File: loo2-lfo.html

package info (click to toggle)
r-cran-loo 2.4.1-1
links: PTS, VCS
area: main
in suites: bullseye
size: 4,296 kB
sloc: sh: 15; makefile: 2
file content (819 lines) | stat: -rw-r--r-- 445,860 bytes
<!DOCTYPE html>

<html>

<head>

<meta charset="utf-8" />
<meta name="generator" content="pandoc" />
<meta http-equiv="X-UA-Compatible" content="IE=EDGE" />

<meta name="viewport" content="width=device-width, initial-scale=1" />

<meta name="author" content="Paul Bürkner, Jonah Gabry, Aki Vehtari" />

<meta name="date" content="2020-12-07" />

<title>Approximate leave-future-out cross-validation for Bayesian time series models</title>

<script>// Pandoc 2.9 adds attributes on both header and div. We remove the former (to
// be compatible with the behavior of Pandoc < 2.8).
document.addEventListener('DOMContentLoaded', function(e) {
  var hs = document.querySelectorAll("div.section[class*='level'] > :first-child");
  var i, h, a;
  for (i = 0; i < hs.length; i++) {
    h = hs[i];
    if (!/^h[1-6]$/i.test(h.tagName)) continue;  // it should be a header h1-h6
    a = h.attributes;
    while (a.length > 0) h.removeAttribute(a[0].name);
  }
});
</script>


<style type="text/css">code{white-space: pre;}</style>
<style type="text/css" data-origin="pandoc">
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; }
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;
    color: #aaaaaa;
  }
pre.numberSource { margin-left: 3em; border-left: 1px solid #aaaaaa;  padding-left: 4px; }
div.sourceCode
  {   }
@media screen {
pre > code.sourceCode > span > a:first-child::before { text-decoration: underline; }
}
code span.al { color: #ff0000; font-weight: bold; } /* Alert */
code span.an { color: #60a0b0; font-weight: bold; font-style: italic; } /* Annotation */
code span.at { color: #7d9029; } /* Attribute */
code span.bn { color: #40a070; } /* BaseN */
code span.bu { } /* BuiltIn */
code span.cf { color: #007020; font-weight: bold; } /* ControlFlow */
code span.ch { color: #4070a0; } /* Char */
code span.cn { color: #880000; } /* Constant */
code span.co { color: #60a0b0; font-style: italic; } /* Comment */
code span.cv { color: #60a0b0; font-weight: bold; font-style: italic; } /* CommentVar */
code span.do { color: #ba2121; font-style: italic; } /* Documentation */
code span.dt { color: #902000; } /* DataType */
code span.dv { color: #40a070; } /* DecVal */
code span.er { color: #ff0000; font-weight: bold; } /* Error */
code span.ex { } /* Extension */
code span.fl { color: #40a070; } /* Float */
code span.fu { color: #06287e; } /* Function */
code span.im { } /* Import */
code span.in { color: #60a0b0; font-weight: bold; font-style: italic; } /* Information */
code span.kw { color: #007020; font-weight: bold; } /* Keyword */
code span.op { color: #666666; } /* Operator */
code span.ot { color: #007020; } /* Other */
code span.pp { color: #bc7a00; } /* Preprocessor */
code span.sc { color: #4070a0; } /* SpecialChar */
code span.ss { color: #bb6688; } /* SpecialString */
code span.st { color: #4070a0; } /* String */
code span.va { color: #19177c; } /* Variable */
code span.vs { color: #4070a0; } /* VerbatimString */
code span.wa { color: #60a0b0; font-weight: bold; font-style: italic; } /* Warning */

</style>
<script>
// apply pandoc div.sourceCode style to pre.sourceCode instead
(function() {
  var sheets = document.styleSheets;
  for (var i = 0; i < sheets.length; i++) {
    if (sheets[i].ownerNode.dataset["origin"] !== "pandoc") continue;
    try { var rules = sheets[i].cssRules; } catch (e) { continue; }
    for (var j = 0; j < rules.length; j++) {
      var rule = rules[j];
      // check if there is a div.sourceCode rule
      if (rule.type !== rule.STYLE_RULE || rule.selectorText !== "div.sourceCode") continue;
      var style = rule.style.cssText;
      // check if color or background-color is set
      if (rule.style.color === '' && rule.style.backgroundColor === '') continue;
      // replace div.sourceCode by a pre.sourceCode rule
      sheets[i].deleteRule(j);
      sheets[i].insertRule('pre.sourceCode{' + style + '}', j);
    }
  }
})();
</script>



<style type="text/css">body {
background-color: #fff;
margin: 1em auto;
max-width: 700px;
overflow: visible;
padding-left: 2em;
padding-right: 2em;
font-family: "Open Sans", "Helvetica Neue", Helvetica, Arial, sans-serif;
font-size: 14px;
line-height: 1.35;
}
#TOC {
clear: both;
margin: 0 0 10px 10px;
padding: 4px;
width: 400px;
border: 1px solid #CCCCCC;
border-radius: 5px;
background-color: #f6f6f6;
font-size: 13px;
line-height: 1.3;
}
#TOC .toctitle {
font-weight: bold;
font-size: 15px;
margin-left: 5px;
}
#TOC ul {
padding-left: 40px;
margin-left: -1.5em;
margin-top: 5px;
margin-bottom: 5px;
}
#TOC ul ul {
margin-left: -2em;
}
#TOC li {
line-height: 16px;
}
table {
margin: 1em auto;
border-width: 1px;
border-color: #DDDDDD;
border-style: outset;
border-collapse: collapse;
}
table th {
border-width: 2px;
padding: 5px;
border-style: inset;
}
table td {
border-width: 1px;
border-style: inset;
line-height: 18px;
padding: 5px 5px;
}
table, table th, table td {
border-left-style: none;
border-right-style: none;
}
table thead, table tr.even {
background-color: #f7f7f7;
}
p {
margin: 0.5em 0;
}
blockquote {
background-color: #f6f6f6;
padding: 0.25em 0.75em;
}
hr {
border-style: solid;
border: none;
border-top: 1px solid #777;
margin: 28px 0;
}
dl {
margin-left: 0;
}
dl dd {
margin-bottom: 13px;
margin-left: 13px;
}
dl dt {
font-weight: bold;
}
ul {
margin-top: 0;
}
ul li {
list-style: circle outside;
}
ul ul {
margin-bottom: 0;
}
pre, code {
background-color: #f7f7f7;
border-radius: 3px;
color: #333;
white-space: pre-wrap; 
}
pre {
border-radius: 3px;
margin: 5px 0px 10px 0px;
padding: 10px;
}
pre:not([class]) {
background-color: #f7f7f7;
}
code {
font-family: Consolas, Monaco, 'Courier New', monospace;
font-size: 85%;
}
p > code, li > code {
padding: 2px 0px;
}
div.figure {
text-align: center;
}
img {
background-color: #FFFFFF;
padding: 2px;
border: 1px solid #DDDDDD;
border-radius: 3px;
border: 1px solid #CCCCCC;
margin: 0 5px;
}
h1 {
margin-top: 0;
font-size: 35px;
line-height: 40px;
}
h2 {
border-bottom: 4px solid #f7f7f7;
padding-top: 10px;
padding-bottom: 2px;
font-size: 145%;
}
h3 {
border-bottom: 2px solid #f7f7f7;
padding-top: 10px;
font-size: 120%;
}
h4 {
border-bottom: 1px solid #f7f7f7;
margin-left: 8px;
font-size: 105%;
}
h5, h6 {
border-bottom: 1px solid #ccc;
font-size: 105%;
}
a {
color: #0033dd;
text-decoration: none;
}
a:hover {
color: #6666ff; }
a:visited {
color: #800080; }
a:visited:hover {
color: #BB00BB; }
a[href^="http:"] {
text-decoration: underline; }
a[href^="https:"] {
text-decoration: underline; }

code > span.kw { color: #555; font-weight: bold; } 
code > span.dt { color: #902000; } 
code > span.dv { color: #40a070; } 
code > span.bn { color: #d14; } 
code > span.fl { color: #d14; } 
code > span.ch { color: #d14; } 
code > span.st { color: #d14; } 
code > span.co { color: #888888; font-style: italic; } 
code > span.ot { color: #007020; } 
code > span.al { color: #ff0000; font-weight: bold; } 
code > span.fu { color: #900; font-weight: bold; } 
code > span.er { color: #a61717; background-color: #e3d2d2; } 
</style>




</head>

<body>




<h1 class="title toc-ignore">Approximate leave-future-out cross-validation for Bayesian time series models</h1>
<h4 class="author">Paul Bürkner, Jonah Gabry, Aki Vehtari</h4>
<h4 class="date">2020-12-07</h4>


<div id="TOC">
<ul>
<li><a href="#introduction">Introduction</a></li>
<li><a href="#m-step-ahead-predictions"><span class="math inline">\(M\)</span>-step-ahead predictions</a></li>
<li><a href="#approximate_MSAP">Approximate <span class="math inline">\(M\)</span>-SAP using importance-sampling</a></li>
<li><a href="#autoregressive-models">Autoregressive models</a></li>
<li><a href="#case-study-annual-measurements-of-the-level-of-lake-huron">Case Study: Annual measurements of the level of Lake Huron</a></li>
<li><a href="#step-ahead-predictions-leaving-out-all-future-values">1-step-ahead predictions leaving out all future values</a>
<ul>
<li><a href="#exact-1-step-ahead-predictions">Exact 1-step-ahead predictions</a></li>
<li><a href="#approximate-1-step-ahead-predictions">Approximate 1-step-ahead predictions</a></li>
</ul></li>
<li><a href="#m-step-ahead-predictions-leaving-out-all-future-values"><span class="math inline">\(M\)</span>-step-ahead predictions leaving out all future values</a>
<ul>
<li><a href="#exact-m-step-ahead-predictions">Exact <span class="math inline">\(M\)</span>-step-ahead predictions</a></li>
<li><a href="#approximate-m-step-ahead-predictions">Approximate <span class="math inline">\(M\)</span>-step-ahead predictions</a></li>
</ul></li>
<li><a href="#conclusion">Conclusion</a></li>
<li><a href="#references">References</a></li>
<li><a href="#appendix">Appendix</a>
<ul>
<li><a href="#appendix-session-information">Appendix: Session information</a></li>
<li><a href="#appendix-licenses">Appendix: Licenses</a></li>
</ul></li>
</ul>
</div>

<!--
%\VignetteEngine{knitr::rmarkdown}
%\VignetteIndexEntry{Approximate leave-future-out cross-validation for Bayesian time series models}
-->
<div id="introduction" class="section level2">
<h2>Introduction</h2>
<p>One of the most common goals of a time series analysis is to use the observed series to inform predictions for future observations. We will refer to this task of predicting a sequence of <span class="math inline">\(M\)</span> future observations as <span class="math inline">\(M\)</span>-step-ahead prediction (<span class="math inline">\(M\)</span>-SAP). Fortunately, once we have fit a model and can sample from the posterior predictive distribution, it is straightforward to generate predictions as far into the future as we want. It is also straightforward to evaluate the <span class="math inline">\(M\)</span>-SAP performance of a time series model by comparing the predictions to the observed sequence of <span class="math inline">\(M\)</span> future data points once they become available.</p>
<p>Unfortunately, we are often in the position of having to use a model to inform decisions <em>before</em> we can collect the future observations required for assessing the predictive performance. If we have many competing models we may also need to first decide which of the models (or which combination of the models) we should rely on for predictions. In these situations the best we can do is to use methods for approximating the expected predictive performance of our models using only the observations of the time series we already have.</p>
<p>If there were no time dependence in the data or if the focus is to assess the non-time-dependent part of the model, we could use methods like leave-one-out cross-validation (LOO-CV). For a data set with <span class="math inline">\(N\)</span> observations, we refit the model <span class="math inline">\(N\)</span> times, each time leaving out one of the <span class="math inline">\(N\)</span> observations and assessing how well the model predicts the left-out observation. LOO-CV is very expensive computationally in most realistic settings, but the Pareto smoothed importance sampling (PSIS, Vehtari et al, 2017, 2019) algorithm provided by the <em>loo</em> package allows for approximating exact LOO-CV with PSIS-LOO-CV. PSIS-LOO-CV requires only a single fit of the full model and comes with diagnostics for assessing the validity of the approximation.</p>
<p>With a time series we can do something similar to LOO-CV but, except in a few cases, it does not make sense to leave out observations one at a time because then we are allowing information from the future to influence predictions of the past (i.e., times <span class="math inline">\(t + 1, t+2, \ldots\)</span> should not be used to predict for time <span class="math inline">\(t\)</span>). To apply the idea of cross-validation to the <span class="math inline">\(M\)</span>-SAP case, instead of leave-<em>one</em>-out cross-validation we need some form of leave-<em>future</em>-out cross-validation (LFO-CV). As we will demonstrate in this case study, LFO-CV does not refer to one particular prediction task but rather to various possible cross-validation approaches that all involve some form of prediction for new time series data. Like exact LOO-CV, exact LFO-CV requires refitting the model many times to different subsets of the data, which is computationally very costly for most nontrivial examples, in particular for Bayesian analyses where refitting the model means estimating a new posterior distribution rather than a point estimate.</p>
<p>Although PSIS-LOO-CV provides an efficient approximation to exact LOO-CV, until now there has not been an analogous approximation to exact LFO-CV that drastically reduces the computational burden while also providing informative diagnostics about the quality of the approximation. In this case study we present PSIS-LFO-CV, an algorithm that typically only requires refitting the time-series model a small number times and will make LFO-CV tractable for many more realistic applications than previously possible.</p>
<p>More details can be found in our paper about approximate LFO-CV (Bürkner, Gabry, &amp; Vehtari, 2020), which is available as a preprint on arXiv (<a href="https://arxiv.org/abs/1902.06281" class="uri">https://arxiv.org/abs/1902.06281</a>).</p>
</div>
<div id="m-step-ahead-predictions" class="section level2">
<h2><span class="math inline">\(M\)</span>-step-ahead predictions</h2>
<p>Assume we have a time series of observations <span class="math inline">\(y = (y_1, y_2, \ldots, y_N)\)</span> and let <span class="math inline">\(L\)</span> be the <em>minimum</em> number of observations from the series that we will require before making predictions for future data. Depending on the application and how informative the data is, it may not be possible to make reasonable predictions for <span class="math inline">\(y_{i+1}\)</span> based on <span class="math inline">\((y_1, \dots, y_{i})\)</span> until <span class="math inline">\(i\)</span> is large enough so that we can learn enough about the time series to predict future observations. Setting <span class="math inline">\(L=10\)</span>, for example, means that we will only assess predictive performance starting with observation <span class="math inline">\(y_{11}\)</span>, so that we always have at least 10 previous observations to condition on.</p>
<p>In order to assess <span class="math inline">\(M\)</span>-SAP performance we would like to compute the predictive densities</p>
<p><span class="math display">\[
p(y_{i+1:M} \,|\, y_{1:i}) = 
  p(y_{i+1}, \ldots, y_{i + M} \,|\, y_{1},...,y_{i}) 
\]</span></p>
<p>for each <span class="math inline">\(i \in \{L, \ldots, N - M\}\)</span>. The quantities <span class="math inline">\(p(y_{i+1:M} \,|\, y_{1:i})\)</span> can be computed with the help of the posterior distribution <span class="math inline">\(p(\theta \,|\, y_{1:i})\)</span> of the parameters <span class="math inline">\(\theta\)</span> conditional on only the first <span class="math inline">\(i\)</span> observations of the time-series:</p>
<p><span class="math display">\[
p(y_{i+1:M} \,| \, y_{1:i}) = 
  \int p(y_{i+1:M} \,| \, y_{1:i}, \theta) \, p(\theta\,|\,y_{1:i}) \,d\theta. 
\]</span></p>
<p>Having obtained <span class="math inline">\(S\)</span> draws <span class="math inline">\((\theta_{1:i}^{(1)}, \ldots, \theta_{1:i}^{(S)})\)</span> from the posterior distribution <span class="math inline">\(p(\theta\,|\,y_{1:i})\)</span>, we can estimate <span class="math inline">\(p(y_{i+1:M} | y_{1:i})\)</span> as</p>
<p><span class="math display">\[
p(y_{i+1:M} \,|\, y_{1:i}) \approx \frac{1}{S}\sum_{s=1}^S p(y_{i+1:M} \,|\, y_{1:i}, \theta_{1:i}^{(s)}).
\]</span></p>
</div>
<div id="approximate_MSAP" class="section level2">
<h2>Approximate <span class="math inline">\(M\)</span>-SAP using importance-sampling</h2>
<p>Unfortunately, the math above makes use of the posterior distributions from many different fits of the model to different subsets of the data. That is, to obtain the predictive density <span class="math inline">\(p(y_{i+1:M} \,|\, y_{1:i})\)</span> requires fitting a model to only the first <span class="math inline">\(i\)</span> data points, and we will need to do this for every value of <span class="math inline">\(i\)</span> under consideration (all <span class="math inline">\(i \in \{L, \ldots, N - M\}\)</span>).</p>
<p>To reduce the number of models that need to be fit for the purpose of obtaining each of the densities <span class="math inline">\(p(y_{i+1:M} \,|\, y_{1:i})\)</span>, we propose the following algorithm. First, we refit the model using the first <span class="math inline">\(L\)</span> observations of the time series and then perform a single exact <span class="math inline">\(M\)</span>-step-ahead prediction step for <span class="math inline">\(p(y_{L+1:M} \,|\, y_{1:L})\)</span>. Recall that <span class="math inline">\(L\)</span> is the minimum number of observations we have deemed acceptable for making predictions (setting <span class="math inline">\(L=0\)</span> means the first data point will be predicted only based on the prior). We define <span class="math inline">\(i^\star = L\)</span> as the current point of refit. Next, starting with <span class="math inline">\(i = i^\star + 1\)</span>, we approximate each <span class="math inline">\(p(y_{i+1:M} \,|\, y_{1:i})\)</span> via</p>
<p><span class="math display">\[
 p(y_{i+1:M} \,|\, y_{1:i}) \approx
   \frac{ \sum_{s=1}^S w_i^{(s)}\, p(y_{i+1:M} \,|\, y_{1:i}, \theta^{(s)})}
        { \sum_{s=1}^S w_i^{(s)}},
\]</span></p>
<p>where <span class="math inline">\(\theta^{(s)} = \theta^{(s)}_{1:i^\star}\)</span> are draws from the posterior distribution based on the first <span class="math inline">\(i^\star\)</span> observations and <span class="math inline">\(w_i^{(s)}\)</span> are the PSIS weights obtained in two steps. First, we compute the raw importance ratios</p>
<p><span class="math display">\[
r_i^{(s)} =
\frac{f_{1:i}(\theta^{(s)})}{f_{1:i^\star}(\theta^{(s)})} 
\propto \prod_{j \in (i^\star + 1):i} p(y_j \,|\, y_{1:(j-1)}, \theta^{(s)}),
\]</span></p>
<p>and then stabilize them using PSIS. The function <span class="math inline">\(f_{1:i}\)</span> denotes the posterior distribution based on the first <span class="math inline">\(i\)</span> observations, that is, <span class="math inline">\(f_{1:i} = p(\theta \,|\, y_{1:i})\)</span>, with <span class="math inline">\(f_{1:i^\star}\)</span> defined analogously. The index set <span class="math inline">\((i^\star + 1):i\)</span> indicates all observations which are part of the data for the model <span class="math inline">\(f_{1:i}\)</span> whose predictive performance we are trying to approximate but not for the actually fitted model <span class="math inline">\(f_{1:i^\star}\)</span>. The proportional statement arises from the fact that we ignore the normalizing constants <span class="math inline">\(p(y_{1:i})\)</span> and <span class="math inline">\(p(y_{1:i^\star})\)</span> of the compared posteriors, which leads to a self-normalized variant of PSIS (see Vehtari et al, 2017).</p>
<p>Continuing with the next observation, we gradually increase <span class="math inline">\(i\)</span> by <span class="math inline">\(1\)</span> (we move forward in time) and repeat the process. At some observation <span class="math inline">\(i\)</span>, the variability of the importance ratios <span class="math inline">\(r_i^{(s)}\)</span> will become too large and importance sampling will fail. We will refer to this particular value of <span class="math inline">\(i\)</span> as <span class="math inline">\(i^\star_1\)</span>. To identify the value of <span class="math inline">\(i^\star_1\)</span>, we check for which value of <span class="math inline">\(i\)</span> does the estimated shape parameter <span class="math inline">\(k\)</span> of the generalized Pareto distribution first cross a certain threshold <span class="math inline">\(\tau\)</span> (Vehtari et al, 2019). Only then do we refit the model using the observations up to <span class="math inline">\(i^\star_1\)</span> and restart the process from there by setting <span class="math inline">\(\theta^{(s)} = \theta^{(s)}_{1:i^\star_1}\)</span> and <span class="math inline">\(i^\star = i^\star_1\)</span> until the next refit.</p>
<p>In some cases we may only need to refit once and in other cases we will find a value <span class="math inline">\(i^\star_2\)</span> that requires a second refitting, maybe an <span class="math inline">\(i^\star_3\)</span> that requires a third refitting, and so on. We refit as many times as is required (only when <span class="math inline">\(k &gt; \tau\)</span>) until we arrive at observation <span class="math inline">\(i = N - M\)</span>. For LOO, we recommend to use a threshold of <span class="math inline">\(\tau = 0.7\)</span> (Vehtari et al, 2017, 2019) and it turns out this is a reasonable threshold for LFO as well (Bürkner et al. 2020).</p>
</div>
<div id="autoregressive-models" class="section level2">
<h2>Autoregressive models</h2>
<p>Autoregressive (AR) models are some of the most commonly used time-series models. An AR(p) model —an autoregressive model of order <span class="math inline">\(p\)</span>— can be defined as</p>
<p><span class="math display">\[
y_i = \eta_i + \sum_{k = 1}^p \varphi_k y_{i - k} + \varepsilon_i,
\]</span></p>
<p>where <span class="math inline">\(\eta_i\)</span> is the linear predictor for the <span class="math inline">\(i\)</span>th observation, <span class="math inline">\(\phi_k\)</span> are the autoregressive parameters and <span class="math inline">\(\varepsilon_i\)</span> are pairwise independent errors, which are usually assumed to be normally distributed with equal variance <span class="math inline">\(\sigma^2\)</span>. The model implies a recursive formula that allows for computing the right-hand side of the above equation for observation <span class="math inline">\(i\)</span> based on the values of the equations for previous observations.</p>
</div>
<div id="case-study-annual-measurements-of-the-level-of-lake-huron" class="section level2">
<h2>Case Study: Annual measurements of the level of Lake Huron</h2>
<p>To illustrate the application of PSIS-LFO-CV for estimating expected <span class="math inline">\(M\)</span>-SAP performance, we will fit a model for 98 annual measurements of the water level (in feet) of <a href="https://en.wikipedia.org/wiki/Lake_Huron">Lake Huron</a> from the years 1875–1972. This data set is found in the <strong>datasets</strong> R package, which is installed automatically with <strong>R</strong>.</p>
<p>In addition to the <strong>loo</strong> package, for this analysis we will use the <strong>brms</strong> interface to Stan to generate a Stan program and fit the model, and also the <strong>bayesplot</strong> and <strong>ggplot2</strong> packages for plotting.</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;loo&quot;</span>)</span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;brms&quot;</span>)</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;bayesplot&quot;</span>)</span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;ggplot2&quot;</span>)</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a><span class="fu">color_scheme_set</span>(<span class="st">&quot;brightblue&quot;</span>)</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a><span class="fu">theme_set</span>(<span class="fu">theme_default</span>())</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a>CHAINS <span class="ot">&lt;-</span> <span class="dv">4</span></span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a>SEED <span class="ot">&lt;-</span> <span class="dv">5838296</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(SEED)</span></code></pre></div>
<p>Before fitting a model, we will first put the data into a data frame and then look at the time series.</p>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a>N <span class="ot">&lt;-</span> <span class="fu">length</span>(LakeHuron)</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a>df <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">y =</span> <span class="fu">as.numeric</span>(LakeHuron),</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a>  <span class="at">year =</span> <span class="fu">as.numeric</span>(<span class="fu">time</span>(LakeHuron)),</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a>  <span class="at">time =</span> <span class="dv">1</span><span class="sc">:</span>N</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb2-7"><a href="#cb2-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-8"><a href="#cb2-8" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(df, <span class="fu">aes</span>(<span class="at">x =</span> year, <span class="at">y =</span> y)) <span class="sc">+</span> </span>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="at">size =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(</span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a>    <span class="at">y =</span> <span class="st">&quot;Water Level (ft)&quot;</span>, </span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a>    <span class="at">x =</span> <span class="st">&quot;Year&quot;</span>,</span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a>    <span class="at">title =</span> <span class="st">&quot;Water Level in Lake Huron (1875-1972)&quot;</span></span>
<span id="cb2-14"><a href="#cb2-14" aria-hidden="true" tabindex="-1"></a>  ) </span></code></pre></div>
<p><img src="data:image/png;base64,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" width="60%" style="display: block; margin: auto;" /></p>
<p>The above plot shows rather strong autocorrelation of the time-series as well as some trend towards lower levels for later points in time.</p>
<p>We can specify an AR(4) model for these data using the <strong>brms</strong> package as follows:</p>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1" aria-hidden="true" tabindex="-1"></a>fit <span class="ot">&lt;-</span> <span class="fu">brm</span>(</span>
<span id="cb3-2"><a href="#cb3-2" aria-hidden="true" tabindex="-1"></a>  y <span class="sc">~</span> <span class="fu">ar</span>(time, <span class="at">p =</span> <span class="dv">4</span>), </span>
<span id="cb3-3"><a href="#cb3-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">data =</span> df, </span>
<span id="cb3-4"><a href="#cb3-4" aria-hidden="true" tabindex="-1"></a>  <span class="at">prior =</span> <span class="fu">prior</span>(<span class="fu">normal</span>(<span class="dv">0</span>, <span class="fl">0.5</span>), <span class="at">class =</span> <span class="st">&quot;ar&quot;</span>),</span>
<span id="cb3-5"><a href="#cb3-5" aria-hidden="true" tabindex="-1"></a>  <span class="at">control =</span> <span class="fu">list</span>(<span class="at">adapt_delta =</span> <span class="fl">0.99</span>), </span>
<span id="cb3-6"><a href="#cb3-6" aria-hidden="true" tabindex="-1"></a>  <span class="at">seed =</span> SEED, </span>
<span id="cb3-7"><a href="#cb3-7" aria-hidden="true" tabindex="-1"></a>  <span class="at">chains =</span> CHAINS</span>
<span id="cb3-8"><a href="#cb3-8" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>The model implied predictions along with the observed values can be plotted, which reveals a rather good fit to the data.</p>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1" aria-hidden="true" tabindex="-1"></a>preds <span class="ot">&lt;-</span> <span class="fu">posterior_predict</span>(fit)</span>
<span id="cb4-2"><a href="#cb4-2" aria-hidden="true" tabindex="-1"></a>preds <span class="ot">&lt;-</span> <span class="fu">cbind</span>(</span>
<span id="cb4-3"><a href="#cb4-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">Estimate =</span> <span class="fu">colMeans</span>(preds), </span>
<span id="cb4-4"><a href="#cb4-4" aria-hidden="true" tabindex="-1"></a>  <span class="at">Q5 =</span> <span class="fu">apply</span>(preds, <span class="dv">2</span>, quantile, <span class="at">probs =</span> <span class="fl">0.05</span>),</span>
<span id="cb4-5"><a href="#cb4-5" aria-hidden="true" tabindex="-1"></a>  <span class="at">Q95 =</span> <span class="fu">apply</span>(preds, <span class="dv">2</span>, quantile, <span class="at">probs =</span> <span class="fl">0.95</span>)</span>
<span id="cb4-6"><a href="#cb4-6" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb4-7"><a href="#cb4-7" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb4-8"><a href="#cb4-8" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(<span class="fu">cbind</span>(df, preds), <span class="fu">aes</span>(<span class="at">x =</span> year, <span class="at">y =</span> Estimate)) <span class="sc">+</span></span>
<span id="cb4-9"><a href="#cb4-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_smooth</span>(<span class="fu">aes</span>(<span class="at">ymin =</span> Q5, <span class="at">ymax =</span> Q95), <span class="at">stat =</span> <span class="st">&quot;identity&quot;</span>, <span class="at">size =</span> <span class="fl">0.5</span>) <span class="sc">+</span></span>
<span id="cb4-10"><a href="#cb4-10" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">y =</span> y)) <span class="sc">+</span> </span>
<span id="cb4-11"><a href="#cb4-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(</span>
<span id="cb4-12"><a href="#cb4-12" aria-hidden="true" tabindex="-1"></a>    <span class="at">y =</span> <span class="st">&quot;Water Level (ft)&quot;</span>, </span>
<span id="cb4-13"><a href="#cb4-13" aria-hidden="true" tabindex="-1"></a>    <span class="at">x =</span> <span class="st">&quot;Year&quot;</span>,</span>
<span id="cb4-14"><a href="#cb4-14" aria-hidden="true" tabindex="-1"></a>    <span class="at">title =</span> <span class="st">&quot;Water Level in Lake Huron (1875-1972)&quot;</span>,</span>
<span id="cb4-15"><a href="#cb4-15" aria-hidden="true" tabindex="-1"></a>    <span class="at">subtitle =</span> <span class="st">&quot;Mean (blue) and 90% predictive intervals (gray) vs. observed data (black)&quot;</span></span>
<span id="cb4-16"><a href="#cb4-16" aria-hidden="true" tabindex="-1"></a>  ) </span></code></pre></div>
<p><img src="data:image/png;base64,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" width="60%" style="display: block; margin: auto;" /></p>
<p>To allow for reasonable predictions of future values, we will require at least <span class="math inline">\(L = 20\)</span> historical observations (20 years) to make predictions.</p>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1" aria-hidden="true" tabindex="-1"></a>L <span class="ot">&lt;-</span> <span class="dv">20</span></span></code></pre></div>
<p>We first perform approximate leave-one-out cross-validation (LOO-CV) for the purpose of later comparison with exact and approximate LFO-CV for the 1-SAP case.</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1" aria-hidden="true" tabindex="-1"></a>loo_cv <span class="ot">&lt;-</span> <span class="fu">loo</span>(<span class="fu">log_lik</span>(fit)[, (L <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>N])</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a><span class="fu">print</span>(loo_cv)</span></code></pre></div>
<pre><code>
Computed from 4000 by 78 log-likelihood matrix

         Estimate   SE
elpd_loo    -88.6  6.4
p_loo         4.7  1.0
looic       177.2 12.7
------
Monte Carlo SE of elpd_loo is 0.0.

All Pareto k estimates are good (k &lt; 0.5).
See help(&#39;pareto-k-diagnostic&#39;) for details.</code></pre>
</div>
<div id="step-ahead-predictions-leaving-out-all-future-values" class="section level2">
<h2>1-step-ahead predictions leaving out all future values</h2>
<p>The most basic version of <span class="math inline">\(M\)</span>-SAP is 1-SAP, in which we predict only one step ahead. In this case, <span class="math inline">\(y_{i+1:M}\)</span> simplifies to <span class="math inline">\(y_{i}\)</span> and the LFO-CV algorithm becomes considerably simpler than for larger values of <span class="math inline">\(M\)</span>.</p>
<div id="exact-1-step-ahead-predictions" class="section level3">
<h3>Exact 1-step-ahead predictions</h3>
<p>Before we compute approximate LFO-CV using PSIS we will first compute exact LFO-CV for the 1-SAP case so we can use it as a benchmark later. The initial step for the exact computation is to calculate the log-predictive densities by refitting the model many times:</p>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1" aria-hidden="true" tabindex="-1"></a>loglik_exact <span class="ot">&lt;-</span> <span class="fu">matrix</span>(<span class="at">nrow =</span> <span class="fu">nsamples</span>(fit), <span class="at">ncol =</span> N)</span>
<span id="cb8-2"><a href="#cb8-2" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> L<span class="sc">:</span>(N <span class="sc">-</span> <span class="dv">1</span>)) {</span>
<span id="cb8-3"><a href="#cb8-3" aria-hidden="true" tabindex="-1"></a>  past <span class="ot">&lt;-</span> <span class="dv">1</span><span class="sc">:</span>i</span>
<span id="cb8-4"><a href="#cb8-4" aria-hidden="true" tabindex="-1"></a>  oos <span class="ot">&lt;-</span> i <span class="sc">+</span> <span class="dv">1</span></span>
<span id="cb8-5"><a href="#cb8-5" aria-hidden="true" tabindex="-1"></a>  df_past <span class="ot">&lt;-</span> df[past, , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb8-6"><a href="#cb8-6" aria-hidden="true" tabindex="-1"></a>  df_oos <span class="ot">&lt;-</span> df[<span class="fu">c</span>(past, oos), , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb8-7"><a href="#cb8-7" aria-hidden="true" tabindex="-1"></a>  fit_i <span class="ot">&lt;-</span> <span class="fu">update</span>(fit, <span class="at">newdata =</span> df_past, <span class="at">recompile =</span> <span class="cn">FALSE</span>)</span>
<span id="cb8-8"><a href="#cb8-8" aria-hidden="true" tabindex="-1"></a>  loglik_exact[, i <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_i, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)[, oos]</span>
<span id="cb8-9"><a href="#cb8-9" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<p>Then we compute the exact expected log predictive density (ELPD):</p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1" aria-hidden="true" tabindex="-1"></a><span class="co"># some helper functions we&#39;ll use throughout</span></span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a><span class="co"># more stable than log(sum(exp(x))) </span></span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>log_sum_exp <span class="ot">&lt;-</span> <span class="cf">function</span>(x) {</span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a>  max_x <span class="ot">&lt;-</span> <span class="fu">max</span>(x)  </span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a>  max_x <span class="sc">+</span> <span class="fu">log</span>(<span class="fu">sum</span>(<span class="fu">exp</span>(x <span class="sc">-</span> max_x)))</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb9-8"><a href="#cb9-8" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-9"><a href="#cb9-9" aria-hidden="true" tabindex="-1"></a><span class="co"># more stable than log(mean(exp(x)))</span></span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a>log_mean_exp <span class="ot">&lt;-</span> <span class="cf">function</span>(x) {</span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">log_sum_exp</span>(x) <span class="sc">-</span> <span class="fu">log</span>(<span class="fu">length</span>(x))</span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a><span class="co"># compute log of raw importance ratios</span></span>
<span id="cb9-15"><a href="#cb9-15" aria-hidden="true" tabindex="-1"></a><span class="co"># sums over observations *not* over posterior samples</span></span>
<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a>sum_log_ratios <span class="ot">&lt;-</span> <span class="cf">function</span>(loglik, <span class="at">ids =</span> <span class="cn">NULL</span>) {</span>
<span id="cb9-17"><a href="#cb9-17" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> (<span class="sc">!</span><span class="fu">is.null</span>(ids)) loglik <span class="ot">&lt;-</span> loglik[, ids, drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb9-18"><a href="#cb9-18" aria-hidden="true" tabindex="-1"></a>  <span class="fu">rowSums</span>(loglik)</span>
<span id="cb9-19"><a href="#cb9-19" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb9-20"><a href="#cb9-20" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb9-21"><a href="#cb9-21" aria-hidden="true" tabindex="-1"></a><span class="co"># for printing comparisons later</span></span>
<span id="cb9-22"><a href="#cb9-22" aria-hidden="true" tabindex="-1"></a>rbind_print <span class="ot">&lt;-</span> <span class="cf">function</span>(...) {</span>
<span id="cb9-23"><a href="#cb9-23" aria-hidden="true" tabindex="-1"></a>  <span class="fu">round</span>(<span class="fu">rbind</span>(...), <span class="at">digits =</span> <span class="dv">2</span>)</span>
<span id="cb9-24"><a href="#cb9-24" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1" aria-hidden="true" tabindex="-1"></a>exact_elpds_1sap <span class="ot">&lt;-</span> <span class="fu">apply</span>(loglik_exact, <span class="dv">2</span>, log_mean_exp)</span>
<span id="cb10-2"><a href="#cb10-2" aria-hidden="true" tabindex="-1"></a>exact_elpd_1sap <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="at">ELPD =</span> <span class="fu">sum</span>(exact_elpds_1sap[<span class="sc">-</span>(<span class="dv">1</span><span class="sc">:</span>L)]))</span>
<span id="cb10-3"><a href="#cb10-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb10-4"><a href="#cb10-4" aria-hidden="true" tabindex="-1"></a><span class="fu">rbind_print</span>(</span>
<span id="cb10-5"><a href="#cb10-5" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;LOO&quot;</span> <span class="ot">=</span> loo_cv<span class="sc">$</span>estimates[<span class="st">&quot;elpd_loo&quot;</span>, <span class="st">&quot;Estimate&quot;</span>],</span>
<span id="cb10-6"><a href="#cb10-6" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;LFO&quot;</span> <span class="ot">=</span> exact_elpd_1sap</span>
<span id="cb10-7"><a href="#cb10-7" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<pre><code>      ELPD
LOO -88.58
LFO -92.45</code></pre>
<p>We see that the ELPD from LFO-CV for 1-step-ahead predictions is lower than the ELPD estimate from LOO-CV, which should be expected since LOO-CV is making use of more of the time series. That is, since the LFO-CV approach only uses observations from before the left-out data point but LOO-CV uses <em>all</em> data points other than the left-out observation, we should expect to see the larger ELPD from LOO-CV.</p>
</div>
<div id="approximate-1-step-ahead-predictions" class="section level3">
<h3>Approximate 1-step-ahead predictions</h3>
<p>We compute approximate 1-SAP with refit at observations where the Pareto <span class="math inline">\(k\)</span> estimate exceeds the threshold of <span class="math inline">\(0.7\)</span>.</p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1" aria-hidden="true" tabindex="-1"></a>k_thres <span class="ot">&lt;-</span> <span class="fl">0.7</span></span></code></pre></div>
<p>The code becomes a little bit more involved as compared to the exact LFO-CV. Note that we can compute exact 1-SAP at the refitting points, which comes with no additional computational costs since we had to refit the model anyway.</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1" aria-hidden="true" tabindex="-1"></a>approx_elpds_1sap <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="cn">NA</span>, N)</span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a><span class="co"># initialize the process for i = L</span></span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a>past <span class="ot">&lt;-</span> <span class="dv">1</span><span class="sc">:</span>L</span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a>oos <span class="ot">&lt;-</span> L <span class="sc">+</span> <span class="dv">1</span></span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a>df_past <span class="ot">&lt;-</span> df[past, , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a>df_oos <span class="ot">&lt;-</span> df[<span class="fu">c</span>(past, oos), , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a>fit_past <span class="ot">&lt;-</span> <span class="fu">update</span>(fit, <span class="at">newdata =</span> df_past, <span class="at">recompile =</span> <span class="cn">FALSE</span>)</span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a>loglik <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_past, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)</span>
<span id="cb13-10"><a href="#cb13-10" aria-hidden="true" tabindex="-1"></a>approx_elpds_1sap[L <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">log_mean_exp</span>(loglik[, oos])</span>
<span id="cb13-11"><a href="#cb13-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb13-12"><a href="#cb13-12" aria-hidden="true" tabindex="-1"></a><span class="co"># iterate over i &gt; L</span></span>
<span id="cb13-13"><a href="#cb13-13" aria-hidden="true" tabindex="-1"></a>i_refit <span class="ot">&lt;-</span> L</span>
<span id="cb13-14"><a href="#cb13-14" aria-hidden="true" tabindex="-1"></a>refits <span class="ot">&lt;-</span> L</span>
<span id="cb13-15"><a href="#cb13-15" aria-hidden="true" tabindex="-1"></a>ks <span class="ot">&lt;-</span> <span class="cn">NULL</span></span>
<span id="cb13-16"><a href="#cb13-16" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> (L <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(N <span class="sc">-</span> <span class="dv">1</span>)) {</span>
<span id="cb13-17"><a href="#cb13-17" aria-hidden="true" tabindex="-1"></a>  past <span class="ot">&lt;-</span> <span class="dv">1</span><span class="sc">:</span>i</span>
<span id="cb13-18"><a href="#cb13-18" aria-hidden="true" tabindex="-1"></a>  oos <span class="ot">&lt;-</span> i <span class="sc">+</span> <span class="dv">1</span></span>
<span id="cb13-19"><a href="#cb13-19" aria-hidden="true" tabindex="-1"></a>  df_past <span class="ot">&lt;-</span> df[past, , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb13-20"><a href="#cb13-20" aria-hidden="true" tabindex="-1"></a>  df_oos <span class="ot">&lt;-</span> df[<span class="fu">c</span>(past, oos), , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb13-21"><a href="#cb13-21" aria-hidden="true" tabindex="-1"></a>  loglik <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_past, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)</span>
<span id="cb13-22"><a href="#cb13-22" aria-hidden="true" tabindex="-1"></a>  </span>
<span id="cb13-23"><a href="#cb13-23" aria-hidden="true" tabindex="-1"></a>  logratio <span class="ot">&lt;-</span> <span class="fu">sum_log_ratios</span>(loglik, (i_refit <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>i)</span>
<span id="cb13-24"><a href="#cb13-24" aria-hidden="true" tabindex="-1"></a>  psis_obj <span class="ot">&lt;-</span> <span class="fu">suppressWarnings</span>(<span class="fu">psis</span>(logratio))</span>
<span id="cb13-25"><a href="#cb13-25" aria-hidden="true" tabindex="-1"></a>  k <span class="ot">&lt;-</span> <span class="fu">pareto_k_values</span>(psis_obj)</span>
<span id="cb13-26"><a href="#cb13-26" aria-hidden="true" tabindex="-1"></a>  ks <span class="ot">&lt;-</span> <span class="fu">c</span>(ks, k)</span>
<span id="cb13-27"><a href="#cb13-27" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> (k <span class="sc">&gt;</span> k_thres) {</span>
<span id="cb13-28"><a href="#cb13-28" aria-hidden="true" tabindex="-1"></a>    <span class="co"># refit the model based on the first i observations</span></span>
<span id="cb13-29"><a href="#cb13-29" aria-hidden="true" tabindex="-1"></a>    i_refit <span class="ot">&lt;-</span> i</span>
<span id="cb13-30"><a href="#cb13-30" aria-hidden="true" tabindex="-1"></a>    refits <span class="ot">&lt;-</span> <span class="fu">c</span>(refits, i)</span>
<span id="cb13-31"><a href="#cb13-31" aria-hidden="true" tabindex="-1"></a>    fit_past <span class="ot">&lt;-</span> <span class="fu">update</span>(fit_past, <span class="at">newdata =</span> df_past, <span class="at">recompile =</span> <span class="cn">FALSE</span>)</span>
<span id="cb13-32"><a href="#cb13-32" aria-hidden="true" tabindex="-1"></a>    loglik <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_past, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)</span>
<span id="cb13-33"><a href="#cb13-33" aria-hidden="true" tabindex="-1"></a>    approx_elpds_1sap[i <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">log_mean_exp</span>(loglik[, oos])</span>
<span id="cb13-34"><a href="#cb13-34" aria-hidden="true" tabindex="-1"></a>  } <span class="cf">else</span> {</span>
<span id="cb13-35"><a href="#cb13-35" aria-hidden="true" tabindex="-1"></a>    lw <span class="ot">&lt;-</span> <span class="fu">weights</span>(psis_obj, <span class="at">normalize =</span> <span class="cn">TRUE</span>)[, <span class="dv">1</span>]</span>
<span id="cb13-36"><a href="#cb13-36" aria-hidden="true" tabindex="-1"></a>    approx_elpds_1sap[i <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">log_sum_exp</span>(lw <span class="sc">+</span> loglik[, oos])</span>
<span id="cb13-37"><a href="#cb13-37" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb13-38"><a href="#cb13-38" aria-hidden="true" tabindex="-1"></a>} </span></code></pre></div>
<p>We see that the final Pareto-<span class="math inline">\(k\)</span>-estimates are mostly well below the threshold and that we only needed to refit the model a few times:</p>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1" aria-hidden="true" tabindex="-1"></a>plot_ks <span class="ot">&lt;-</span> <span class="cf">function</span>(ks, ids, <span class="at">thres =</span> <span class="fl">0.6</span>) {</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a>  dat_ks <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(<span class="at">ks =</span> ks, <span class="at">ids =</span> ids)</span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggplot</span>(dat_ks, <span class="fu">aes</span>(<span class="at">x =</span> ids, <span class="at">y =</span> ks)) <span class="sc">+</span> </span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a>    <span class="fu">geom_point</span>(<span class="fu">aes</span>(<span class="at">color =</span> ks <span class="sc">&gt;</span> thres), <span class="at">shape =</span> <span class="dv">3</span>, <span class="at">show.legend =</span> <span class="cn">FALSE</span>) <span class="sc">+</span> </span>
<span id="cb14-5"><a href="#cb14-5" aria-hidden="true" tabindex="-1"></a>    <span class="fu">geom_hline</span>(<span class="at">yintercept =</span> thres, <span class="at">linetype =</span> <span class="dv">2</span>, <span class="at">color =</span> <span class="st">&quot;red2&quot;</span>) <span class="sc">+</span> </span>
<span id="cb14-6"><a href="#cb14-6" aria-hidden="true" tabindex="-1"></a>    <span class="fu">scale_color_manual</span>(<span class="at">values =</span> <span class="fu">c</span>(<span class="st">&quot;cornflowerblue&quot;</span>, <span class="st">&quot;darkblue&quot;</span>)) <span class="sc">+</span> </span>
<span id="cb14-7"><a href="#cb14-7" aria-hidden="true" tabindex="-1"></a>    <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">&quot;Data point&quot;</span>, <span class="at">y =</span> <span class="st">&quot;Pareto k&quot;</span>) <span class="sc">+</span> </span>
<span id="cb14-8"><a href="#cb14-8" aria-hidden="true" tabindex="-1"></a>    <span class="fu">ylim</span>(<span class="sc">-</span><span class="fl">0.5</span>, <span class="fl">1.5</span>)</span>
<span id="cb14-9"><a href="#cb14-9" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<div class="sourceCode" id="cb15"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb15-1"><a href="#cb15-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span>(<span class="st">&quot;Using threshold &quot;</span>, k_thres, </span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>    <span class="st">&quot;, model was refit &quot;</span>, <span class="fu">length</span>(refits), </span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a>    <span class="st">&quot; times, at observations&quot;</span>, refits)</span></code></pre></div>
<pre><code>Using threshold  0.7 , model was refit  2  times, at observations 20 57</code></pre>
<div class="sourceCode" id="cb17"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb17-1"><a href="#cb17-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot_ks</span>(ks, (L <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(N <span class="sc">-</span> <span class="dv">1</span>))</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="60%" style="display: block; margin: auto;" /></p>
<p>The approximate 1-SAP ELPD is remarkably similar to the exact 1-SAP ELPD computed above, which indicates our algorithm to compute approximate 1-SAP worked well for the present data and model.</p>
<div class="sourceCode" id="cb18"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb18-1"><a href="#cb18-1" aria-hidden="true" tabindex="-1"></a>approx_elpd_1sap <span class="ot">&lt;-</span> <span class="fu">sum</span>(approx_elpds_1sap, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a><span class="fu">rbind_print</span>(</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;approx LFO&quot;</span> <span class="ot">=</span> approx_elpd_1sap,</span>
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;exact LFO&quot;</span> <span class="ot">=</span> exact_elpd_1sap</span>
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<pre><code>             ELPD
approx LFO -92.60
exact LFO  -92.45</code></pre>
<p>Plotting exact against approximate predictions, we see that no approximation value deviates far from its exact counterpart, providing further evidence for the good quality of our approximation.</p>
<div class="sourceCode" id="cb20"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb20-1"><a href="#cb20-1" aria-hidden="true" tabindex="-1"></a>dat_elpd <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(</span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>  <span class="at">approx_elpd =</span> approx_elpds_1sap,</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">exact_elpd =</span> exact_elpds_1sap</span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(dat_elpd, <span class="fu">aes</span>(<span class="at">x =</span> approx_elpd, <span class="at">y =</span> exact_elpd)) <span class="sc">+</span></span>
<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_abline</span>(<span class="at">color =</span> <span class="st">&quot;gray30&quot;</span>) <span class="sc">+</span></span>
<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="at">size =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb20-9"><a href="#cb20-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">&quot;Approximate ELPDs&quot;</span>, <span class="at">y =</span> <span class="st">&quot;Exact ELPDs&quot;</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="60%" style="display: block; margin: auto;" /></p>
<p>We can also look at the maximum difference and average difference between the approximate and exact ELPD calculations, which also indicate a ver close approximation:</p>
<div class="sourceCode" id="cb21"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb21-1"><a href="#cb21-1" aria-hidden="true" tabindex="-1"></a>max_diff <span class="ot">&lt;-</span> <span class="fu">with</span>(dat_elpd, <span class="fu">max</span>(<span class="fu">abs</span>(approx_elpd <span class="sc">-</span> exact_elpd), <span class="at">na.rm =</span> <span class="cn">TRUE</span>))</span>
<span id="cb21-2"><a href="#cb21-2" aria-hidden="true" tabindex="-1"></a>mean_diff <span class="ot">&lt;-</span> <span class="fu">with</span>(dat_elpd, <span class="fu">mean</span>(<span class="fu">abs</span>(approx_elpd <span class="sc">-</span> exact_elpd), <span class="at">na.rm =</span> <span class="cn">TRUE</span>))</span>
<span id="cb21-3"><a href="#cb21-3" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb21-4"><a href="#cb21-4" aria-hidden="true" tabindex="-1"></a><span class="fu">rbind_print</span>(</span>
<span id="cb21-5"><a href="#cb21-5" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;Max diff&quot;</span> <span class="ot">=</span> <span class="fu">round</span>(max_diff, <span class="dv">2</span>), </span>
<span id="cb21-6"><a href="#cb21-6" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;Mean diff&quot;</span> <span class="ot">=</span>  <span class="fu">round</span>(mean_diff, <span class="dv">3</span>)</span>
<span id="cb21-7"><a href="#cb21-7" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<pre><code>          [,1]
Max diff  0.19
Mean diff 0.02</code></pre>
</div>
</div>
<div id="m-step-ahead-predictions-leaving-out-all-future-values" class="section level2">
<h2><span class="math inline">\(M\)</span>-step-ahead predictions leaving out all future values</h2>
<p>To illustrate the application of <span class="math inline">\(M\)</span>-SAP for <span class="math inline">\(M &gt; 1\)</span>, we next compute exact and approximate LFO-CV for the 4-SAP case.</p>
<div id="exact-m-step-ahead-predictions" class="section level3">
<h3>Exact <span class="math inline">\(M\)</span>-step-ahead predictions</h3>
<p>The necessary steps are the same as for 1-SAP with the exception that the log-density values of interest are now the sums of the log predictive densities of four consecutive observations. Further, the stability of the PSIS approximation actually stays the same for all <span class="math inline">\(M\)</span> as it only depends on the number of observations we leave out, not on the number of observations we predict.</p>
<div class="sourceCode" id="cb23"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb23-1"><a href="#cb23-1" aria-hidden="true" tabindex="-1"></a>M <span class="ot">&lt;-</span> <span class="dv">4</span></span>
<span id="cb23-2"><a href="#cb23-2" aria-hidden="true" tabindex="-1"></a>loglikm <span class="ot">&lt;-</span> <span class="fu">matrix</span>(<span class="at">nrow =</span> <span class="fu">nsamples</span>(fit), <span class="at">ncol =</span> N)</span>
<span id="cb23-3"><a href="#cb23-3" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> L<span class="sc">:</span>(N <span class="sc">-</span> M)) {</span>
<span id="cb23-4"><a href="#cb23-4" aria-hidden="true" tabindex="-1"></a>  past <span class="ot">&lt;-</span> <span class="dv">1</span><span class="sc">:</span>i</span>
<span id="cb23-5"><a href="#cb23-5" aria-hidden="true" tabindex="-1"></a>  oos <span class="ot">&lt;-</span> (i <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(i <span class="sc">+</span> M)</span>
<span id="cb23-6"><a href="#cb23-6" aria-hidden="true" tabindex="-1"></a>  df_past <span class="ot">&lt;-</span> df[past, , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb23-7"><a href="#cb23-7" aria-hidden="true" tabindex="-1"></a>  df_oos <span class="ot">&lt;-</span> df[<span class="fu">c</span>(past, oos), , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb23-8"><a href="#cb23-8" aria-hidden="true" tabindex="-1"></a>  fit_past <span class="ot">&lt;-</span> <span class="fu">update</span>(fit, <span class="at">newdata =</span> df_past, <span class="at">recompile =</span> <span class="cn">FALSE</span>)</span>
<span id="cb23-9"><a href="#cb23-9" aria-hidden="true" tabindex="-1"></a>  loglik <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_past, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)</span>
<span id="cb23-10"><a href="#cb23-10" aria-hidden="true" tabindex="-1"></a>  loglikm[, i <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">rowSums</span>(loglik[, oos])</span>
<span id="cb23-11"><a href="#cb23-11" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<div class="sourceCode" id="cb24"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb24-1"><a href="#cb24-1" aria-hidden="true" tabindex="-1"></a>exact_elpds_4sap <span class="ot">&lt;-</span> <span class="fu">apply</span>(loglikm, <span class="dv">2</span>, log_mean_exp)</span>
<span id="cb24-2"><a href="#cb24-2" aria-hidden="true" tabindex="-1"></a>(exact_elpd_4sap <span class="ot">&lt;-</span> <span class="fu">c</span>(<span class="at">ELPD =</span> <span class="fu">sum</span>(exact_elpds_4sap, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)))</span></code></pre></div>
<pre><code>     ELPD 
-405.1963 </code></pre>
</div>
<div id="approximate-m-step-ahead-predictions" class="section level3">
<h3>Approximate <span class="math inline">\(M\)</span>-step-ahead predictions</h3>
<p>Computing the approximate PSIS-LFO-CV for the 4-SAP case is a little bit more involved than the approximate version for the 1-SAP case, although the underlying principles remain the same.</p>
<div class="sourceCode" id="cb26"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb26-1"><a href="#cb26-1" aria-hidden="true" tabindex="-1"></a>approx_elpds_4sap <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="cn">NA</span>, N)</span>
<span id="cb26-2"><a href="#cb26-2" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-3"><a href="#cb26-3" aria-hidden="true" tabindex="-1"></a><span class="co"># initialize the process for i = L</span></span>
<span id="cb26-4"><a href="#cb26-4" aria-hidden="true" tabindex="-1"></a>past <span class="ot">&lt;-</span> <span class="dv">1</span><span class="sc">:</span>L</span>
<span id="cb26-5"><a href="#cb26-5" aria-hidden="true" tabindex="-1"></a>oos <span class="ot">&lt;-</span> (L <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(L <span class="sc">+</span> M)</span>
<span id="cb26-6"><a href="#cb26-6" aria-hidden="true" tabindex="-1"></a>df_past <span class="ot">&lt;-</span> df[past, , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb26-7"><a href="#cb26-7" aria-hidden="true" tabindex="-1"></a>df_oos <span class="ot">&lt;-</span> df[<span class="fu">c</span>(past, oos), , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb26-8"><a href="#cb26-8" aria-hidden="true" tabindex="-1"></a>fit_past <span class="ot">&lt;-</span> <span class="fu">update</span>(fit, <span class="at">newdata =</span> df_past, <span class="at">recompile =</span> <span class="cn">FALSE</span>)</span>
<span id="cb26-9"><a href="#cb26-9" aria-hidden="true" tabindex="-1"></a>loglik <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_past, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)</span>
<span id="cb26-10"><a href="#cb26-10" aria-hidden="true" tabindex="-1"></a>loglikm <span class="ot">&lt;-</span> <span class="fu">rowSums</span>(loglik[, oos])</span>
<span id="cb26-11"><a href="#cb26-11" aria-hidden="true" tabindex="-1"></a>approx_elpds_1sap[L <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">log_mean_exp</span>(loglikm)</span>
<span id="cb26-12"><a href="#cb26-12" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb26-13"><a href="#cb26-13" aria-hidden="true" tabindex="-1"></a><span class="co"># iterate over i &gt; L</span></span>
<span id="cb26-14"><a href="#cb26-14" aria-hidden="true" tabindex="-1"></a>i_refit <span class="ot">&lt;-</span> L</span>
<span id="cb26-15"><a href="#cb26-15" aria-hidden="true" tabindex="-1"></a>refits <span class="ot">&lt;-</span> L</span>
<span id="cb26-16"><a href="#cb26-16" aria-hidden="true" tabindex="-1"></a>ks <span class="ot">&lt;-</span> <span class="cn">NULL</span></span>
<span id="cb26-17"><a href="#cb26-17" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> (L <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(N <span class="sc">-</span> M)) {</span>
<span id="cb26-18"><a href="#cb26-18" aria-hidden="true" tabindex="-1"></a>  past <span class="ot">&lt;-</span> <span class="dv">1</span><span class="sc">:</span>i</span>
<span id="cb26-19"><a href="#cb26-19" aria-hidden="true" tabindex="-1"></a>  oos <span class="ot">&lt;-</span> (i <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(i <span class="sc">+</span> M)</span>
<span id="cb26-20"><a href="#cb26-20" aria-hidden="true" tabindex="-1"></a>  df_past <span class="ot">&lt;-</span> df[past, , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb26-21"><a href="#cb26-21" aria-hidden="true" tabindex="-1"></a>  df_oos <span class="ot">&lt;-</span> df[<span class="fu">c</span>(past, oos), , drop <span class="ot">=</span> <span class="cn">FALSE</span>]</span>
<span id="cb26-22"><a href="#cb26-22" aria-hidden="true" tabindex="-1"></a>  loglik <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_past, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)</span>
<span id="cb26-23"><a href="#cb26-23" aria-hidden="true" tabindex="-1"></a>  </span>
<span id="cb26-24"><a href="#cb26-24" aria-hidden="true" tabindex="-1"></a>  logratio <span class="ot">&lt;-</span> <span class="fu">sum_log_ratios</span>(loglik, (i_refit <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>i)</span>
<span id="cb26-25"><a href="#cb26-25" aria-hidden="true" tabindex="-1"></a>  psis_obj <span class="ot">&lt;-</span> <span class="fu">suppressWarnings</span>(<span class="fu">psis</span>(logratio))</span>
<span id="cb26-26"><a href="#cb26-26" aria-hidden="true" tabindex="-1"></a>  k <span class="ot">&lt;-</span> <span class="fu">pareto_k_values</span>(psis_obj)</span>
<span id="cb26-27"><a href="#cb26-27" aria-hidden="true" tabindex="-1"></a>  ks <span class="ot">&lt;-</span> <span class="fu">c</span>(ks, k)</span>
<span id="cb26-28"><a href="#cb26-28" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> (k <span class="sc">&gt;</span> k_thres) {</span>
<span id="cb26-29"><a href="#cb26-29" aria-hidden="true" tabindex="-1"></a>    <span class="co"># refit the model based on the first i observations</span></span>
<span id="cb26-30"><a href="#cb26-30" aria-hidden="true" tabindex="-1"></a>    i_refit <span class="ot">&lt;-</span> i</span>
<span id="cb26-31"><a href="#cb26-31" aria-hidden="true" tabindex="-1"></a>    refits <span class="ot">&lt;-</span> <span class="fu">c</span>(refits, i)</span>
<span id="cb26-32"><a href="#cb26-32" aria-hidden="true" tabindex="-1"></a>    fit_past <span class="ot">&lt;-</span> <span class="fu">update</span>(fit_past, <span class="at">newdata =</span> df_past, <span class="at">recompile =</span> <span class="cn">FALSE</span>)</span>
<span id="cb26-33"><a href="#cb26-33" aria-hidden="true" tabindex="-1"></a>    loglik <span class="ot">&lt;-</span> <span class="fu">log_lik</span>(fit_past, <span class="at">newdata =</span> df_oos, <span class="at">oos =</span> oos)</span>
<span id="cb26-34"><a href="#cb26-34" aria-hidden="true" tabindex="-1"></a>    loglikm <span class="ot">&lt;-</span> <span class="fu">rowSums</span>(loglik[, oos])</span>
<span id="cb26-35"><a href="#cb26-35" aria-hidden="true" tabindex="-1"></a>    approx_elpds_4sap[i <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">log_mean_exp</span>(loglikm)</span>
<span id="cb26-36"><a href="#cb26-36" aria-hidden="true" tabindex="-1"></a>  } <span class="cf">else</span> {</span>
<span id="cb26-37"><a href="#cb26-37" aria-hidden="true" tabindex="-1"></a>    lw <span class="ot">&lt;-</span> <span class="fu">weights</span>(psis_obj, <span class="at">normalize =</span> <span class="cn">TRUE</span>)[, <span class="dv">1</span>]</span>
<span id="cb26-38"><a href="#cb26-38" aria-hidden="true" tabindex="-1"></a>    loglikm <span class="ot">&lt;-</span> <span class="fu">rowSums</span>(loglik[, oos])</span>
<span id="cb26-39"><a href="#cb26-39" aria-hidden="true" tabindex="-1"></a>    approx_elpds_4sap[i <span class="sc">+</span> <span class="dv">1</span>] <span class="ot">&lt;-</span> <span class="fu">log_sum_exp</span>(lw <span class="sc">+</span> loglikm)</span>
<span id="cb26-40"><a href="#cb26-40" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb26-41"><a href="#cb26-41" aria-hidden="true" tabindex="-1"></a>} </span></code></pre></div>
<p>Again, we see that the final Pareto-<span class="math inline">\(k\)</span>-estimates are mostly well below the threshold and that we only needed to refit the model a few times:</p>
<div class="sourceCode" id="cb27"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb27-1"><a href="#cb27-1" aria-hidden="true" tabindex="-1"></a><span class="fu">cat</span>(<span class="st">&quot;Using threshold &quot;</span>, k_thres, </span>
<span id="cb27-2"><a href="#cb27-2" aria-hidden="true" tabindex="-1"></a>    <span class="st">&quot;, model was refit &quot;</span>, <span class="fu">length</span>(refits), </span>
<span id="cb27-3"><a href="#cb27-3" aria-hidden="true" tabindex="-1"></a>    <span class="st">&quot; times, at observations&quot;</span>, refits)</span></code></pre></div>
<pre><code>Using threshold  0.7 , model was refit  2  times, at observations 20 57</code></pre>
<div class="sourceCode" id="cb29"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb29-1"><a href="#cb29-1" aria-hidden="true" tabindex="-1"></a><span class="fu">plot_ks</span>(ks, (L <span class="sc">+</span> <span class="dv">1</span>)<span class="sc">:</span>(N <span class="sc">-</span> M))</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="60%" style="display: block; margin: auto;" /></p>
<p>The approximate ELPD computed for the 4-SAP case is not as close to its exact counterpart as in the 1-SAP case. In general, the larger <span class="math inline">\(M\)</span>, the larger the variation of the approximate ELPD around the exact ELPD. It turns out that the ELPD estimates of AR-models with <span class="math inline">\(M&gt;1\)</span> show particular variation due to their predictions’ dependency on other predicted values. In Bürkner et al. (2020) we provide further explanation and simulations for these cases.</p>
<div class="sourceCode" id="cb30"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb30-1"><a href="#cb30-1" aria-hidden="true" tabindex="-1"></a>approx_elpd_4sap <span class="ot">&lt;-</span> <span class="fu">sum</span>(approx_elpds_4sap, <span class="at">na.rm =</span> <span class="cn">TRUE</span>)</span>
<span id="cb30-2"><a href="#cb30-2" aria-hidden="true" tabindex="-1"></a><span class="fu">rbind_print</span>(</span>
<span id="cb30-3"><a href="#cb30-3" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;Approx LFO&quot;</span> <span class="ot">=</span> approx_elpd_4sap,</span>
<span id="cb30-4"><a href="#cb30-4" aria-hidden="true" tabindex="-1"></a>  <span class="st">&quot;Exact LFO&quot;</span> <span class="ot">=</span> exact_elpd_4sap</span>
<span id="cb30-5"><a href="#cb30-5" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<pre><code>              ELPD
Approx LFO -401.39
Exact LFO  -405.20</code></pre>
<p>Plotting exact against approximate pointwise predictions confirms that, for a few specific data points, the approximate predictions underestimate the exact predictions.</p>
<div class="sourceCode" id="cb32"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb32-1"><a href="#cb32-1" aria-hidden="true" tabindex="-1"></a>dat_elpd_4sap <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(</span>
<span id="cb32-2"><a href="#cb32-2" aria-hidden="true" tabindex="-1"></a>  <span class="at">approx_elpd =</span> approx_elpds_4sap,</span>
<span id="cb32-3"><a href="#cb32-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">exact_elpd =</span> exact_elpds_4sap</span>
<span id="cb32-4"><a href="#cb32-4" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb32-5"><a href="#cb32-5" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb32-6"><a href="#cb32-6" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(dat_elpd_4sap, <span class="fu">aes</span>(<span class="at">x =</span> approx_elpd, <span class="at">y =</span> exact_elpd)) <span class="sc">+</span></span>
<span id="cb32-7"><a href="#cb32-7" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_abline</span>(<span class="at">color =</span> <span class="st">&quot;gray30&quot;</span>) <span class="sc">+</span></span>
<span id="cb32-8"><a href="#cb32-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="at">size =</span> <span class="dv">2</span>) <span class="sc">+</span></span>
<span id="cb32-9"><a href="#cb32-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">labs</span>(<span class="at">x =</span> <span class="st">&quot;Approximate ELPDs&quot;</span>, <span class="at">y =</span> <span class="st">&quot;Exact ELPDs&quot;</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="60%" style="display: block; margin: auto;" /></p>
</div>
</div>
<div id="conclusion" class="section level2">
<h2>Conclusion</h2>
<p>In this case study we have shown how to do carry out exact and approximate leave-future-out cross-validation for <span class="math inline">\(M\)</span>-step-ahead prediction tasks. For the data and model used in our example, the PSIS-LFO-CV algorithm provides reasonably stable and accurate results despite not requiring us to refit the model nearly as many times. For more details on approximate LFO-CV, we refer to Bürkner et al. (2020).</p>
<p><br /></p>
</div>
<div id="references" class="section level2">
<h2>References</h2>
<p>Bürkner P. C., Gabry J., &amp; Vehtari A. (2020). Approximate leave-future-out cross-validation for Bayesian time series models. <em>Journal of Statistical Computation and Simulation</em>. :10.1080/00949655.2020.1783262. <a href="https://www.tandfonline.com/doi/full/10.1080/00949655.2020.1783262">Online</a>. <a href="https://arxiv.org/abs/1902.06281">arXiv preprint</a>.</p>
<p>Vehtari A., Gelman A., &amp; Gabry J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. <em>Statistics and Computing</em>, 27(5), 1413–1432. :10.1007/s11222-016-9696-4. <a href="https://link.springer.com/article/10.1007/s11222-016-9696-4">Online</a>. <a href="https://arxiv.org/abs/1507.04544">arXiv preprint arXiv:1507.04544</a>.</p>
<p>Vehtari, A., Simpson, D., Gelman, A., Yao, Y., and Gabry, J. (2019). Pareto smoothed importance sampling. <a href="https://arxiv.org/abs/1507.02646">arXiv preprint arXiv:1507.02646</a>.</p>
<p><br /></p>
</div>
<div id="appendix" class="section level2">
<h2>Appendix</h2>
<div id="appendix-session-information" class="section level3">
<h3>Appendix: Session information</h3>
<div class="sourceCode" id="cb33"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb33-1"><a href="#cb33-1" aria-hidden="true" tabindex="-1"></a><span class="fu">sessionInfo</span>()</span></code></pre></div>
<pre><code>R version 4.0.2 (2020-06-22)
Platform: x86_64-apple-darwin17.0 (64-bit)
Running under: macOS Catalina 10.15.7

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRblas.dylib
LAPACK: /Library/Frameworks/R.framework/Versions/4.0/Resources/lib/libRlapack.dylib

locale:
[1] C/en_US.UTF-8/en_US.UTF-8/C/en_US.UTF-8/en_US.UTF-8

attached base packages:
[1] stats     graphics  grDevices utils     datasets  methods   base     

other attached packages:
[1] brms_2.14.4          bayesplot_1.7.2.9000 rstanarm_2.21.1     
[4] Rcpp_1.0.5           loo_2.4.1            rstan_2.21.3        
[7] ggplot2_3.3.2        StanHeaders_2.21.0-6 knitr_1.29          

loaded via a namespace (and not attached):
  [1] TH.data_1.0-10       minqa_1.2.4          colorspace_2.0-0    
  [4] ellipsis_0.3.1       ggridges_0.5.2       rsconnect_0.8.16    
  [7] estimability_1.3     markdown_1.1         base64enc_0.1-3     
 [10] farver_2.0.3         DT_0.14              fansi_0.4.1         
 [13] mvtnorm_1.1-1        bridgesampling_1.0-0 codetools_0.2-16    
 [16] splines_4.0.2        shinythemes_1.1.2    projpred_2.0.2      
 [19] jsonlite_1.7.1       nloptr_1.2.2.2       shiny_1.5.0         
 [22] compiler_4.0.2       emmeans_1.4.8        backports_1.2.0     
 [25] assertthat_0.2.1     Matrix_1.2-18        fastmap_1.0.1       
 [28] cli_2.2.0            later_1.1.0.1        htmltools_0.5.0     
 [31] prettyunits_1.1.1    tools_4.0.2          igraph_1.2.5        
 [34] coda_0.19-3          gtable_0.3.0         glue_1.4.2          
 [37] reshape2_1.4.4       dplyr_1.0.2          V8_3.4.0            
 [40] vctrs_0.3.5          nlme_3.1-148         crosstalk_1.1.0.1   
 [43] xfun_0.15            stringr_1.4.0        ps_1.4.0            
 [46] lme4_1.1-23          mime_0.9             miniUI_0.1.1.1      
 [49] lifecycle_0.2.0      gtools_3.8.2         statmod_1.4.34      
 [52] MASS_7.3-51.6        zoo_1.8-8            scales_1.1.1        
 [55] colourpicker_1.0     promises_1.1.1       Brobdingnag_1.2-6   
 [58] parallel_4.0.2       sandwich_2.5-1       inline_0.3.17       
 [61] shinystan_3.0.0      gamm4_0.2-6          yaml_2.2.1          
 [64] curl_4.3             gridExtra_2.3        stringi_1.4.6       
 [67] dygraphs_1.1.1.6     checkmate_2.0.0      boot_1.3-25         
 [70] pkgbuild_1.1.0       rlang_0.4.9          pkgconfig_2.0.3     
 [73] matrixStats_0.57.0   evaluate_0.14        lattice_0.20-41     
 [76] purrr_0.3.4          rstantools_2.1.1     htmlwidgets_1.5.1   
 [79] labeling_0.4.2       processx_3.4.5       tidyselect_1.1.0    
 [82] plyr_1.8.6           magrittr_2.0.1       R6_2.5.0            
 [85] generics_0.0.2       multcomp_1.4-15      pillar_1.4.7        
 [88] withr_2.3.0          mgcv_1.8-31          xts_0.12-0          
 [91] survival_3.1-12      abind_1.4-5          tibble_3.0.4        
 [94] crayon_1.3.4.9000    rmarkdown_2.3        grid_4.0.2          
 [97] callr_3.5.1          threejs_0.3.3        digest_0.6.27       
[100] xtable_1.8-4         httpuv_1.5.4         RcppParallel_5.0.2  
[103] stats4_4.0.2         munsell_0.5.0        shinyjs_1.1         </code></pre>
</div>
<div id="appendix-licenses" class="section level3">
<h3>Appendix: Licenses</h3>
<ul>
<li>Code © 2018, Paul Bürkner, Jonah Gabry, Aki Vehtari (licensed under BSD-3).</li>
<li>Text © 2018, Paul Bürkner, Jonah Gabry, Aki Vehtari (licensed under CC-BY-NC 4.0).</li>
</ul>
</div>
</div>



<!-- code folding -->


<!-- dynamically load mathjax for compatibility with self-contained -->
<script>
  (function () {
    var script = document.createElement("script");
    script.type = "text/javascript";
    script.src  = "https://mathjax.rstudio.com/latest/MathJax.js?config=TeX-AMS-MML_HTMLorMML";
    document.getElementsByTagName("head")[0].appendChild(script);
  })();
</script>

</body>
</html>