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

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</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">2025-12-22</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>

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<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, 2024) 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, 2024). 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, assuming posterior sample size is 4000 or larger, we recommend to use a threshold of <span class="math inline">\(\tau = 0.7\)</span> (Vehtari et al, 2017, 2024) 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;brms&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;loo&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 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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">linewidth =</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 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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         4.8  1.0
looic       177.3 12.8
------
MCSE of elpd_loo is 0.0.
MCSE and ESS estimates assume independent draws (r_eff=1).

All Pareto k estimates are good (k &lt; 0.7).
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">ndraws</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 -88.64
LFO -92.43</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 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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 -92.98
exact LFO  -92.43</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  0.42
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">ndraws</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 
-404.8864 </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_4sap[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 55</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 -408.49
Exact LFO  -404.89</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 time series models. <em>Journal of Statistical Computation and Simulation</em>, 90(14):2499-2523. :/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. (2024). Pareto smoothed importance sampling. <em>Journal of Machine Learning Research</em>, 25(72):1-58. <a href="https://jmlr.org/papers/v25/19-556.html">PDF</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 4.4.2 (2024-10-31)
Platform: x86_64-apple-darwin20
Running under: macOS Sequoia 15.4.1

Matrix products: default
BLAS:   /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRblas.0.dylib 
LAPACK: /Library/Frameworks/R.framework/Versions/4.4-x86_64/Resources/lib/libRlapack.dylib;  LAPACK version 3.12.0

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

time zone: America/Denver
tzcode source: internal

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

other attached packages:
[1] ggplot2_4.0.0           brms_2.23.1             bayesplot_1.14.0.9000  
[4] rstanarm_2.32.1         Rcpp_1.1.0              loo_2.9.0              
[7] rstan_2.36.0.9000       StanHeaders_2.36.0.9000 knitr_1.50             

loaded via a namespace (and not attached):
  [1] gridExtra_2.3        inline_0.3.19        sandwich_3.1-1      
  [4] rlang_1.1.6          magrittr_2.0.3       multcomp_1.4-26     
  [7] matrixStats_1.5.0    compiler_4.4.2       callr_3.7.6         
 [10] vctrs_0.6.5          reshape2_1.4.4       stringr_1.5.1       
 [13] pkgconfig_2.0.3      fastmap_1.2.0        backports_1.5.0     
 [16] labeling_0.4.3       threejs_0.3.3        promises_1.3.3      
 [19] rmarkdown_2.29       markdown_1.13        ps_1.9.1            
 [22] nloptr_2.1.0         xfun_0.53            cachem_1.1.0        
 [25] jsonlite_2.0.0       later_1.4.3          parallel_4.4.2      
 [28] R6_2.6.1             dygraphs_1.1.1.6     bslib_0.9.0         
 [31] stringi_1.8.7        RColorBrewer_1.1-3   boot_1.3-31         
 [34] jquerylib_0.1.4      estimability_1.5.1   zoo_1.8-14          
 [37] base64enc_0.1-3      httpuv_1.6.16        Matrix_1.7-1        
 [40] splines_4.4.2        igraph_2.1.4         tidyselect_1.2.1    
 [43] abind_1.4-8          yaml_2.3.10          codetools_0.2-20    
 [46] miniUI_0.1.1.1       curl_7.0.0           processx_3.8.6      
 [49] pkgbuild_1.4.8       lattice_0.22-6       tibble_3.3.0        
 [52] plyr_1.8.9           shiny_1.11.1         withr_3.0.2         
 [55] bridgesampling_1.1-2 S7_0.2.0             posterior_1.6.1     
 [58] coda_0.19-4.1        evaluate_1.0.4       survival_3.7-0      
 [61] RcppParallel_5.1.10  xts_0.14.1           pillar_1.11.0       
 [64] tensorA_0.36.2.1     checkmate_2.3.3      DT_0.33             
 [67] stats4_4.4.2         shinyjs_2.1.0        distributional_0.5.0
 [70] generics_0.1.4       rstantools_2.5.0     scales_1.4.0        
 [73] minqa_1.2.7          gtools_3.9.5         xtable_1.8-4        
 [76] glue_1.8.0           emmeans_1.10.2       tools_4.4.2         
 [79] shinystan_2.7.0      lme4_1.1-35.4        colourpicker_1.3.0  
 [82] mvtnorm_1.3-3        grid_4.4.2           QuickJSR_1.2.2      
 [85] crosstalk_1.2.1      nlme_3.1-166         cli_3.6.5           
 [88] Brobdingnag_1.2-9    dplyr_1.1.4          V8_4.4.2            
 [91] gtable_0.3.6         sass_0.4.10          digest_0.6.37       
 [94] TH.data_1.1-2        htmlwidgets_1.6.4    farver_2.1.2        
 [97] htmltools_0.5.8.1    lifecycle_1.0.4      mime_0.13           
[100] shinythemes_1.2.0    MASS_7.3-61         </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>



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