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  64       <img src="../logo.svg" class="logo" alt=""><h1>Sequential Bayes: Utilizing the Posterior Distribution</h1>
  65
  66
  67       <small class="dont-index">Source: <a href="https://github.com/MI2YorkU/Rnaught/blob/master/vignettes/seq_bayes_post.Rmd" class="external-link"><code>vignettes/seq_bayes_post.Rmd</code></a></small>
  68       <div class="d-none name"><code>seq_bayes_post.Rmd</code></div>
  69     </div>
  70
  71
  72
  73 <p>In the Sequential Bayes method, the probability distribution of R0 is
  74 updated sequentially from one case count to the next, starting from a
  75 (discretized) uniform prior. By default, the function
  76 <code><a href="../reference/seq_bayes.html">seq_bayes()</a></code> returns the mean of the last updated posterior
  77 distribution as its estimate of R0. However, by setting the parameter
  78 <code>post</code> to <code>TRUE</code>, it is possible to return the
  79 final distribution itself:</p>
  80 <div class="sourceCode" id="cb1"><pre class="downlit sourceCode r">
  81 <code class="sourceCode R"><span><span class="co"># Daily case counts.</span></span>
  82 <span><span class="va">cases</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/c.html" class="external-link">c</a></span><span class="op">(</span><span class="fl">1</span>, <span class="fl">4</span>, <span class="fl">10</span>, <span class="fl">5</span>, <span class="fl">3</span>, <span class="fl">4</span>, <span class="fl">19</span>, <span class="fl">3</span>, <span class="fl">3</span>, <span class="fl">14</span>, <span class="fl">4</span><span class="op">)</span></span>
  83 <span></span>
  84 <span><span class="va">posterior</span> <span class="op">&lt;-</span> <span class="fu"><a href="../reference/seq_bayes.html">seq_bayes</a></span><span class="op">(</span><span class="va">cases</span>, mu <span class="op">=</span> <span class="fl">8</span>, kappa <span class="op">=</span> <span class="fl">7</span>, post <span class="op">=</span> <span class="cn">TRUE</span><span class="op">)</span></span></code></pre></div>
  85 <p>First, the distribution can be used to retrieve the original estimate
  86 (had <code>post</code> been left to its default value of
  87 <code>FALSE</code>) by calculating its mean:</p>
  88 <div class="sourceCode" id="cb2"><pre class="downlit sourceCode r">
  89 <code class="sourceCode R"><span><span class="co"># `supp` is the support of the distribution, and `pmf` is its probability mass</span></span>
  90 <span><span class="co"># function.</span></span>
  91 <span><span class="va">post_mean</span> <span class="op">&lt;-</span> <span class="fu"><a href="https://rdrr.io/r/base/sum.html" class="external-link">sum</a></span><span class="op">(</span><span class="va">posterior</span><span class="op">$</span><span class="va">supp</span> <span class="op">*</span> <span class="va">posterior</span><span class="op">$</span><span class="va">pmf</span><span class="op">)</span></span>
  92 <span><span class="va">post_mean</span></span>
  93 <span><span class="co">#&gt; [1] 1.476652</span></span>
  94 <span></span>
  95 <span><span class="co"># Verify that the following is true:</span></span>
  96 <span><span class="va">post_mean</span> <span class="op">==</span> <span class="fu"><a href="../reference/seq_bayes.html">seq_bayes</a></span><span class="op">(</span><span class="va">cases</span>, mu <span class="op">=</span> <span class="fl">8</span>, kappa <span class="op">=</span> <span class="fl">7</span><span class="op">)</span></span>
  97 <span><span class="co">#&gt; [1] TRUE</span></span></code></pre></div>
  98 <p>Another use of the posterior is to obtain an alternative estimate of
  99 R0. For instance, the following extracts the posterior mode rather than
 100 the mean:</p>
 101 <div class="sourceCode" id="cb3"><pre class="downlit sourceCode r">
 102 <code class="sourceCode R"><span><span class="va">post_mode</span> <span class="op">&lt;-</span> <span class="va">posterior</span><span class="op">$</span><span class="va">supp</span><span class="op">[</span><span class="fu"><a href="https://rdrr.io/r/base/which.min.html" class="external-link">which.max</a></span><span class="op">(</span><span class="va">posterior</span><span class="op">$</span><span class="va">pmf</span><span class="op">)</span><span class="op">]</span></span>
 103 <span><span class="va">post_mode</span></span>
 104 <span><span class="co">#&gt; [1] 1.36</span></span></code></pre></div>
 105 <p>Returning the posterior is suitable for visualization purposes. Below
 106 is a graph containing the uniform prior, final posterior distribution,
 107 posterior mean and posterior mode:</p>
 108 <p><img src="seq_bayes_post_files/figure-html/unnamed-chunk-5-1.png" width="1400"></p>
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