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test.html
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<!DOCTYPE html>
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en"><head>
<meta http-equiv="Content-Type" content="text/html; charset=UTF-8">
<meta charset="utf-8">
<meta name="generator" content="quarto-1.3.450">
<meta name="viewport" content="width=device-width, initial-scale=1.0, user-scalable=yes">
<meta name="author" content="SM">
<meta name="dcterms.date" content="2024-03-24">
<title>Statistical_Rethinking_RM</title>
<style>
code{white-space: pre-wrap;}
span.smallcaps{font-variant: small-caps;}
div.columns{display: flex; gap: min(4vw, 1.5em);}
div.column{flex: auto; overflow-x: auto;}
div.hanging-indent{margin-left: 1.5em; text-indent: -1.5em;}
ul.task-list{list-style: none;}
ul.task-list li input[type="checkbox"] {
width: 0.8em;
margin: 0 0.8em 0.2em -1em; /* quarto-specific, see https://github.com/quarto-dev/quarto-cli/issues/4556 */
vertical-align: middle;
}
/* CSS for syntax highlighting */
pre > code.sourceCode { white-space: pre; position: relative; }
pre > code.sourceCode > span { display: inline-block; line-height: 1.25; }
pre > code.sourceCode > span:empty { height: 1.2em; }
.sourceCode { overflow: visible; }
code.sourceCode > span { color: inherit; text-decoration: inherit; }
div.sourceCode { margin: 1em 0; }
pre.sourceCode { margin: 0; }
@media screen {
div.sourceCode { overflow: auto; }
}
@media print {
pre > code.sourceCode { white-space: pre-wrap; }
pre > code.sourceCode > span { text-indent: -5em; padding-left: 5em; }
}
pre.numberSource code
{ counter-reset: source-line 0; }
pre.numberSource code > span
{ position: relative; left: -4em; counter-increment: source-line; }
pre.numberSource code > span > a:first-child::before
{ content: counter(source-line);
position: relative; left: -1em; text-align: right; vertical-align: baseline;
border: none; display: inline-block;
-webkit-touch-callout: none; -webkit-user-select: none;
-khtml-user-select: none; -moz-user-select: none;
-ms-user-select: none; user-select: none;
padding: 0 4px; width: 4em;
}
pre.numberSource { margin-left: 3em; padding-left: 4px; }
div.sourceCode
{ }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
</style>
<script src="test_files/libs/clipboard/clipboard.min.js"></script>
<script src="test_files/libs/quarto-html/quarto.js"></script>
<script src="test_files/libs/quarto-html/popper.min.js"></script>
<script src="test_files/libs/quarto-html/tippy.umd.min.js"></script>
<script src="test_files/libs/quarto-html/anchor.min.js"></script>
<link href="test_files/libs/quarto-html/tippy.css" rel="stylesheet">
<link href="test_files/libs/quarto-html/quarto-syntax-highlighting.css" rel="stylesheet" id="quarto-text-highlighting-styles">
<script src="test_files/libs/bootstrap/bootstrap.min.js"></script>
<link href="test_files/libs/bootstrap/bootstrap-icons.css" rel="stylesheet">
<link href="test_files/libs/bootstrap/bootstrap.min.css" rel="stylesheet" id="quarto-bootstrap" data-mode="light"><style>html{ scroll-behavior: smooth; }</style>
<script src="https://polyfill.io/v3/polyfill.min.js?features=es6"></script><script src="https://cdn.jsdelivr.net/npm/mathjax@3/es5/tex-chtml-full.js" type="text/javascript"></script>
</head>
<body>
<div id="quarto-content" class="page-columns page-rows-contents page-layout-article toc-left">
<div id="quarto-sidebar-toc-left" class="sidebar toc-left">
</div>
<div id="quarto-margin-sidebar" class="sidebar margin-sidebar">
</div>
<main class="content" id="quarto-document-content"><header id="title-block-header" class="quarto-title-block default"><div class="quarto-title">
<div class="quarto-title-block"><div><h1 class="title">Statistical_Rethinking_RM</h1><button type="button" class="btn code-tools-button" id="quarto-code-tools-source"><i class="bi"></i> Code</button></div></div>
</div>
<div class="quarto-title-meta">
<div>
<div class="quarto-title-meta-heading">Author</div>
<div class="quarto-title-meta-contents">
<p>SM </p>
</div>
</div>
<div>
<div class="quarto-title-meta-heading">Published</div>
<div class="quarto-title-meta-contents">
<p class="date">March 24, 2024</p>
</div>
</div>
</div>
</header><p>Linear model with n number of predictor variables:</p>
<p><span class="math display">\[\mu_i = \alpha + \beta_1 \text{x}_{1i} + \beta_2 \text{x}_{2i} + ... + \beta_n \text{x}_{ni}\]</span></p>
<div class="quarto-figure quarto-figure-center">
<figure class="figure"><p><embed src="https://latex.codecogs.com/svg.latex?x%3D%5Cfrac%7B-b%5Cpm%5Csqrt%7Bb%5E2-4ac%7D%7D%7B2a%7D" class="img-fluid"></p>
<figcaption class="figure-caption"></figcaption></figure>
</div>
<p>wrong</p>
<div class="quarto-figure quarto-figure-center">
<figure class="figure"><p><img src="https://latex.codecogs.com/svg.latex?%5Cboldsymbol%7B%5Cgamma%20=%20%5Cbeta_R%20+%20%5Cbeta_%7BAR%7D(1)%20=%20-0.18%20+%200.35%20=%200.17%7D" class="img-fluid figure-img"></p>
<figcaption class="figure-caption"></figcaption></figure>
</div>
<p><img src="https://latex.codecogs.com/svg.latex?%5Cdpi%7B220%7D%5Ctext%7BPosterior%20=%7D%5Cfrac%7B%5Ctext%7BLikelihood%20x%20Prior%7D%7D%7B%5Ctext%7BAverage%20Likelihood%7D%7D" title="\text{Posterior =}\frac{\text{Likelihood x Prior}}{\text{Average Likelihood}}"></p>
<p><img src="https://latex.codecogs.com/svg.latex?%5Cdpi%7B110%7D%5Ctext%7BPosterior%7D%20=%20%5Cfrac%7B%5Ctextbf%7BLikelihood%7D%20%5Ctimes%20%5Ctextbf%7BPrior%7D%7D%7B%5Ctext%7BAverage%20Likelihood%7D%7D" title="\text{Posterior} = \frac{\textbf{Likelihood} \times \textbf{Prior}}{\text{Average Likelihood}}"></p>
<p>test</p>
<p><img src="https://latex.codecogs.com/svg.latex?%5Cinline&space;%5Cdpi%7B110%7D%5Cboldsymbol%7B%5Cbegin%7Balign*%7Dh_i%20&%5Csim%20Normal(%5Cmu_i,%20%5Csigma)%20%5C%20&&&%20height%20&%5Csim%20dnorm(mu,%20sigma)%20%5C%5C%5Cmu_i%20&=%20%5Calpha%20+%20%5Cbeta%20x_i%20%5C%20&&&%20mu%20&%5Cleftarrow%20a%20+%20b%20%5Ctimes%20weight%20%5C%5C%5Calpha%20&%5Csim%20Normal(178,%20100)%20%5C%20&&&%20a%20&%5Csim%20dnorm(178,%20100)%5C%5C%5Cbeta%20&%5Csim%20Normal(0,%2010)%20%5C%20&&&%20b%20&%5Csim%20dnorm(0,%2010)%5C%5C%5Csigma%20&%5Csim%20Uniform(0,%2050)%20%5C%20&&&%20sigma%20&%5Csim%20dunif(0,%2050)%5C%5C%5Cend%7Balign*%7D" title=""></p>
<p>new</p>
<p><img src="https://latex.codecogs.com/svg.latex?%5Cdpi%7B110%7D%5Cinline&space;%5Cdpi%7B110%7D%5Cboldsymbol%7B%5Cbegin%7Balign*%7DPr(p%7Cw,n)%20=%20%5Cfrac%7BBinomial(w%7Cn,p)%20~%20Uniform(p%7C0,1)%7D%7B%5Cint%20Binomial(w%7Cn,p)%20~%20Uniform(p%7C0,1)dp%7D%5C%5C%20%5Cend%7Balign*%7D" title=""></p>
<p><img src="https://latex.codecogs.com/svg.latex?%5Cdpi%7B110%7D%5Cmathbf%7BPosterior%7D%20=%20%5Cfrac%7B%5Cmathbf%7BLikelihood%7D%20%5Ctimes%20%5Cmathbf%7BPrior%7D%7D%7B%5Cmathbf%7BAverage%5C%20Likelihood%7D%7D" title="\mathbf{Posterior} = \frac{\mathbf{Likelihood} \times \mathbf{Prior}}{\mathbf{Average\ Likelihood}}"></p>
<p>Now since both right-hand sides are equal to the same thing, we can set them equal to one another and solve for the posterior probability: <img src="https://latex.codecogs.com/svg.latex?%5Cmathbf%7BPr(s%7Cy)%7D%20=%20%5Cfrac%7B%5Cmathbf%7BPr(y%7Cs)~Pr(s)%7D%7D%7B%5Cmathbf%7BPr(y)%7D%7D" class="img-fluid"></p>
<div class="quarto-figure quarto-figure-center">
<figure class="figure"><p><img src="https://latex.codecogs.com/svg.latex?%5Cmathbf%7Bw_i%20=%20%5Cfrac%7Bexp%20%5Cleft(-%20%5Cfrac%7B1%7D%7B2%7DdWAIC_i%20%5Cright)%7D%7B%5Csum_%7Bj=1%7D%5Em%20exp%5Cleft(-%20%5Cfrac%7B1%7D%7B2%7DdWAIC_j%20%5Cright)%7D%7D" class="img-fluid figure-img"></p>
<figcaption class="figure-caption"></figcaption></figure>
</div>
<p>mu, sigma symbol</p>
<p><img src="https://latex.codecogs.com/svg.image?%5Cboldsymbol%7B%5Csigma%7D" title=""></p>
<p>take</p>
<p><img src="https://latex.codecogs.com/svg.latex?%5Cboldsymbol%7B%5Cmu_i%20=%20%5Calpha%20+%20%5Cbeta_x%20x_i%20+%20%5Cbeta_z%20Z_i%7D" class="img-fluid"></p>
<p><img src="https://latex.codecogs.com/svg.latex?%5Cdpi%7B110%7D%5Ctextbf%7Bplausibility%20of%20p%20after%20D%7D_%7B%5Ctextbf%7Bnew%7D%7D%20%5Cboldsymbol%7B=%7D%20%5Cfrac%7B%5Ctextbf%7Bways%20p%20can%20produce%20D%7D_%7B%5Ctextbf%7Bnew%7D%7D%20%5Cboldsymbol%7B%5Ctimes%7D%20%5Ctextbf%7Bprior%20plausibility%20p%7D%7D%7B%5Ctextbf%7Bsum%20of%20products%7D%7D" title=""></p>
<p>test deployment</p>
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<div class="sourceCode" id="cb1" data-shortcodes="false"><pre class="sourceCode markdown code-with-copy"><code class="sourceCode markdown"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="co">---</span></span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="an">title:</span><span class="co"> "Statistical_Rethinking_RM"</span></span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="an">author:</span><span class="co"> "SM"</span></span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="an">date:</span><span class="co"> "`r format(Sys.time(), '%B %d, %Y')`"</span></span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="an">format:</span></span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="co"> html:</span></span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a><span class="co"> toc: true</span></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a><span class="co"> toc_float: true</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a><span class="co"> toc-title: "Contents"</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a><span class="co"> toc-depth: 5</span></span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a><span class="co"> toc-location: left</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a><span class="co"> number_sections: true</span></span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a><span class="co"> fig_caption: true</span></span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a><span class="co"> code-tools: true</span></span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a><span class="co"> code-fold: true</span></span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a><span class="co"> code-summary: 'Show code'</span></span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a><span class="co"> code-link: true</span></span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a><span class="co"> code_highlight: tango</span></span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a><span class="co"> code_download: true</span></span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a><span class="co"> theme: sandstone</span></span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a><span class="co"> highlight: tango</span></span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a><span class="co"> smooth-scroll: true</span></span>
<span id="cb1-23"><a href="#cb1-23" aria-hidden="true" tabindex="-1"></a><span class="co"> mathjax: local</span></span>
<span id="cb1-24"><a href="#cb1-24" aria-hidden="true" tabindex="-1"></a><span class="co"> self_contained: false</span></span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a><span class="co">---</span></span>
<span id="cb1-26"><a href="#cb1-26" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-27"><a href="#cb1-27" aria-hidden="true" tabindex="-1"></a><span class="in">```{r setup, include=FALSE}</span></span>
<span id="cb1-28"><a href="#cb1-28" aria-hidden="true" tabindex="-1"></a>knitr<span class="sc">::</span>opts_chunk<span class="sc">$</span><span class="fu">set</span>(<span class="at">echo =</span> <span class="cn">TRUE</span>)</span>
<span id="cb1-29"><a href="#cb1-29" aria-hidden="true" tabindex="-1"></a><span class="in">```</span></span>
<span id="cb1-30"><a href="#cb1-30" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-31"><a href="#cb1-31" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-32"><a href="#cb1-32" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-33"><a href="#cb1-33" aria-hidden="true" tabindex="-1"></a>Linear model with n number of predictor variables:</span>
<span id="cb1-34"><a href="#cb1-34" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-35"><a href="#cb1-35" aria-hidden="true" tabindex="-1"></a>$$\mu_i = \alpha + \beta_1 \text{x}_{1i} + \beta_2 \text{x}_{2i} + ... + \beta_n \text{x}_{ni}$$</span>
<span id="cb1-36"><a href="#cb1-36" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-37"><a href="#cb1-37" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-38"><a href="#cb1-38" aria-hidden="true" tabindex="-1"></a><span class="al"></span></span>
<span id="cb1-39"><a href="#cb1-39" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-40"><a href="#cb1-40" aria-hidden="true" tabindex="-1"></a>wrong</span>
<span id="cb1-41"><a href="#cb1-41" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-42"><a href="#cb1-42" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-43"><a href="#cb1-43" aria-hidden="true" tabindex="-1"></a>!<span class="co">[</span><span class="ot">\large </span><span class="co">]</span>(https://latex.codecogs.com/svg.latex?\boldsymbol{\gamma = \beta_R + \beta_{AR}(1) = -0.18 + 0.35 = 0.17})</span>
<span id="cb1-44"><a href="#cb1-44" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-45"><a href="#cb1-45" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-46"><a href="#cb1-46" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-47"><a href="#cb1-47" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-48"><a href="#cb1-48" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-49"><a href="#cb1-49" aria-hidden="true" tabindex="-1"></a><span class="kw"><img</span> <span class="er">src</span><span class="ot">=</span><span class="st">"https://latex.codecogs.com/svg.latex?\dpi{220}\text{Posterior =}\frac{\text{Likelihood x Prior}}{\text{Average Likelihood}}"</span><span class="er">title</span><span class="ot">=</span><span class="st">"\text{Posterior =}\frac{\text{Likelihood x Prior}}{\text{Average Likelihood}}"</span><span class="kw">/></span></span>
<span id="cb1-50"><a href="#cb1-50" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-51"><a href="#cb1-51" aria-hidden="true" tabindex="-1"></a><span class="kw"><img</span> <span class="er">src</span><span class="ot">=</span><span class="st">"https://latex.codecogs.com/svg.latex?\dpi{110}\text{Posterior} = \frac{\textbf{Likelihood} \times \textbf{Prior}}{\text{Average Likelihood}}"</span> <span class="er">title</span><span class="ot">=</span><span class="st">"\text{Posterior} = \frac{\textbf{Likelihood} \times \textbf{Prior}}{\text{Average Likelihood}}"</span><span class="kw">/></span></span>
<span id="cb1-52"><a href="#cb1-52" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-53"><a href="#cb1-53" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-54"><a href="#cb1-54" aria-hidden="true" tabindex="-1"></a>test</span>
<span id="cb1-55"><a href="#cb1-55" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-56"><a href="#cb1-56" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-57"><a href="#cb1-57" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-58"><a href="#cb1-58" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-59"><a href="#cb1-59" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-60"><a href="#cb1-60" aria-hidden="true" tabindex="-1"></a><span class="kw"><img</span> <span class="er">src</span><span class="ot">=</span><span class="st">"https://latex.codecogs.com/svg.latex?\inline</span><span class="dv">&space;</span><span class="st">\dpi{110}\boldsymbol{\begin{align*}h_i </span><span class="er">&</span><span class="st">\sim Normal(\mu_i, \sigma) \ </span><span class="er">&&&</span><span class="st"> height </span><span class="er">&</span><span class="st">\sim dnorm(mu, sigma) \\\mu_i </span><span class="er">&</span><span class="st">= \alpha + \beta x_i \ </span><span class="er">&&&</span><span class="st"> mu </span><span class="er">&</span><span class="st">\leftarrow a + b \times weight \\\alpha </span><span class="er">&</span><span class="st">\sim Normal(178, 100) \ </span><span class="er">&&&</span><span class="st"> a </span><span class="er">&</span><span class="st">\sim dnorm(178, 100)\\\beta </span><span class="er">&</span><span class="st">\sim Normal(0, 10) \ </span><span class="er">&&&</span><span class="st"> b </span><span class="er">&</span><span class="st">\sim dnorm(0, 10)\\\sigma </span><span class="er">&</span><span class="st">\sim Uniform(0, 50) \ </span><span class="er">&&&</span><span class="st"> sigma </span><span class="er">&</span><span class="st">\sim dunif(0, 50)\\\end{align*}"</span> <span class="er">title</span><span class="ot">=</span><span class="st">""</span> <span class="kw">/></span></span>
<span id="cb1-61"><a href="#cb1-61" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-62"><a href="#cb1-62" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-63"><a href="#cb1-63" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-64"><a href="#cb1-64" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-65"><a href="#cb1-65" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-66"><a href="#cb1-66" aria-hidden="true" tabindex="-1"></a>new</span>
<span id="cb1-67"><a href="#cb1-67" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-68"><a href="#cb1-68" aria-hidden="true" tabindex="-1"></a><span class="kw"><img</span> <span class="er">src</span><span class="ot">=</span><span class="st">"https://latex.codecogs.com/svg.latex?\dpi{110}\inline</span><span class="dv">&space;</span><span class="st">\dpi{110}\boldsymbol{\begin{align*}Pr(p|w,n) = \frac{Binomial(w|n,p) ~ Uniform(p|0,1)}{\int Binomial(w|n,p) ~ Uniform(p|0,1)dp}\\ \end{align*}"</span> <span class="er">title</span><span class="ot">=</span><span class="st">""</span> <span class="kw">/></span></span>
<span id="cb1-69"><a href="#cb1-69" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-70"><a href="#cb1-70" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-71"><a href="#cb1-71" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-72"><a href="#cb1-72" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-73"><a href="#cb1-73" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-74"><a href="#cb1-74" aria-hidden="true" tabindex="-1"></a><span class="kw"><img</span> <span class="er">src</span><span class="ot">=</span><span class="st">"https://latex.codecogs.com/svg.latex?\dpi{110}\mathbf{Posterior} = \frac{\mathbf{Likelihood} \times \mathbf{Prior}}{\mathbf{Average\ Likelihood}}"</span> <span class="er">title</span><span class="ot">=</span><span class="st">"\mathbf{Posterior} = \frac{\mathbf{Likelihood} \times \mathbf{Prior}}{\mathbf{Average\ Likelihood}}"</span><span class="kw">/></span></span>
<span id="cb1-75"><a href="#cb1-75" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-76"><a href="#cb1-76" aria-hidden="true" tabindex="-1"></a>Now since both right-hand sides are equal to the same thing, we can set them equal to one another and solve for the posterior probability: } = \frac{\mathbf{Pr(y|s)~Pr(s)}}{\mathbf{Pr(y)}})</span>
<span id="cb1-77"><a href="#cb1-77" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-78"><a href="#cb1-78" aria-hidden="true" tabindex="-1"></a>!<span class="co">[</span><span class="ot">\large</span><span class="co">]</span>(https://latex.codecogs.com/svg.latex?\mathbf{w_i = \frac{exp \left(- \frac{1}{2}dWAIC_i \right)}{\sum_{j=1}^m exp\left(- \frac{1}{2}dWAIC_j \right)}})</span>
<span id="cb1-79"><a href="#cb1-79" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-80"><a href="#cb1-80" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-81"><a href="#cb1-81" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-82"><a href="#cb1-82" aria-hidden="true" tabindex="-1"></a>mu, sigma symbol</span>
<span id="cb1-83"><a href="#cb1-83" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-84"><a href="#cb1-84" aria-hidden="true" tabindex="-1"></a><span class="kw"><img</span> <span class="er">src</span><span class="ot">=</span><span class="st">"https://latex.codecogs.com/svg.image?\boldsymbol{\sigma}"</span> <span class="er">title</span><span class="ot">=</span><span class="st">""</span> <span class="kw">/></span></span>
<span id="cb1-85"><a href="#cb1-85" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-86"><a href="#cb1-86" aria-hidden="true" tabindex="-1"></a>take</span>
<span id="cb1-87"><a href="#cb1-87" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-88"><a href="#cb1-88" aria-hidden="true" tabindex="-1"></a><span class="al"></span></span>
<span id="cb1-89"><a href="#cb1-89" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-90"><a href="#cb1-90" aria-hidden="true" tabindex="-1"></a><span class="kw"><img</span> <span class="er">src</span><span class="ot">=</span><span class="st">"https://latex.codecogs.com/svg.latex?\dpi{110}\textbf{plausibility of p after D}_{\textbf{new}} \boldsymbol{=} \frac{\textbf{ways p can produce D}_{\textbf{new}} \boldsymbol{\times} \textbf{prior plausibility p}}{\textbf{sum of products}}"</span><span class="er">title</span><span class="ot">=</span><span class="st">""</span> <span class="kw">/></span></span>
<span id="cb1-91"><a href="#cb1-91" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-92"><a href="#cb1-92" aria-hidden="true" tabindex="-1"></a>test deployment</span></code><button title="Copy to Clipboard" class="code-copy-button"><i class="bi"></i></button></pre></div>
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