https://github.com/cran/bayestestR
Revision 40f7c88ddf855896018cf20ec8a7ac5fbd0ea2fb authored by Dominique Makowski on 27 January 2020, 05:30 UTC, committed by cran-robot on 27 January 2020, 05:30 UTC
1 parent d8462ad
Raw File
Tip revision: 40f7c88ddf855896018cf20ec8a7ac5fbd0ea2fb authored by Dominique Makowski on 27 January 2020, 05:30 UTC
version 0.5.1
Tip revision: 40f7c88
probability_of_direction.html
<!DOCTYPE html>

<html xmlns="http://www.w3.org/1999/xhtml">

<head>

<meta charset="utf-8">
<meta http-equiv="Content-Type" content="text/html; charset=utf-8" />
<meta name="generator" content="pandoc" />
<meta name="viewport" content="width=device-width, initial-scale=1">

<style type="text/css">
@font-face {
font-family: octicons-link;
src: url(data:font/woff;charset=utf-8;base64,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) format('woff');
}
body {
-webkit-text-size-adjust: 100%;
text-size-adjust: 100%;
color: #333;
font-family: "Helvetica Neue", Helvetica, "Segoe UI", Arial, freesans, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol";
font-size: 16px;
line-height: 1.6;
word-wrap: break-word;
}
a {
background-color: transparent;
}
a:active,
a:hover {
outline: 0;
}
strong {
font-weight: bold;
}
h1 {
font-size: 2em;
margin: 0.67em 0;
}
img {
border: 0;
}
hr {
box-sizing: content-box;
height: 0;
}
pre {
overflow: auto;
}
code,
kbd,
pre {
font-family: monospace, monospace;
font-size: 1em;
}
input {
color: inherit;
font: inherit;
margin: 0;
}
html input[disabled] {
cursor: default;
}
input {
line-height: normal;
}
input[type="checkbox"] {
box-sizing: border-box;
padding: 0;
}
table {
border-collapse: collapse;
border-spacing: 0;
}
td,
th {
padding: 0;
}
* {
box-sizing: border-box;
}
input {
font: 13px / 1.4 Helvetica, arial, nimbussansl, liberationsans, freesans, clean, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol";
}
a {
color: #4078c0;
text-decoration: none;
}
a:hover,
a:active {
text-decoration: underline;
}
hr {
height: 0;
margin: 15px 0;
overflow: hidden;
background: transparent;
border: 0;
border-bottom: 1px solid #ddd;
}
hr:before {
display: table;
content: "";
}
hr:after {
display: table;
clear: both;
content: "";
}
h1,
h2,
h3,
h4,
h5,
h6 {
margin-top: 15px;
margin-bottom: 15px;
line-height: 1.1;
}
h1 {
font-size: 30px;
}
h2 {
font-size: 21px;
}
h3 {
font-size: 16px;
}
h4 {
font-size: 14px;
}
h5 {
font-size: 12px;
}
h6 {
font-size: 11px;
}
blockquote {
margin: 0;
}
ul,
ol {
padding: 0;
margin-top: 0;
margin-bottom: 0;
}
ol ol,
ul ol {
list-style-type: lower-roman;
}
ul ul ol,
ul ol ol,
ol ul ol,
ol ol ol {
list-style-type: lower-alpha;
}
dd {
margin-left: 0;
}
code {
font-family: Consolas, "Liberation Mono", Menlo, Courier, monospace;
font-size: 12px;
}
pre {
margin-top: 0;
margin-bottom: 0;
font: 12px Consolas, "Liberation Mono", Menlo, Courier, monospace;
}
.select::-ms-expand {
opacity: 0;
}
.octicon {
font: normal normal normal 16px/1 octicons-link;
display: inline-block;
text-decoration: none;
text-rendering: auto;
-webkit-font-smoothing: antialiased;
-moz-osx-font-smoothing: grayscale;
-webkit-user-select: none;
-moz-user-select: none;
-ms-user-select: none;
user-select: none;
}
.octicon-link:before {
content: '\f05c';
}
.markdown-body:before {
display: table;
content: "";
}
.markdown-body:after {
display: table;
clear: both;
content: "";
}
.markdown-body>*:first-child {
margin-top: 0 !important;
}
.markdown-body>*:last-child {
margin-bottom: 0 !important;
}
a:not([href]) {
color: inherit;
text-decoration: none;
}
.anchor {
display: inline-block;
padding-right: 2px;
margin-left: -18px;
}
.anchor:focus {
outline: none;
}
h1,
h2,
h3,
h4,
h5,
h6 {
margin-top: 1em;
margin-bottom: 16px;
font-weight: bold;
line-height: 1.4;
}
h1 .octicon-link,
h2 .octicon-link,
h3 .octicon-link,
h4 .octicon-link,
h5 .octicon-link,
h6 .octicon-link {
color: #000;
vertical-align: middle;
visibility: hidden;
}
h1:hover .anchor,
h2:hover .anchor,
h3:hover .anchor,
h4:hover .anchor,
h5:hover .anchor,
h6:hover .anchor {
text-decoration: none;
}
h1:hover .anchor .octicon-link,
h2:hover .anchor .octicon-link,
h3:hover .anchor .octicon-link,
h4:hover .anchor .octicon-link,
h5:hover .anchor .octicon-link,
h6:hover .anchor .octicon-link {
visibility: visible;
}
h1 {
padding-bottom: 0.3em;
font-size: 2.25em;
line-height: 1.2;
border-bottom: 1px solid #eee;
}
h1 .anchor {
line-height: 1;
}
h2 {
padding-bottom: 0.3em;
font-size: 1.75em;
line-height: 1.225;
border-bottom: 1px solid #eee;
}
h2 .anchor {
line-height: 1;
}
h3 {
font-size: 1.5em;
line-height: 1.43;
}
h3 .anchor {
line-height: 1.2;
}
h4 {
font-size: 1.25em;
}
h4 .anchor {
line-height: 1.2;
}
h5 {
font-size: 1em;
}
h5 .anchor {
line-height: 1.1;
}
h6 {
font-size: 1em;
color: #777;
}
h6 .anchor {
line-height: 1.1;
}
p,
blockquote,
ul,
ol,
dl,
table,
pre {
margin-top: 0;
margin-bottom: 16px;
}
hr {
height: 4px;
padding: 0;
margin: 16px 0;
background-color: #e7e7e7;
border: 0 none;
}
ul,
ol {
padding-left: 2em;
}
ul ul,
ul ol,
ol ol,
ol ul {
margin-top: 0;
margin-bottom: 0;
}
li>p {
margin-top: 16px;
}
dl {
padding: 0;
}
dl dt {
padding: 0;
margin-top: 16px;
font-size: 1em;
font-style: italic;
font-weight: bold;
}
dl dd {
padding: 0 16px;
margin-bottom: 16px;
}
blockquote {
padding: 0 15px;
color: #777;
border-left: 4px solid #ddd;
}
blockquote>:first-child {
margin-top: 0;
}
blockquote>:last-child {
margin-bottom: 0;
}
table {
display: block;
width: 100%;
overflow: auto;
word-break: normal;
word-break: keep-all;
}
table th {
font-weight: bold;
}
table th,
table td {
padding: 6px 13px;
border: 1px solid #ddd;
}
table tr {
background-color: #fff;
border-top: 1px solid #ccc;
}
table tr:nth-child(2n) {
background-color: #f8f8f8;
}
img {
max-width: 100%;
box-sizing: content-box;
background-color: #fff;
}
code {
padding: 0;
padding-top: 0.2em;
padding-bottom: 0.2em;
margin: 0;
font-size: 85%;
background-color: rgba(0,0,0,0.04);
border-radius: 3px;
}
code:before,
code:after {
letter-spacing: -0.2em;
content: "\00a0";
}
pre>code {
padding: 0;
margin: 0;
font-size: 100%;
word-break: normal;
white-space: pre;
background: transparent;
border: 0;
}
.highlight {
margin-bottom: 16px;
}
.highlight pre,
pre {
padding: 16px;
overflow: auto;
font-size: 85%;
line-height: 1.45;
background-color: #f7f7f7;
border-radius: 3px;
}
.highlight pre {
margin-bottom: 0;
word-break: normal;
}
pre {
word-wrap: normal;
}
pre code {
display: inline;
max-width: initial;
padding: 0;
margin: 0;
overflow: initial;
line-height: inherit;
word-wrap: normal;
background-color: transparent;
border: 0;
}
pre code:before,
pre code:after {
content: normal;
}
kbd {
display: inline-block;
padding: 3px 5px;
font-size: 11px;
line-height: 10px;
color: #555;
vertical-align: middle;
background-color: #fcfcfc;
border: solid 1px #ccc;
border-bottom-color: #bbb;
border-radius: 3px;
box-shadow: inset 0 -1px 0 #bbb;
}
.pl-c {
color: #969896;
}
.pl-c1,
.pl-s .pl-v {
color: #0086b3;
}
.pl-e,
.pl-en {
color: #795da3;
}
.pl-s .pl-s1,
.pl-smi {
color: #333;
}
.pl-ent {
color: #63a35c;
}
.pl-k {
color: #a71d5d;
}
.pl-pds,
.pl-s,
.pl-s .pl-pse .pl-s1,
.pl-sr,
.pl-sr .pl-cce,
.pl-sr .pl-sra,
.pl-sr .pl-sre {
color: #183691;
}
.pl-v {
color: #ed6a43;
}
.pl-id {
color: #b52a1d;
}
.pl-ii {
background-color: #b52a1d;
color: #f8f8f8;
}
.pl-sr .pl-cce {
color: #63a35c;
font-weight: bold;
}
.pl-ml {
color: #693a17;
}
.pl-mh,
.pl-mh .pl-en,
.pl-ms {
color: #1d3e81;
font-weight: bold;
}
.pl-mq {
color: #008080;
}
.pl-mi {
color: #333;
font-style: italic;
}
.pl-mb {
color: #333;
font-weight: bold;
}
.pl-md {
background-color: #ffecec;
color: #bd2c00;
}
.pl-mi1 {
background-color: #eaffea;
color: #55a532;
}
.pl-mdr {
color: #795da3;
font-weight: bold;
}
.pl-mo {
color: #1d3e81;
}
kbd {
display: inline-block;
padding: 3px 5px;
font: 11px Consolas, "Liberation Mono", Menlo, Courier, monospace;
line-height: 10px;
color: #555;
vertical-align: middle;
background-color: #fcfcfc;
border: solid 1px #ccc;
border-bottom-color: #bbb;
border-radius: 3px;
box-shadow: inset 0 -1px 0 #bbb;
}
.task-list-item {
list-style-type: none;
}
.task-list-item+.task-list-item {
margin-top: 3px;
}
.task-list-item input {
margin: 0 0.35em 0.25em -1.6em;
vertical-align: middle;
}
:checked+.radio-label {
z-index: 1;
position: relative;
border-color: #4078c0;
}
.sourceLine {
display: inline-block;
}
code .kw { color: #000000; }
code .dt { color: #ed6a43; }
code .dv { color: #009999; }
code .bn { color: #009999; }
code .fl { color: #009999; }
code .ch { color: #009999; }
code .st { color: #183691; }
code .co { color: #969896; }
code .ot { color: #0086b3; }
code .al { color: #a61717; }
code .fu { color: #63a35c; }
code .er { color: #a61717; background-color: #e3d2d2; }
code .wa { color: #000000; }
code .cn { color: #008080; }
code .sc { color: #008080; }
code .vs { color: #183691; }
code .ss { color: #183691; }
code .im { color: #000000; }
code .va {color: #008080; }
code .cf { color: #000000; }
code .op { color: #000000; }
code .bu { color: #000000; }
code .ex { color: #000000; }
code .pp { color: #999999; }
code .at { color: #008080; }
code .do { color: #969896; }
code .an { color: #008080; }
code .cv { color: #008080; }
code .in { color: #008080; }
</style>
<style>
body {
  box-sizing: border-box;
  min-width: 200px;
  max-width: 980px;
  margin: 0 auto;
  padding: 45px;
  padding-top: 0px;
}
</style>

</head>

<body>

<h1 id="probability-of-direction-pd">Probability of Direction (pd)</h1>
<ul>
<li><a href="#what-is-the-pd">What is the <em>pd?</em></a></li>
<li><a href="#relationship-with-the-p-value">Relationship with the <em>p</em>-value</a></li>
<li><a href="#methods-of-computation">Methods of computation</a></li>
<li><a href="#methods-comparison">Methods comparison</a>
<ul>
<li><a href="#correlation">Correlation</a></li>
<li><a href="#accuracy">Accuracy</a></li>
<li><a href="#can-the-pd-be-100">Can the pd be 100%?</a></li>
</ul></li>
</ul>
<p>This vignette can be referred to by citing the package:</p>
<ul>
<li>Makowski, D., Ben-Shachar, M. S., &amp; Lüdecke, D. (2019). <em>bayestestR: Describing Effects and their Uncertainty, Existence and Significance within the Bayesian Framework</em>. Journal of Open Source Software, 4(40), 1541. <a href="https://doi.org/10.21105/joss.01541">https://doi.org/10.21105/joss.01541</a></li>
<li>Makowski, D., Ben-Shachar, M. S., Chen, S. H. A., &amp; Lüdecke, D. (2019). <em>Indices of Effect Existence and Significance in the Bayesian Framework</em>. Frontiers in Psychology 2019;10:2767. <a href="https://doi.org/10.3389/fpsyg.2019.02767">10.3389/fpsyg.2019.02767</a></li>
</ul>
<hr />
<h1 id="what-is-the-pd">What is the <em>pd?</em></h1>
<p>The <strong>Probability of Direction (pd)</strong> is an index of <strong>effect existence</strong>, ranging from 50% to 100%, representing the certainty with which an effect goes in a particular direction (<em>i.e.</em>, is positive or negative).</p>
<p>Beyond its <strong>simplicity of interpretation, understanding and computation</strong>, this index also presents other interesting properties:</p>
<ul>
<li>It is <strong>independent from the model</strong>: It is solely based on the posterior distributions and does not require any additional information from the data or the model.</li>
<li>It is <strong>robust</strong> to the scale of both the response variable and the predictors.</li>
<li>It is strongly correlated with the frequentist <strong><em>p</em>-value</strong>, and can thus be used to draw parallels and give some reference to readers non-familiar with Bayesian statistics.</li>
</ul>
<p>However, this index is not relevant to assess the magnitude and importance of an effect (the meaning of “significance”), which is better achieved through other indices such as the <a href="https://easystats.github.io/bayestestR/articles/region_of_practical_equivalence.html">ROPE percentage</a>. In fact, indices of significance and existence are totally independent. You can have an effect with a <em>pd</em> of <strong>99.99%</strong>, for which the whole posterior distribution is concentrated within the <code>[0.0001, 0.0002]</code> range. In this case, the effect is <strong>positive with a high certainty</strong>, but also <strong>not significant</strong> (<em>i.e.</em>, very small).</p>
<p>Indices of effect existence, such as the <em>pd</em>, are particularly useful in exploratory research or clinical studies, for which the focus is to make sure that the effect of interest is not in the opposite direction (for clinical studies, that a treatment is not harmful). However, once the effect’s direction is confirmed, the focus should shift toward its significance, including a precise estimation of its magnitude, relevance and importance.</p>
<h1 id="relationship-with-the-p-value">Relationship with the <em>p</em>-value</h1>
<p>In most cases, it seems that the <em>pd</em> has a direct correspondence with the frequentist <strong>one-sided <em>p</em>-value</strong> through the formula: [p_{one-sided} = 1-p_d] Similarly, the <strong>two-sided <em>p</em>-value</strong> (the most commonly reported one) is equivalent through the formula: [p_{two-sided} = 2*(1-p_d)] Thus, the two-sided <em>p</em>-value of respectively <strong>.1</strong>, <strong>.05</strong>, <strong>.01</strong> and <strong>.001</strong> would correspond approximately to a <em>pd</em> of <strong>95%</strong>, <strong>97.5%</strong>, <strong>99.5%</strong> and <strong>99.95%</strong> .</p>
<div class="figure" style="text-align: center">

<img src="data:image/png;base64,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" alt="Correlation between the frequentist p-value and the probability of direction (pd)" />

<p class="caption">

<p>Correlation between the frequentist p-value and the probability of direction (pd)</p>
</p>

</div>

<blockquote>
<p><strong>But if it’s like the <em>p</em>-value, it must be bad because the <em>p</em>-value is bad [<em>insert reference to the reproducibility crisis</em>].</strong></p>
</blockquote>
<p>In fact, this aspect of the reproducibility crisis might have been misunderstood. Indeed, it is not that the <em>p</em>-value is an intrinsically bad or wrong. Instead, it is its <strong>misuse</strong>, <strong>misunderstanding</strong> and <strong>misinterpretation</strong> that fuels the decay of the situation. For instance, the fact that the <strong>pd</strong> is highly correlated with the <em>p</em>-value suggests that the latter is more an index of effect <em>existence</em> than <em>significance</em> (<em>i.e.</em>, “worth of interest”). The Bayesian version, the <strong>pd</strong>, has an intuitive meaning and makes obvious the fact that <strong>all thresholds are arbitrary</strong>. Additionally, the <strong>mathematical and interpretative transparency</strong> of the <strong>pd</strong>, and its reconceptualisation as an index of effect existence, offers a valuable insight into the characterization of Bayesian results. Moreover, its concomitant proximity with the frequentist <em>p</em>-value makes it a perfect metric to ease the transition of psychological research into the adoption of the Bayesian framework.</p>
<h1 id="methods-of-computation">Methods of computation</h1>
<p>The most <strong>simple and direct</strong> way to compute the <strong>pd</strong> is to 1) look at the median’s sign, 2) select the portion of the posterior of the same sign and 3) compute the percentage that this portion represents. This “simple” method is the most straightforward, but its precision is directly tied to the number of posterior draws.</p>
<p>The second approach relies on <a href="https://easystats.github.io/bayestestR/reference/estimate_density.html"><strong>density estimation</strong></a>. It starts by estimating the density function (for which many methods are available), and then computing the <a href="https://easystats.github.io/bayestestR/reference/area_under_curve.html"><strong>area under the curve</strong></a> (AUC) of the density curve on the other side of 0. The density-based method could hypothetically be considered as more precise, but strongly depends on the method used to estimate the density function.</p>
<h1 id="methods-comparison">Methods comparison</h1>
<p>Let’s compare the 4 available methods, the <strong>direct</strong> method and 3 <strong>density-based</strong> methods differing by their density estimation algorithm (see <a href="https://easystats.github.io/bayestestR/reference/estimate_density.html"><code>estimate_density</code></a>).</p>
<h2 id="correlation">Correlation</h2>
<p>Let’s start by testing the proximity and similarity of the results obtained by different methods.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb1-1" title="1"><span class="kw">library</span>(bayestestR)</a>
<a class="sourceLine" id="cb1-2" title="2"><span class="kw">library</span>(logspline)</a>
<a class="sourceLine" id="cb1-3" title="3"><span class="kw">library</span>(KernSmooth)</a>
<a class="sourceLine" id="cb1-4" title="4"></a>
<a class="sourceLine" id="cb1-5" title="5"><span class="co"># Compute the correlations</span></a>
<a class="sourceLine" id="cb1-6" title="6">data &lt;-<span class="st"> </span><span class="kw">data.frame</span>()</a>
<a class="sourceLine" id="cb1-7" title="7"><span class="cf">for</span>(the_mean <span class="cf">in</span> <span class="kw">runif</span>(<span class="dv">25</span>, <span class="dv">0</span>, <span class="dv">4</span>)){</a>
<a class="sourceLine" id="cb1-8" title="8">  <span class="cf">for</span>(the_sd <span class="cf">in</span> <span class="kw">runif</span>(<span class="dv">25</span>, <span class="fl">0.5</span>, <span class="dv">4</span>)){</a>
<a class="sourceLine" id="cb1-9" title="9">    x &lt;-<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">100</span>, the_mean, <span class="kw">abs</span>(the_sd))</a>
<a class="sourceLine" id="cb1-10" title="10">    data &lt;-<span class="st"> </span><span class="kw">rbind</span>(data,</a>
<a class="sourceLine" id="cb1-11" title="11">      <span class="kw">data.frame</span>(<span class="st">&quot;direct&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x),</a>
<a class="sourceLine" id="cb1-12" title="12">                 <span class="st">&quot;kernel&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;kernel&quot;</span>),</a>
<a class="sourceLine" id="cb1-13" title="13">                 <span class="st">&quot;logspline&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;logspline&quot;</span>),</a>
<a class="sourceLine" id="cb1-14" title="14">                 <span class="st">&quot;KernSmooth&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(x, <span class="dt">method=</span><span class="st">&quot;KernSmooth&quot;</span>)</a>
<a class="sourceLine" id="cb1-15" title="15">                 ))</a>
<a class="sourceLine" id="cb1-16" title="16">  }</a>
<a class="sourceLine" id="cb1-17" title="17">}</a>
<a class="sourceLine" id="cb1-18" title="18">data &lt;-<span class="st"> </span><span class="kw">as.data.frame</span>(<span class="kw">sapply</span>(data, as.numeric))</a>
<a class="sourceLine" id="cb1-19" title="19"></a>
<a class="sourceLine" id="cb1-20" title="20"><span class="co"># Visualize the correlations</span></a>
<a class="sourceLine" id="cb1-21" title="21"><span class="kw">library</span>(ggplot2)</a>
<a class="sourceLine" id="cb1-22" title="22"><span class="kw">library</span>(GGally)</a>
<a class="sourceLine" id="cb1-23" title="23"></a>
<a class="sourceLine" id="cb1-24" title="24">GGally<span class="op">::</span><span class="kw">ggpairs</span>(data) <span class="op">+</span></a>
<a class="sourceLine" id="cb1-25" title="25"><span class="st">  </span><span class="kw">theme_classic</span>()</a></code></pre></div>
<img src="data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAA8cAAAJACAMAAACXE+S8AAABRFBMVEUAAAAZGUgZGXEZSHEZSJcZcZcZcboaGhozMzNIGRlIGUhIGXFISBlISHFISJdIl5dIl91NTU1NTW5NTY5NbqtNjshuTU1uTW5uTY5ubqtuq8huq+RxGRlxGUhxGXFxSBlxSEhxSJdxcRlxcUhxcbpxuv9/f39/f5V/f6t/lZV/lcF/q9aOTU2OTW6OTY6ObquOyP+Vf3+Vf5WVf6uVlZWVweuXSBmXSEiXcRmXl0iXl3GX3bqX3d2X3f+rbk2rbm6rbo6rf3+rf5Wrjk2ryKur1v+r5P+6cRm63Ze6/7q6/926///BlX/BwZXB1sHB6//Ijk3I///Wq3/W68HW/+vW///dl0jdl5fd3Zfd///kq27k///rwZXr////unH/yI7/1qv/3Zf/3d3/5Kv/68H//7r//8j//9b//93//+T//+v///+0XKQeAAAACXBIWXMAAA7DAAAOwwHHb6hkAAAgAElEQVR4nO2d+3/USJblsxgWu6Zma528ChaqZmdnyWZ5tatryszsLu6muzDdZboL0w2z2IDxGIyN/v/fJxV6hZRSKCTF694430+VlSil0D2KOLqK0CNnCQCAOjPfAQAAJgMfA0Af+BgA+sDHANAHPgaAPvAxAPTp8fGMNfFo5C0yBo19Rp30NWlKH/sNwypVG/cahlVi0JjAx53AxzyIQSN83A18zIMYNMLH3cDHPIhBI3zcDXzMgxg0wsfdwMc8iEEjfNwNfMyDGDTCx93AxzyIQSMFH59u3Tr6andldts8o7jx8enDR6qvLau02sZ7Yl9+bb0OU2xoFIGfbl1o+erjzbW1c7vKVS3IpuHjttnwsQE8+9jCRlex5eP2dvnx5nLuq/OvVatG6OPl0e3v/jHNx0f/9R/P7S7/lR7qlpMv/u9N5VHPAM58fLp1/nWmLBX5x6//dW3tlhCZziHu46rG/u5/PEreiVT18bt/W/viUd6gj2pybWDJx5mNV+pNVNjHbx+dPvw/a2sbS8EbibQTsib8x6/+p9BskNB9/HRjWfnCx1/eEv96dUEcCN+d//9s8vFSVa4sFXn05VLy8niezyHu46elmHdfPPr43W6q6ePN86/fndvNfVyTawM7Pv45y8Yr9ZYelNMv0pPuoy8vNHfC+deSZoME7uO05rP+sTi4f/sonZO1bTbn1f+wkcjK8v9rWq1h28dp/S2ViGp8+CjVlGSnnst/5T6uybUQhR0f//0/rKVHndV6S9KTjuXZRtpfSv/P1VeTSrO5cIL3sVD7tPTxzbV0Hx19/Trh4+Ot//ZPr0tlko+rORax7WPRj3woaixt1Edfpk1c2Lmo1LpcC1HY8fGXGx9vZmfMjXrLvv77R5KPi51QTuLzcSMfZwdsZvn40asNWVnRsGWt1nCbj9OZy/PJ1Mcr+dhOLk6xNc61NGtLvb0TnYOnt5CPa1T9Y5GZ8y5IOpzwRzY+Tqu77DuVbaKaYxG3/eP0U+rjmxeKjmLVpp8a7zIWWLvu9Eru81bnUbfyca7Sx6v94/h8fLpVjFeLccCb4txLTE63uIxX5+eV2RBu+X81xyIOx6v/S3q0ysarv/1naby6JtcGFq8fi+sMq/XW6B/XxquXa537Y3w+9gju5zJK1XDz4S5X4H6uBD5O4tBofTBPHsSCj80DH3cCH/MgBo3wcTfwMQ9i0DjZx6yJRyNvkTFohI+7iUcjb5ExaOxC08fqrwEATmh3InwMACXgYwDoAx8DQB/4GAD6wMeJPK4HAEmi93HmYTgZkCZ2H0tXF73GAcAUIvexJABGBnSJ28e1+GFkQJaofdxwLnE1IGJi9nEzeiRkQJWIfbxqW9JyQMzE6+O22CnrATETrY9bT6IJ6wFRE6uPO/rCdAWBqInUx11DWmQFgbjR9fHx1fl8U3w6uTe/fKBcO3y6R6apKgJxo+njk/s7yfE3O8tPZ9ubyf4V5drh0x03VUUgbjR9fJg693makE8e7CXH1/ZUa4eO8joxTUkgcgb0j9OcvDzBvn6Qf1pfX6fZ6JVR05QEIkffx2fbN9LJ4eXCx51rB446aJKSQOxo+/jknrCxlI871w6aiW/6BSBE9Mers9Fq6v3j3nuo6UkCQNfHpY3F6TXd8er+RyHISQJA28f785TNNBFTvn6s8UQTNUkAJHHdz6X1XCItSQAIuPh45Rdt2pbQKshcTAC4woWPW343yii1gjs2o71p+BgQxLqP6wYy7+X2Aus/Njdko/AxIIhlH3ekRmNeVpc05iQAPgYEsevjTgsZ8bKV03T4GBDEqo/VPpvoZVudbRuFAmAXmz7Wuswz0s3WfsgFPgYEsehjfUcM7cba/DUm+BgQxJ6PBxtC082Wfx0RPgYEsebj0WZTDjLb/4lT+BgQxJ6Px8UjhdDGxEJ1tmt/EwCYxpaPydqBbOAgZiz5mK4b6EYOIgY+bkA3chAx+j4uXgKSPop8qed9IITNQDh0EC/aPj4szPt8U1puSKE0oBw7iBZdHz+/+FOWj89+u9O3NmkvUI4dRMvg8+qTe/P8F2I6319N2gqkgwexMtjH6a/DlDm5dW0XV3ntQTp4ECvDx7lSij5yu4+NBOYL2tGDSIGPG7iP/s1isfjVL8436xRotMxgH6e/C3P2O8V1J9o2dh7+52d33qZt4Inj7boEGq2TNduna2tr519Lczt8nP6/P59f3Fn9emVVorgO/0Va/csGkE14Ao3WSZvt6dbG8u8rycgT7ucibmPX8X96XB3APz9bLO4myYcf/ry4/df0z9+e/eg2GjtAo32NabP9+N1u+TefCx874sNvyh7V52d3xf8fvr+bZH+YAI32Ec32qcjHF6S5o31M3cbOffzDy+Lj+9svxZ8P3z9J659PZxIa7SPy8c21jHO7xVz42BHScfx92rVa/lvMkuaTBxrtY/h5J/I29tU//vT7X9i2cWi0D3zcwLWCfIDzze2X79OLj+n5GLc2Do32kc6rz/2pHOka62P6NvZ4/bgcH2HXxqHROmbzMXw8ghfFfUDF9Yqy/j/zuCaTQKOT604tc+FjAAghn1fvVnPH+ZiDBzhoANFRNdujryffz8XBAxw0gOiomu30+7lYWICFCBAbJvvHLCzAQgSIDdFsT7c0nnfqXLvjX0RhIQLERv680+nDR5Ofd+LhAB4qQGTkzzstfTy5f8zDATxUgMjI8vEtjXxcvNfn5N788sHq11wMwEQGiAvRbI+++nmrr39cvIf+bHsz2b+y8jUbAzCRAeJCd7y6fA/9yYO96pV78PFkXiwWxatgPj1eLH6Uph++X1RfUkehkwVqfdZvsx78nr3j6wfJyf30BV3199AzsbFrHW/uvE3vqU9J77RP78QtptmDrExQ6eSAWt/nZ7ZfpCmarbgxU7ots+99mZmPa19Tf71eiVsd4rFV8QKJ5SR/3q2YJm/uOo3FJkqdDOjR9+Z/u8jHp1u3ln/f6Y1zVfm49jUXGzsWIs638mfQRZUvZxTT5AWTXJX06GSAWt+HH/7qwscfv32UpINdu9Xcbh939I/h41GIui7qXxy/F0+K6afH/7JY8EhXSp2+YzOBUt/nZ0/c9I+PvtxI3q3dkuZ2+/hs+0bbeDV8PIq8/kXi/fQ4ff489W82/fD9j7X3t1FGpdN3bCZQ6ntzN7RxrvT/9uvH8PEo5ON4Or75q78sK7yYZvM4tfNuncRR6UsPxQ59PO1+Lvh4FHK/qpohTZn4uFcncVT60t99WmK3HrNxrvy9t+VIF3zsCHmcU1T9mztvi2l2jP89i3au0uk7NhP06XOSj8vfk/gP+Ni1kBfydce74rXl1fQJn2vICp0s6NEXUP9YvTZ8PJIX4p1s4n6B9P6ftNrlKRMbK3WyQK0PPnYNGyEgJuDjBmyEgJiAjxuwEQJiAj5uwEYIiAn4uAEbISAm4OMGbISAmICPG7ARAmICPm7ARgiICfi4ARshICbg4wZshICYgI8bsBECYkLXx9VTx/vzef4KXPgYgDDQ9LH01urnm21rs2n+bISAmND0cfVWrrPf7rStzab5sxECYkLTx9VbMpcn2PO5SMm191ezaf5shICY0PRx9dbq4292qpwMHwMQAoPzsaDoI8PHAITA4P6xAD4GICS0x6uLt1anZ9hnv8N1JwACYtj14zQl78/nF3eaX/Np/myEgJjA/VwN2AgBMQEfN2AjBMQEfNyAjRAQE/BxAzZCQEzAxw3YCAExAR83YCMExAR83ICNEBAT8HEDNkJATMDHDdgIATEBHzdgIwTEBHzcgI0QEBPwcQM2QkBMwMcN2AgBMQEfN2AjBMQEfNyAjRAQE/BxAzZCQEwMe49A/RN8DEAYaL/Xp3gPvfRGevgYgDAY/J692hv34GMAQkDTx9V7b6tP9ffQs8Hm3gbADpo+rt5DX33qXBsA4JYJ+bhzbQCAW0z1jwEA/tAer75RjlffaBuvBgD4Y9j14zQRt18/BgD4o2fUFkYFgADwMQDsgY8BoA98DAB94GMA6AMfA0Af+BgA+mi/RwAA4I9p153gYwBCwNR7fQAA/tD3cfFwBO7LBCA0tH18OL8kfNzxXh8u4EUCgCK6Pn5+8acsHzN+bhFvBAFUGXxe3fFeHwZwfbMPT1WgxmAfM32vD9s3dJV6mOkCNSbk4861CcL2TXuSGl7CQI3BPubZP2bq44YWRspAncE+Zvhen457YOjTlMJIGqgzzMcs3+vTdS8beVaVsJEGGsR+P5finlTqtOngog00iNzHqnvLadMug4c2sAJ8bN7GIRwNurZPvsZAK/CxeRNLJU8ubmwQw78BlInVx6nHLOTi5oUeP2ZWbZJulQEFkfrYUr+4tQzXZlZvjGyVARWx+Thv5HZ8rPSPIzf3boRenYF+IvNxq39d2Fje/uQNKcvvXcTi5oEv4GNjiVK3jNGb64lbt1xylQb6gY+N9Y2HxjFw8fY1RmggV2mgH/jYlI2HlqG1WXNnC1KZRksDQQAfG3LJmFKU27bg4KJkG4UCr8TkY3vJePyeaN2+PQtnxVsrGfgiBh/PFNeafKbjKrwyChvn0asbtFs88EAEPu7yr0nDGLgRzIWD82252AhwSsw+NrgJc0W5gFi4oB/OPnZxPp1vyWBZDiAWLuiHsY8Ls9o2ceC7oQVq8YJeuPvYQTIOfDe0QC1e0EukPja7IaOlOYBcwKAPxj520THOtmO6QNuQCxj0wdHHs+wdAa58TO8VG+QCBn0w9LHyfBrpOKEYMeghJh/b2p6lcu1BL2LQA3w8eXN2irUJwZCBGm4+VvSLbW3RUrkWIRgyUMPJx8qOsbWNWivZHhRjBkoY+diLjcPaBZpQjBko4eJjLx4WG7ZbvBUoxgyUUPexoj/swMQh7IERkAwaqCDuY5WF4eMuSAYNVHD1cfGd7e1bLt8ONKMGChj72Ma9Wyvbt70BK9CMGijQ9fHJvfnlA/Hp+Or80p5ybZf4Op8uNu9oO2ahGTVQoOnjs+3NZP9K+unk/k6yn1s6jAYBGw+FaNigm7RKP95cyzi3W8xt+vjkwV5yfC1Nw8fXD8S/al97xZOHxaYdbssg7sN+s1gsfvWL8806xavGokpfXajNbfpYuHeZieV8vL6+7r8de0zGZG3sPO7Pz+68Tdv5E8fbdYlnjXmVvvrin8+/luY2fXx4ufCx1FP23ZA99419yx+P67hfpE182cizCU88axRVevTlxtLKkpEV+fj4m53k8JLX8+pqOBo+HoXjuD89rpLU52eLxd0k+fDDnxe3/5r++duzH91GYwffGkX/+J+Eg/99t5rb3T+WMrOnhqz0r9P+MXysxYfflL3Gz8/uiv8/fH83yf4wwbdG7fHqG/l4tf987D8PF4G43qApXPv4h5fFx/e3X4o/H75/krZxPh1m3xpFlZ5ura2tKfvHea84TcmH8/nFnebXLoGPp+IvH79Pu4/Lf4tZ0nzy+NaYVunp1sbpw0fK/rFibXcE0y/Ow3G8PXN46h9/+v0vbH3sW6PoH3+3u/Tx8m81N0Qfd/oXPh6I68jzQdw3t1++Ty+wpuec3HzsW2OWj28Fn497TYzTan38XT8ux4DY+dizxuy601c/b/X0jxVruyA4E1O2sYfQXxT3OhXXZMo2/pnHdafEs0YKzzv1WdiLjeFjEBAEfBxYHi7D8rfpqRAOHbQjPSdRPiUBH+tE5W3L06EcO2ilqtKjrwMd54KPTUM5dtBKVaXhXnfq8i9Oq0dCOXbQSuj94+DycBGX7wCmQDp40Ebg/ePwzqeLwHwHMAXSwYM2qiqV3yQQho+7LByAjWlbgXTwoI1Q+8eh5uGCYAIZA+ngQRtVlb7zfl4t2RQ2tgnt6EELUv/4ljTXh49lowZt4oS6E2hHD1oIaLy6z8cmtzWRkGIZgevwXywWxWurPj1eLH6UpuJJP8fhWEGhsdJqjxB9HLaHU0KLZyCOw39z5236/E9K+lRQ+tRAMV3ygsX7cBUaJa32EFWq8T4QxdrGQskNG/o5dQIfD0I8Yi9edrOc5M/mFtM0V3HwsUpjqdUm2fPHQbwPpGtsKzwfhxXNcNzGLx7dy9+XIZrzckYxTd7fZfEUskpjqdUmYpzL8/tAZj2/YQwfG8Zt/KIdF21c5KbFk2KaMHmbgEqjpNUeWT72+j6QPgsHZ2P4eBB5GxcdxE+P03dlLJ4U04SXj1s1SlrtIarU7/tAaHk4oW9jj/lY9If/snRuMeXl43aNlVZ7+ByvnvW8/zJIEyfw8UDkvmM1o5yy8HGPRjf945a5Lnxc+BQ+do2/8WrRnN/ceVtMEyY+VmmUtNpDup9L9bupirXHb5qoj0OMaRiOFbyQr63eFT+xUEwTJj5WaZS02sN3PqbWN07g4+G8EO+PFPdCpPc2pU26mHLxsUpjpdUePnys0S8O4tnEdkKNawAMJIA6Hnzcdz49pkyHhB6fBgwkgDq+fEzsXFoi9Pg0YCAB1AnQx2G3srCj04ODBlADPh5I2NHpwUEDqAEfDyPo4HRhIQLIuPTxrP95iIDHqTPCjk4TFiKAjK6PT+7NLx+IT2fb84s7yrW7NkU5DxeQCLIPFiKAjKaPz7Y3k/0r4uPzzeQwt/SABtFrYtjYHTxUAAlNH5882EuOr+3ln3rWbi2QgYkTLg7goQJIaPr4+PpBcnJ/R3z6Q35evb6+HpuPiYTZBxMZoELTx+mZdO7jq5vC1Yq1WwvkYGMuBmAiA1SMyMfFp861V0tjYeKEjQGYyAAVw/vHvx7k4z4Lw8Ye4KIDlGiPV9+Qxqv1z6uZ5OEcehG3w0UHKBl2/ThNyctPl/aaX9dXnpVT+DhEuOgAJebv5yosqvQvfOwTLjpAiSUf96Vh+NgnXHSAEg8+Low8IWpPEAy5FS46QIlhH/ebmKSBc+hGXoeLDlBi1sdaNqbbiuhGXoeLDlACHw+AbuR1uOgAJQZ9rOVfyjZm0/656AAl5nys9C/tPFxAX0EGFx2gxJGPaefhAgYSBFx0gBJXPmYBFyVcdIAS+HgAXJRw0QFKDPm408KcbMym/XPRAUrM+Jh/KhZwkcNFByix62NjYYYBFz1cdIASiz42FmMwcJHERQcosdg/NhViOHCRxEUHKLGTj3kNb5Vw0cRFByix4GNjsQUHF2lcdIAS+HgAXKRx0QFKzPqY6fl0ARdtXHSAEsPjXKbCChMu8rjoACWGz6uNxRUkXORx0QFK4OMBdN3uQg7fOxKYxnD/GADgAXP9Y1MRAQCGYu65RQCAL+BjAOgDHwNAn54RTRgVAALAxwCwBz4GgD7wMQD0gY8BoA98DAB94GMA6IPrxwAQYNp1J/gYgBDQv5/r+NqemJ7cm18+UK4NAHCLto8P55eEj8+2N5P9K8q1AQBu0fXx84s/Zfn45MFemZoZ+jiCBzDxoDhDBp9XH18/SE7u7yw/ra+v82oPUbwNIQaNETLYx4eXCx93rk2UCN56w/XNPgwlDWRCPu5cmyIxvL2Kq8ZMDTNRAxnsY57947Zrbpzouq7IgEoLJ1VDGezjs+0bDMermbbxgs77A+gjS2EkayjDfJz+z+v68aw8KWPYxnNWXcxGY0MIG12Dify9Pm1NnLyoBow1ruhgoms4Mfu4tYGzaeMC3hJbdDBRNphYfdzVwDk18lm3St/BGaFNBg9lw4nNx7OW/jDDRq7Ux0JhV2eYh7bBRObjnvZN/odf+w9TviM0RpcSPgqHAB9zauLlsahNHAuFBd1aGIkcAHzMyMYKeb4jM4xCEDepesTkY+YmjsnGo7/kSgw+nsUxthWNjXv0MFOrRwQ+Lloydx8zllajTxE7wTrE4uMefMdoAMbSavQLYidZg5h9nFS5mjazfDg6AhvrCOKmWYcIfKzKVByaOvcTDRk9QdxUa8Ddx31tnHxTj8fD+pXFT3kvXH08i32M2ndgFtAWxVF8D0x9rPQvo6bOVtgqQ2Tx3AMquPlYMw+Tb+6SDNh4dWFrYYQKMx9rp2Hizb1XHzMGymK5D5Rw8rGuh+kTgcQag1Wx3AsqGPkYJuajscYIWSz3gwr4mBoxaKwxRhTH/aAkIh/7js8QnfI4iawYJ4nffuiBi4+jMHG3fXnc09LCWEn89oQaJj5WWphL++46PnHRt8p4YVz3SBfcfew7MHMwl9fCJHm8d80KjH3MK09FZ+OJ6ljvm1Uo+7hoyNxbOPczjRam6+O9f1Yg7OPOc2lmrTwCiQ1MiGO8e9qAj0MnAol1zEhju3vaSeV+vLmWcW63mBu0j2eRPJOYEoHEGsZ08dw9nRDMx2UjjqCNd8ljJFHGoCyW+6cbqj7us7KPwEzD/zBVw6wunvuoEyH3dGt5Un3+tTR3xcfVr5cfX51f2mt+7RK5NTNu6d0u5qBuBdOqOO4jBanc062N5d9XkpFXfHy2vZnsX0k/ndzfSfZzS/vrH6saOIOW3qaMs48tSGK3j9SIca7vdsu/+dymj08e7CXH19I0fHz9QPyr9rVTerMU+YbeKi44GysOp91101GOhejMFxkymvlYuHeZieV8vL6+HqaPydPt43AOUgNf0NFVQ9bqLYy95AzN/vHh5cLHUk/Zx84aecynRbu4kBSOfJpQrijLlRbOvnKC5nh1lY+Pv9lJDi85P6+e9V8zdhaLZQiIm3rvswNJ7vfYm8Vi8atfnG82Q9PHVf9YysyudpbUllubeHDNfCxF2g3bxDRynesYPz+78zb18hPH281Zyn13bvdp33n12faNfLzafT5W5WAKLUobKiJDi6cV10G+SG28NHI2cc4sOX34//rHufJecZqSD+fzizvNr62GGIWPO8QFKDKwcDpwHOWnx1Ui/vxssbibJB9++PPi9l/TP3979qPt7c+Sj9/9qf+6U+faDuj1cXAtfTDd6sLzcVjRdOI4zA+/KXvGn5/dFf9/+P5ukv1xwDIfb916KvLxBWkuBR/Xxr5cBGIN1WEqNG2BhdOJax//8LL4+P72S/Hnw/dPUh+76TDPqsedyqedQvKxKg/Li1gPxCbq042gCDCkdvzl4/dpF3n5bzFLmm+VUJ+TkHMtdx932zg8WeFF1IGn/vGn3/8CH8sBzPSfgwixvQ9AYePgdIUXUReuA80Hqt/cfvk+vYicnlc79/G7tVvv1tY2pLlefCy1W2XbDrB9j0WlM0AfBxdQN/6uH5fjXK59/PHbR6dbG97Hq+WGS6lxT6DrKBWq1NDiUeA+1BfF/VzFdafSx59dXHcSPj76anf5XzUXPnZCl7hAlQYXkAJCoZogP69e28geeirmevWx0sThte5x1NJuW1IOUGd4EXVDKVYDhDTO1WdjaRnyqPw7C3QMIMCQuqEUqwFC8zH7PCxQ5+FQpYYZVQekgp3OrOWtt6583GivKguH27iH06szUKlBBtUJrWgnI+SK+zKfuu4fNxtsa2IKvG2PQO3fgKWGGVUXtKKdjBiv9vOchMrHXE3cl4x9h6cg5NhaIBbuVKp8rH5uUbH26E0XDbcj/85moXcYh0PXxtSMQSzcqWRye98joFx79LY1x6cDb+BDIOlgQfgR1qEW70R8j1f3ZCcabVwPqok4g0CINajFOxHPPu5r23TaeS/dMinoCz/CBq4DfrFYFK/0+fR4sfhRmoqnoCxvXoxzOf69xaLdqkxML2H10amMhL7gA2ziOOA3d96mz0akpE9MpHdUF9MlL6y/R9NDPi7a7RAbk2tGTRTKKOgLPb5V3EYsHj8WLwJZTvLnFotpmpej97G0PF3UCinoCz2+VdxGLB5ryt8lIOy8nFFMk/d37T+9KJ1Xn/tTeQU5KB+T6D+q6NZW7gjfIfYQenwtuA1ZeLbwscjDiyfFNHHxFLKPca4yCantS6B9a9AnkgSEQi3w4mPRGf70OH2PwOJJMU24+jiJ5N6tFBZCyQQq4S8fi/7wX5bOLaaufFycV+9Wc437eCbdz6GTi+kz6+88+A5RFzKBSvjrH1czyqnLfGz1/dVy09Vq2oRaeTs9xypKPiYTqIy/8Wph2jd33hbTxK2PrT4noe3jmXT/h7aIEOkTSUgfmUBlHAf9Qr5+fFe8fr6YJm59/M7aeXXDpH0+ZnCtqVciJW2UYq3wcD/X3fyNeul9XKl9i6nj/vEtaa5JHzfTEH8f62mkAqVYK2hGPRoH49W9fm1r47SaegNWNibqCJpRjyYkH+cLa8ceKlwMnEEw5BSiYY9FyD3dsvr8sapN027jLXDKxAJ6EQuIhj2WVO7p1sbpw0c6v2OecrY95HfMe1o07SZeZ5bfacnLyNTiLaAa90jEONd3u0sfK687nW1vJvtXxMfnm8lhbun+ndXXoim38AaZhFaZM/k733EOhFq8BVTjHkmWj2/15eOTB3vJ8bW9/FNtbXXxOj6WpoTp9HEpl6KPiYVbQTbwcQi5R1/9vKXuHx9fP0hO7u+IT3/Iz6vX19eVO6unWdfGtQi28CZKqZWPfYc5EGrxlpANfBya49XpmXTu46ubwtWKtYsymnm3w8rF0hOVeKfPxhRFUou3gm7ko9D0sZyPi0+daxdl6GBIRgiosjBRnVTjTuDjbK6if/xrHR/rmZhs+65RqOgSSFgl2cBJhz4GTR+fbd+Qxqu7z6tnLZeTOPu4kXW5CSQcPeHQx6B7P1d2/ThNyctPl/aaX5fr6ViXSytneLW4DuXoKcc+ArP3ZWr5mMl1phTePkbwdPDkY8qdRgnWNqZtBdLBD8fwcxLaPmYCZ5W0FdCOfjCGfZxwP9dswFgn8fhpRz8YD/l4asghwVgp7eiphz8Ugz7W8TCjvnEGWyOTDj6Bj7O5Q32s49/mlC6lji7d5Q7xHeloCIeeQT3+gZjxsX4eZpCp+p9sqr72Hepo6EaeQ17AMBz6eMXXVOlXWxrZd6hjoRt5AXkBw3Dk4+YSxuL3gaaDKcukG3kBfQWDcNE/bn5vKHRf6B2zfDGRR6IAAA9bSURBVEc5CdrRCxhIGILlfNx8cIJ0ksqQvKo4avmOchK0o8/goGEAdn0sFUi9bZfkUvoUE4aFCg4aBmDPx80S6e/YWdVFSGTNSZdomjBR4TsAt1jysbH4AqJx1tz0MYtDVcLFxvCxmDvRx8bCC4mmMkksI8lclDCRoYtBH0tTTg27ROFjRoKZyGCjQxNz153yCeOk3NQkKeUjmIcKPjo0MeTjakXGPm6h3kPmAA8VfHRoAh8PRz6Xho8DhYsOTQz6OIrBrqTtwhPxmzBrMJHBRocm5nwcg42rvnDZJ+YmlYsYLjo0seRjI7EFh3QOzWpsS4aLIi46NDHvYz6nmCs0DMxSKBdJXHRoYtjHRmIKFtnAXMVyUcVFhybw8RAqhWzVchHFRYcm8PE42KptDleSxfeOdAt8PI641ILQMXv92ERERIhLLQgcw/dzAQA8AB8DQB/4GAD69Iz2wagAEAA+BoA98DEA9IGPAaAPfAwAfeBjAOgDHwNAH1w/BoAA0647wccAhID+/VzH1/bE9OTe/PKBcm0AgFu0fXw4vyR8fLa9mexfUa4NAHCLro+fX/wpy8cnD/bK1MzQx/wfR2T+5HSkLxIYfF59fP0gObm/s/y0vr7Oa1/F0AC4a4z1jSCDfXx4ufBx59pEiaH+mWtsHavlglLWhHzcuTZFGNe/BHON7ddceFDqaRc22Mc8+8d867+CvcaGjVlplNUY8fHZ9g2G49Vs67+AcRMvMG7jcPZW8wd7W5ZQr9fwcfo/v+vHnI/jGfwVJqY7x3IZvvfZysZXg8F7fVZvafMdkHGYy8swbePW8qcWO4q2WFbmqNdk7+MVEzNs6LzVFZi1sXIjU0sfFopWdzhyH0dgY87aCgxXYU8BLvdk15b6z7SztZVf96xNCO4mjmF8y3gt6qzvaGd2bgQ+ruCfi2Mc4JosU3t16ztUVfxM+c9mAZx9HJmJ+d46bljmkNUnbayn1amLho8FLbmYrph2OGuTMF2JQ0sYs00p1I64+6X0XlJOIvBxm43JiumAsbQS85U40pVTl66dT2gVGLeP8z3E3Md8ldWxUIfjStDbtEaEAxTMOv+xWho3H7f6l11r56prhVBsXMYy+usxG+z8h7RR5dc9awcMbMwIG9l46lD3ShQWa2HW8VneuPLrnrUDhr2HE9h4UpnTi3C3/+Fjzi2dtzoJG/VIam/Bx1xbOm91dUJNx+6I1cdtjZxVQ+etrqL1aBydjWvxRuRj7pmKt7oKWy4m1pyT6Hw8q66uM27pvNUJhKp2G8PHrQtw8nFHxfNq6bzVZWSyWpRGauNYfDxT3LvFrKXzVpdjuxrJ7bKGjz/eXMs4t1vM5eDjTv8aPISHAG91ErBxg5Z8/K70sJjL2se+AzMLb3UStiuT3p5rO69+KhuZvo+VyZgRrMXVsF2RBPfcqo+PvrzwSjIyeR+rbBxs0CPgrK2B7XokuOtWfPxq7dbyT2Vk1j72HZtBWItrAB+vsDLOlTn4FZNxrjg8vHrjBzd9DWDjJk0f/6/8H/++W8yl7OMoTcxMXQuW1VLcf4yvH0eai3mJW8W6XJI7sOnj0621tbXzr6W5JH2s8HBYgU6Hubwm9uWS3IMNH59ubZw+fPRKMjJJH6tsHFSgE+Gtrg0Haknuwmb/+LvdpY+Xf6u53HzsOzaDNJXxUtcGbNzBSj6+RTofz+K5jzqWM+pZ/mRT4kgwzd3Y7B8fffXzFtH+sSoJM2zprMVV1E83HOiluR/5jFfH5OFoXOz+zIrojhzh45N788sH4tPx1fmlPeXaDonIxLGMb/moUKI7cuV+rvpTiy0+PtveTPavpJ9O7u8k+7ml/euHjbnhpT6J7snWfHz0tWKc6+TBXnJ8LU3Dx9cPxL+aBXkiEhPH4uLOCrW7Taul26PVx8rrTsK9y0ws5+P19fUgdsBKlTNs4802zVBiTlmF8HEvw/vHh5cLH0s9Zd87YNZxvclrUBbgra4JbKzN8P5xlY+Pv9lJDi+FcF7dcQbGrqWzFteK4/oku09b8/GrC9Lc7v6xlJl97QFFHmbX1LkfpFbwIJjsPh3ePz7bvpGPV/vPxzXPNmucWUuPxsaFNB9nV2R3aquP3ynf65P1itOUfDifX9xZLcgdZQWzb+Pc9VW0VyhsrKa9f3xLmhvy/Vxttc2ynfNWV8NnldLds7Tvy4zEx6zFNYGNx0DUx7OOUy+OTZ2xNIlKmb/KJLxvV3z89Nzu6dZa4O/LVFmYWVvnq0xGFgcfj6Dp46cXkuTV+dfvykcXw/NxRCZuuUONJTV9/iQT3rvNca5vH6Xv9pGuPAXn4z4bE66MFViLq6gL9CaY8s5t+njp39TLofq4x7/Mmjrvg5Rg1hzo8NiRoLxzV86rN5L0nLq6oysoH6tszM7HK/IYaStoqUV/xy3Ke7fp44831754JP9SGykf82nqrer4oapO16JJ72Ja1516fcwFxtJqSAq9Sya9l2n52MubXnzAWFodKfX61kx6N7fflxnk76ZGmouZqZPIHezrZupmNM63aJLWfPxqQ5obio/jsDFvdTVUFYp0PJBWH/v/PQm5JmcdzxhzbObM5SVSzYbkYRGPn80aotXHR1/tVnN9+FiuTuVhm1lDZy4vkWo2tAolvp/b+8e+z6t1fFx0r0xu1y/tEnlR1GxoNmbm4wzv/eNeH5vcWCCwFyjo9bG3wHxt2AyB94+78jA7QmnO1pm1XCsOQDX1HR5m/1g5tmV0Q4EQg8aS0DwsYvK7+cm09499v9enqNgAK9wO/BXmdGVi36Kp7/PA7udS5eEwKtw47AWmzLr7SUGoJr/Pmz4+3VqmY2+/f6z0bxAVbhzW4gpKaaFWK/n93vBx+g4B8UKQai58bBPO2ir6atS3cvr7vdk/FiPV7ser+w/XLJs6X2V1Qq9S/xFMJYx8XNRmTB6OJxUHb2N+PvbUP+7zbyDVbRTW4kpo1GsIMUwjjPHq6HzMWVsNElUaShwT8OzjGfrF7MTVbqslUaXBBDIev+fVOv4NqcLNEI8+dQ37jrMgmEAm4HecK0ITx/GIMakqDSycUfi97tRb38HV+WSaDZqfQiJjWxVhRTOOwPPxmEKDhre6DGI+DiqYsQTePx5TaMCwFpej4eKwpAcVzFg8jVfP+u8OCK6+J8NZW0l/hQYmPahgRtPqY3X/+OTe/PKB+HS2Pb+4s1qQxlZ1/BtYfU+Gv4dTyB2XQ4xpOCv947WM7t9NPdveTPaviI/PN5PD3NIDdkeviYOt8gmsiGOnMIVinQYZ1GC6xqv/o9PHJw/2kuNre/mntoJ6tthVx7PGPSEjFQVJm1heClMoHptDjGkEw/vHx9cPkpP7O+LTH/Lz6vX19ck+Lis64EofR0PgrLw/wndgZul1cZCCQ4xpBM18fDM/ry5/GWbFx+mZdO7jq5vC1c2CeraoUdehVvooWhsyF4WVip5KDVVwiDGNoDUfK997K+fj4lOiuz80jtm8xrg6ExIPhZKovjoNU3CIMY1h+Hi11D/+9VAfK6t6ta3Tp+0YxYPSnIWw3mNzkIQb2TBafax87+3Z9g1pvFp9Xt3MQH3VHHadD4ZQex5K92GYlI25+ljnvbfZ9eM0JS8/Xdprfi0XXtRhXz3LRjalzDstDd13SOZQ1iYZF7P1ccsCE+7nKmqRdlWPhLdETQMHrzvw8LSBj+3AXiKTOqURZT/2fKx1wJ5xO9/MaJPJh9Kk8HEwWPOxjo2J1PVgeGvUq1kiumlE2Q98bBauEme1sUg+VUskzF7s+Fj3kM1lL5Zw1SeJ4VWzVOLsw4qPtWqZUm1rQ7Mx91OpUVcrOelU4uzDj4/LhSZEHhpdOllQCeqr1nxpn8EOgUygPfjLx5RqW4OmPlY2lu6/1PExISjG3IZjHyf88nAO+RatonmA4mNkgiG3Ah+bgXyDViIJU9mYoGyCIbfi3sfMzqczyLdnFTVh8HGQmPdxZx2TrGctGLRnBZIopYlJyqYYcxvGfcypkjVhrrVS1FmtdFWTDLoFZz6eHGm4MNVaM2n1qVUrWdU0o17FjY8nhxkqjKXW7CvN4qWXevwF1n3MuFvM9zbMlFzQStrlpZi8gBy7Pp4cXtiw1loehRvqeImmryADPp4Ab6FyOoaPA8eqjydHFzBSsvIdik1WJZb/ZqGcgQSBvevHUyMLmpl01uk7FpvUBc6Ki8j+AjINFyn28vHk0AImAokZNZkcNXPRAx+PIQKJGfx9zAVJUodQ5dcra6+Wy5AIJObM6qfVcYimjbn+samIwiUKkSvEqZoahnwMAPAIfAwAfeBjAOjTMxLW5+OSdd0hNt0F/S/Xs4eMbtVXUX3NYEyZoRVkRGPoFdmFno8r1k0vGPpyzksLsyjzZYZXkOHCfBQFH0+DePX7KDO8ggwXBh+HtJzz0sIsynyZ4RVkuLCgfQwACBb4GAD6wMcA0Ac+BoA+8DEA9On18cm9+eUD8Wl/Pp9f2tNY8Gx7fnGnf7m0vPl8s7+846t621Uvt/z+2l5jjfHoqh1UVJ8ADUxqTBolTVRqUKdBlUwqss/HZ9ubyf4V8fF5p+VWFzzs3La03BKd5U7u7yT7Osvd21Qst9xWvm/rEYxDV+2gotRCtTCpsRneRKUGdRpUyaUi+3x88mAvPzSc/VZ5sKoWTD/pLJdkgnuXO75+oCizsVx3gc8v/pRtthbBSHTVDipKLVQHoxqb4U1Uak6nSZVcKrLPx5U5lglecRYsLXh8/Q+KE5Sa2xRHGmnDyqObvF2lj8tTld7lNNBVO6goA4dxkxqb4U1UalKnOZVcKrLPx+mZRq7zmx1VTpYWvLopNt+3nDIdy8spuwjVcuK8WlUT+a6RIxiLrtpBRZno7hnUmGFMqUmd5lRyqUj9fCzo7iPr5kX5W1V3RCpveQA57Bw2kMo7vjr/76qTf0v5eGJpukI1S7OZjyeVaVKnnXxMuSL1+8eCbh9LHY1fqzYtF/j8hs6G1YekeoDKXsmxlf6xUu2gokwkUYMam+FNVGpSpzmVXCqyf7z6Rt6LTYM7+11nidWCqdm7T1Ck5ZQjZ9Vy6qNbtZzolaiG9vL9IUUwGl21g4oyeBg3oTHDmFKTOs2p5FKRmteP01L358pxgGrB5afe671iOeUhq1ruULnh2nLKXkm6TB6foevH/WoHFaUWqoVJjc3wJio1qNOgSiYVifu5AKAPfAwAfeBjAOgDHwNAH/gYAPrAxwDQBz4GgD7wMQD0gY8BoM9/AhIn+UkjyjJmAAAAAElFTkSuQmCC" style="display: block; margin: auto;" />

<p>All methods give are highly correlated and give very similar results. That means that the method choice is not a drastic game changer and cannot be used to tweak the results too much.</p>
<h2 id="accuracy">Accuracy</h2>
<p>To test the accuracy of each methods, we will start by computing the <strong>direct <em>pd</em></strong> from a very dense distribution (with a large amount of observations). This will be our baseline, or “true” <em>pd</em>. Then, we will iteratively draw smaller samples from this parent distribution, and we will compute the <em>pd</em> with different methods. The closer this estimate is from the reference one, the better.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb2-1" title="1">data &lt;-<span class="st"> </span><span class="kw">data.frame</span>()</a>
<a class="sourceLine" id="cb2-2" title="2"><span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">25</span>){</a>
<a class="sourceLine" id="cb2-3" title="3">  the_mean &lt;-<span class="st"> </span><span class="kw">runif</span>(<span class="dv">1</span>, <span class="dv">0</span>, <span class="dv">4</span>)</a>
<a class="sourceLine" id="cb2-4" title="4">  the_sd &lt;-<span class="st"> </span><span class="kw">abs</span>(<span class="kw">runif</span>(<span class="dv">1</span>, <span class="fl">0.5</span>, <span class="dv">4</span>))</a>
<a class="sourceLine" id="cb2-5" title="5">  parent_distribution &lt;-<span class="st"> </span><span class="kw">rnorm</span>(<span class="dv">100000</span>, the_mean, the_sd)</a>
<a class="sourceLine" id="cb2-6" title="6">  true_pd &lt;-<span class="st"> </span><span class="kw">pd</span>(parent_distribution)</a>
<a class="sourceLine" id="cb2-7" title="7">  </a>
<a class="sourceLine" id="cb2-8" title="8">  <span class="cf">for</span>(j <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">25</span>){</a>
<a class="sourceLine" id="cb2-9" title="9">    sample_size &lt;-<span class="st"> </span><span class="kw">round</span>(<span class="kw">runif</span>(<span class="dv">1</span>, <span class="dv">25</span>, <span class="dv">5000</span>))</a>
<a class="sourceLine" id="cb2-10" title="10">    subsample &lt;-<span class="st"> </span><span class="kw">sample</span>(parent_distribution, sample_size)</a>
<a class="sourceLine" id="cb2-11" title="11">    data &lt;-<span class="st"> </span><span class="kw">rbind</span>(data,</a>
<a class="sourceLine" id="cb2-12" title="12">      <span class="kw">data.frame</span>(<span class="st">&quot;sample_size&quot;</span> =<span class="st"> </span>sample_size, </a>
<a class="sourceLine" id="cb2-13" title="13">                 <span class="st">&quot;true&quot;</span> =<span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-14" title="14">                 <span class="st">&quot;direct&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample) <span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-15" title="15">                 <span class="st">&quot;kernel&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;kernel&quot;</span>)<span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-16" title="16">                 <span class="st">&quot;logspline&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;logspline&quot;</span>) <span class="op">-</span><span class="st"> </span>true_pd,</a>
<a class="sourceLine" id="cb2-17" title="17">                 <span class="st">&quot;KernSmooth&quot;</span> =<span class="st"> </span><span class="kw">pd</span>(subsample, <span class="dt">method=</span><span class="st">&quot;KernSmooth&quot;</span>) <span class="op">-</span><span class="st"> </span>true_pd</a>
<a class="sourceLine" id="cb2-18" title="18">                 ))</a>
<a class="sourceLine" id="cb2-19" title="19">  }</a>
<a class="sourceLine" id="cb2-20" title="20">}</a>
<a class="sourceLine" id="cb2-21" title="21">data &lt;-<span class="st"> </span><span class="kw">as.data.frame</span>(<span class="kw">sapply</span>(data, as.numeric))</a></code></pre></div>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><a class="sourceLine" id="cb3-1" title="1"><span class="kw">library</span>(tidyr)</a>
<a class="sourceLine" id="cb3-2" title="2"><span class="kw">library</span>(dplyr)</a>
<a class="sourceLine" id="cb3-3" title="3"></a>
<a class="sourceLine" id="cb3-4" title="4">data <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-5" title="5"><span class="st">  </span>tidyr<span class="op">::</span><span class="kw">gather</span>(Method, Distance, <span class="op">-</span>sample_size, <span class="op">-</span>true) <span class="op">%&gt;%</span><span class="st"> </span></a>
<a class="sourceLine" id="cb3-6" title="6"><span class="st">  </span><span class="kw">ggplot</span>(<span class="kw">aes</span>(<span class="dt">x=</span>sample_size, <span class="dt">y =</span> Distance, <span class="dt">color =</span> Method, <span class="dt">fill=</span> Method)) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-7" title="7"><span class="st">  </span><span class="kw">geom_point</span>(<span class="dt">alpha=</span><span class="fl">0.3</span>, <span class="dt">stroke=</span><span class="dv">0</span>, <span class="dt">shape=</span><span class="dv">16</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-8" title="8"><span class="st">  </span><span class="kw">geom_smooth</span>(<span class="dt">alpha=</span><span class="fl">0.2</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-9" title="9"><span class="st">  </span><span class="kw">geom_hline</span>(<span class="dt">yintercept=</span><span class="dv">0</span>) <span class="op">+</span></a>
<a class="sourceLine" id="cb3-10" title="10"><span class="st">  </span><span class="kw">theme_classic</span>() <span class="op">+</span></a>
<a class="sourceLine" id="cb3-11" title="11"><span class="st">  </span><span class="kw">xlab</span>(<span class="st">&quot;</span><span class="ch">\n</span><span class="st">Distribution Size&quot;</span>)</a></code></pre></div>
<img src="data:image/png;base64,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" style="display: block; margin: auto;" />

<p>The “Kernel” based density methods seems to consistently underestimate the <em>pd</em>. Interestingly, the “direct” method appears as being the more reliable, even in the case of small number of posterior draws.</p>
<h2 id="can-the-pd-be-100">Can the pd be 100%?</h2>
<p><code>p = 0.000</code> is coined as one of the term to avoid when reporting results (Lilienfeld et al., 2015), even if often displayed by statistical software. The rationale is that for every probability distribution, there is no value with a probability of exactly 0. There is always some infinitesimal probability associated with each data point, and the <code>p = 0.000</code> returned by software is due to approximations related, among other, to finite memory hardware.</p>
<p>One could apply this rationale for the <em>pd</em>: since all data points have a non-null probability density, then the <em>pd</em> (a particular portion of the probability density) can <em>never</em> be 100%. While this is an entirely valid point, people using the <em>direct</em> method might argue that their <em>pd</em> is based on the posterior draws, rather than on the theoretical, hidden, true posterior distribution (which is only approximated by the posterior draws). These posterior draws represent a finite sample for which <code>pd = 100%</code> is a valid statement.</p>
<div id="refs" class="references">

<div id="ref-lilienfeld2015fifty">

<p>Lilienfeld, S. O., Sauvigné, K. C., Lynn, S. J., Cautin, R. L., Latzman, R. D., &amp; Waldman, I. D. (2015). Fifty psychological and psychiatric terms to avoid: A list of inaccurate, misleading, misused, ambiguous, and logically confused words and phrases. <em>Frontiers in Psychology</em>, <em>6</em>, 1100. <a href="https://doi.org/10.3389/fpsyg.2015.01100">https://doi.org/10.3389/fpsyg.2015.01100</a></p>
</div>

</div>

</body>
</html>
back to top