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  <title>Bayesian statistics with R: Untitled</title>


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  }

  .figure img.external {
    background: white;
    border: 1px solid rgba(0, 0, 0, 0.1);
    box-shadow: 0 1px 8px rgba(0, 0, 0, 0.1);
    padding: 18px;
    box-sizing: border-box;
  }

  .figure .caption a {
    color: rgba(0, 0, 0, 0.6);
  }

  .figure .caption b,
  .figure .caption strong, {
    font-weight: 600;
    color: rgba(0, 0, 0, 1.0);
  }

  /* Citations */

  d-article .citation {
    color: inherit;
    cursor: inherit;
  }

  div.hanging-indent{
    margin-left: 1em; text-indent: -1em;
  }

  /* Citation hover box */

  .tippy-box[data-theme~=light-border] {
    background-color: rgba(250, 250, 250, 0.95);
  }

  .tippy-content > p {
    margin-bottom: 0;
    padding: 2px;
  }


  /* Tweak 1000px media break to show more text */

  @media(min-width: 1000px) {
    .base-grid,
    distill-header,
    d-title,
    d-abstract,
    d-article,
    d-appendix,
    distill-appendix,
    d-byline,
    d-footnote-list,
    d-citation-list,
    distill-footer {
      grid-template-columns: [screen-start] 1fr [page-start kicker-start] 80px [middle-start] 50px [text-start kicker-end] 65px 65px 65px 65px 65px 65px 65px 65px [text-end gutter-start] 65px [middle-end] 65px [page-end gutter-end] 1fr [screen-end];
      grid-column-gap: 16px;
    }

    .grid {
      grid-column-gap: 16px;
    }

    d-article {
      font-size: 1.06rem;
      line-height: 1.7em;
    }
    figure .caption, .figure .caption, figure figcaption {
      font-size: 13px;
    }
  }

  @media(min-width: 1180px) {
    .base-grid,
    distill-header,
    d-title,
    d-abstract,
    d-article,
    d-appendix,
    distill-appendix,
    d-byline,
    d-footnote-list,
    d-citation-list,
    distill-footer {
      grid-template-columns: [screen-start] 1fr [page-start kicker-start] 60px [middle-start] 60px [text-start kicker-end] 60px 60px 60px 60px 60px 60px 60px 60px [text-end gutter-start] 60px [middle-end] 60px [page-end gutter-end] 1fr [screen-end];
      grid-column-gap: 32px;
    }

    .grid {
      grid-column-gap: 32px;
    }
  }


  /* Get the citation styles for the appendix (not auto-injected on render since
     we do our own rendering of the citation appendix) */

  d-appendix .citation-appendix,
  .d-appendix .citation-appendix {
    font-size: 11px;
    line-height: 15px;
    border-left: 1px solid rgba(0, 0, 0, 0.1);
    padding-left: 18px;
    border: 1px solid rgba(0,0,0,0.1);
    background: rgba(0, 0, 0, 0.02);
    padding: 10px 18px;
    border-radius: 3px;
    color: rgba(150, 150, 150, 1);
    overflow: hidden;
    margin-top: -12px;
    white-space: pre-wrap;
    word-wrap: break-word;
  }

  /* Include appendix styles here so they can be overridden */

  d-appendix {
    contain: layout style;
    font-size: 0.8em;
    line-height: 1.7em;
    margin-top: 60px;
    margin-bottom: 0;
    border-top: 1px solid rgba(0, 0, 0, 0.1);
    color: rgba(0,0,0,0.5);
    padding-top: 60px;
    padding-bottom: 48px;
  }

  d-appendix h3 {
    grid-column: page-start / text-start;
    font-size: 15px;
    font-weight: 500;
    margin-top: 1em;
    margin-bottom: 0;
    color: rgba(0,0,0,0.65);
  }

  d-appendix h3 + * {
    margin-top: 1em;
  }

  d-appendix ol {
    padding: 0 0 0 15px;
  }

  @media (min-width: 768px) {
    d-appendix ol {
      padding: 0 0 0 30px;
      margin-left: -30px;
    }
  }

  d-appendix li {
    margin-bottom: 1em;
  }

  d-appendix a {
    color: rgba(0, 0, 0, 0.6);
  }

  d-appendix > * {
    grid-column: text;
  }

  d-appendix > d-footnote-list,
  d-appendix > d-citation-list,
  d-appendix > distill-appendix {
    grid-column: screen;
  }

  /* Include footnote styles here so they can be overridden */

  d-footnote-list {
    contain: layout style;
  }

  d-footnote-list > * {
    grid-column: text;
  }

  d-footnote-list a.footnote-backlink {
    color: rgba(0,0,0,0.3);
    padding-left: 0.5em;
  }


  /* Anchor.js */

  .anchorjs-link {
    /*transition: all .25s linear; */
    text-decoration: none;
    border-bottom: none;
  }
  *:hover > .anchorjs-link {
    margin-left: -1.125em !important;
    text-decoration: none;
    border-bottom: none;
  }

  /* Social footer */

  .social_footer {
    margin-top: 30px;
    margin-bottom: 0;
    color: rgba(0,0,0,0.67);
  }

  .disqus-comments {
    margin-right: 30px;
  }

  .disqus-comment-count {
    border-bottom: 1px solid rgba(0, 0, 0, 0.4);
    cursor: pointer;
  }

  #disqus_thread {
    margin-top: 30px;
  }

  .article-sharing a {
    border-bottom: none;
    margin-right: 8px;
  }

  .article-sharing a:hover {
    border-bottom: none;
  }

  .sidebar-section.subscribe {
    font-size: 12px;
    line-height: 1.6em;
  }

  .subscribe p {
    margin-bottom: 0.5em;
  }


  .article-footer .subscribe {
    font-size: 15px;
    margin-top: 45px;
  }


  .sidebar-section.custom {
    font-size: 12px;
    line-height: 1.6em;
  }

  .custom p {
    margin-bottom: 0.5em;
  }

  /* Styles for listing layout (hide title) */
  .layout-listing d-title, .layout-listing .d-title {
    display: none;
  }

  /* Styles for posts lists (not auto-injected) */


  .posts-with-sidebar {
    padding-left: 45px;
    padding-right: 45px;
  }

  .posts-list .description h2,
  .posts-list .description p {
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
  }

  .posts-list .description h2 {
    font-weight: 700;
    border-bottom: none;
    padding-bottom: 0;
  }

  .posts-list h2.post-tag {
    border-bottom: 1px solid rgba(0, 0, 0, 0.2);
    padding-bottom: 12px;
  }
  .posts-list {
    margin-top: 60px;
    margin-bottom: 24px;
  }

  .posts-list .post-preview {
    text-decoration: none;
    overflow: hidden;
    display: block;
    border-bottom: 1px solid rgba(0, 0, 0, 0.1);
    padding: 24px 0;
  }

  .post-preview-last {
    border-bottom: none !important;
  }

  .posts-list .posts-list-caption {
    grid-column: screen;
    font-weight: 400;
  }

  .posts-list .post-preview h2 {
    margin: 0 0 6px 0;
    line-height: 1.2em;
    font-style: normal;
    font-size: 24px;
  }

  .posts-list .post-preview p {
    margin: 0 0 12px 0;
    line-height: 1.4em;
    font-size: 16px;
  }

  .posts-list .post-preview .thumbnail {
    box-sizing: border-box;
    margin-bottom: 24px;
    position: relative;
    max-width: 500px;
  }
  .posts-list .post-preview img {
    width: 100%;
    display: block;
  }

  .posts-list .metadata {
    font-size: 12px;
    line-height: 1.4em;
    margin-bottom: 18px;
  }

  .posts-list .metadata > * {
    display: inline-block;
  }

  .posts-list .metadata .publishedDate {
    margin-right: 2em;
  }

  .posts-list .metadata .dt-authors {
    display: block;
    margin-top: 0.3em;
    margin-right: 2em;
  }

  .posts-list .dt-tags {
    display: block;
    line-height: 1em;
  }

  .posts-list .dt-tags .dt-tag {
    display: inline-block;
    color: rgba(0,0,0,0.6);
    padding: 0.3em 0.4em;
    margin-right: 0.2em;
    margin-bottom: 0.4em;
    font-size: 60%;
    border: 1px solid rgba(0,0,0,0.2);
    border-radius: 3px;
    text-transform: uppercase;
    font-weight: 500;
  }

  .posts-list img {
    opacity: 1;
  }

  .posts-list img[data-src] {
    opacity: 0;
  }

  .posts-more {
    clear: both;
  }


  .posts-sidebar {
    font-size: 16px;
  }

  .posts-sidebar h3 {
    font-size: 16px;
    margin-top: 0;
    margin-bottom: 0.5em;
    font-weight: 400;
    text-transform: uppercase;
  }

  .sidebar-section {
    margin-bottom: 30px;
  }

  .categories ul {
    list-style-type: none;
    margin: 0;
    padding: 0;
  }

  .categories li {
    color: rgba(0, 0, 0, 0.8);
    margin-bottom: 0;
  }

  .categories li>a {
    border-bottom: none;
  }

  .categories li>a:hover {
    border-bottom: 1px solid rgba(0, 0, 0, 0.4);
  }

  .categories .active {
    font-weight: 600;
  }

  .categories .category-count {
    color: rgba(0, 0, 0, 0.4);
  }


  @media(min-width: 768px) {
    .posts-list .post-preview h2 {
      font-size: 26px;
    }
    .posts-list .post-preview .thumbnail {
      float: right;
      width: 30%;
      margin-bottom: 0;
    }
    .posts-list .post-preview .description {
      float: left;
      width: 45%;
    }
    .posts-list .post-preview .metadata {
      float: left;
      width: 20%;
      margin-top: 8px;
    }
    .posts-list .post-preview p {
      margin: 0 0 12px 0;
      line-height: 1.5em;
      font-size: 16px;
    }
    .posts-with-sidebar .posts-list {
      float: left;
      width: 75%;
    }
    .posts-with-sidebar .posts-sidebar {
      float: right;
      width: 20%;
      margin-top: 60px;
      padding-top: 24px;
      padding-bottom: 24px;
    }
  }


  /* Improve display for browsers without grid (IE/Edge <= 15) */

  .downlevel {
    line-height: 1.6em;
    font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Oxygen, Ubuntu, Cantarell, "Fira Sans", "Droid Sans", "Helvetica Neue", Arial, sans-serif;
    margin: 0;
  }

  .downlevel .d-title {
    padding-top: 6rem;
    padding-bottom: 1.5rem;
  }

  .downlevel .d-title h1 {
    font-size: 50px;
    font-weight: 700;
    line-height: 1.1em;
    margin: 0 0 0.5rem;
  }

  .downlevel .d-title p {
    font-weight: 300;
    font-size: 1.2rem;
    line-height: 1.55em;
    margin-top: 0;
  }

  .downlevel .d-byline {
    padding-top: 0.8em;
    padding-bottom: 0.8em;
    font-size: 0.8rem;
    line-height: 1.8em;
  }

  .downlevel .section-separator {
    border: none;
    border-top: 1px solid rgba(0, 0, 0, 0.1);
  }

  .downlevel .d-article {
    font-size: 1.06rem;
    line-height: 1.7em;
    padding-top: 1rem;
    padding-bottom: 2rem;
  }


  .downlevel .d-appendix {
    padding-left: 0;
    padding-right: 0;
    max-width: none;
    font-size: 0.8em;
    line-height: 1.7em;
    margin-bottom: 0;
    color: rgba(0,0,0,0.5);
    padding-top: 40px;
    padding-bottom: 48px;
  }

  .downlevel .footnotes ol {
    padding-left: 13px;
  }

  .downlevel .base-grid,
  .downlevel .distill-header,
  .downlevel .d-title,
  .downlevel .d-abstract,
  .downlevel .d-article,
  .downlevel .d-appendix,
  .downlevel .distill-appendix,
  .downlevel .d-byline,
  .downlevel .d-footnote-list,
  .downlevel .d-citation-list,
  .downlevel .distill-footer,
  .downlevel .appendix-bottom,
  .downlevel .posts-container {
    padding-left: 40px;
    padding-right: 40px;
  }

  @media(min-width: 768px) {
    .downlevel .base-grid,
    .downlevel .distill-header,
    .downlevel .d-title,
    .downlevel .d-abstract,
    .downlevel .d-article,
    .downlevel .d-appendix,
    .downlevel .distill-appendix,
    .downlevel .d-byline,
    .downlevel .d-footnote-list,
    .downlevel .d-citation-list,
    .downlevel .distill-footer,
    .downlevel .appendix-bottom,
    .downlevel .posts-container {
    padding-left: 150px;
    padding-right: 150px;
    max-width: 900px;
  }
  }

  .downlevel pre code {
    display: block;
    border-left: 2px solid rgba(0, 0, 0, .1);
    padding: 0 0 0 20px;
    font-size: 14px;
  }

  .downlevel code, .downlevel pre {
    color: black;
    background: none;
    font-family: Consolas, Monaco, 'Andale Mono', 'Ubuntu Mono', monospace;
    text-align: left;
    white-space: pre;
    word-spacing: normal;
    word-break: normal;
    word-wrap: normal;
    line-height: 1.5;

    -moz-tab-size: 4;
    -o-tab-size: 4;
    tab-size: 4;

    -webkit-hyphens: none;
    -moz-hyphens: none;
    -ms-hyphens: none;
    hyphens: none;
  }

  .downlevel .posts-list .post-preview {
    color: inherit;
  }


  </style>

  <script type="application/javascript">

  function is_downlevel_browser() {
    if (bowser.isUnsupportedBrowser({ msie: "12", msedge: "16"},
                                   window.navigator.userAgent)) {
      return true;
    } else {
      return window.load_distill_framework === undefined;
    }
  }

  // show body when load is complete
  function on_load_complete() {

    // add anchors
    if (window.anchors) {
      window.anchors.options.placement = 'left';
      window.anchors.add('d-article > h2, d-article > h3, d-article > h4, d-article > h5');
    }


    // set body to visible
    document.body.style.visibility = 'visible';

    // force redraw for leaflet widgets
    if (window.HTMLWidgets) {
      var maps = window.HTMLWidgets.findAll(".leaflet");
      $.each(maps, function(i, el) {
        var map = this.getMap();
        map.invalidateSize();
        map.eachLayer(function(layer) {
          if (layer instanceof L.TileLayer)
            layer.redraw();
        });
      });
    }

    // trigger 'shown' so htmlwidgets resize
    $('d-article').trigger('shown');
  }

  function init_distill() {

    init_common();

    // create front matter
    var front_matter = $('<d-front-matter></d-front-matter>');
    $('#distill-front-matter').wrap(front_matter);

    // create d-title
    $('.d-title').changeElementType('d-title');

    // separator
    var separator = '<hr class="section-separator" style="clear: both"/>';
    // prepend separator above appendix
    $('.d-byline').before(separator);
    $('.d-article').before(separator);

    // create d-byline
    var byline = $('<d-byline></d-byline>');
    $('.d-byline').replaceWith(byline);

    // create d-article
    var article = $('<d-article></d-article>');
    $('.d-article').wrap(article).children().unwrap();

    // move posts container into article
    $('.posts-container').appendTo($('d-article'));

    // create d-appendix
    $('.d-appendix').changeElementType('d-appendix');

    // flag indicating that we have appendix items
    var appendix = $('.appendix-bottom').children('h3').length > 0;

    // replace footnotes with <d-footnote>
    $('.footnote-ref').each(function(i, val) {
      appendix = true;
      var href = $(this).attr('href');
      var id = href.replace('#', '');
      var fn = $('#' + id);
      var fn_p = $('#' + id + '>p');
      fn_p.find('.footnote-back').remove();
      var text = fn_p.html();
      var dtfn = $('<d-footnote></d-footnote>');
      dtfn.html(text);
      $(this).replaceWith(dtfn);
    });
    // remove footnotes
    $('.footnotes').remove();

    // move refs into #references-listing
    $('#references-listing').replaceWith($('#refs'));

    $('h1.appendix, h2.appendix').each(function(i, val) {
      $(this).changeElementType('h3');
    });
    $('h3.appendix').each(function(i, val) {
      var id = $(this).attr('id');
      $('.d-contents a[href="#' + id + '"]').parent().remove();
      appendix = true;
      $(this).nextUntil($('h1, h2, h3')).addBack().appendTo($('d-appendix'));
    });

    // show d-appendix if we have appendix content
    $("d-appendix").css('display', appendix ? 'grid' : 'none');

    // localize layout chunks to just output
    $('.layout-chunk').each(function(i, val) {

      // capture layout
      var layout = $(this).attr('data-layout');

      // apply layout to markdown level block elements
      var elements = $(this).children().not('details, div.sourceCode, pre, script');
      elements.each(function(i, el) {
        var layout_div = $('<div class="' + layout + '"></div>');
        if (layout_div.hasClass('shaded')) {
          var shaded_content = $('<div class="shaded-content"></div>');
          $(this).wrap(shaded_content);
          $(this).parent().wrap(layout_div);
        } else {
          $(this).wrap(layout_div);
        }
      });


      // unwrap the layout-chunk div
      $(this).children().unwrap();
    });

    // remove code block used to force  highlighting css
    $('.distill-force-highlighting-css').parent().remove();

    // remove empty line numbers inserted by pandoc when using a
    // custom syntax highlighting theme, except when numbering line
    // in code chunk
    $('pre:not(.numberLines) code.sourceCode a:empty').remove();

    // load distill framework
    load_distill_framework();

    // wait for window.distillRunlevel == 4 to do post processing
    function distill_post_process() {

      if (!window.distillRunlevel || window.distillRunlevel < 4)
        return;

      // hide author/affiliations entirely if we have no authors
      var front_matter = JSON.parse($("#distill-front-matter").html());
      var have_authors = front_matter.authors && front_matter.authors.length > 0;
      if (!have_authors)
        $('d-byline').addClass('hidden');

      // article with toc class
      $('.d-contents').parent().addClass('d-article-with-toc');

      // strip links that point to #
      $('.authors-affiliations').find('a[href="#"]').removeAttr('href');

      // add orcid ids
      $('.authors-affiliations').find('.author').each(function(i, el) {
        var orcid_id = front_matter.authors[i].orcidID;
        var author_name = front_matter.authors[i].author
        if (orcid_id) {
          var a = $('<a></a>');
          a.attr('href', 'https://orcid.org/' + orcid_id);
          var img = $('<img></img>');
          img.addClass('orcid-id');
          img.attr('alt', author_name ? 'ORCID ID for ' + author_name : 'ORCID ID');
          img.attr('src','data:image/png;base64,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');
          a.append(img);
          $(this).append(a);
        }
      });

      // hide elements of author/affiliations grid that have no value
      function hide_byline_column(caption) {
        $('d-byline').find('h3:contains("' + caption + '")').parent().css('visibility', 'hidden');
      }

      // affiliations
      var have_affiliations = false;
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<h1 id="mit-license">MIT License</h1>
<p>Copyright (c) 2021 Olivier Gimenez</p>
<p>Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the “Software”), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
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copies or substantial portions of the Software.</p>
<p>THE SOFTWARE IS PROVIDED “AS IS”, WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
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