.zoomed .reveal :before,.zoomed .reveal :after{-webkit-transform:none!important;-moz-transform:none!important;-ms-transform:none!important;transform:none!important;-webkit-backface-visibility:visible!important;-moz-backface-visibility:visible!important;-ms-backface-visibility:visible!important;backface-visibility:visible!important}.zoomed .reveal .progress,.zoomed .reveal .controls{opacity:0}.zoomed .reveal .roll span{background:0}.zoomed .reveal .roll span:after{visibility:hidden}
</style>
<style type="text/css" >
/**
* A simple theme for reveal.js presentations, similar
* to the default theme. The accent color is darkblue.
*
* This theme is Copyright (C) 2012 Owen Versteeg, https://github.com/StereotypicalApps. It is MIT licensed.
* reveal.js is Copyright (C) 2011-2012 Hakim El Hattab, http://hakim.se
*/
/*********************************************
* GLOBAL STYLES
*********************************************/
body {
background: white;
background-color: white; }
.reveal {
font-family: "Lato", sans-serif;
font-size: 36px;
font-weight: 200;
letter-spacing: -0.02em;
color: black; }
::selection {
color: white;
background: rgba(0, 0, 0, 0.99);
text-shadow: none; }
/*********************************************
* HEADERS
*********************************************/
.reveal h1,
.reveal h2,
.reveal h3,
.reveal h4,
.reveal h5,
.reveal h6 {
margin: 0 0 20px 0;
color: black;
font-family: "News Cycle", Impact, sans-serif;
line-height: 0.9em;
letter-spacing: 0.02em;
text-transform: none;
text-shadow: none; }
.reveal h1 {
text-shadow: 0px 0px 6px rgba(0, 0, 0, 0.2); }
/*********************************************
* LINKS
*********************************************/
.reveal a:not(.image) {
color: darkblue;
text-decoration: none;
-webkit-transition: color .15s ease;
-moz-transition: color .15s ease;
-ms-transition: color .15s ease;
-o-transition: color .15s ease;
transition: color .15s ease; }
.reveal a:not(.image):hover {
color: #0000f1;
text-shadow: none;
border: none; }
.reveal .roll span:after {
color: #fff;
background: #00003f; }
/*********************************************
* IMAGES
*********************************************/
.reveal section img {
margin: 15px 0px;
background: rgba(255, 255, 255, 0.12);
border: 4px solid black;
box-shadow: 0 0 10px rgba(0, 0, 0, 0.15);
-webkit-transition: all .2s linear;
-moz-transition: all .2s linear;
-ms-transition: all .2s linear;
-o-transition: all .2s linear;
transition: all .2s linear; }
.reveal a:hover img {
background: rgba(255, 255, 255, 0.2);
border-color: darkblue;
box-shadow: 0 0 20px rgba(0, 0, 0, 0.55); }
/*********************************************
* NAVIGATION CONTROLS
*********************************************/
.reveal .controls div.navigate-left,
.reveal .controls div.navigate-left.enabled {
border-right-color: darkblue; }
.reveal .controls div.navigate-right,
.reveal .controls div.navigate-right.enabled {
border-left-color: darkblue; }
.reveal .controls div.navigate-up,
.reveal .controls div.navigate-up.enabled {
border-bottom-color: darkblue; }
.reveal .controls div.navigate-down,
.reveal .controls div.navigate-down.enabled {
border-top-color: darkblue; }
.reveal .controls div.navigate-left.enabled:hover {
border-right-color: #0000f1; }
.reveal .controls div.navigate-right.enabled:hover {
border-left-color: #0000f1; }
.reveal .controls div.navigate-up.enabled:hover {
border-bottom-color: #0000f1; }
.reveal .controls div.navigate-down.enabled:hover {
border-top-color: #0000f1; }
/*********************************************
* PROGRESS BAR
*********************************************/
.reveal .progress {
background: rgba(0, 0, 0, 0.2); }
.reveal .progress span {
background: darkblue;
-webkit-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
-moz-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
-ms-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
-o-transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985);
transition: width 800ms cubic-bezier(0.26, 0.86, 0.44, 0.985); }
</style>
<style type="text/css">
.reveal h1 {
font-size: 2.5em;
}
.reveal h1,
.reveal h2,
.reveal h3,
.reveal h4,
.reveal h5,
.reveal h6 {
margin-bottom: .6em;
}
.reveal p,
.reveal table {
margin-bottom: 1em;
}
.reveal li {
margin-bottom: .4em;
}
.reveal ul ul,
.reveal ul ol,
.reveal ol ol,
.reveal ol ul {
margin-top: .4em;
}
.reveal .slides {
text-align: left;
}
.reveal small {
font-size: 0.85em;
}
.reveal pre {
margin-top: 0;
max-width: 95%;
border: 1px solid #ccc;
white-space: pre-wrap;
margin-bottom: 1em;
}
.reveal pre code {
display: block; padding: 0.5em;
font-size: 1.6em;
line-height: 1.1em;
background-color: white;
overflow: visible;
max-height: none;
word-wrap: normal;
}
.reveal code {
overflow: visible;
max-height: none;
}
.reveal code.r {
background-color: #F8F8F8;
}
.reveal code.cpp {
background-color: #F8F8F8;
}
.reveal section del {
text-decoration: none;
color: #AAB1BA;
}
.reveal section img {
border: none;
}
.reveal section .fieldError {
margin-bottom: 25px;
}
.reveal section .fieldError span {
color: red;
}
.prompt .reveal .state-background {
background: #C6D7DC;
}
.quiz-multichoice .reveal .state-background {
background: rgba(254,220,179,1);
}
.quiz-multichoice .reveal ul {
list-style-type: none;
margin-bottom: 30px;
}
.quiz-multichoice .reveal li {
margin-top: 15px;
}
.quiz-multichoice .reveal .quizFeedback {
margin-bottom: 30px;
}
.quiz-multichoice .reveal .quizFeedback img {
border: none;
box-shadow: none;
background: transparent;
float: left;
margin-top: -15px;
}
.quiz-multichoice .reveal .quizFeedback span {
font-size: 1.4em;
margin-left: 12px;
}
.section .reveal .state-background {
background: #96A2B6;
}
.section .reveal h1,
.section .reveal h2,
.section .reveal p {
color: white;
margin-top: 50px;
}
.sub-section .reveal .state-background {
background: #E7E8EA
}
.sub-section .reveal h2,
.sub-section .reveal p {
color: #63717B;
margin-top: 50px;
}
.reveal strong {
color: #25679E;
}
.reveal .controls {
right: -20px;
bottom: 5px;
}
.reveal .controls div.navigate-left {
top: 75px;
}
.reveal .controls div.navigate-right {
left: 54px;
top: 75px;
}
.reveal .controls div.navigate-up {
display: none;
}
.reveal .controls div.navigate-down {
display: none;
}
/*********************************************
* NAVIGATION CONTROLS
*********************************************/
.reveal .controls div.navigate-left,
.reveal .controls div.navigate-left.enabled {
border-right-color: #25679E;
}
.reveal .controls div.navigate-right,
.reveal .controls div.navigate-right.enabled {
border-left-color: #25679E;
}
.reveal .controls div.navigate-up,
.reveal .controls div.navigate-up.enabled {
border-bottom-color: #25679E;
}
.reveal .controls div.navigate-down,
.reveal .controls div.navigate-down.enabled {
border-top-color: #25679E;
}
.reveal .controls div.navigate-left.enabled:hover {
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<h1>Bayesian Regression Models with RStanARM</h1><p>TJ Mahr<br/>Sept. 21, 2016</p>
<div class="slideContent" >
<p>Madison R Users Group</p>
<p><small>
<a href="https://github.com/tjmahr/MadR_RStanARM">Github repository</a>
<br/>
<a href="https://twitter.com/tjmahr">@tjmahr</a>
</small></p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<h3>Overview</h3>
<div class="slideContent" >
<ul>
<li><a href="http://rpubs.com/tjmahr/rep-crisis">How I got into Bayesian statistics</a></li>
<li><strong><a href="http://rpubs.com/tjmahr/bayes-theorem">Some intuition-building about Bayes theorem</a></strong></li>
<li><a href="http://rpubs.com/tjmahr/rstanarm-tour">Tour of RStanARM</a></li>
<li><a href="http://rpubs.com/tjmahr/bayes-learn-more">Where to learn more about Bayesian statistics</a></li>
</ul>
</div>
</section>
<section data-state="section" data-transition="linear" data-transition-speed="default">
<h2>Building mathematical intuitions</h2>
<div class="slideContent" >
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<h3>Caveat</h3>
<div class="slideContent" >
<ul>
<li>These slides and these examples are meant to illustrate the pieces of Bayes
theorem.</li>
<li>This is not a rigorous mathematical description of Bayesian probability
or regression.</li>
</ul>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<h3>Classifying emails</h3>
<div class="slideContent" >
<p>I got an email with the word “cialis” in it. Is it spam?</p>
<p>\[ P(\mathrm{spam} \mid \mathrm{cialis}) = \frac{ P(\mathrm{cialis} \mid \mathrm{spam}) \, P(\mathrm{spam})}{P(\mathrm{cialis})} \]</p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<div class="slideContent noTitle" >
<p>The two unconditional probabilities are base rates that need to be accounted for.</p>
<p>\[ P(\mathrm{spam} \mid \mathrm{cialis}) = \frac{\mathrm{cialis\ freq.\ in\ spam} \, * \mathrm{spam\ rate}}{\mathrm{cialis\ freq.}} \]</p>
<p>This example is just counting events. We can think more broadly about the
probabilities.</p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<div class="slideContent noTitle" >
<p>I saw a creature, and it just <em>quacked</em> at me! Was it a duck?</p>
<p>\[ P(\mathrm{duck} \mid \mathrm{quacks}) = \frac{ P(\mathrm{quacks} \mid \mathrm{duck}) \, P(\mathrm{duck})}{P(\mathrm{quacks})} \]</p>
<ul>
<li>If it quacks like a duck…</li>
<li>and after taking into account how common ducks are and
how often animals quack…</li>
<li>then it probably is a duck.</li>
</ul>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<h3>General structure</h3>
<div class="slideContent" >
<p>How plausible is some hypothesis given the data?</p>
<p>\[ P(\mathrm{hypothesis} \mid \mathrm{data}) = \frac{ P(\mathrm{data} \mid \mathrm{hypothesis}) \, P(\mathrm{hypothesis})}{P(\mathrm{data})} \]</p>
<p>Pieces of the equation:</p>
<p>\[ \mathrm{posterior} = \frac{ \mathrm{likelihood} * \mathrm{prior}}{\mathrm{average\ likelihood}} \]</p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<h3>Likelihood measures fit</h3>
<div class="slideContent" >
<p>We found some IQ scores in an old, questionable dataset.</p>
<pre><code class="r">library(dplyr)
iqs <- car::Burt$IQbio
iqs
#> [1] 82 80 88 108 116 117 132 71 75 93 95 88 111 63 77 86 83
#> [18] 93 97 87 94 96 112 113 106 107 98
</code></pre>
<p>IQs are designed to have a normal distribution with a population mean of 100
and an SD of 15.</p>
<p>How well do these data <em>fit</em> in that kind of bell curve?</p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<h3>Density is a measure of relative likelihood</h3>
<div class="column column1 slideContent" style="width: 38%;" >
<ul>
<li>Draw the data on a hypothetical bell curve with a mean of 100 and SD of 15.</li>
<li>Height of each point on curve is density around that point.</li>
<li>Higher density regions are more likely.</li>
<li>Data farther from center is less likely.</li>
</ul>
</div>
<div class="column column2 slideContent" style="width: 58%;" >
<p><img src="data:image/png;base64,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" title="Density of IQ scores drawn a bell curve with mean 100." alt="Density of IQ scores drawn a bell curve with mean 100." width="70%" style="display: block; margin: auto;" /></p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<div class="slideContent noTitle" >
<p>In comparison, the data are less likely in a bell curve with a mean of 130.</p>
<p><img 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xARerCBgrrJglwgxZFYqQJygRaPVMCDiNCDDRTUTRbkAimOxEoVkAv0mgjX+mGCQIQObKCgbrIgF0hxJFaqgFygpSNV8CAi9GADBXWTBblAiiOxUgXkAi0cqYQHEaEHGyiomyzIBVIciZUqIBdo2UgVniB8Q4QubKCgbrIgF0hxJFaqgFygRSMV8SAi9GADBXWTBblAiiOxUgXkAi0X4Zo/TBCI0IENFNRNFuQCKY7EShWQC7RkpCoeRIQebKCgbrIgF0hxJFaqgFygBSOV8SAi9GADBXWTBblAiiOxUgXkAvWPVOUJwjdE6MIGCuomC3KBFEdipQrIBVoowpV/mCAQoQMbKKibLMgFUhyJlSogF6h7pEIeRIQebKCgbrIgF0hxJFaqgFyg3pEqeRARerCBgrrJglwgxZFYqQJygTpHKvQE4RsidGEDBXWTBblAiiOxUgXkAvWNVMuDiNCDDRTUTRbkAimOxEoVkAu0QIQb/DBBIEIHNlBQN1mQC6Q4EitVQC5Q10jFPIgIPdhAQd1kQS6Q4kisVAG5QD0jVfMgIvRgAwV1kwW5QIojsVIF5AJ1jFTsCcI3ROjCBgrqJgtygRRHYqUKyAXqFeE2P0wQiNCBDRTUTRbkAimOxEoVkAv0fKR6HkSEHmygoG6yIBdIcSRWqoBcoKcjFfQgIvRgAwV1kwW5QIojsVIF5AI9G6neE4RviNCFDRTUTRbkAimOxEoVkAvUJcLNfpggEKEDGyiomyzIBVIciZUqIBfoyUglPYgIPdhAQd1kQS6Q4kisVAG5QI9HqulBROjBBgrqJgtygRRHYqUKyAV6OFLJJwjfEKELGyiomyzIBVIciZUqIBfouQi3/GGCQIQObKCgbrIgF0hxJFaqgFygRyNV9SAi9GADBXWTBblAiiOxUgXkAj0YqawHEaEHGyiomyzIBVIciZUqIBdofqSqTxC+IUIXNlBQN1mQC6Q4EitVQC7QExFu/MMEgQgd2EBB3WRBLpDiSKxUAblAsyMV9iAi9GADBXWTBblAiiOxUgXkAs2NVNmDiNCDDRTUTRbkAimOxEoVkAs0M1LhJwjfEKELGyiomyzIBVIciZUqIBfokQi3/2GCQIQObKCgbrIgF0hxJFaqgFyg6ZFqexARerCBgrrJglwgxZFYqQJygSZHKu5BROjBBgrqJgtygRRHYqUKyAWaGqn2E4RviNCFDRTUTRbkAimOxEoVkAs0K8JdfpggEKEDGyiomyzIBVIciZUqIBdoYqTyHkSEHmygoG6yIBdIcSRWqoBcoHak+h5EhB5soKBusiAXSHEkVqqAXKBmpPJPEL4hQhc2UFA3WZALpDgSK1VALtC0CPf6YYJAhA5soKBusiAXSHEkVqqAXKD7kRQ8iAg92EBB3WRBLpDiSKxUAblAdyNJeBARerCBgrrJglwgxZFYqQJygRBh2N85CSJMhFwgxZFYqQJygW5H0vAgIvRgAwV1kwW5QIojsVIF5ALdjCTiQUTowQYK6iYLcoEUR2KlCsgFsiMpvHPiBCJ0YAMFdZMFuUCKI7FSBeQCNSLc9YcJAhE6sIGCusmCXCDFkVipAnKBzEgyHkSEHmygoG6yIBdIcSRWqoBcoI+RdDyICD3YQEHdZEEukOJIrFQBuUCIMOzvnAQRJkIukOJIrFQBuUDvIwl5EBF6sIGCusmCXCDFkVipAnKBriMpeRARerCBgrrJglwgxZFYqQJygS4jybxz4gQidGADBXWTBblAiiOxUgXkAlkR7v2jhIEIHdhAQd1kQS6Q4kisVAG5QOeRtDyICD3YQEHdZEEukOJIrFQBuUCnkcQ8iAg92EBB3WRBLpDiSKxUAblAiDDs75wEESZCLpDiSKxUAblAx5HUPIgIPdhAQd1kQS6Q4kisVAG5QFcR7v1jhIIIHdhAQd1kQS6Q4kisVAG5QG+CHkSEHmygoG6yIBdIcSRWqoBcoDe9B0YRoQsbKKibLMgFUhyJlSogF+hN8A4hIvRgAwV1kwW5QIojsVIF5AJFuiANiNCBDRTUTRbkAimOxEoVkAuECMP+zkkQYSLkAimOxEoVkAt0VIFaJkTowQYK6iYLcoEUR2KlCqgFOiDCsL9zEkSYCLlAiiOxUgXUAp08KJYJEbqwgYK6yYJcIMWRWKkCYoHOHtTK9IYIXdhAQd1kQS6Q4kisVAGtQAdEiAjvsYGCusmCXCDFkVipAlqBLh6UynQEETqwgYK6yYJcIMWRWKkCUoFOGhAcCRF6sIGCusmCXCDFkVipAkqBDogQEbbYQEHdZEEukOJIrFQBpUBnCwiOhAg92EBB3WRBLpDiSKxUAaFAFwkIjoQIPdhAQd1kQS6Q4kisVAGhQIgQEU5hAwV1kwW5QIojsVIFdAJdHSA4EiL0YAMFdZMFuUCKI7FSBWQCHRDhGyKcwgYK6iYLcoEUR2KlCsgEeleA4EiI0IMNFNRNFuQCKY7EShVQCfRhAMGREKEHGyiomyzIBVIciZUqIBLogAhPIMIWGyiomyzIBVIciZUqIBLICEBwJETowQYK6iYLcoEUR2KlCmgEsud/wZEQoQcbKKibLMgFUhyJlSogEeiACC8gwhYbKKibLMgFUhyJlSogEejm9C84EiL0YAMFdZMFuUCKI7FSBRQC3Z79BUdChB5soKBusiAXSHEkVqqAQKADInwHEbbYQEHdZEEukOJIrFQBgUB3J3/BkRChBxsoqJssyAVSHImVKlA/0P25X3AkROjBBgrqJgtygRRHYqUKlA90QIQGRNhiAwV1kwW5QIojsVIFygdqTv2CIyFCDzZQUDdZkAukOBIrVaB6oPbMLzgSIvRgAwV1kwW5QIojsVIFqgdChDeUFuH//tun7/zqP5Zc/dffHy/89I//Nf9tbaCgbrIgF0hxJFaqQPFAEyd+wZHGEOGXTxemrTZ19UWDj1VoAwV1kwW5QIojsVIFagdqXinzJjnSECJ8F92nT//wx76r//LbT49vdMIGCuomC3KBFEdipQrUDjR13hccaQQRfr087Hl6APTXXVef7g+e7gl+/GkCGyiomyzIBVIciZUqUDrQ5GlfcKQBRHgU3MVkXyaeJ5y8+ngn8XeXL/j8/c9/mP7WNlBQN1mQC6Q4EitVoHKgqQdGJUcaQIRfP+x3lN79XcKpq2++7nifsL0fecIGCuomC3KBFEdipQpUDjR91hccaQARfjYPbX5tn/Cbuvrovo87gV9mHxu1gYK6yYJcIMWRWKkChQPNnPQFR9IX4fHe3fVRztNrYP7w/Orv/2seQv0y+3IZGyiomyzIBVIciZUqUDfQ9AOjkiPpi/Dm3t2N9nquPsI9QgkER2KlCtQNNHfOFxxJX4Q39+7aJwmfXD134RkbKKibLMgFUhyJlSpQNtDsKV9wJH0R3j4t+Pleak+uPn/FzcOpf/dB/E8LAJCB0wOje/8Q+Vi/lY1EePsw55Orz4+d3lyGCAFAHjw4SVUR3r7UpXm+78nV57fZ37y+BhECgDp4cJpBRfj50/3rZxAhAIjDA6MzDCnCmU9lu2Kf9Ax6/jQLcoEUR2KlCtQM9Og1IYIjDfhimQXPET7xICKshOBIrFSBkoEenu4FRxpQhP2vGj39Cor2fYUf2EBB3WRBLpDiSKxUgYqB5t5Kf0ZwJH0Rvv4+wuP7Jh56EBFWQnAkVqpAxUCPz/aCI+mL8OVPljn9msKZXztxwQYK6iYLcoEUR2KlChQM9ORkLziSvghf+azRI58/TfzOpjtsoKBusiAXSHEkVqpAvUCPHxiVHElfhK/89onzxfO/mf6KDRTUTRbkAimOxEoVqBfo2blecKQBRPjC7yM8Py4693vpP7CBgrrJglwgxZFYqQLlAj091QuONIAIj3q73Lf7MvGs3+TVX7s8iAgrITgSK1WgXCBE+IiyIjxZ7Xinb+ZdgRNXGzk+xAYK6iYLcoEUR2KlClQL9PxMLzjSCCI8Pd934aq3o+qud/naq79+uoNfzFsfwZFYqQLFAj17pcyb5EhDiPD8TogboVkRtld/RoRygRRHYqUKFAvUcaIXHGkMEZ4f9rTvhrgR4f3V5/+LCLUQHImVKlArUM95XnCkQUS4EjZQUDdZkAukOBIrVaBUoI4HRiVHQoQebKCgbrIgF0hxJFaqQKlAXad5wZEQoQcbKKibLMgFUhyJlSpQKVDfWV5wJETowQYK6iYLcoEUR2KlChQK1PXAqORIiNCDDRTUTRbkAimOxEoVKBSo8yQvOBIi9GADBXWTBblAiiOxUgXqBOo9xwuOhAg92EBB3WRBLpDiSKxUgTKBOh8YlRwJEXqwgYK6yYJcIMWRWKkCZQJ1n+IFR0KEHmygoG6yIBdIcSRWqkCVQP1neMGREKEHGyiomyzIBVIciZUqUCUQIuwCEbbYQEHdZEEukOJIrFSBIoEWnOAFR0KEHmygoG6yIBdIcSRWqkCNQN2vlHmTHAkRerCBgrrJglwgxZFYqQI1Ai05vwuOhAg92EBB3WRBLpDiSKxUgRKBFp3eBUdChB5soKBusiAXSHEkVqpAiUCIEBG+jg0U1E0W5AIpjsRKFagQaNnZXXAkROjBBgrqJgtygRRHYqUKVAiECBGhAxsoqJssyAVSHImVKlAg0MKTu+BIiNCDDRTUTRbkAimOxEoVyB9oyVsnjgiOhAg92EBB3WRBLpDiSKxUgfyBlp7bBUdChB5soKBusiAXSHEkVqpA+kCLT+2CIyFCDzZQUDdZkAukOBIrVSB9IET4hghd2EBB3WRBLpDiSKxUgeyBlp/ZBUdChB5soKBusiAXSHEkVqpA8kBLXynzJjkSIvRgAwV1kwW5QIojsVIFkgd64cQuOBIi9GADBXWTBblAiiOxUgVyB3rlvC44EiL0YAMFdZMFuUCKI7FSBXIHQoRnEKEDGyiomyzIBVIciZUqkDrQS6d1wZEQoQcbKKibLMgFUhyJlSqQOhAivIAIHdhAQd1kQS6Q4kisVIHMgV47qwuOhAg92EBB3WRBLpDiSKxUgcSBXnjrxBHBkRChBxsoqJssyAVSHImVKpA40IsndcGREKEHGyiomyzIBVIciZUqkDfQq+d0wZEQoQcbKKibLMgFUhyJlSqQNtCLD4xKjoQIPdhAQd1kQS6Q4kisVIF0gQ6Gl76B4EiI0IMNFNRNFuQCKY7EShVIFujg9qDiSIjQgw0U1E0W5AIpjsRKFUgWCBFOgggd2EBB3WRBLpDiSKxUgVyBDohwEkTowAYK6iYLcoEUR2KlCqQKdDgEmFBwJETowQYK6iYLcoEUR2KlCqQKhAhnQIQObKCgbrIgF0hxJFaqQKpAiHAGROjABgrqJgtygRRHYqUKpAqECGdAhA5soKBusiAXSHEkVqpAqkCIcAZE6MAGCuomC3KBFEdipQqkCoQIZ0CEDmygoG6yIBdIcSRWqkCqQIhwBkTowAYK6iYLcoEUR2KlCqQKhAhnQIQObKCgbrIgF0hxJFaqQK5AAR5UHAkRerCBgrrJglwgxZFYqQLJAvk9qDgSIvRgAwV1kwW5QIojsVIFkgVChJMgQgc2UFA3WZALpDgSK1UgWSC3BiVHQoQebKCgbrIgF0hxJFaqQLJAbg1KjoQIPdhAQd1kQS6Q4kisVIFcgU7ncUTYgAgd2EBB3WRBLpDiSKxUgVyBEOE0iNCBDRTUTRbkAimOxEoVSBXofBpHhA2I0IENFNRNFuQCKY7EShXIFOiACGdAhA5soKBusiAXSHEkVqpApkCXszgibECEDmygoG6yIBdIcSRWqkCiQNeTOCJsQIQObKCgbrIgF0hxJFaqQJ5AB0Q4CyJ0YAMFdZMFuUCKI7FSBfIEej+HI8IGROjABgrqJgtygRRHYqUKpAn0cQpHhA2I0IENFNRNFuQCKY7EShVIEwgRPgAROrCBgrrJglwgxZFYqQJZApkzOCJsQIQObKCgbrIgF0hxJFaqQJJAB0T4CETowAYK6iYLcoEUR2KlCiQJZE/giLABETqwgYK6yYJcIMWRWKkCOQLdnL8RYQMidGADBXWTBblAiiOxUgVSBDogwscgQgc2UFA3WZALpDgSK1UgRaDb0zcibECEDmygoG6yIBdIcSRWqkCGQHdnb0TYgAgd2EBB3WRBLpDiSKxUgQyBEOEzEKEDGyiomyzIBVIciZUqsGegwwf3Fzu+q+BIiNCDDRTUTRbkAimOxEoV2C/Q4YAIe0GEDmygoG6yIBdIcSRWqrtMfO8AACAASURBVEAOETZXOL6v4EiI0IMNFNRNFuQCKY7EShXYLdCBe4T9IEIHNlBQN1mQC6Q4EitVYK9Ah8OsCRFhAyJ0YAMFdZMFuUCKI7FSBRBhBRChAxsoqJssyAVSHImVKoAIK4AIHdhAQd1kQS6Q4kisVAFEWAFE6MAGCuomC3KBFEdipQogwgogQgc2UFA3WZALpDgSK1UAEVYAETqwgYK6yYJcIMWRWKkCiLACiNCBDRTUTRbkAimOxEoVQIQVQIQObKCgbrIgF0hxJFaqAG+orwAidGADBXWTBblAiiOxUgX4iLUKIEIHNlBQN1mQC6Q4EitVABFWABE6sIGCusmCXCDFkVipAhlEOHGF4/sKjoQIPdhAQd1kQS6Q4kisVIFdnyOcPm8jwgZE6MAGCuomC3KBFEdipQrs+qpRRNgJInRgAwV1kwW5QIojsVIF9hThzHkbETYgQgc2UFA3WZALpDgSK1Vgp0CXEzYi7AMROrCBgrrJglwgxZFYqQL7BDogwkUgQgc2UFA3WZALpDgSK1VgPxHa/5288kUER0KEHmygoG6yIBdIcSRWqsAugd5P14iwD0TowAYK6iYLcoEUR2KlCiDCCiBCBzZQUDdZkAukOBIrVWCPQB9na0TYByJ0YAMFdZMFuUCKI7FSBXYIdECES0GEDmygoG6yIBdIcSRWqsBOImz/OHn9KwiOhAg92EBB3WRBLpDiSKxUge0D2XM1IuwDETqwgYK6yYJcIMWRWKkCmwc6IMLlIEIHNlBQN1mQC6Q4EitVYBcRTv+fhxf2IzgSIvRgAwV1kwW5QIojsVIFtg50e6ZGhH0gQgc2UFA3WZALpDgSK1UAEVYAETqwgYK6yYJcIMWRWKkCGwe6O1Ejwj4QoQMbKKibLMgFUhyJlSqwbaADInwJROjABgrqJgtygRRHYqUKbC/CR/9//sJ+BEdChB5soKBusiAXSHEkVqrApoGa0zQi7AMROrCBgrrJglwgxZFYqQKIsAKI0IENFNRNFuQCKY7EShXYMlB7lkaEfSBCBzZQUDdZkAukOBIrVQARVgAROrCBgrrJglwgxZFYqQIbBpo4SSPCPhChAxsoqJssyAVSHImVKoAIK4AIHdhAQd1kQS6Q4kisVIHtAk2doxFhH4jQgQ0U1E0W5AIpjsRKFdgs0P176d8vnPxKx18kOBIi9GADBXWTBblAiiOxUgU2FaHjwn4ER0KEHmygoG6yIBdIcSRWqsBWgabP0IiwD0TowAYK6iYLcoEUR2KlCiDCCiBCBzZQUDdZkAukOBIrVWCjQDMnaETYByJ0YAMFdZMFuUCKI7FSBRBhBRChAxsoqJssyAVSHImVKrBNoLnzMyLsAxE6sIGCusmCXCDFkVipApsEmnzrxPWKvgv7ERwJEXqwgYK6yYJcIMWRWKkCm4mw/wpE2IAIHdhAQd1kQS6Q4kisVIEtAs2fnRFhH4jQgQ0U1E0W5AIpjsRKFUCEFUCEDmygoG6yIBdIcSRWqsAGgR6cnBFhH4jQgQ0U1E0W5AIpjsRKFUCEFUCEDmygoG6yIBdIcSRWqsD6gR6dmxFhH4jQgQ0U1E0W5AIpjsRKFUCEFUCEDmygoG6yIBdIcSRWqsDqgR6emhFhH4jQgQ0U1E0W5AIpjsRKFVg70Ox76d+v7buwH8GREKEHGyiomyzIBVIciZUqsIUIF16LCBsQoQMbKKibLMgFUhyJlSqwcqAnJ2ZE2AcidGADBXWTBblAiiOxUgXWDfT4gVFE2AsidGADBXWTBblAiiOxUgXWF+Hi6xFhAyJ0YAMFdZMFuUCKI7FSBVYN9PS0jAj7KCnC//6nX/oMFoQNFNRNFuQCKY7EShVAhBUoKsLvP8xvfBKLwAYK6iYLcoEUR2KlCqwZ6PlZGRH2UVeECVxoAwV1kwW5QIojsVIFVgz07JUyb4iwl9Ii3NuFNlBQN1mQC6Q4EitVYGURvvIliLChpAi/ffvp3YSHv/lXj8tc2EBB3WRBLpDiSKxUgfUC9ZyTEWEfRUX4LYULbaCgbrIgF0hxJFaqwGqBOh4YRYS91BXht/1daAMFdZMFuUCKI7FSBVYV4WtfhAgbSovw240L//Y/X/kGHmygoG6yIBdIcSRWqsBagfrOyIiwj+oi/Hbjwl/86cXv8Ro2UFA3WZALpDgSK1UAEVZAQITf+fPf7/IQqQ0U1E0W5AIpjsRKFVgpUOcJGRH2oSFCY8It31FhAwV1kwW5QIojsVIF1gnU9UqZN0TYi4IIzWOjJ3549RstxQYK6iYLcoEUR2KlCqwnwpe/DhE2lBfhzaOil/+zlQltoKBusiAXSHEkVqrAKoG6T8eIsI/aIjQfMfODvWSjR0dtoKBusiAXSHEkVqrAGoF6HxhFhL0UFuH//MvkOyd+3O7VozZQUDdZkAukOBIrVWAtETq+EhE2lBXhj3Ovjjk+PLr9WwoBALbheNbzfOmC28Md63e34Nubl8c0d/6OD44iQgBQBRHuRyYRvj81OPWuweMjpjw06kUukOJIrFSB+EBLHp3jodE+Sj40ehHh9K+pP1650ctGbaCgbrIgF0hxJFaqQHig/lfKvCHCXsqKcPbRzz//Pe8j9CMXSHEkVqrAKiL0fTEibCgqwr1/N/0ZGyiomyzIBVIciZUqEB1o2ZkYEfZRUoRZsIGCusmCXCDFkVipAoiwAkIi3PAx0Qs2UFA3WZALpDgSK1UgONDCEzEi7KOkCP/7n9rXix6fN9z4tzAhwkoIjsRKFYgNtOiVMm+IsBcZER7fNbH12wdtoKBusiAXSHEkVqpAvAjdX48IG2REuMf76G2goG6yIBdIcSRWqkBooMWnYUTYh4wIfzogwkDkAimOxEoVQIQVKCVC88smJuE5wjDkAimOxEoViAy0/CyMCPsoJcLmV/DesfW7C22goG6yIBdIcSRWqkBgoKWvlHlDhL3UEqH5zUsJ7hAiwkoIjsRKFQgWYcRNEGFDLRGa30ffMv3Ro2tiAwV1kwW5QIojsVIF4gK9cg5GhH0UE+GZqRfL7IENFNRNFuQCKY7EShVAhBVAhA5soKBusiAXSHEkVqpAWKCXTsGIsA9E6MAGCuomC3KBFEdipQpEBXrhlTJviLCXkiLMgg0U1E0W5AIpjsRKFYgUYdCtEGEDInRgAwV1kwW5QIojsVIFggK9eAJGhH0gQgc2UFA3WZALpDgSK1UAEVYAETqwgYK6yYJcIMWRWKkCMYFePf8iwj4qifD0CWs/fJv/qDU+azQMuUCKI7FSBUICvfZKmTdE2AsidGADBXWTBblAiiOxUgXCRBh3Q0TYgAgd2EBB3WRBLpDiSKxUgYhAr599EWEfiNCBDRTUTRbkAimOxEoVcAUyZ7fXv0Hfhf0IjlRKhOmwgYK6yYJcIMWRWKkCjkAHtwcRYSeI0IENFNRNFuQCKY7EShVAhBVAhA5soKBusiAXSHEkVqrA64Fun/h5/Xv0XdiP4EiI0IMNFNRNFuQCKY7EShV4OdD9SyBe/iZ9F/YjOBIi9GADBXWTBblAiiOxUgUQYQUERHj6Zb1bv2D0hA0U1E0W5AIpjsRKFUCEFSgrwp+v7vvx8s/kF396UWevYwMFdZMFuUCKI7FSBRBhBYqK8Hgv8PwrCX96/3eyvQltoKBusiAXSHEkVqoAIqxATRGeHg09idC+t/6XHqm9gg0U1E0W5AIpjsRKFUCEFSgpwv/5l9M/jN98u9wh/M3xkdIdnie0gYK6yYJcIMWRWKkCiLACJUV4tN7ps9bOSvzl9bKt7xLaQEHdZEEukOJIrFQBRFiBkiL88XJ30D5XeLzwh1eN9iI2UFA3WZALpDgSK1WAN9RXoKIIj3cDL8776eNFMj9t/3IZGyiomyzIBVIciZUqwEesVaCiCI8vkDnfIfx4ZPT02Ci/fSIMuUCKI7FSBRBhBWqL0DwyighDkQukOBIrVSBEhK5v0XdhP4IjFReheWQUEYYiF0hxJFaqgO85Qu+JFxH2UVGExwdEf3n9w/tLRX/kOcJA5AIpjsRKFUCEFagownfn2UdGj3cTedVoGHKBFEdipQq43j7hPvEiwj5KivDn8yOip0+VudwLPN05/I1Daq9gAwV1kwW5QIojsVIFXg10QIQbUlKE9nPVzvI7vcWeT5aJQy6Q4kisVAGPCN8Q4UaUFOHZeyfeHyI98FmjkcgFUhyJlSrwYqDrCRcRbkJNEb6b8Hwn8CzCrZ8hRISlEByJlSqACCtQVISXX0N4eVLw9FDp1k8QfkOEpRAciZUq8Fqg9/MtItyEsiK0/M+/7KFBRFgKwZFYqQKIsAISItwLGyiomyzIBVIciZUq8FKgj9MtItwEROjABgrqJgtygRRHYqUKvBLogAg3BhE6sIGCusmCXCDFkVipAq+KsP3jKyDCPhChAxsoqJssyAVSHImVKvBCIHuyRYSbgAgd2EBB3WRBLpDiSKxUgeWBDohwc8qK0H66zBV++0QYcoEUR2KlCrwmwun/sxxE2EdREV4+SwYRroVcIMWRWKkCiwPdnmoR4SbUFOG0BxFhHHKBFEdipQosDXRAhDtQUoSnXzWBCNdELpDiSKxUgVdEOP9/l4II+ygpwvMnje7yYTI32EBB3WRBLpDiSKxUgd5A5r/o7y92/O2IsI+SIjx+zujWv41+ChsoqJssyAVSHImVKtAX6OahrfsrHH87IuyjogiPj4xefzH9rthAQd1kQS6Q4kisVIHlImyucPztiLCPiiI8vnPiB6fDQrCBgrrJglwgxZFYqQJdgW5f7HB/jeNvR4R9VBXh5r+EdwobKKibLMgFUhyJlSrQE+j+ZX93Vzn+dkTYByJ0YAMFdZMFuUCKI7FSBRBhBSqK8PgcIQ+NrotcIMWRWKkCiLACFUX47accLxpFhJUQHImVKoAIK1BShP/9T7xqdGXkAimOxEoVQIQVKCnC4zvqM9wltIGCusmCXCDFkVipAoiwAjVFeHxwNMGzhDZQUDdZkAukOBIrVQARVqCoCE+fsra7Cm2goG6yIBdIcSRWqgAirEBJEU79LsIjfOh2GHKBFEdipQrwhvoKIEIHNlBQN1mQC6Q4EitVgI9YqwAidGADBXWTBblAiiOxUgUQYQUQoQMbKKibLMgFUhyJlSqw9KHRiWscfzsi7KOkCLNgAwV1kwW5QIojsVIFukW4irQQYR+I0IENFNRNFuQCKY7EShXofdXoOtJChH0gQgc2UFA3WZALpDgSK1WgI9ABEe4NInRgAwV1kwW5QIojsVIFOkX4hgj3BBE6sIGCusmCXCDFkVipAs8DXc+tiHA/Kovw/OLR428m/HGfX09oAwV1kwW5QIojsVIFngY6IML9qSvCny6vNv7l+RcU7qFCGyiomyzIBVIciZUq0CXC2z9MXvsaiLCPqiL8898fPkR4umu4w6+jsIGCusmCXCDFkVipAs8CfZxZEeF+FBXhhwePIjz/v+1NaAMFdZMFuUCKI7FSBZ4EOiDCDNQU4fnZwR/eHxM9m3DzR0dtoKBusiAXSHEkVqpAhwjbP05e/wqIsI+aIvzxcgfw48nB4zOGW3/CGiKshOBIrFSBx4HseRUR7kdJER7vAJ4eCDWvkjm68TcvK+01bKCgbrIgF0hxJFaqACKsQEkRfr/79zf/evyDEeHx0dIfXjXai9hAQd1kQS6Q4kisVIGHgW5Oq4hwPyqK8Ki/H97/dH1m8MftXy5jAwV1kwW5QIojsVIFHgU6IMIkVBTh8c7fWX9WhD/za5gCkQukOBIrVeCZCOf+36ML+0GEfVQV4fnpQES4FnKBFEdipQo8CHR3UkWE+4EIHdhAQd1kQS6Q4kisVIH5QAdEmIaKIvzQnxXhTzxHGIhcIMWRWKkCbaCD4f7y5uaIcBMqivDjdTFGhB+voNkOGyiomyzIBVIciZUqcB/oMOdBRLgjJUU49faJ75dt/tEyNlBQN1mQC6Q4EitVABFWoKQIj2+oPz0f+CHC40VnOW6IDRTUTRbkAimOxEoVuAt0QIQZKSnC08fIHE34LsLj/cHNHxlFhJUQHImVKnAb6HCYNyEi3I+aIjx/6PYv/nQR4Y+nf1Kbf9QoIqyE4EisVAFEWIGaIryY8IbNHxhFhKUQHImVKoAIK1BUhK0Jd/AgIqyE4EisVAFEWIGqIjy9gd6w+fODR2ygoG6yIBdIcSRWqgAirEBdEX67Pje4x7ODZ2ygoG6yIBdIcSRWqgAirEBpEe6NDRTUTRbkAimOxEoVQIQVQIQObKCgbrIgF0hxJFaqACKsACJ0YAMFdZMFuUCKI7FSBXhDfQUQoQMbKKibLMgFUhyJlSrw6CPW2muamyPCTUCEDmygoG6yIBdIcSRWqgAirEAlEU68i/4Wfh9hGHKBFEdipQrMi/D+KxHhfiBCBzZQUDdZkAukOBIrVWBOhO1XIsL9QIQObKCgbrIgF0hxJFaqwMSLZWbOpohwPxChAxsoqJssyAVSHImVKjDx9glEmI5KIjScP1/t+ot4j7+MkA/dDkUukOJIrFSBVoRzZ1NEuB81Rdj8Gt7jncXtTWgDBXWTBblAiiOxUgVuAl1Oo4gwGyVFePw1hHcPg05ctD42UFA3WZALpDgSK1UAEVagpAh/nrj7d7yT+MvJr14PGyiomyzIBVIciZUqYANdz6KIMBslRfjj1K9dmrxwXWygoG6yIBdIcSRWqoAJdECEWakowuMTgu2dv5951WggcoEUR2KlCtyJ8PYPNyDC/agqwt80lyLCSOQCKY7EShX4CPRxDkWE2agqQu4RrotcIMWRWKkCiLACFUV4fIXo5HOEv/jTUpX5sIGCusmCXCDFkVipAu+BzCkUEWajogiPzpt81SgvlglDLpDiSKxUgWugAyJMTEkRHj9X5u7e3y7vqLeBgrrJglwgxZFYqQJWhNfLEGE2Sorw+Njo7ROCpw9Z2/oOISKshOBIrFSBS6CbEygizEZJEZ699/HS0fMnj27+wTKIsBKCI7FSBc6BDogwNTVFeFHfDXzodiRygRRHYqUKfIjw4zJEmI2iImxNuP39QURYCsGRWKkCp0B3p09EmI2qIjy9dNTQvsF+A2ygoG6yIBdIcSRWqsAx0AERJqeuCC+vmTns8SqZCzZQUDdZkAukOBIrVeAqQnsZIsxGZRHujg0U1E0W5AIpjsRKFfgeqDl5IsJsIEIHNlBQN1mQC6Q4EitV4PuZDRGmBxE6sIGCusmCXCDFkVipAhMeRITpQIQObKCgbrIgF0hxJFaqwLeJUycizAYidGADBXWTBblAiiOxUgWmzpyIMBuI0IENFNRNFuQCKY7ESgWYeGAUEeYDETqwgYK6yYJcIMWRWKkAC0yECPcDETqwgYK6yYJcIMWRWCk/C5SHCHcEETqwgYK6yYJcIMWRWCk9kw+MIsJ8IEIHNlBQN1mQC6Q4Eiul53janAiECLOBCB3YQEHdZEEukOJIrJSdkwcRYQEQoQMbKKibLMgFUhyJlZJzQIRVQIQObKCgbrIgF0hxJFZKzumkiQgrgAgd2EBB3WRBLpDiSKyUm/M5ExFWABE6sIGCusmCXCDFkVgpNQdEWAdE6MAGCuomC3KBFEdipdRcTpmIsAKI0IENFNRNFuQCKY7ESpm5njERYQUQoQMbKKibLMgFUhyJlRJzQISVQIQObKCgbrIgF0hxJFZKzPsJExFWABE6sIGCusmCXCDFkVgpLx/nS0RYAUTowAYK6iYLcoEUR2KltBwQYS0QoQMbKKibLMgFUhyJldJiTpeIsAKI0IENFNRNFuQCKY7ESlmxZ0tEWIExRPi///bpO7/6j8VXf/30D3+c/7Y2UFA3WZALpDgSKyXlgAirMYQIv3y68I//tezqv/wWEaogOBIr5eTGg4iwBCOI8F10nya1Nn/1X38/fYsrNlBQN1mQC6Q4Eivl5PZciQgrMIAIv14e9jw9APrrBVcfPYgIVRAciZVScneqRIQV0BfhUXCXxzy/TDwROH/1X347dx/yig0U1E0W5AIpjsRKGTkgwoLoi/Drh96O0ru/Szh79ef5B1Ov2EBB3WRBLpDiSKyUkfszJSKsgL4IP5sXwXxtxTZz9emJw1/9OyKUQXAkVkpIc6JEhBWQF+Hxbt7vrv/n+GjnH3quPj09+OspcVpsoKBusiAXSHEkVsrH/QOjiLAG8iI8Ku3dfTfae3T194uPD5giQh0ER2KlfLTnSURYAXkRfr+X9/EKmPZJwpmr//rPpwsRoQ6CI7FSOiZOk4iwAvIivHXZ53sRPr56SoR/90H8TwsAdTk9MNr5dZ2Xdn7HRX+T83sOzfrdbSTC24+PeXw1IgSAbnrPkoiwLFVF+OXGZV/uRfj4akQIAL10nyQRYVkQ4QVECAAT9D4wiggLgwhb7JOeQc+fZkEukOJIrJSL6ddR8GKZCoz3Yhnvc4QGGyiomyzIBVIciZVSMXOKRIQVGE+E3leNGmygoG6yIBdIcSRWysQBERZGXoSvvY/wAiLUQXAkVsrE3BkSEVZAXoSvfbLMBUSog+BIrJSI2RMkIqyAvAhf+6zRC4hQB8GRWCkPcw+MIsIayIvwxd8+Mfv1FhsoqJssyAVSHImV8jB/fkSEFdAX4au/j/ByJSIUQXAkVkrDg9MjIqyAvgiPervY7PhLBv+w5GpEqIPgSKyUhfkHRhFhDfRFeLTZ6U7fUXnNHcLHVyNCHQRHYqUsPDo7IsIKDCDC49OAV65aO1rv+tTgxNVXEKEOgiOxUhIenhwRYQVGEOHpMc9b0VkRTlx9BRHqIDgSK+Xg0QOjiLAGQ4jw/LCneef8rQjbq68gQh0ER2KlHDw+NyLCCowhwpWwgYK6yYJcIMWRWCkFT06NiLACiNCBDRTUTRbkAimOxEoZePzAKCKsASJ0YAMFdZMFuUCKI7FSBp6dGRFhBRChAxsoqJssyAVSHImVEvD0xIgIK4AIHdhAQd1kQS6Q4kistD/PHhhFhDVAhA5soKBusiAXSHEkVtqf5+dFRFgBROjABgrqJgtygRRHYqXd6TgtIsIKIEIHNlBQN1mQC6Q4EivtzfMHRhFhDRChAxsoqJssyAVSHImVduJgefbFiLACiNCBDRTUTRbkAimOxEq7cDggwvQjLQUROrCBgrrJglwgxZFYaReWeRARlgAROrCBgrrJglwgxZFYaQ8WehARlgAROrCBgrrJglwgxZFYaQfuHhjlHqEGiNCBDRTUTRbkAimOxEo7gAgLjLQcROjABgrqJgtygRRHYqUdQIQFRloOInRgAwV1kwW5QIojsdIOIMICIy0HETqwgYK6yYJcIMWRWGkHEGGBkZaDCB3YQEHdZEEukOJIrLQDiLDASMtBhA5soKBusiAXSHEkVtoBRFhgpOUgQgc2UFA3WZALpDgSK+0AIiww0nIQoQMbKKibLMgFUhyJlfZgoQcRYQkQoQMbKKibLMgFUhyJlXZhmQcRYQkQoQMbKKibLMgFUhyJlXYBERYYaSmI0IENFNRNFuQCKY7ESnuwTIOIsAaI0IENFNRNFuQCKY7ESjtwNuCC0yEirAAidGADBXWTBblAiiOx0vYcEGH+kV4AETqwgYK6yYJcIMWRWGl7Lg+JIkIxEKEDGyiomyzIBVIciZU25/rUICIUAxE6sIGCusmCXCDFkVhpa95fIoMIxUCEDmygoG6yIBdIcSRW2pgDIjySe6TXQIQObKCgbrIgF0hxJFbaFvOeCUQoBiJ0YAMFdZMFuUCKI7HStnx4EBE6bp4SROjABgrqJgtygRRHYqVNMR5EhI6bpwQROrCBgrrJglwgxZFYaUusBxGh4+YpQYQObKCgbrIgF0hxJFbakAMivJJ3pNdBhA5soKBusiAXSHEkVtqOWw8iQsfNU4IIHdhAQd1kQS6Q4kistD4Hy+3Fnd8BEVYAETqwgYK6yYJcIMWRWGltDjMeRISOm6cEETqwgYK6yYJcIMWRWGlt5jyICB03TwkidGADBXWTBblAiiOx0srM3iFEhI6bpwQROrCBgrrJglwgxZFYaV0Oh1kTIkIxEKEDGyiomyzIBVIciZXWBRFOk2qkIBChAxsoqJssyAVSHImV1gURTpNqpCAQoQMbKKibLMgFUhyJldYFEU6TaqQgEKEDGyiomyzIBVIciZXWBRFOk2qkIBChAxsoqJssyAVSHImV1gURTpNqpCAQoQMbKKibLMgFUhyJldYFEU6TaqQgEKEDGyiomyzIBVIciZXWBRFOk2qkIBChAxsoqJssyAVSHImVVmbWg4jQcfOUIEIHNlBQN1mQC6Q4EiutzZwHEaHj5ilBhA5soKBusiAXSHEkVlqZ2TuEiNBx85QgQgc2UFA3WZALpDgSK63LrAYRYZ6RgkCEDmygoG6yIBdIcSRWWpWLAb0qQYQVQIQObKCgbrIgF0hxJFZalcs9QUR4T6aRokCEDmygoG6yIBdIcSRWWpPrI6KI8J5EI4WBCB3YQEHdZEEukOJIrLQi788MIsJ78owUByJ0YAMFdZMFuUCKI7HSiiDCWfKMFAcidGADBXWTBblAiiOx0np8vFQUEd6TZqRAEKEDGyiomyzIBVIciZVW48ODiLAhy0iRIEIHNlBQN1mQC6Q4EiutxQERPiDJSKEgQgc2UFA3WZALpDgSK62F8SAibEgyUiiI0IENFNRNFuQCKY7ESithPYgIG3KMFAsidGADBXWTBblAiiOx0jrceBARNqQYKRhE6MAGCuomC3KBFEdipVAON9xcPPm1nd8WEVYAETqwgYK6yYJcIMWRWCmQw4wHEWHD0IcSImyxgYK6yYJcIMWRWCmQOQ8iwoahDyVE2GIDBXWTBblAiiOxUhyzHkSEDUMfSoiwxQYK6iYLcoEUR2KlMO4eGOUe4SOGPpQQYYsNFNRNFuQCKY7ESmEgwgUMfSghwhYbKKibLMgFUhyJlcJAhAsY+lBCj89eiAAAIABJREFUhC02UFA3WZALpDgSK4WBCBcw9KGECFtsoKBusiAXSHEkVgoDES5g6EMJEbbYQEHdZEEukOJIrBQGIlzA0IcSImyxgYK6yYJcIMWRWCkMRLiAoQ8lRNhiAwV1kwW5QIojsVIYiHABQx9KiLDFBgrqJgtygRRHYqU4Zj2ICBuGPpQQYYsNFNRNFuQCKY7ESoHMeRARNgx9KCHCFhsoqJssyAVSHImV4pi9Q4gIG4Y+lBBhiw0U1E0W5AIpjsRKYcxqEBG2DH0oIcIWGyiomyzIBVIciZWiuBiw3xqIUAxE6MAGCuomC3KBFEdipSCu9wQRYRdDH0qIsMUGCuomC3KBFEdipRjeHxFFhF0MfSghwhYbKKibLMgFUhyJlWJ4f2YQEXYx9KGECFtsoKBusiAXSHEkVgrh4xUyiLCLoQ8lRNhiAwV1kwW5QIojsVIE5pWiiLCLoQ8lRNhiAwV1kwW5QIojsVIAB0S4lKEPJUTYYgMFdZMFuUCKI7GSH+tBRNjH0IcSImyxgYK6yYJcIMWRWMnNjQcRYR9DH0qIsMUGCuomC3KBFEdiJS+3HkSEfQx9KCHCFhsoqJssyAVSHImVnNx5EBH2MfShhAhbbKCgbrIgF0hxJFbyce9BRNjH0IcSImyxgYK6yYJcIMWRWMnHvQcRYR9DH0qIsMUGCuomC3KBFEdiJReNBxFhH0MfSoiwxQYK6iYLcoEUR2IlD60HEWEfQx9KiLDFBgrqJgtygRRHYiUHzROEb4iwk6EPJUTYYgMFdZMFuUCKI7HS60x5EBH2MfShhAhbbKCgbrIgF0hxJFZ6mUkPIsI+hj6UEGGLDRTUTRbkAimOxEqvMu1BRNjH0IcSImyxgYK6yYJcIMWRWOlFZjyICPsY+lBChC02UFA3WZALpDgSK73IjAcRYR9DH0qIsMUGCuomC3KBFEdipdeY8yAi7GPoQwkRtthAQd1kQS6Q4kis9BKzHkSEfQx9KCHCFhsoqJssyAVSHImVXmHuCcI3RNjJ0IcSImyxgYK6yYJcIMWRWOkFHngQEfYx9KGECFtsoKBusiAXSHEkVlrOIw8iwj6GPpQQYYsNFNRNFuQCKY7ESot56EFE2MfQhxIibLGBgrrJglwgxZFYaSmPPYgI+xj6UEKELTZQUDdZkAukOBIrLeSJBxFhH0MfSoiwxQYK6iYLcoEUR2KlZTzzICLsY+hDCRG22EBB3WRBLpDiSKy0iKceRIR9DH0oIcIWGyiomyzIBVIciZWW8NyDiLCPoQ8lRNhiAwV1kwW5QIojsdICOjyICPsY+lBChC02UFA3WZALpDgSK/XT40FE2MfQhxIibLGBgrrJglwgxZFYqZsuDyLCPoY+lBBhiw0U1E0W5AIpjsRKvfR5EBH2MfShhAhbbKCgbrIgF0hxJFbqpc+DiLCPoQ8lRNhiAwV1kwW5QIojsVInnR5EhH0MfSghwhYbKKibLMgFUhyJlfro9SAi7GPoQwkRtthAQd1kQS6Q4kis1EXnE4RviLCToQ8lRNhiAwV1kwW5QIojsVIP/R5EhH0MfSghwhYbKKibLMgFUhyJlTpY4EFE2MfQhxIibLGBgrrJglwgxZFY6TlLPIgI+xj6UEKELTZQUDdZkAukOBIrPWWRBxFhH0MfSoiwxQYK6iYLcoEUR2KlZyzzICLsY+hDCRG22EBB3WRBLpDiSKz0hIUeRIR9DH0oIcIWGyiomyzIBVIciZUes9SDiLCPoQ8lRNhiAwV1kwW5QIojsdJDFnsQEfYx9KGECFtsoKBusiAXSHEkVnrEcg8iwj6GPpQQYYsNFNRNFuQCKY7ESg94wYOIsI+hDyVE2GIDBXWTBblAiiOx0jyveBAR9jH0oYQIW2ygoG6yIBdIcSRWmuUlDyLCPoY+lBBhiw0U1E0W5AIpjsRKc7zmQUTYx9CHEiJssYGCusmCXCDFkVhphhc9iAj7GPpQQoQtNlBQN1mQC6Q4EitN86oHEWEfQx9KiLDFBgrqJgtygRRHYqVJXvYgIuxj6EMJEbbYQEHdZEEukOJIrDTF6x5EhH0MfSghwhYbKKibLMgFUhyJlSZweBAR9jH0oYQIW2ygoG6yIBdIcSRWavF4EBH2MfShhAhbbKCgbrIgF0hxJFZqcHkQEfYx9KGECFtsoKBusiAXSHEkVrrH50FE2MfQhxIibLGBgrrJglwgxZFY6Q6nBxFhH0MfSoiwxQYK6iYLcoEUR2KlW7weRIR9DH0oIcIWGyiomyzIBVIciZVucHsQEfYx9KGECFtsoKBusiAXSHEkVrL4PYgI+xj6UEKELTZQUDdZkAukOBIrGQI8iAj7GPpQQoQtNlBQN1mQC6Q4Eit9EOFBRNjH0IcSImyxgYK6yYJcIMWRWOmdEA8iwj6GPpQQYYsNFNRNFuQCKY7ESldiPIgI+xj6UEKEAJCSswdjvo/jQudftN3fFNPWmKzfHdMAwHKiPIgI4SmIsMXexQ26t5wFuUCKI7HSiaDHRd94aLSToQ8lHhptsYGCusmCXCDFkVjp7arBmHMTIuxi6EMJEbbYQEHdZEEukOJIrBTrQUTYx9CHEiJssYGCusmCXCDFkVgp1oOIsI+hDyVE2GIDBXWTBblAiiOxUqgGEWEnQx9KiLDFBgrqJgtygRRHGn6lYA8iwj6GPpQQYYsNFNRNFuQCKY40+krRHkSEfQx9KCHCFhsoqJssyAVSHGnwlcI9iAj7GPpQQoQtNlBQN1mQC6Q40tArxb5M5uN7Oi6cBhFWABE6sIGCusmCXCDFkUZeaQ0PIsI+hj6UEGGLDRTUTRbkAimONPBKq3gQEfYx9KGECFtsoKBusiAXSHGkcVdaRYOIsJOhDyVE2GIDBXWTBblAiiMNu9JKHkSEfQx9KCHCFhsoqJssyAVSHGnUldbyICLsY+hDCRG22EBB3WRBLpDiSIOutJoHEWEfQx9KiLDFBgrqJgtygRRHGnOl9TyICPsY+lBChC02UFA3WZALpDjSkCut6EFE2MfQhxIibLGBgrrJglwgxZFGXGlNDyLCPoY+lBBhiw0U1E0W5AIpjjTgSqt6EBH2MfShhAhbbKCgbrIgF0hxpPFWWteDiLCPoQ8lRNhiAwV1kwW5QIojDbfSyh5EhH0MfSghwhYbKKibLMgFUhxpsJUOa3sQEfYx9KGECFtsoKBusiAXSHGksVZa34OIsI+hDyVE2GIDBXWTBblAiiMNtdIGHkSEfQx9KCHCFhsoqJssyAVSHGmklTbQICLsZOhDCRG22EBB3WRBLpDiSOOstMXdwTdE2MnQhxIibLGBgrrJglwgxZGGWWkjDyLCPoY+lBBhiw0U1E0W5AIpjjTKSlt5EBH2MfShhAhbbKCgbrIgF0hxpEFW2kqDiLCToQ8lRNhiAwV1kwW5QIojDbHSZncH3xBhJ0MfSoiwxQYK6iYLcoEURxphpS09iAj7GPpQQoQtNlBQN1mQC6Q40gArbepBRNjH0IcSImyxgYK6yYJcIMWR9FfaVIOIsJOhDyVE2GIDBXWTBblAiiOpr7Tt3cE3RNjJ0IcSImyxgYK6yYJcIMWRxFfa3IOIsI+hDyVE2GIDBXWTBblAiiNpr7S9BxFhH0MfSoiwxQYK6iYLcoEUR5JeaXsNIsJOhj6UEGGLDRTUTRbkAimOJLzSDncH3xBhJ0MfSoiwxQYK6iYLcoEUR9JdaR8PIsI+hj6UEGGLDRTUTRbkAimOJLvSTh5EhH0MfSghwhYbKKibLMgFUhxJdaWdNIgIOxn6UEKELTZQUDdZkAukOJLmSnvdHXxDhJ0MfSghwhYbKKibLMgFUhxJcqUdPYgI+xj6UEKELTZQUDdZkAukOJLiSnt6EBH2MfShhAhbbKCgbrIgF0hxJMGV9tQgIuxk6EMJEbbYQEHdZEEukOJIeivt60FE2MfQhxIibLGBgrrJglwgxZHUVtr1YdHrD+C4cBpEWAFE6MAGCuomC3KBFEcSW+niwR0zIcIuhj6UEGGLDRTUTRbkAimOpLXSRYN7ZkKEXQx9KCHCFhsoqJssyAVSHElppcujovuuhAi7GPpQQoQtNlBQN1mQC6Q4ktBK12cH910JEXYx9KGECFtsoKBusiAXSHEkmZU+XiWz70qIsIuhDyVE2GIDBXWTBblAiiOprPSuwb1XQoRdDH0oIcIWGyiomyzIBVIcSWQl40FE6PmbpkCEfSBCBzZQUDdZkAukOJLESlaDe6+ECLsY+lBChC02UFA3WZALpDiSwkq3HkSEnr9pCkTYByJ0YAMFdZMFuUCKI9Vf6XDnQUTo+ZumQIR9IEIHNlBQN1mQC6Q4UvmV7jW490qIsIuhDyVE2GIDBXWTBblAiiMVX6m5O/i290qIsIuhDyVE2GIDBXWTBblAiiPVXmlCg3uvhAi7GPpQQoQtNlBQN1mQC6Q4UuWVpu4Ovu29EiLsYuhDCRG22EBB3WRBLpDiSIVXmtbg3ishwi6GPpQQYYsNFNRNFuQCKY5UdqWZu4Nve6+ECLsY+lBChC02UFA3WZALpDhS1ZVmNbj3Soiwi6EPJUTYYgMFdZMFuUCKI9Vcaf7u4NveKyHCLoY+lBBhiw0U1E0W5AIpjlRkpcON+h5pcO+VEGEXQx9KiLDFBgrqJgtygRRHKrHSwfDk7uDb3ishwi6GPpQQYYsNFNRNFuQCKY5UYqVDy4Ov3nclRNjF0IcSImyxgYK6yYJcIMWRKqy0zIOI0PM3TYEI+0CEDmygoG6yIBdIcaQCKy3T4N4rIcIuhj6UEGGLDRTUTRbkAimOVGClZRrceyVE2MXQhxIibLGBgrrJglwgxZEKrIQIEWEJEKEDGyiomyzIBVIcqcBKiBARlgAROrCBgrrJglwgxZEKrIQIEWEJEKEDGyiomyzIBVIcqcBKiBARlgAROrCBgrrJglwgxZEKrIQIEWEJEKEDGyiomyzIBVIcKf9K9x5EhI9ujgj3AxE6sIGCusmCXCDFkdKtdKe7RoPPzyD7roQIuxj6UEKELTZQUDdZkAukOFKyle6N94IHEaHnb5oCEfaBCB3YQEHdZEEukOJIyVa6Vd71D4gQERYAETqwgYK6yYJcIMWRcq3U3gG8nDH6Nbj3Soiwi6EPJUTYYgMFdZMFuUCKI6VaadaDb0tOHvuuhAi7GPpQQoQtNlBQN1mQC6Q4UqqV5jWICDtvjgj3AxE6sIGCusmCXCDFkVKtNK9BRNh5c0S4H4jQgQ0U1E0W5AIpjpRqJUQ4AyKsACJ0YAMFdZMFuUCKI6VaCRHOgAgrgAgd2EBB3WRBLpDiSKlWQoQzIMIKIEIHNlBQN1mQC6Q4UqqVEOEMiLACiNCBDRTUTRbkAimOtOdKd7671yAifAcRVgAROrCBgrrJglwgxZH2W+nOeK0GD82X933jfVdChF0MfSghwhYbKKibLMgFUhwpiQgnNHhov7zvG++7EiLsYuhDCRG22EBB3WRBLpDiSLutNKU+RDgDIqwAInRgAwV1kwW5QIoj7bXSrPqmNYgIO2+OCPcDETqwgYK6yYJcIMWREonQXjV9g75vve9KiLCLoQ8lRNhiAwV1kwW5QIojpRHh7VXTN+j71vuuhAi7GPpQQoQtNlBQN1mQC6Q4UhYR3l01fYO+b73vSoiwi6EPJUTYYgMFdZMFuUCKIyHCYBBhF0MfSoiwxQYK6iYLcoEUR9popcZ3iBAROm6eEkTowAYK6iYLcoEUR9pkpcZ49xpEhI9BhBVAhA5soKBusiAXSHGkPUTYahARPgYRVgAROrCBgrrJglwgxZG2WGlKfPMeRIQtiLACiNCBDRTUTRbkAimOtMFKCz2ICFsQYQUQoQMbKKibLMgFUhxpLxFOPHFov376u/T9ffuuhAi7GPpQQoQtNlBQN1mQC6Q40j4ivL1i4uunv0vf37fvSoiwi6EPJUTYYgMFdZMFuUCKI+0hwturJr9++rv0/X37roQIuxj6UEKELTZQUDdZkAukOFL8So3u5j2ICDu/KSKsACJ0YAMFdZMFuUCKI0WvNGE8RIgIG4Y+lBBhiw0U1E0W5AIpjrS+CO89iAgfXTgNIqwAInRgAwV1kwW5QIojBa/UKK/RICJ8eOE0iLACiNCBDRTUTRbkAimOFLvShPYeeRARdn5TRFgBROjABgrqJgtygRRH2lyEzddPfpPpb933Q+y7EiLsYuhDCRG22EBB3WRBLpDiSFuIcOF75xFhAyKsACJ0YAMFdZMFuUCKI60vwpsrJr5+8ptMf+u+H2LflRBhF0MfSoiwxQYK6iYLcoEUR3Kt1Oht2oLvV01+g74LEWHfzRHhfiBCBzZQUDdZkAukOJJjpQnhzXsQEfZdOA0irAAidGADBXWTBblAiiNFirC5P4gIF184DSKsACJ0YAMFdZMFuUCKI72+0p3yWgsiwhcunAYRVgAROrCBgrrJglwgxZFeXmlSfPMeRIR9F06DCCuACB3YQEHdZEEukOJIa4qw+frJb9J3ISLsuzki3A9E6MAGCuomC3KBFEcKFeHdxc3XT36TvgsRYd/NEeF+IEIHNlBQN1mQC6Q4UpwI76+Y+PrJb9J3ISLsuzki3A9E6MAGCuomC3KBFEcKE+HdVZNf77gQEfbdHBHuByJ0YAMFdZMFuUCKI722UnN3EBFeQYRdDH0oIcIWGyiomyzIBVIcaflKExJEhB8gwi6GPpQQYYsNFNRNFuQCKY60cKUZCyLCdxBhF0MfSoiwxQYK6iYLcoEUR1qy0rwFQ98yiAgbEGEFEKEDGyiomyzIBVIcqXul1ntzHkSEjgunQYQVQIQObKCgbrIgF0hxpL6VJu/8IcIpEGEXwx5KRxBhiw0U1E0W5AIpjtSx0qQFb66ZuMHkd3FciAj7bo4I9wMROrCBgrrJglwgxZEer3S4ZfoLNrkQEfbdHBHuByJ0YAMFdZMFuUCKI82udLhn9qs2uRAR9t0cEe4HInRgAwV1kwW5QIojTa3UOHD+sEWE9yDCLgY5lKZBhC02UFA3WZALpDjS/UoTEnx0zCLCexBhFwMcSvMgwhYbKKibLMgFUhzpZqVFDny/xSYXIsK+myPC/UCEDmygoG6yIBdIcaT3lRY78P1Wm1yICPtujgj3AxE6sIGCusmCXCDFkc4rveLAE4jwHkTYheyh1AMibLGBgrrJglwgxZGae4LLb73JhYiw7+aIcD8QoQMbKKibLMgFqjJSr9PuHfjC0YkI70GEXRQ5lBaBCB3YQEHdZEEuUI2RusTWOvC1IxMR3oMIuyhxKC0EETqwgYK6yYJcoBojPZbbhAE9hyUivAcRdlHiUFoIInRgAwV1kwW5QAlHakU2I7gZAX7HlQgR3oMIu8h3KPlBhA5soKBusiAXKN1IE8qbuKs378DjDXyJEOE9iLCLbIdSBIjQgQ0U1E0W5ALtO9Kd8exFD0T4QIFnEGEsiLALwfMdIvRgAwV1kwW5QHuONGWxKbf1G/ACIowFEXYheL5DhB5soKBusiAXKJkIJx3Xb8ALiDAWRNiF4PkOEXqwgYK6yYJcoB1HmpLarPN6HXgCEcaCCLsQPN8hQg82UFA3WZALtN9Ik2rzS/AIIowFEXYheL5DhB5soKBusiAXCBFO/mCbXIgI+26OCPcDETqwgYK6yYJcIN9I3Wp6cNvlPP3WiDAWRNiF4PkOEXqwgYK6yYJcoO6RJiy0SE6z37DDeQs9iAiDQYRdCJ7vBhHh//7bp+/86j+WXP3kNkdsoKBusiAXqHOkSRG9KMIuA95+24V/EyKMBRF2IXi+G0OEXz5d+Mf/6r76yW1O2EBB3WRBLVCvXaZMNKmsZzdeyIO//gGIMBZE2IXg+W4IEb477dOnf/hj59VPbnPGBgrqJgtagbr9MmWnGWfN36zLeXPfc4EGEWE0iLALwfPdCCL8enmE8/RY56/7rn5ymws2UFA3WdgoUP9pf5Eg5m787BtMOmtaZNM36OHZz+Q8x/bTf450XogI+27u/ZumWON7Cp7vBhDh0WWXhze/TDznN3n1k9tcsYFebqPnBL09E4Hif9BZFzi+8tmtFz22OXHRAh7/9bM/0oKMiDAWb85JEGEF9EX49cNkR7/d372bvPrJba7YQC92MXs63Jkm0Bo/aP/3dP3tc4J6/pVLWfbTz9xqQUZEGIs35ySIsAL6IvxsXu/ytX3Gb/LqJ7e5YgO92EXfCXp7thBhl0QWfuXzW7e3n9PaAvp/gOaKya/uTIYIY/HmnAQRVkBehMd7dL+7/p+//PbTpz88v/rJbd6xgV6rYsnpdFPuA63wg/bLZJl2nt48kKU/wsTFk1/b+W0RYSzenJMgwgrIi/CvvzceuzHc/NVPbvOODfRSE6+eV9fnLtAaP2j/95z8yueWCiEq++Qt+y+cBhHGstlIC2p6/Z/cat9z35HWQV6E3+/QfbzYpX3Cb/LqJ7d5xwZ6qYmYc+warCbCV2S0G4HZJ2/Zf+E0iDCWzUZaUNPr/+RW+577jrQO8iK8fYrv873UJq9+eJu/+8D9w0WfuOEV5veYutQxtePCNXD+SAt++M0iOdlspAU1rfE3VdkjI+t3t5EIbz8pZvLqh7dBhNXpHmTqUs/UjgvXwPkjLfjhN4vkZLORFtS0xt9UZY+MrN/dOt/+y43UvtyLcPLqh7dBhDl4veXer318IQBAPIhwBObD99fkq7n7SycuXvo3AwAsoogIDfZJz5eeLb0/wwc9CRtA/leNvvpX9X7t4r9kBxRfsyCXSS6Q4ki7rDSjrCLPERpsoJeaGFqEm72hPu/HFnhRPB/JZZILpDjSgCL0vmrUYAO9VkVWD27xhvrNPmLNfoOXbpwWxfORXCa5QIoj6Ysw9fsI895XUfqs0TOOkdKimEguk1wgxZH0RZj6k2UGF+GSO2ruv9sxUloUE8llkgukOJK+CHN/1uhb1gftNvk1TJviGikpionkMskFUhxJX4TJf/tEVuQCKY7EShWQC6Q40gAizP37CLMiF0hxJFaqgFwgxZEGEOHRZJe7dF8+tY9yTl795DZXbKDta1wVuUCKI7FSBeQCKY40gAiPd+9O9++Odpu4czd59ZPbXLCBtq9xVeQCKY7EShWQC6Q40ggiPD7jd+X6bN9RcNdnASeunrnwHhto+xpXRS6Q4kisVAG5QIojDSHC08Obt06zIpy4eu7CO2yg7WtcFblAiiOxUgXkAimONIYIz49wmjfJ34qwvXr2wltsoO1rXBW5QIojsVIF5AIpjjSICFfCBtq+xlWRC6Q4EitVQC6Q4kiI0IMNtH2NqyIXSHEkVqqAXCDFkRChBxto+xpXRS6Q4kisVAG5QIojIUIPNtD2Na6KXCDFkVipAnKBFEdChB5soO1rXBW5QIojsVIF5AIpjoQIPdhA29e4KnKBFEdipQrIBVIcCRF6sIG2r3FV5AIpjsRKFZALpDgSIvRgA21f46rIBVIciZUqIBdIcSRE6MEG2r7GVZELpDgSK1VALpDiSIjQgw20fY2rIhdIcSRWqoBcIMWREKEHG2j7GldFLpDiSKxUAblAiiMhQg820PY1ropcIMWRWKkCcoEUR0KEHmyg7WtcFblAiiOxUgXkAimOhAg92EDb17gqcoEUR2KlCsgFUhwJEXqwgbavcVXkAimOxEoVkAukOBIi9GADbV/jqsgFUhyJlSogF0hxJETowQbavsZVkQukOBIrVUAukOJIiNCDDbR9jasiF0hxJFaqgFwgxZEQoQcbaPsaV0UukOJIrFQBuUCKIyFCDzbQ9jWuilwgxZFYqQJygRRHQoQebKDta1wVuUCKI7FSBeQCKY6ECD3YQNvXuCpygRRHYqUKyAVSHAkRerCBtq9xVeQCKY7EShWQC6Q4EiL0YANtX+OqyAVSHImVKiAXSHEkROjBBtq+xlWRC6Q4EitVQC6Q4kiI0IMNtH2NqyIXSHEkVqqAXCDFkRChBxto+xpXRS6Q4kisVAG5QIojIUIPNtD2Na6KXCDFkVipAnKBFEdChB5soO1rXBW5QIojsVIF5AIpjoQII/i77+z9M8ATGKkCrFQARloVRAgrwkgVYKUCMNKqIEJYEUaqACsVgJFWBRHCijBSBVipAIy0KogQVoSRKsBKBWCkVUGEsCKMVAFWKgAjrQoihBVhpAqwUgEYaVUQIawII1WAlQrASKuCCGFFGKkCrFQARloVRAgrwkgVYKUCMNKqIEJYEUaqACsVgJFWpa4IAQAAAkCEAAAwNIgQAACGBhECAMDQIEIAABgaRAgAAEODCAEAYGgQIQAADA0iBACAoUGEAAAwNIgQAACGppYI//r7T9/51X/Yy/7339rLYD/OG336w82FjJSGr5/+4Y/2/09Ow177cj/S5aD6x/+yFzJSIJVEePnXcPsP4svEZbAb54Pz/gBlpDT85be359jJadhrX+5G+jjxceZbi0Ii/P6v4533fyZfJi6D3fjwoDUhI6XheE61G0xOw177cjeSPfFx5luJOiI8/WfR8QG308n21+cLv15OuPYy2I8v18Pyszk+GSkNp4PInDcnp2Gvfbkb6fR/T/f6Pv7ESNHUEeHnj38cn693N47/Ci7/ML7waPn+HI/Ujz0+/e70J0ZKw/m+xcc5dnIa9tqX+5E+jqTzf1+enn1npGDKiPD4z+P6Aozj+fb0T+Prx7+B478M/sNoZyb3YKQsfL5/JI298nE/0s0GxzPf6f8wUjBlRPjFPin8+TL9Z3PhVx4r3x070vufGSkHpyeVfvXvdoHJadhrR9qRju77g73+NA4jBVNFhMf/7PnD1IXXBw1u7jLCPnydECEj5eD0BNOvb86ak9Ow145MjPR9AvPI55fzNYwUTRURfv8X0j4QfvMfSzf/NmAXph6wYaQcXI6gr3N3Nq7TsNeOTIx0y+U/LxkpmioivLyz5svNw+c3/7HEQ+X7Y57C/3p9Wp+RcvDozYddAAAFwklEQVTXfz6tMHtn4zoNe+3IxEg3MNJaVBHh6UG3r3dvIb399/KZfw6789W+feL9tReMlAc7x+Q07LU/syK8/uclI0VTRYTHhwT+3/1bSJt/DnzGwt6YN/9+vNWTkfLwUITHadhrf+ZE+P72JEaKppAIP10fbPt8vU/45eafwxf+OSTg+tky74/cMFIq7Cl0chr22p8ZEZ6OrdMpkJGiKSXC69rXBwj455CNiY9YY6RUIMICzIjw8/tb6xkpmkoivHn/06+/8c8hHZdXf387/7cK//GaEERYgEkR2g9TY6RoKonw4yXCl38oPFKejPdPgDoftqdxGCkVPEdYgCkR3n8cLCOFUkmEH28avbx6mNdO5eL4Spn3/1q5fg4eI6WCV40WYEKEp1eh/W76CxjJTxURfr35ZNmLCHk3TS4m/zuVkVLB+wgL0Irw9FTDx0NijBRNFRHeftDQ5f/x+Qq5uH2u4nI0M1Iq+GSZAjQi/PLp5hExRgqnighvP3r2IkI+cS8XkyJkpFTwWaMFuBfh5093v2qJkaKpIkLz4V3f+Az2pNw+fs1IGblZgN8+kZO72j9/amZgpGCqiPDm1TLv/z3Eb+VKRfNiGX51Wjpuzpr8PsKc3Krty6f2VaGMFEwZER7Pq9d/HF/sb6i/XHj7slLYhbu3TzBSPm7OsZPTsNfu3P/XSvvuCEYKpowIT/8eTmfW0xtqfnd74c2bbGAvTq/xPh20pz99fNooI2Xh9s7G5DTstTf3T+ROPPLJSLHUEeH140btr5843we5+SBu2JOvnxgpNxNPPzXTsNfO3L3Z85bLNYwUSiERmn8S5r+AvvCvIRPmt0+YV3QzUhruX1kxOQ177YsdyQjvdhNGiqSSCK8qvH0g4Pw5z+2vr4d9uKjw9o1NjJSF5iWGk9Ow166YkezH2N95j5ECqSVCAACAYBAhAAAMDSIEAIChQYQAADA0iBAAAIYGEQIAwNAgQgAAGBpECAAAQ4MIAQBgaBAhAAAMDSIEAIChQYQAADA0iBAAAIYGEQIAwNAgQgAAGBpECAAAQ4MIAQBgaBAhAAAMDSIEAIChQYQAADA0iBCgMv/9T4fD3/zr3j8FQGkQIUBlECGAG0QIUBlECOAGEQJUBhECuEGEAAAwNIgQAACGBhECAMDQIEIAABgaRAigxJ///vCdX/xp758DoBCIEKAyt68a/flw5Zff/udfECJAF4gQoDI3Ivzx8MEPiBCgE0QIUBkrQuvBw+H/IkKAPhAhQGWMCM+Pi57cd32IFBECdIAIASrzIcLjQ6GHw28ul/+ICAF6QYQAlfkQ4c/WgxcTIkKADhAhQGU+RHg03w+3VyBCgB4QIUBl3kV4Et9vzDU/IUKAPhAhQGXeRXh8J/3Nr6H4GREC9IEIASpzI8K//c+7axAhQAeIEKAy7yJs7gAiQoBOECFAZeZFyCfLAHSCCAEqwz1CADeIEKAyPEcI4AYRAlTm5u0TN68aPZoREQJ0gAgBKvPuv9MnrNn3EfL2CYBOECFAZT7uCN69gf4kRkQI0AEiBKjMhwhPv5v+l+9X/MRnjQJ0gggBKmOeGvzxYEz4M799AqAXRAhQGSPC06eNnl85ev4jIgToAhECVMa+WPT663jP/B9ECNAHIgSozM27JqwJf+BVowCdIEKAyty+ffD6kOjxNxMiQoBOECFAZe7fR39618RJgIgQoBNECKAJIgToBBECaIIIATpBhACaIEKAThAhgCaIEKATRAigCSIE6AQRAmiCCAE6QYQAmiBCgE4QIYAmiBCgE0QIoAkiBOgEEQIAwNAgQgAAGBpECAAAQ4MIAQBgaBAhAAAMDSIEAIChQYQAADA0iBAAAIYGEQIAwNAgQgAAGBpECAAAQ4MIAQBgaBAhAAAMDSIEAIChQYQAADA0iBAAAIYGEQIAwNAgQgAAGBpECAAAQ4MIAQBgaBAhAAAMDSIEAICh+f9JscrKwZSm2gAAAABJRU5ErkJggg==" title="Density of IQ scores drawn a bell curve with mean 130. The fit is terrible." alt="Density of IQ scores drawn a bell curve with mean 130. The fit is terrible." width="70%" style="display: block; margin: auto;" /></p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<div class="slideContent noTitle" >
<p>Density function <code>dnorm(xs, mean = 100, sd = 15)</code> tells us the height of each
value in <code>xs</code> when drawn on a normal bell curve.</p>
<pre><code class="r"># likelihood (density) of each point
dnorm(iqs, 100, 15) %>% round(3)
#> [1] 0.013 0.011 0.019 0.023 0.015 0.014 0.003 0.004 0.007 0.024 0.025
#> [12] 0.019 0.020 0.001 0.008 0.017 0.014 0.024 0.026 0.018 0.025 0.026
#> [23] 0.019 0.018 0.025 0.024 0.026
</code></pre>
<p>Likelihood of all points is the product. These quantities get vanishingly small
<a href="https://math.stackexchange.com/questions/892832/why-we-consider-log-likelihood-instead-of-likelihood-in-gaussian-distribution">so we sum their logs instead</a>. (Hence, <em>log-likelihoods</em>.)</p>
<pre><code class="r"># vanishingly small!
prod(dnorm(iqs, 100, 15))
#> [1] 2.276823e-50
# log scale
sum(dnorm(iqs, 100, 15, log = TRUE))
#> [1] -114.3065
</code></pre>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<div class="slideContent noTitle" >
<p>Log-likelihoods provide a measure of how well the data fit a given normal
distribution.</p>
<p>Which mean best fits the data? Below average IQ (85), average IQ (100), or above
average IQ (115)?</p>
<pre><code class="r">sum(dnorm(iqs, 85, 15, log = TRUE))
#> [1] -119.0065
sum(dnorm(iqs, 100, 15, log = TRUE))
#> [1] -114.3065
sum(dnorm(iqs, 115, 15, log = TRUE))
#> [1] -136.6065
</code></pre>
<p>The data fit best with the “population average” mean (100).</p>
<p>We just used a <em>maximum likelihood</em> criterion to choose among these
alternatives!</p>
</div>
</section>
<section data-transition="linear" data-transition-speed="default">
<h3>Likelihood summary</h3>
<div class="slideContent" >
<ul>
<li>We have some model of how the data could be generated. This model has
tuneable parameters.
<ul>
<li>“The IQs are drawn from a normal distribution with an SD of 15 and some
unknown mean.”</li>
</ul></li>
<li>Likelihood is how well the observed data fit in a particular data-generating
model.</li>
<li>Classical regression's “line of best fit” finds model parameters that
maximize the likelihood of the data.</li>
</ul>
</div>
</section>
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<h3>Bayesian models</h3>
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