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<title>Leave-one-out cross-validation for non-factorized models</title>

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</head>

<body>




<h1 class="title toc-ignore">Leave-one-out cross-validation for non-factorized models</h1>
<h4 class="author">Aki Vehtari, Paul Bürkner and Jonah Gabry</h4>
<h4 class="date">2025-12-22</h4>


<div id="TOC">
<ul>
<li><a href="#introduction">Introduction</a></li>
<li><a href="#loo-cv-for-multivariate-normal-models">LOO-CV for multivariate normal models</a>
<ul>
<li><a href="#approximate-loo-cv-using-integrated-importance-sampling">Approximate LOO-CV using integrated importance-sampling</a></li>
<li><a href="#exact-loo-cv-with-re-fitting">Exact LOO-CV with re-fitting</a></li>
</ul></li>
<li><a href="#lagged-sar-models">Lagged SAR models</a>
<ul>
<li><a href="#case-study-neighborhood-crime-in-columbus-ohio">Case Study: Neighborhood Crime in Columbus, Ohio</a>
<ul>
<li><a href="#fit-lagged-sar-model">Fit lagged SAR model</a></li>
<li><a href="#approximate-loo-cv">Approximate LOO-CV</a></li>
<li><a href="#exact-loo-cv">Exact LOO-CV</a></li>
</ul></li>
</ul></li>
<li><a href="#working-with-stan-directly">Working with Stan directly</a></li>
<li><a href="#conclusion">Conclusion</a></li>
<li><a href="#references">References</a></li>
</ul>
</div>

<!--
%\VignetteEngine{knitr::rmarkdown}
%\VignetteIndexEntry{Leave-one-out cross-validation for non-factorized models}
-->
<div id="introduction" class="section level1">
<h1>Introduction</h1>
<p>When computing ELPD-based LOO-CV for a Bayesian model we need to compute the log leave-one-out predictive densities <span class="math inline">\(\log{p(y_i | y_{-i})}\)</span> for every response value <span class="math inline">\(y_i, \: i = 1, \ldots, N\)</span>, where <span class="math inline">\(y_{-i}\)</span> denotes all response values except observation <span class="math inline">\(i\)</span>. To obtain <span class="math inline">\(p(y_i | y_{-i})\)</span>, we need to have access to the pointwise likelihood <span class="math inline">\(p(y_i\,|\, y_{-i}, \theta)\)</span> and integrate over the model parameters <span class="math inline">\(\theta\)</span>:</p>
<p><span class="math display">\[
p(y_i\,|\,y_{-i}) =
  \int p(y_i\,|\, y_{-i}, \theta) \, p(\theta\,|\, y_{-i}) \,d \theta
\]</span></p>
<p>Here, <span class="math inline">\(p(\theta\,|\, y_{-i})\)</span> is the leave-one-out posterior distribution for <span class="math inline">\(\theta\)</span>, that is, the posterior distribution for <span class="math inline">\(\theta\)</span> obtained by fitting the model while holding out the <span class="math inline">\(i\)</span>th observation (we will later show how refitting the model to data <span class="math inline">\(y_{-i}\)</span> can be avoided).</p>
<p>If the observation model is formulated directly as the product of the pointwise observation models, we call it a <em>factorized</em> model. In this case, the likelihood is also the product of the pointwise likelihood contributions <span class="math inline">\(p(y_i\,|\, y_{-i}, \theta)\)</span>. To better illustrate possible structures of the observation models, we formally divide <span class="math inline">\(\theta\)</span> into two parts, observation-specific latent variables <span class="math inline">\(f = (f_1, \ldots, f_N)\)</span> and hyperparameters <span class="math inline">\(\psi\)</span>, so that <span class="math inline">\(p(y_i\,|\, y_{-i}, \theta) = p(y_i\,|\, y_{-i}, f_i, \psi)\)</span>. Depending on the model, one of the two parts of <span class="math inline">\(\theta\)</span> may also be empty. In very simple models, such as linear regression models, latent variables are not explicitly presented and response values are conditionally independent given <span class="math inline">\(\psi\)</span>, so that <span class="math inline">\(p(y_i\,|\, y_{-i}, f_i, \psi) = p(y_i \,|\, \psi)\)</span>. The full likelihood can then be written in the familiar form</p>
<p><span class="math display">\[
p(y \,|\, \psi) = \prod_{i=1}^N p(y_i \,|\, \psi),
\]</span></p>
<p>where <span class="math inline">\(y = (y_1, \ldots, y_N)\)</span> denotes the vector of all responses. When the likelihood factorizes this way, the conditional pointwise log-likelihood can be obtained easily by computing <span class="math inline">\(p(y_i\,|\, \psi)\)</span> for each <span class="math inline">\(i\)</span> with computational cost <span class="math inline">\(O(n)\)</span>.</p>
<p>Yet, there are several reasons why a <em>non-factorized</em> observation model may be necessary or preferred. In non-factorized models, the joint likelihood of the response values <span class="math inline">\(p(y \,|\, \theta)\)</span> is not factorized into observation-specific components, but rather given directly as one joint expression. For some models, an analytic factorized formulation is simply not available in which case we speak of a <em>non-factorizable</em> model. Even in models whose observation model can be factorized in principle, it may still be preferable to use a non-factorized form for reasons of efficiency and numerical stability (Bürkner et al. 2020).</p>
<p>Whether a non-factorized model is used by necessity or for efficiency and stability, it comes at the cost of having no direct access to the leave-one-out predictive densities and thus to the overall leave-one-out predictive accuracy. In theory, we can express the observation-specific likelihoods in terms of the joint likelihood via</p>
<p><span class="math display">\[
p(y_i \,|\, y_{i-1}, \theta) = 
  \frac{p(y \,|\, \theta)}{p(y_{-i} \,|\, \theta)} = 
  \frac{p(y \,|\, \theta)}{\int p(y \,|\, \theta) \, d y_i},
\]</span></p>
<p>but the expression on the right-hand side may not always have an analytical solution. Computing <span class="math inline">\(\log p(y_i \,|\, y_{-i}, \theta)\)</span> for non-factorized models is therefore often impossible, or at least inefficient and numerically unstable. However, there is a large class of multivariate normal and Student-<span class="math inline">\(t\)</span> models for which there are efficient analytical solutions available.</p>
<p>More details can be found in our paper about LOO-CV for non-factorized models (Bürkner, Gabry, &amp; Vehtari, 2020), which is available as a preprint on arXiv (<a href="https://arxiv.org/abs/1810.10559" class="uri">https://arxiv.org/abs/1810.10559</a>).</p>
</div>
<div id="loo-cv-for-multivariate-normal-models" class="section level1">
<h1>LOO-CV for multivariate normal models</h1>
<p>In this vignette, we will focus on non-factorized multivariate normal models. Based on results of Sundararajan and Keerthi (2001), Bürkner et al. (2020) show that, for multivariate normal models with coriance matrix <span class="math inline">\(C\)</span>, the LOO predictive mean and standard deviation can be computed as follows:</p>
<p><span class="math display">\[\begin{align}
  \mu_{\tilde{y},-i} &amp;= y_i-\bar{c}_{ii}^{-1} g_i \nonumber \\
  \sigma_{\tilde{y},-i} &amp;= \sqrt{\bar{c}_{ii}^{-1}},
\end{align}\]</span> where <span class="math inline">\(g_i\)</span> and <span class="math inline">\(\bar{c}_{ii}\)</span> are <span class="math display">\[\begin{align}
  g_i &amp;= \left[C^{-1} y\right]_i \nonumber \\
  \bar{c}_{ii} &amp;= \left[C^{-1}\right]_{ii}.
\end{align}\]</span></p>
<p>Using these results, the log predictive density of the <span class="math inline">\(i\)</span>th observation is then computed as</p>
<p><span class="math display">\[
  \log p(y_i \,|\, y_{-i},\theta)
  = - \frac{1}{2}\log(2\pi)
  - \frac{1}{2}\log \sigma^2_{-i}
  - \frac{1}{2}\frac{(y_i-\mu_{-i})^2}{\sigma^2_{-i}}.
\]</span></p>
<p>Expressing this same equation in terms of <span class="math inline">\(g_i\)</span> and <span class="math inline">\(\bar{c}_{ii}\)</span>, the log predictive density becomes:</p>
<p><span class="math display">\[
  \log p(y_i \,|\, y_{-i},\theta)
  = - \frac{1}{2}\log(2\pi)
  + \frac{1}{2}\log \bar{c}_{ii}
  - \frac{1}{2}\frac{g_i^2}{\bar{c}_{ii}}.
\]</span> (Note that Vehtari et al. (2016) has a typo in the corresponding Equation 34.)</p>
<p>From these equations we can now derive a recipe for obtaining the conditional pointwise log-likelihood for <em>all</em> models that can be expressed conditionally in terms of a multivariate normal with invertible covariance matrix <span class="math inline">\(C\)</span>.</p>
<div id="approximate-loo-cv-using-integrated-importance-sampling" class="section level2">
<h2>Approximate LOO-CV using integrated importance-sampling</h2>
<p>The above LOO equations for multivariate normal models are conditional on parameters <span class="math inline">\(\theta\)</span>. Therefore, to obtain the leave-one-out predictive density <span class="math inline">\(p(y_i \,|\, y_{-i})\)</span> we need to integrate over <span class="math inline">\(\theta\)</span>,</p>
<p><span class="math display">\[
p(y_i\,|\,y_{-i}) =
  \int p(y_i\,|\,y_{-i}, \theta) \, p(\theta\,|\,y_{-i}) \,d\theta.
\]</span></p>
<p>Here, <span class="math inline">\(p(\theta\,|\,y_{-i})\)</span> is the leave-one-out posterior distribution for <span class="math inline">\(\theta\)</span>, that is, the posterior distribution for <span class="math inline">\(\theta\)</span> obtained by fitting the model while holding out the <span class="math inline">\(i\)</span>th observation.</p>
<p>To avoid the cost of sampling from <span class="math inline">\(N\)</span> leave-one-out posteriors, it is possible to take the posterior draws <span class="math inline">\(\theta^{(s)}, \, s=1,\ldots,S\)</span>, from the  posterior <span class="math inline">\(p(\theta\,|\,y)\)</span>, and then approximate the above integral using integrated importance sampling (Vehtari et al., 2016, Section 3.6.1):</p>
<p><span class="math display">\[
 p(y_i\,|\,y_{-i}) \approx
   \frac{ \sum_{s=1}^S p(y_i\,|\,y_{-i},\,\theta^{(s)}) \,w_i^{(s)}}{ \sum_{s=1}^S w_i^{(s)}},
\]</span></p>
<p>where <span class="math inline">\(w_i^{(s)}\)</span> are importance weights. First we compute the raw importance ratios</p>
<p><span class="math display">\[
  r_i^{(s)} \propto \frac{1}{p(y_i \,|\, y_{-i}, \,\theta^{(s)})},
\]</span></p>
<p>and then stabilize them using Pareto smoothed importance sampling (PSIS, Vehtari et al, 2019) to obtain the weights <span class="math inline">\(w_i^{(s)}\)</span>. The resulting approximation is referred to as PSIS-LOO (Vehtari et al, 2017).</p>
</div>
<div id="exact-loo-cv-with-re-fitting" class="section level2">
<h2>Exact LOO-CV with re-fitting</h2>
<p>In order to validate the approximate LOO procedure, and also in order to allow exact computations to be made for a small number of leave-one-out folds for which the Pareto <span class="math inline">\(k\)</span> diagnostic (Vehtari et al, 2024) indicates an unstable approximation, we need to consider how we might to do <em>exact</em> leave-one-out CV for a non-factorized model. In the case of a Gaussian process that has the marginalization property, we could just drop the one row and column of <span class="math inline">\(C\)</span> corresponding to the held out out observation. This does not hold in general for multivariate normal models, however, and to keep the original prior we may need to maintain the full covariance matrix <span class="math inline">\(C\)</span> even when one of the observations is left out.</p>
<p>The solution is to model <span class="math inline">\(y_i\)</span> as a missing observation and estimate it along with all of the other model parameters. For a conditional multivariate normal model, <span class="math inline">\(\log p(y_i\,|\,y_{-i})\)</span> can be computed as follows. First, we model <span class="math inline">\(y_i\)</span> as missing and denote the corresponding parameter <span class="math inline">\(y_i^{\mathrm{mis}}\)</span>. Then, we define</p>
<p><span class="math display">\[
y_{\mathrm{mis}(i)} = (y_1, \ldots, y_{i-1}, y_i^{\mathrm{mis}}, y_{i+1}, \ldots, y_N).
\]</span> to be the same as the full set of observations <span class="math inline">\(y\)</span>, except replacing <span class="math inline">\(y_i\)</span> with the parameter <span class="math inline">\(y_i^{\mathrm{mis}}\)</span>.</p>
<p>Second, we compute the LOO predictive mean and standard deviations as above, but replace <span class="math inline">\(y\)</span> with <span class="math inline">\(y_{\mathrm{mis}(i)}\)</span> in the computation of <span class="math inline">\(\mu_{\tilde{y},-i}\)</span>:</p>
<p><span class="math display">\[
\mu_{\tilde{y},-i} = y_{{\mathrm{mis}}(i)}-\bar{c}_{ii}^{-1}g_i,
\]</span></p>
<p>where in this case we have</p>
<p><span class="math display">\[
g_i = \left[ C^{-1} y_{\mathrm{mis}(i)} \right]_i.
\]</span></p>
<p>The conditional log predictive density is then computed with the above <span class="math inline">\(\mu_{\tilde{y},-i}\)</span> and the left out observation <span class="math inline">\(y_i\)</span>:</p>
<p><span class="math display">\[
  \log p(y_i\,|\,y_{-i},\theta)
  = - \frac{1}{2}\log(2\pi)
  - \frac{1}{2}\log \sigma^2_{\tilde{y},-i}
  - \frac{1}{2}\frac{(y_i-\mu_{\tilde{y},-i})^2}{\sigma^2_{\tilde{y},-i}}.
\]</span></p>
<p>Finally, the leave-one-out predictive distribution can then be estimated as</p>
<p><span class="math display">\[
 p(y_i\,|\,y_{-i}) \approx \sum_{s=1}^S p(y_i\,|\,y_{-i}, \theta_{-i}^{(s)}),
\]</span></p>
<p>where <span class="math inline">\(\theta_{-i}^{(s)}\)</span> are draws from the posterior distribution <span class="math inline">\(p(\theta\,|\,y_{\mathrm{mis}(i)})\)</span>.</p>
</div>
</div>
<div id="lagged-sar-models" class="section level1">
<h1>Lagged SAR models</h1>
<p>A common non-factorized multivariate normal model is the simultaneously autoregressive (SAR) model, which is frequently used for spatially correlated data. The lagged SAR model is defined as</p>
<p><span class="math display">\[
y = \rho Wy + \eta + \epsilon
\]</span> or equivalently <span class="math display">\[
(I - \rho W)y = \eta + \epsilon,
\]</span> where <span class="math inline">\(\rho\)</span> is the spatial correlation parameter and <span class="math inline">\(W\)</span> is a user-defined weight matrix. The matrix <span class="math inline">\(W\)</span> has entries <span class="math inline">\(w_{ii} = 0\)</span> along the diagonal and the off-diagonal entries <span class="math inline">\(w_{ij}\)</span> are larger when areas <span class="math inline">\(i\)</span> and <span class="math inline">\(j\)</span> are closer to each other. In a linear model, the predictor term <span class="math inline">\(\eta\)</span> is given by <span class="math inline">\(\eta = X \beta\)</span> with design matrix <span class="math inline">\(X\)</span> and regression coefficients <span class="math inline">\(\beta\)</span>. However, since the above equation holds for arbitrary <span class="math inline">\(\eta\)</span>, these results are not restricted to linear models.</p>
<p>If we have <span class="math inline">\(\epsilon \sim {\mathrm N}(0, \,\sigma^2 I)\)</span>, it follows that <span class="math display">\[
(I - \rho W)y \sim {\mathrm N}(\eta, \sigma^2 I),
\]</span> which corresponds to the following log PDF coded in <strong>Stan</strong>:</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="sc">/</span><span class="er">**</span> </span>
<span id="cb1-2"><a href="#cb1-2" aria-hidden="true" tabindex="-1"></a> <span class="er">*</span> Normal log<span class="sc">-</span>pdf <span class="cf">for</span> spatially lagged responses</span>
<span id="cb1-3"><a href="#cb1-3" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> </span>
<span id="cb1-4"><a href="#cb1-4" aria-hidden="true" tabindex="-1"></a> <span class="er">*</span> <span class="er">@</span>param y Vector of response values.</span>
<span id="cb1-5"><a href="#cb1-5" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param mu Mean parameter vector.</span>
<span id="cb1-6"><a href="#cb1-6" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param sigma Positive scalar residual standard deviation.</span>
<span id="cb1-7"><a href="#cb1-7" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param rho Positive scalar autoregressive parameter.</span>
<span id="cb1-8"><a href="#cb1-8" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param W Spatial weight matrix.</span>
<span id="cb1-9"><a href="#cb1-9" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span></span>
<span id="cb1-10"><a href="#cb1-10" aria-hidden="true" tabindex="-1"></a> <span class="er">*</span> <span class="er">@</span>return A scalar to be added to the log posterior.</span>
<span id="cb1-11"><a href="#cb1-11" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span><span class="er">/</span></span>
<span id="cb1-12"><a href="#cb1-12" aria-hidden="true" tabindex="-1"></a>real <span class="fu">normal_lagsar_lpdf</span>(vector y, vector mu, real sigma, </span>
<span id="cb1-13"><a href="#cb1-13" aria-hidden="true" tabindex="-1"></a>                        real rho, matrix W) {</span>
<span id="cb1-14"><a href="#cb1-14" aria-hidden="true" tabindex="-1"></a>  int N <span class="ot">=</span> <span class="fu">rows</span>(y);</span>
<span id="cb1-15"><a href="#cb1-15" aria-hidden="true" tabindex="-1"></a>  real inv_sigma2 <span class="ot">=</span> <span class="dv">1</span> <span class="sc">/</span> <span class="fu">square</span>(sigma);</span>
<span id="cb1-16"><a href="#cb1-16" aria-hidden="true" tabindex="-1"></a>  matrix[N, N] W_tilde <span class="ot">=</span> <span class="sc">-</span>rho <span class="sc">*</span> W;</span>
<span id="cb1-17"><a href="#cb1-17" aria-hidden="true" tabindex="-1"></a>  vector[N] half_pred;</span>
<span id="cb1-18"><a href="#cb1-18" aria-hidden="true" tabindex="-1"></a>  </span>
<span id="cb1-19"><a href="#cb1-19" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> (n <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>N) W_tilde[n,n] <span class="sc">+</span><span class="er">=</span> <span class="dv">1</span>;</span>
<span id="cb1-20"><a href="#cb1-20" aria-hidden="true" tabindex="-1"></a>  </span>
<span id="cb1-21"><a href="#cb1-21" aria-hidden="true" tabindex="-1"></a>  half_pred <span class="ot">=</span> W_tilde <span class="sc">*</span> (y <span class="sc">-</span> <span class="fu">mdivide_left</span>(W_tilde, mu));</span>
<span id="cb1-22"><a href="#cb1-22" aria-hidden="true" tabindex="-1"></a>  </span>
<span id="cb1-23"><a href="#cb1-23" aria-hidden="true" tabindex="-1"></a>  return <span class="fl">0.5</span> <span class="sc">*</span> <span class="fu">log_determinant</span>(<span class="fu">crossprod</span>(W_tilde) <span class="sc">*</span> inv_sigma2) <span class="sc">-</span></span>
<span id="cb1-24"><a href="#cb1-24" aria-hidden="true" tabindex="-1"></a>         <span class="fl">0.5</span> <span class="sc">*</span> <span class="fu">dot_self</span>(half_pred) <span class="sc">*</span> inv_sigma2;</span>
<span id="cb1-25"><a href="#cb1-25" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<p>For the purpose of computing LOO-CV, it makes sense to rewrite the SAR model in slightly different form. Conditional on <span class="math inline">\(\rho\)</span>, <span class="math inline">\(\eta\)</span>, and <span class="math inline">\(\sigma\)</span>, if we write</p>
<p><span class="math display">\[\begin{align}
y-(I-\rho W)^{-1}\eta &amp;\sim {\mathrm N}(0, \sigma^2(I-\rho W)^{-1}(I-\rho W)^{-T}),
\end{align}\]</span> or more compactly, with <span class="math inline">\(\widetilde{W}=(I-\rho W)\)</span>, <span class="math display">\[\begin{align}
y-\widetilde{W}^{-1}\eta &amp;\sim {\mathrm N}(0, \sigma^2(\widetilde{W}^{T}\widetilde{W})^{-1}),
\end{align}\]</span></p>
<p>then this has the same form as the zero mean Gaussian process from above. Accordingly, we can compute the leave-one-out predictive densities with the equations from Sundararajan and Keerthi (2001), replacing <span class="math inline">\(y\)</span> with <span class="math inline">\((y-\widetilde{W}^{-1}\eta)\)</span> and taking the covariance matrix <span class="math inline">\(C\)</span> to be <span class="math inline">\(\sigma^2(\widetilde{W}^{T}\widetilde{W})^{-1}\)</span>.</p>
<div id="case-study-neighborhood-crime-in-columbus-ohio" class="section level2">
<h2>Case Study: Neighborhood Crime in Columbus, Ohio</h2>
<p>In order to demonstrate how to carry out the computations implied by these equations, we will first fit a lagged SAR model to data on crime in 49 different neighborhoods of Columbus, Ohio during the year 1980. The data was originally described in Aneslin (1988) and ships with the <strong>spdep</strong> R package.</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="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;loo&quot;</span>)</span>
<span id="cb2-2"><a href="#cb2-2" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;brms&quot;</span>)</span>
<span id="cb2-3"><a href="#cb2-3" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;bayesplot&quot;</span>)</span>
<span id="cb2-4"><a href="#cb2-4" aria-hidden="true" tabindex="-1"></a><span class="fu">library</span>(<span class="st">&quot;ggplot2&quot;</span>)</span>
<span id="cb2-5"><a href="#cb2-5" aria-hidden="true" tabindex="-1"></a><span class="fu">color_scheme_set</span>(<span class="st">&quot;brightblue&quot;</span>)</span>
<span id="cb2-6"><a href="#cb2-6" aria-hidden="true" tabindex="-1"></a><span class="fu">theme_set</span>(<span class="fu">theme_default</span>())</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>
<span id="cb2-9"><a href="#cb2-9" aria-hidden="true" tabindex="-1"></a>SEED <span class="ot">&lt;-</span> <span class="dv">10001</span> </span>
<span id="cb2-10"><a href="#cb2-10" aria-hidden="true" tabindex="-1"></a><span class="fu">set.seed</span>(SEED) <span class="co"># only sets seed for R (seed for Stan set later)</span></span>
<span id="cb2-11"><a href="#cb2-11" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb2-12"><a href="#cb2-12" aria-hidden="true" tabindex="-1"></a><span class="co"># loads COL.OLD data frame and COL.nb neighbor list</span></span>
<span id="cb2-13"><a href="#cb2-13" aria-hidden="true" tabindex="-1"></a><span class="fu">data</span>(oldcol, <span class="at">package =</span> <span class="st">&quot;spdep&quot;</span>) </span></code></pre></div>
<p>The three variables in the data set relevant to this example are:</p>
<ul>
<li><code>CRIME</code>: the number of residential burglaries and vehicle thefts per thousand households in the neighbood</li>
<li><code>HOVAL</code>: housing value in units of $1000 USD</li>
<li><code>INC</code>: household income in units of $1000 USD</li>
</ul>
<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><span class="fu">str</span>(COL.OLD[, <span class="fu">c</span>(<span class="st">&quot;CRIME&quot;</span>, <span class="st">&quot;HOVAL&quot;</span>, <span class="st">&quot;INC&quot;</span>)])</span></code></pre></div>
<pre><code>&#39;data.frame&#39;:   49 obs. of  3 variables:
 $ CRIME: num  18.802 32.388 38.426 0.178 15.726 ...
 $ HOVAL: num  44.6 33.2 37.1 75 80.5 ...
 $ INC  : num  21.23 4.48 11.34 8.44 19.53 ...</code></pre>
<p>We will also use the object <code>COL.nb</code>, which is a list containing information about which neighborhoods border each other. From this list we will be able to construct the weight matrix to used to help account for the spatial dependency among the observations.</p>
<div id="fit-lagged-sar-model" class="section level3">
<h3>Fit lagged SAR model</h3>
<p>A model predicting <code>CRIME</code> from <code>INC</code> and <code>HOVAL</code>, while accounting for the spatial dependency via an SAR structure, can be specified in <strong>brms</strong> as follows.</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>fit <span class="ot">&lt;-</span> <span class="fu">brm</span>(</span>
<span id="cb5-2"><a href="#cb5-2" aria-hidden="true" tabindex="-1"></a>  CRIME <span class="sc">~</span> INC <span class="sc">+</span> HOVAL <span class="sc">+</span> <span class="fu">sar</span>(COL.nb, <span class="at">type =</span> <span class="st">&quot;lag&quot;</span>), </span>
<span id="cb5-3"><a href="#cb5-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">data =</span> COL.OLD,</span>
<span id="cb5-4"><a href="#cb5-4" aria-hidden="true" tabindex="-1"></a>  <span class="at">data2 =</span> <span class="fu">list</span>(<span class="at">COL.nb =</span> COL.nb),</span>
<span id="cb5-5"><a href="#cb5-5" aria-hidden="true" tabindex="-1"></a>  <span class="at">chains =</span> <span class="dv">4</span>,</span>
<span id="cb5-6"><a href="#cb5-6" aria-hidden="true" tabindex="-1"></a>  <span class="at">seed =</span> SEED</span>
<span id="cb5-7"><a href="#cb5-7" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>The code above fits the model in <strong>Stan</strong> using a log PDF equivalent to the <code>normal_lagsar_lpdf</code> function we defined above. In the summary output below we see that both higher income and higher housing value predict lower crime rates in the neighborhood. Moreover, there seems to be substantial spatial correlation between adjacent neighborhoods, as indicated by the posterior distribution of the <code>lagsar</code> parameter.</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>lagsar <span class="ot">&lt;-</span> <span class="fu">as.matrix</span>(fit, <span class="at">pars =</span> <span class="st">&quot;lagsar&quot;</span>)</span>
<span id="cb6-2"><a href="#cb6-2" aria-hidden="true" tabindex="-1"></a>estimates <span class="ot">&lt;-</span> <span class="fu">quantile</span>(lagsar, <span class="at">probs =</span> <span class="fu">c</span>(<span class="fl">0.25</span>, <span class="fl">0.5</span>, <span class="fl">0.75</span>))</span>
<span id="cb6-3"><a href="#cb6-3" aria-hidden="true" tabindex="-1"></a><span class="fu">mcmc_hist</span>(lagsar) <span class="sc">+</span> </span>
<span id="cb6-4"><a href="#cb6-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">vline_at</span>(estimates, <span class="at">linetype =</span> <span class="dv">2</span>, <span class="at">size =</span> <span class="dv">1</span>) <span class="sc">+</span></span>
<span id="cb6-5"><a href="#cb6-5" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ggtitle</span>(<span class="st">&quot;lagsar: posterior median and 50% central interval&quot;</span>)</span></code></pre></div>
<p><img 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" width="60%" style="display: block; margin: auto;" /></p>
</div>
<div id="approximate-loo-cv" class="section level3">
<h3>Approximate LOO-CV</h3>
<p>After fitting the model, the next step is to compute the pointwise log-likelihood values needed for approximate LOO-CV. To do this we will use the recipe laid out in the previous sections.</p>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1" aria-hidden="true" tabindex="-1"></a>posterior <span class="ot">&lt;-</span> <span class="fu">as.data.frame</span>(fit)</span>
<span id="cb7-2"><a href="#cb7-2" aria-hidden="true" tabindex="-1"></a>y <span class="ot">&lt;-</span> fit<span class="sc">$</span>data<span class="sc">$</span>CRIME</span>
<span id="cb7-3"><a href="#cb7-3" aria-hidden="true" tabindex="-1"></a>N <span class="ot">&lt;-</span> <span class="fu">length</span>(y)</span>
<span id="cb7-4"><a href="#cb7-4" aria-hidden="true" tabindex="-1"></a>S <span class="ot">&lt;-</span> <span class="fu">nrow</span>(posterior)</span>
<span id="cb7-5"><a href="#cb7-5" aria-hidden="true" tabindex="-1"></a>loglik <span class="ot">&lt;-</span> yloo <span class="ot">&lt;-</span> sdloo <span class="ot">&lt;-</span> <span class="fu">matrix</span>(<span class="at">nrow =</span> S, <span class="at">ncol =</span> N)</span>
<span id="cb7-6"><a href="#cb7-6" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-7"><a href="#cb7-7" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (s <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>S) {</span>
<span id="cb7-8"><a href="#cb7-8" aria-hidden="true" tabindex="-1"></a>  p <span class="ot">&lt;-</span> posterior[s, ]</span>
<span id="cb7-9"><a href="#cb7-9" aria-hidden="true" tabindex="-1"></a>  eta <span class="ot">&lt;-</span> p<span class="sc">$</span>b_Intercept <span class="sc">+</span> p<span class="sc">$</span>b_INC <span class="sc">*</span> fit<span class="sc">$</span>data<span class="sc">$</span>INC <span class="sc">+</span> p<span class="sc">$</span>b_HOVAL <span class="sc">*</span> fit<span class="sc">$</span>data<span class="sc">$</span>HOVAL</span>
<span id="cb7-10"><a href="#cb7-10" aria-hidden="true" tabindex="-1"></a>  W_tilde <span class="ot">&lt;-</span> <span class="fu">diag</span>(N) <span class="sc">-</span> p<span class="sc">$</span>lagsar <span class="sc">*</span> spdep<span class="sc">::</span><span class="fu">nb2mat</span>(COL.nb)</span>
<span id="cb7-11"><a href="#cb7-11" aria-hidden="true" tabindex="-1"></a>  Cinv <span class="ot">&lt;-</span> <span class="fu">t</span>(W_tilde) <span class="sc">%*%</span> W_tilde <span class="sc">/</span> p<span class="sc">$</span>sigma<span class="sc">^</span><span class="dv">2</span></span>
<span id="cb7-12"><a href="#cb7-12" aria-hidden="true" tabindex="-1"></a>  g <span class="ot">&lt;-</span> Cinv <span class="sc">%*%</span> (y <span class="sc">-</span> <span class="fu">solve</span>(W_tilde, eta))</span>
<span id="cb7-13"><a href="#cb7-13" aria-hidden="true" tabindex="-1"></a>  cbar <span class="ot">&lt;-</span> <span class="fu">diag</span>(Cinv)</span>
<span id="cb7-14"><a href="#cb7-14" aria-hidden="true" tabindex="-1"></a>  yloo[s, ] <span class="ot">&lt;-</span> y <span class="sc">-</span> g <span class="sc">/</span> cbar</span>
<span id="cb7-15"><a href="#cb7-15" aria-hidden="true" tabindex="-1"></a>  sdloo[s, ] <span class="ot">&lt;-</span> <span class="fu">sqrt</span>(<span class="dv">1</span> <span class="sc">/</span> cbar)</span>
<span id="cb7-16"><a href="#cb7-16" aria-hidden="true" tabindex="-1"></a>  loglik[s, ] <span class="ot">&lt;-</span> <span class="fu">dnorm</span>(y, yloo[s, ], sdloo[s, ], <span class="at">log =</span> <span class="cn">TRUE</span>)</span>
<span id="cb7-17"><a href="#cb7-17" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb7-18"><a href="#cb7-18" aria-hidden="true" tabindex="-1"></a></span>
<span id="cb7-19"><a href="#cb7-19" aria-hidden="true" tabindex="-1"></a><span class="co"># use loo for psis smoothing</span></span>
<span id="cb7-20"><a href="#cb7-20" aria-hidden="true" tabindex="-1"></a>log_ratios <span class="ot">&lt;-</span> <span class="sc">-</span>loglik</span>
<span id="cb7-21"><a href="#cb7-21" aria-hidden="true" tabindex="-1"></a>psis_result <span class="ot">&lt;-</span> <span class="fu">psis</span>(log_ratios)</span></code></pre></div>
<p>The quality of the PSIS-LOO approximation can be investigated graphically by plotting the Pareto-k estimate for each observation. The approximation is robust up to values of <span class="math inline">\(0.7\)</span> (Vehtari et al, 2017, 2024). In the plot below, we see that the fourth observation is problematic and so may reduce the accuracy of the LOO-CV approximation.</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><span class="fu">plot</span>(psis_result, <span class="at">label_points =</span> <span class="cn">TRUE</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 check that the conditional leave-one-out predictive distribution equations work correctly, for instance, using the last posterior draw:</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>yloo_sub <span class="ot">&lt;-</span> yloo[S, ]</span>
<span id="cb9-2"><a href="#cb9-2" aria-hidden="true" tabindex="-1"></a>sdloo_sub <span class="ot">&lt;-</span> sdloo[S, ]</span>
<span id="cb9-3"><a href="#cb9-3" aria-hidden="true" tabindex="-1"></a>df <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(</span>
<span id="cb9-4"><a href="#cb9-4" aria-hidden="true" tabindex="-1"></a>  <span class="at">y =</span> y, </span>
<span id="cb9-5"><a href="#cb9-5" aria-hidden="true" tabindex="-1"></a>  <span class="at">yloo =</span> yloo_sub,</span>
<span id="cb9-6"><a href="#cb9-6" aria-hidden="true" tabindex="-1"></a>  <span class="at">ymin =</span> yloo_sub <span class="sc">-</span> sdloo_sub <span class="sc">*</span> <span class="dv">2</span>,</span>
<span id="cb9-7"><a href="#cb9-7" aria-hidden="true" tabindex="-1"></a>  <span class="at">ymax =</span> yloo_sub <span class="sc">+</span> sdloo_sub <span class="sc">*</span> <span class="dv">2</span></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="fu">ggplot</span>(<span class="at">data=</span>df, <span class="fu">aes</span>(<span class="at">x =</span> y, <span class="at">y =</span> yloo, <span class="at">ymin =</span> ymin, <span class="at">ymax =</span> ymax)) <span class="sc">+</span></span>
<span id="cb9-10"><a href="#cb9-10" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_errorbar</span>(</span>
<span id="cb9-11"><a href="#cb9-11" aria-hidden="true" tabindex="-1"></a>    <span class="at">width =</span> <span class="dv">1</span>, </span>
<span id="cb9-12"><a href="#cb9-12" aria-hidden="true" tabindex="-1"></a>    <span class="at">color =</span> <span class="st">&quot;skyblue3&quot;</span>, </span>
<span id="cb9-13"><a href="#cb9-13" aria-hidden="true" tabindex="-1"></a>    <span class="at">position =</span> <span class="fu">position_jitter</span>(<span class="at">width =</span> <span class="fl">0.25</span>)</span>
<span id="cb9-14"><a href="#cb9-14" aria-hidden="true" tabindex="-1"></a>  ) <span class="sc">+</span></span>
<span id="cb9-15"><a href="#cb9-15" 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="at">size =</span> <span class="fl">1.2</span>) <span class="sc">+</span></span>
<span id="cb9-16"><a href="#cb9-16" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>()</span></code></pre></div>
<p><img 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kqJirs5UR6TAAmQAAmQAAkgJzcPR89fsksiItgP4uubQgKlicDp06eVh5jFixcrP+x65t6iRQuMGDECrVu31lPcbhkq7nbxMJMESIAESIAESh+BlIwcjJu3w+7Ee91YBcNuqWm3DDNJwFMI7N+/HzNnzsTvv/+OvLw8h9OSFfWOHTti5MiRqFevnsPyegtQcddLiuVIgARIgARIgARIgARKFYEtW7Yol46bNm3SNW8/Pz/06NFDrbCLLbuzhYq7s4myPRIgARIgARJwcwKhAT7496DmplmMnbNdHfe8oTJuqRuljssG+ZnyeUACnkQgNzdX+V6fMmUKDh48qGtqoaGhuPPOOzF48GBERBgCW+mqWMhCVNwLCYzFSYAESIAESMDTCfh4e6Gm5iHFUiJD/a2mW5bjOQm4I4HMzEwsW7ZMrbCfPXtW1xSio6OVst6vXz8EBgbqqnM9hai4Xw891iUBEiABEvBIAtna5sy1++Pszq1KuSDUrRBmtwwzSYAEXJ9AcnIy5s+fj59++gmJiYm6BlyrVi3lIaZbt27w8Sk+dbr4etKFgYVIgARIgARIoOQJZGbn4rs/7D8i796sEhX3kr9UHAEJXDOBc+fOKWV9wYIFyMjI0NVO06ZNlf16u3btdJV3diEq7s4myvZIgARIgARIgARIgARclsCRI0eUh5hff/0VYs/uSMqUKYO2bdti1KhRaNy4saPiRZpPxb1I8bJxEiABEiABdyQQEuCLSQ9fXVF7+Lv1mm/zyxjcpjruuKGKmpK3Vxl3nBrHTAKllsDOnTuV/fr69et1MRATmK5duyqXjtWqVdNVp6gLUXEvasJsnwRIgARIwC0J+PlcjWxoVNG9Nd/M5uluOTEOmgRKEYHLly9j3bp1EA8xe/bs0TXzoKAg9OnTB0OHDkX58uV11SmuQlTci4s0+yEBEiABEiABEiABEigWAtnZ2VixYgWmTp2KkydP6uozMjISAwcOxIABAxAcHKyrTnEXouJe3MTZHwmQAAmQAAmQAAmQQJEQSE1NxaJFi5QN+8WLF3X1UbVqVeUhpmfPnvD19dVVp6QKUXEvKfLslwRIgARIgARIgARIwCkELly4gHnz5mHu3LlIS0vT1WajRo2UOUynTp0gG1DdQai4u8NV4hhJgARIgARIgARIgAQKEDhx4gRmzZqFX375BWIeo0dat26tXDq2aNFCT3GXKkPF3aUuBwdDAiRAAiRAAiRAAiTgiMDu3buVOczq1ashG1Adibe3Nzp37qw8xNSuXdtRcZfNp+LuspeGAyMBEiABEiABEiABEjAnsHHjRkyfPh1bt241T7Z5HBAQALFdHz58OGJiYmyWc5cMKu7ucqU4ThIgARIgARIgARIohQRycnKwatUq5SFGgifpkfDwcPTv3x+DBg1CWFiYnipuUYaKu1tcJg6SBEiABEjAWQQOnE3GLztO2W2ub4uqqBkdarcMM0mABIqWQHp6OpYuXapW2OPi4nR1VrFiRQwePBh9+/aFv7+/rjruVIiKuztdLY6VBEiABEjgugnEp2Zi0xH7buI6NHD/R+rXDYoNkEAJEUhISMD8+fPx008/ISUlRdco6tatqzzEdOnSBWLP7qlCxd1TryznRQIkQAIkYJVAWKAvGlQqq/LSMnNw4mKqOq4RFYIAX8MPfkiAa/tytjoxJpKAmxM4c+aMUtYXLlyIrKwsXbNp3ry58hBz88036yrv7oWouLv7FeT4SYAESIAECkWgUeVwyEvkwNkkvPXzTnX8YKe6EOWdQgIkULwEDhw4oDzErFy5Enl5eQ47F5/rHTp0wKhRo1C/fn2H5T2pABV3T7qanAsJkAAJkAAJkAAJuAmBbdu2Ydq0aRBPMXrEz88P3bt3VyvslStX1lPF48pQcfe4S8oJkQAJkAAJkEDpJZCbdxmxielWAaw7EIc8zee3n48XAv0MZlEXL2WqsrFJ6dh2LB431ihntS4TnUNAVtT//PNPTJkyBfv379fVaGhoqNpsOmTIEEREROiq46mFqLh76pXlvEiABEiABEigFBJITs/CizO3FHrmp+LT8Of+c1TcC01OX4XMzEwsX75crbCLLbseiYqKUu4c77zzTgQFBempUqDMqfhU/H34QoF084S29aJRoWygeZLLHlNxd9lLw4GRAAmQAAmQAAkUBYEyWqOWsTYlzVuznaY4l4B4hVmwYAFmzZqFxMREXY3XqFFDeYgRsxgfn+tTVWXz+bxNJ+z2W0tz/UrF3S4iZpIACZAACZAACZCA8wmEah6BXurbxNTwfxfuUse3N6mIlrUi1XFUaAD+u2gXzidnoFywH+JTs3BTzUg80a2BqR4Pro+A+F2fM2eOcuso/tj1SOPGjZX9evv27SEbUJ0hvl5eCPY3KP9iRpWRnauaDdQ8SHl5GfrwufLujP6Kuo3ru40p6tGxfRIgARIgARKwQ2DXqQT8c9L+Kl7v5lUQqrmAdJbkaT/+2bn2PV/4ajbUXk5SPJw17tLSjo+3F5pUKWgHXTE80Gp6aeFSXPM8evSo8hAjZjG5uQYl2VHfbdu2xciRI9G0aVNHRQud36p2echLZN+ZJLw93+BFamz/ZqhW3v28SFFxL/RHgBVIgARIgARchcDB2BQs2XbK7nA6NYxxquK+8fB5fL7C/qa6Mb0ao3l1bnK0e2E8IHPhlpPYr7kUPXbhkpqN2Mm/v9iwwi8J3tpK7rM9G3vATB1PYdeuXSrCqWw81SNiAiPBkkRhF9MYij4CVNz1cWIpEiABEnBrApu0zVkntU1atkQeS/dvWc1WtsumB2meQcqF+KnxZWqPwFMzDSt8EcG+pkft3tqjcgoJFAWBY+cvYceJBFPTqVpAL/NzdzLBME2iEAeXNQ89f/31l/IQI4q7HgkMDESfPn2UDbtsPqUUjgAV98LxYmkSIAEScEsC4lXhr0PnbY5dLD3dUXHv3qwy5CWyem8svll1UB1/MLwV/K9EQVUJTvxTOyYMD3Wuq1o8q7kdXHxlxX9Aq2qIDPFX6VUjg53YI5tyVQLVo4KVzfRxbcU9KT1bDdNPM9UxRub18XaOnbarzT87OxsSLGnq1Kk4fvy4ruGVK1cOAwYMwMCBAxES4n4mKromWQyFqLgXA2R2QQIkQAIlTUCU2KArG7SycnKRk3sZolIEXknjmrT+KxQdFoDosAqqgtjMGhV32dxY3Q1tZvXPnCUtCfS7SXtKdRPw6fK9JpeD4dpm1xf6XN0ca1nHnc/T0tKwaNEiZcN+4cIFXVOpUqUK7rrrLvTq1QsSQIlyfQSouF8fP9YmARIgAbcg8KC2QiwvkRnrj2DJ9tOI0ExMPr27jVuMn4MkARIoOQLx8fGYO3cu5s2bh0uXDPb8jkbToEEDDBs2DJ06ddK8t3BpwBEvvflU3PWSYjkSIAESIAESIAESKEUETp48idmzZ2PJkiUQ8xg90rJlS+XSUd4pzidAxd35TNkiCZAACZAACdgl8PGyPThxwfZm4SjNHOflvs53jWd3UMwkgSsE9u7dq8xhVq1aBdmA6ki8vb3RsWNHjBo1CnXq1HFUnPnXQYCK+3XAY1USIAESIAESuBYC8ZcyEacF/7El9AFviwzTi5LAxeP78Mwzk7F582Zd3fj7+6Nnz57KJKZixYq66rDQ9RGg4n59/FibBEiABEiABApN4Ja6UahbIUzV23YsXinxEsHTGCgmzIkBowo9OFYoVQRycnJwYvcmnPl9EY4nxuqae1hYGPr374/BgwejbNmyuuqwkHMIUHF3Dke2QgIkQAIkQAK6CdxxQxVT2YsphtX3GC2y56j2tU3pPCCBoiSQkZGBpUuXYsaMGYiN1aewV6hQQSnrffv2RUBAQFEOj23bIEDF3QaYkk6evOYQ5FGqLamgfcEPb1vLVjbTSYAESIAESIAESKAAgaSkJMyfP19tOk1OTi6Qby2hdu3aKmDS7bffDol4Sik5AqRfcuzt9rz7VCIksIctqRXN4AW22DCdBEiABEiABEggPwFZVRcPMQsXLkRmpu2FQfNaN9xwA4YPH462bduaJ/O4BAlQcS9B+Pa6rhMTinLBhgh8ElI5NSsHoQG+qHYlGl/FiEB71ZlHAiRAAiRAAiRAArh49iTefnsGfvvtN+Tm5jokUqZMGbRv3155iGnYsKHD8ixQvASouBcvb929PdKlvqnsfxbsxJ7TSahXMQzP3NHIlM4DEiABEiAB1yEwde0RU3Ra81EFa9FpH76tnnkSj0mgyAmknD2CuE0rMO/Mfn19eXmjUsPW+ODV0ahataq+OixV7ATcVnE/d+4c9uzZg4sXL6J169aoVk0LO3xF8vLyID5Iz549CwkAEB4ebsziOwmQAAmQQCEI7DyRgF2nEuzWkLDvopyWdtl7JskqgrL0EGOVi7snJqRm4lJGjppGWqbhXU5ycvNw8qLBR3+VckGQFeziksuX85B+ei/eefV7HD9yUFe3wcHBqNKsPVJjWqBBzcpU2nVRK7lCbvdNm5aWhkmTJmH79u0YPXq0cvhvHkpXFPZx48Zh4MCBKgjAG2+8gUaNGuGRRx4pOcrsmQRIgATclMD+s0lYuv203dF3a1qJirtGSPYeXdScCiSlZSPA11udC7gQf1+7/JjpngTm/n0cf+w9V2Dw8alZeHnWVpU+6eF28PMpesU9KysLq1Ysw5nFU5Bz6WKBMVlLKF++PAYNGqTcOn639jg2HrpgrRjTXIyAWynuBw8exPPPP4+mTZviiy++gK9v/i/DCxcu4OWXX0a/fv2UuyJhXb16daXEV65cGb1793Yx/BwOCZAACbg2AVlJjwwx7LfJyM5F6pWVRfE5blxJZLAgwzV8oFNdLNtxGn/uj0NFzfPXK/2aufbF5ejcnsClS5fUZtNZs2YhPj5e13xELxoyZAh69OhRQI/S1QALlSgBt1HcU1NTMXbsWAQGBirl3FJpF4qTJ09GYmKiUtyNVMuVK4fbbrsNEydORPfu3fkhNYLhOwmQAAnoINCzeRXIS2TlrrP4XnNVK/LRqNbw9ir6lUTVGf+QgAsS6HVjFbSrF61G9tXvB3BB88cvEh7khye6Gvap+XoXzf+ILFTOmTMH8+bNQ3q6bQ90akBX/oj1gXiI6dChg+mm2zyfx+5BwG0U9//+9784ffo03n//fQQFBRWgKzulV69erWyzRFk3l8aNG+PXX3/FX3/9pT6w5nk8JgESIAESIAESIIHCEqgYHqQ9WTHoI/4+3qbqfj5eaFi5aPbWHT9+HDNnzsSyZcsgEU/1SJV6TfHyU4+iWTM+AdLDy9XLuIXiLptQ//jjD8TExCAiIkJ9aFNSUpTtert27RTjM2fOqNV2uaO0lEqVKqmk3bt3W1Xc5cNv7Y7V+BjYsj2ekwAJkAAJkAAJkEBxERD9Zfr06VizZo2uLr28vRFRqzn86rTHHbfeqCntjMirC5wbFHIbxV1YemsfxE2bNiEsLAxbt27Fjz/+CFHc//Of/5hsu6ytxhvD8sbFxVm9JOLb9KmnniqQJ3ZgFBIgARIgARIgARIobgKXL1/Gxo0bla7zzz//6Oq+jI8fQmq1xCtPPoSfdyXgXFKGrnos5D4E3Epxf/LJJ5WiLnj79OmDF154AevWrcOiRYsQFRWlqPv5+RWgb7SHtxUpTFxGfvfddwXqiU287LqmkAAJkAAJkAAJFJ5ArBYB/Ic/DfsibNW+vUkl3FQz0lZ2qUsXK4CVK1di6tSpOHbsmK75i9vr2+/ogw1ZNeDtF4iISNFd7Ltx1dUwC7kcAbdQ3MUfu0i9elcDWIgZi2yy2LBhA9avX48HHnhAlRGXSJZiVNjNfb2blxHlXKKEWUpGBu9ULZnwnARIgARIgAT0EkjTon7/czLRbvHm1fPvS7Nb2IMzxd31kiVLMGPGDJw/f17XTMUUWDzE9OrVC+dTc7BppsENpa7KLOSWBNxCca9YsSJ27doFowJuJF2rVi11KMGYxP5dRD74lmJMq1GjhmUWz0mABEiABEiABIqIQJDmTtSomGfn5GH3aYMSX6N8CMI1l6IiUaEBRdS7ezSbkJCgvMPMnTsXsn9Pj9SvXx9Dhw5VXvNMsWw0xZ3i+QTcQnE32prL5owqVaqYropE+xK7d1Hay5YtC7nzlE2qlmK0ba9Zs6ZlFs9JgARIgARIgASKiECFsoEY06uxaj1BC0w0+oeN6rjvTVXRunbJm6JmXkrCwd07cEFb4fY7UxNJbSsrfaKIcORrVjzlif91WWW3Zi2Qr/CVkxYtWmDEiBEqYry1fKZ5PgG3UNz79u2rdlOLdxmxOzfK4cOHIW4g27Rpo5LkcdEnn3wCMa2RVXqj7Nu3T7mJrFu3rjGJ7yRAAiRAAiRAAqWUQF5eHv6a9zU2LfwBebnZisJm7e+sj17B22+/jWeeeabIyOzfv195x/v9998h43AksqLesWNHjBw5Mp/JsKN6zPdMAl7uMC1xAfnoo49CPuQSdMAosttazF9EsRfp2bOnipQqLpOMIpHEZAPrY489BtPjJGMm30mABEiABEiABEodgSeeeAIbf/7WpLQbAYhr6GeffRZvvPGGMclp71u2bFFtP/jggxBvdo6UdnG2IZHgxeb9rbfeotLutCvh3g25xYq7IO7fv79yA/n666+jVatWyu+6BCKYMGECfHwM0xC3j5999hnGjx+P1157DQ0bNsTmzZsh3mhuvfVW975SHD0JkECxEhBvGPYk0M8bZbUIiRQSIIHiJXAhJQPxlwxRSm31XCs6FD7e1tcmZTHvyy+/tFpVXDCKyKq72JCLHnE9IlYB4nt9ypQpOHjwoK6mQkNDceedd2Lw4MEqdo2uSixUagi4jeIuV6RLly7qderUKfVhFht3SxEf7++++y7EI4xs+Bg2bBhX2i0h8ZwESMAugTztx3vMdHlwblturR+NR7oYwprbLsUcEiABZxNY8c8ZLNl+2m6zn93bBuE2bqx/+OEHu3UlU1bDp02bphR4h4WtFBBnGhLdVCwArO29s1IF0dHRSlmXVfbAwEBrRZhGAnArxd14vcw3qBrTLN9l9d3czt0yn+ckQAIkQAKeT2DepuP4+/BVE0vLGWdm51omedR5Vo79+XlprpVtrUx7FAizyYiNubiUNq6um2WZDsW0VsoVVnIz03Bm61oMmvWWiuaup754yJPV/a5du5osCPTUY5nSScAtFffSeak4axIggeIiIMrMC72bmLr7fMU+pGbm4OY6UejQwOB6NuKKKztTIR64JAHxZHIqvqCbYJccrJMHlZyehce/N3hxsdV0j2aVMbK9wbWyrTKult7jhsq4pW60Gtb6g3FYqq2+l9HO/j34RtNQQwN8TceWBxJh3ZHiLkq9tUjslm0ZzzNTEhC/9TdcOvQ3Ll/Z7GrMs/XetGlT5SFGIsBTSEAvASruekmxHAmQQKki0KxahGm+Pl6iFgDRYQEwTzcV4IHLEqhfMUxbWTUM79j5Szh24RLkeravb7gBS0rLwrbj8S47fg6sIIGIYH/IS2TfmSRTgRpRIaZjewcScFHMWOyJKO7WAjNa1jly5IjyELNl2XLgsmMPMXLD0LZtW4waNQqNGxvcZFq26azz1KSL2LFoBv7+Yhc+KJOtNrdK4MoBAwY4qwu2UwIEqLiXAHR2SQIkQAIkcH0Edp1KwJyNx/M1kpxucOsnieMX7MTIdrWVgm5U0sVsRhR3P19vPNjZ4B74wNkkj1XcA3x9TPMUJpP+OIg87SZG/Kcbb0Crliu4V0zKerI88sgjeP/995GUnKwp21fu6swmLGYyFSpUUKvhZsn5Dnfu3Kls4CVyux4RJxrdunVTbdqK4q6nHb1lNq5bg+/HDEdWeiq0xwtqnhLIUoI8iSc+8R8vJsUU9yNAxd39rhlHTAIkQAIeQWCPFkVTNgLbkrKBfqgaaV2xvJSeg0PnbEeZPBJ3SZk32Wq7NKT7+XihU8MKpql+v/qQUuDqxITmSzcVKCUH5cuXVwpsj569kZOVUWDW4uRiwYIFBUxlZBVePNKIhxiJK6NHxNymT58+yoZd+i0OuXTxLP415j5kZVzxjHXlf8xo079w4UKMHj0a33zzTXEMh304mQAVdycDZXMkQAIkQAL6CLy/eDeyc22bF7SqFYmnejSy2lhkqL9m5xyl8mSlffepxHzlZFW5XAjddeaDwhMTAfFSN2L8VKye/RXO7FqvVqaDQstixNC7MHbsWBW00Vg4Ozsbv/76q1phP3nypDHZ7ntkZCQGDhyozFKsecCzW/kaMlNSUjDhfx/il6mzkHTmKHKz7bvL/Pbbb/HSSy+hdu3a19Abq5QkASruJUmffZMACZAACVwTgboVwiAvkf2auYul4v7IbfXgr5nEUEjAFoGICtXQ7t6xKKdtNL+QnIbWdWLw9B1XbxRTU1OxaNEiZcN+8eJFW83kS/cJLY/KzTvj+3GPwdfX9gbZfJWu8+TQoUPKI82xY8e0lmQ/ju2nWOZdyc2IBKekuBcBKu7udb04WhIgARLwGALj77rRZGL83uJduKgF1WmneQvpe1NVNUcJckUhgeIg4OV9VR2SCO1iCz5v3jykpenzSBQSXR0BddsiqGpjRJcNKjalXZ4G9O7dGxKQ0iD6lHYpq/dm5ErDfHMRAlc/qS4yIA6DBEiABEigdBCoFBFkmqjRc09wgA8ql7uabirAAxIoYgIpF89pm1aX4JdffoEoxHqkdevWasPprP2XcTpBn5Kvp129ZWbOnHlN/ual/apVDTfIevtiOdcgQMXdNa4DR0ECJEACJEACJFACBFLjjuP8tlU4fnK31rvjFWtvb2907twZI0eONNmIz9q/pQRGDvz2228OfdJbG5i/vz969uxpLYtpLk6AiruLXyAOjwRIgARIgARIwPkEkk7uQ+zm35AZd0RX4+I+UZRd8YUeE2OIA6CrYhEWSkxMvCbFfdy4cYiKioJsal2+fDl+W/YXzmqeIyPaddRGe0MRjphNXy8BKu7XS5D1SYAESIAESIAE3IJATk4OVq1ahalTp0KCJ+mR8PBw9O/fH4MGDYK4inQlqVmzJvLybHtmshyrPC0QrzkvvvgifvjhBzz11FNISroaxGrTzP/h4vph+OqrrxAaGmpZnecuQICKuwtcBA6BBEiABEiABEig6Ajk5WRh0x/L8PW4pYiLi9PVUcWKFXHXXXcpP+xiWmJLTpw4gV+/ewf7t6xB5qVEhEZEwWfnCKUci1vIohQZ3yeffOKwi65duyrzHikvLiAnTZqEBx54QK3WW1aeMWMGZE5yg1NcnnEsx8Bz2wSouNtmwxwSIAESIAESIAE3JiCmJIn/rETKgfU4mXUlIJGD+dStW1cFTBJf77JCbU/+/PNP9OrVS5mcGMslnT+jIrPKqv7vv/+OBg0aGLOc/t62bVvce++9mDx5ss22W3bsrvmhX2bKT0hIUCvtZbSIqsagTKbMKwcSaEp8vdNdpCWZkj+n4l7y14AjIAESIAESIAEScCKBM2fO4KeffoJECc3KytLVcvlq9fDi6Idw88036yov7hT79u0L8fduTWJjY1X+7t27i3TlWsxaAgMD8eWXXxZQxGvdfAceee2DfMMTJpcuXcqXZnkiSr1EiKXibkmm5M+puJf8NeAISIAESIAESIAEnEDg4MGDEFOPlStX6rT9LoOyNZogsH4HtLupmaa0N9I9ClGUZUXflshqtoxHbiBkQ2tRiZ+fHyZOnIgh9zyEZ979BulJF3BHm0a4GNYAuWGV4Wdh5iNjciQy9v379zsqxvwSIEDFvQSgs0sSIAESIAESIAHnEUg/dwRjxizAxo0bdTUqym5Y7Rbwq90OMRUqIj5V36q8eeN//PGHLo8uUq4oFXfjmGrXrYdGtw9Tpw/0bYpJqw/iXFKGMdv0HhISYjq2d8DNqfbolFweFfeSY8+eSYAESIAESIAErpGAeFPZu20jzi6bhayEMzinox1RRsW8ZciQIXhrySGcTy6o2OpoRhURV4qORExOHJmlOGrD2fkdO4rLR8civuoprkeAirvrXROOiARIwIUIHI1LQVK6IYriwq0nIS9LGdmuFnrcUNky2eF5bFI6Tl60bh9rrNy4cjiC/PlVbeTB95IjkJZ4AUf2p+N8RT/lA7ykRpKZmal8j0+bNg1iy65HvAPD0KlHH7zw6N0ICnJOZF7ZxPr333/b7V5MTurUqWO3THFn3nLLLcrDjHiNsSZysyGbcp9//nlr2UwrYQL8NSjhC8DuSYAESi+BrUcvYvr6o3YBvD34RtSI0vdo225DzCSBaySwbNkyLBn/BBLPHMHPWhuPa6927drhww8/RJs2ba6x1cJXkxXuBQsWYNasWXZty81brlGjBlKiWyC45o24pUNdpynt0seIESOUP3jz/iyPRQkeNsxgvmKZV5Ln06dPV8r7vn37LMx9ysDLyws//vgjGjXSb+9fknMpbX17lbYJc74kQAIkUBgCkaH+CPA1fFXWr3g1+ErHBjG4+9ba6tWwctnCNMmyJOA2BMRjyR133IHEs/lvMNevX4/27dtj8eLFRT4X8bv++eefY+DAgSowkL0NocbBNG7cGP/5z3+UAhpSuyXKeNl362isV5j3Hj16KJMbe3VeeuklNGzY0F6REsmrUKECNm/ejLfeegv16tWDl7cP/ILD0LhdV2zdutUlbzZKBJQLdsoVdxe8KBwSCZCA6xAIC/SDv483MrLzUL18CPafTVaDa1Y9Am1qR13XQG9rXBE31zG0sfXYRUxec1i1N/6uGxEa4KuOwwIN79fVkRtVTs3MwcpdZ+2OuEXNSEQE+9ktw8zrJyDeR/71r39ZrMga2hUTELExl1Xno0ePoly5ctffoUUL0u7MmTOVWUxubq5FrvVT8Ws+cuRING3a1HoBJ6fKynR0dDQ+++yzfK4YZfPr66+/jldeecXJPTqvueDgYBVFVSKpTvh1LzYeuoC6FcLQrFkz53XClpxOgIq705GyQRIgARLQRyDA11tbzTesBIZcUdSlpiilcsNQGiUxNRPfrzlkd+qVIgKpuNsl5JzML774Ajk5OTYbE8U9OTlZmYs8+eSTNssVNmPXrl0Q+/W1a9fqq6qtpgdXb4Yv33oWYhpTnCIK+qeffoqsOt2wbYMhcmqMFnF1yr+fUAp9cY6FfZUOAlTcS8d15ixJgARIgARIoFAEtmzZYnW13bwRseEWk4vrFVnBF/MbiTYqirsekaBDTW/ujNNhTeEbVLbYlXbzMZaNqoi67fuopOiwACrt5nB47FQCVNydipONkQAJkAAJXA+ByuWC8GIfg5nDzhMJ+GDpbtXc+8NuQkzZQHXs5VXmerrQXTcpKQnvvfeeMtc4evSYphyG4NStt6HWh+NLxcY9WVHXI6J0X6tkZ2erYEmisB8/flxXMxEREcrefcCAAVh3RFvxX3dEVz0WIgFPIEDF3ROuIudAAiRAAh5DQLxaGBTzMmbuE8poacb04piqKJHix1rsrI2SlZqM1cvm48bflyplvn///sYsj3xv3ry5Q3MVUdqlXGElIz1deYcRG/YLFy7oql6lShXcdddd6NWrF8RExSCGPSe6GmAhEvAAAlTcPeAicgokQALOJ5CUloV1B+JUw5nZho1xx85fDbiy7Wg8YsIC6arR+ehLvEVRRsWDybFjx6yORVaJxcXfnj17gIBIq2U8IfHhhx9W3lxsraiLmYyYq8hmUL2Sm56C5AN/4d8L/kZGWpquag0aNFC8O3XqpFwV6qrEQiTgoQSouHvoheW0SIAEro/AhZTMAj7WD8ReVdzXakp9zegQKu7Xh9kla69YsQJi321LRJGVIEAfffQRnnj5bVvF3D5dPLP897//xYsvvgjN2B2a2xTTnMTXt3D49ttvERMTY0q3dXDy5ElMmTYDp35ZCuTp8xDTsmVL5bVG3ikkQAIGAlTc+UkgARIgASsExFrD+4rJRm7eVYXFWFSyvESZoXgcgdWrV+uak0SefOJlXUXdttALL7yAqlWr4sHHn0Ja4nnTPMT3t3hT6dq1qynN2sHevXsxY8YM/PHHH/ncJVorK2kSsVNW1mUV39UijtoaM9NJoDgJUHEvTtrsiwRIwG0I1IwOxQ+PtlfjfWzSX0jJyO8W74luDa7bj7vbwChlA01NTdU1Y73ldDXmwoXELGhxfGUkaUGYOtQIxJ0dmqugPfaGvGnTJkh0Tr0eZ/z9/dGzZ09lElNRc6dIIQESsE6Airt1LkwlARIgARIopQTq1q3rcOZi312/fn2H5TylgMw3vFIt3NC6lqa0V7Y6LfH5Lk8rpkyZgsOHDcHErBY0SwwLC4Ns8h08eDDKlmUEYjM0PCQBqwSouFvFwkQSIAESIIHSSkA2pj733HPIysqyad4h9t2jRo0qrYjyzTsjIwNLly5VJjGxsbH58mydRERGYdSIYejTpw8CAgJsFWM6CZCABQEq7hZAeEoCJEACrkxg8bZTyM617V+7QtkA3FI32pWn4PJjq1ChAt5//31INFBZabbmVaV79+7KrMN8w7LLT8zJAxQ/9z///DPmzJkDOdYjvuEVENbgVrz40BDcUs/xplY9bbIMCZQmAlTcS9PV5lxJgATcnsDCLSeQlmXbK0fz6hFU3J1wlUePHg2xux4zZgxSUq56ExJF/v7778eECRNKrWtCWVWfPXs2Fi5cqLzr6MF9ww03oN/AIfhhr6G0bEKlkAAJFJ4AFffCM2MNEiABEigxAkH+2te2pjyKpGflaKvBgI/m4sbP16AI+V95L7EBelDH4sd86NChWL58Od6duQo+ASF4cNideLB3Ww+apf6pZCWcxYIffsE7W9YjN9f2zaOxRbnJad++vTIpatiwIRJSszTFfaMxm+8kQALXQICK+zVAYxUSIAESKCkCH49qber6pZlbcCo+DR0axOD+To43VJoq8iAfgYRTh5B45ggW+R5B79s7oGbNmqZ82TwpGyeXxlfUTJQuo0Llaqa80nKwfft2xP0xGelnD+Csjkn7+vqiW7duyge7uJKkkAAJOI8AFXfnsWRLJEACJEACbkRAIp8OGT4Su3ZsU6Ne/wPwpHbUt29ffPPNN4iOLr17BfLy8rB27VpMnToV4otdjwQHB6Nfv3646667EBnpuRFl9bBgGRIoKgJU3IuKLNslARIgARJwWQL79u3DzTffjEuXLhUYo9hu7969G+KLPCIiokC+JyeIJ51ff/0V06ZNw6lTp3RNtXz58hg0aJBy6xgUFKSrDguRAAlcGwEq7tfGjbVIgARIgATcmIDYr4vSbs1jjExL/JCPHTsWn332mRvPUv/QhcWCBQvUptP4+HhdFatXr44hQ4agR48eEPMYCgmQQNEToOJe9IzZAwmQAAmQgAsRSD5/Gn/++afDEf3www/4+OOP4ePjuT+VFy5cUO4c582bh/T0dIdMpECjRo2U/fqtt96q3GXqqsRCJEACTiHgud9GTsHDRkiABEiABDyNQMKZo7qmJKvQp0+fhqwse5ocP34cM2fOxLJlyyART/VIYMV6GDx0OB4a0EVP8RIvIzciYu6TnhyPwLByJT4eDoAEnEGAirszKLINEiABEiABtyHg4+uve6ziy92TJPPCScz95me8s3OTrmmJv/UuXbrgH++G8AuPQbU6tXTVK8lCclPy4osvQp4iZGdnq6GERldFtedeRremj2Lu3LmYPn061mzaAS+/INRo3ArV2t2pleOG2pK8bkXRt5jCyQbr7777Drt27YK3jx8CKjdAwy5DtO5uLIoui7xNKu5FjpgdkAAJkAAJFCUB8Sl+4ehupCWch39oOMrXaGS3u/I1GijzF3srzeKDXFbaJYqqu4soLxs2bMCZX79CxvljiNUxocDAQPTq1UtFhxXvOiMnOjYt0tFskRcRT0HiOz4hISFfXynnT+GdFx/H7K8/VPsXrkbELYPzR3Zh+4pZiHlD289wh/3PTr5GeeLSBOSmTTZNy2bzq9dbG/K5WJzY+ge+C0vEuNdedOk5WBscFXdrVJhGAiRAAiTgFgTmzJmDx/81Gue1H2Oj+AYEo9Xl8Xj26aeMSfne/YNCIZtTJ06cmC/d/ESUXVm1dWeRG5OVK1eqFcdjx47pmkp4eDgGDhyoXqGhobrquEohcWEprigTExMLDkkilWkim45Frm5KNqRnZ6bj23H/wgvDbvNI0yg16VL25+WXX1ZKe/7rrc4UibfGvoT2bVqga9eubkWGirtbXS4OlgRIgARIwEjg66+/xiOPPFJgg2R2Riqee+ZpnDt7Bu+++66xeL73999/HxJYaP369fnSjStz99xzj2o7X6abnKSlpWHJkiXKhj0uLk7XqCtVqqQ8xMgqu7uaB/3+++/KjaeuCVsW0hT7rIw09Xmxd0NnWW3RokXKJGfVpt3QHvegUuM2iLytj2UxnhczAfGM9Mknn9jtVf7Xx40bR8XdLiVmkgAJkAAJuBSB1NRUSOAcdxPZNDp69Oj8j8AtJvHee+9hwIABaNOmjUUOIP7GRdF7+Y3x+OrrrzQzG4OCKx5TnnvuOdx3330F6thKiN23BbEHtuLN7cFI94tEVqUWQFSIreJFli7mIWLXLTbcKSkpuvqpX78+hg4dis6dO0Ps2d1ZxO/+9covv/yiq4nk5GQVUVd83qubPamlLd4f3/o7Dvw+C892/p0r97pIFk2hdevWOdx0LU9d5MY9MzPTrW5WueJeNJ8ZtkoCJEACLkvg3KnjWDf5HZzeuRYT7klXSqxEC5XVp3r16rnsuM0HJhvOJFiQI5FNadYUd6knK8uPPvUc4qp1Rba22jpuUAs0qBblqElTvtw8DO3bHzu2GhRGbc1ViZe3D5KHPQEMLp7NbzKOWbNmqVV2PUxkkDfddJNy6diqVSvDoD3gr709C3qnJ+4x9ciIESNUoCope9XsxlDz4ukj6N69O3bs2OFWCqGeebtLmaSkJF1DlWsn3qPc6SkTFXddl5aFSIAESMAzCIj/8pfu7Y3M9DTThMS0QlwDyiYuefR/2223mfJc9UA8RBjNWmyNUfKlnB7xDQhCgLYhU6/Ij71wOnDgQIEqebmabfnUT/DxTTXw9NNPF8h3VsL+/fsxY8YMrFq1CmLf7VA0HkFVGmPIsOG4v8+tDou7W4FmzZpd95CrVavmsI01a9Zg8eLFdsvJtZGbxscff9xuOWYWDYHatWvrajgsLAzlyrmXq1AvXTNjIRIgARIgAbcnII/3+/fvr9nypludS0ZGhtqUqDdyptVGiilRInVarnRa67qoInpKYCZrSrv5GF555RXoXcE1r+foePPmzXj22Wfx4IMPqs2njpR2Pz8/9OvXD1X7jkFU++GoULWmoy7cMl8iuFapUgVeXteu2gwePNjh3OXm1pHIGBwp947aYP61E5CnbDVq1Ciw/8WyxeHDhzssY1mnpM+v/dNd0iNn/yRAAiRAAoUiMHnyZFy8eNGmwisKoHjk+PbbbwvVbkkUvvnmmx12K4q9LTMZh5UdFJAnFLKib08kANDSpUvtFdGdJy4vZWX9/vvvxzPPPAM99tziFebuu+9WkVHHjBkD3xD3WlnUDedKQTF3mDJlirLVvxblvVxMZXVD5Kjf2NirHoxslZX/pbNnz9rKZnoRE5Dr/+WXX6perP+flkF0TAVlHljEQ3F681TcnY6UDZIACZCAaxKQDVvWf8Sujld+8KScq4uslJUvX97m6qrMU1aai8pUQdwr6lnx1+uGUXgnx8dh69atOHPmjAm/bJybP38+ZL6vv/46Dh48aMqzdSB+15944gm1SfWhhx5CRESEraIel96pUyeIOZil2YyPXwBGPT4GY8eOtboJN7xybTzx3+8hphOOpGLFio6KqP8z8dRDKTkCss9A/nesmcJEVK2LOYuWQ/5X3E1o4+5uV4zjJQESsElg1Z6z2HDQ/uay0d0bICTA12Ybrpyx7kAcjp2/ZBpiYpphc+bB2GRMW3dEUxaA4W1rmfItD2QFWBRaRwqnlHN1CQkJUYrpHXfcARlvvjlpcyyj3YDIE4Ya2uPyohBRhsUjjyPRozQf3LERSz9/BwmnDuK9Kw02bdoUPXv2VO4Nrfolt9JxzZo1VcAk8Uvt41N6f97lKcu2bdsgdubit/3j344isnp9jOjcEN2bVYa4+pw9ezamLfsLOd4BqNOsFcrWaY1yMVFWqBZMErMjcSdqT+TzKBu+KSVLQK6BRNIVsyUJzpWceRn/ZEQipu6NqF7T9ndlyY7afu+l9z/bPhfmkgAJuCGB2MR07D5tJfiK2Vyycw0BV8yS3OZw+/F4/HXwfIHxnoxPg7zEcMOe4t6gQQO1+bRAA2YJ8oi/YcOGZimue9ihQweIvfe/nhmDVSuW43JerjZY7RF4nRsw69tP0alD0W3AFHtqPSZFt99+u12A06ZNwxevPCCeBPPJP//8A3mJlx9Hq4Ki5IuXk3bt2uVro7SfiKtLeU0/lj/qq2xclOA8cVU34XxyBsoF+yE+1bGHIiNP4SxBqsTtpi1p3LhxoVyK2mqH6ddPQNzdDhkyRDW070wS3p6/8/obLcEWqLiXIHx2TQIk4FwClcsFo0UNgx1vnPaDfEpTZkWMaXLs523fLlnKuKqEBfqifKi/Gl5qRg7Ss0VRBQJ8vbWnCD4OzWDE3vmDDz7IvzqtWsj/R1Yk3UXkJmPi99Px5uzNyLiUAP/gshCziFtuaVukU5CoqqJ0y4befKv9Zr2KeYu9myBx4/jAA1eUdm2F1pqIaUzZsmWtuqtr3749Ro4cCVESKcVLQJ7miOtN40ZV8ydZUdXqYdmyZcpUq3hHxd5KAwEq7qXhKnOOJFBKCHRoEAN5iSzfeRpT1mrmI9rxsz09Q7EZ1b425CUyY/0RLNl+Wh23rRuF+zvVVcf2/jRp0gSvvvoq3n77bZvFnn/+ebRo0cJmvqtmePv6ITjCcO2LY4x16tRRK64DtJXXDDPTIqMCV71RS3z11Vd2hyLuAsWG3Z7ITcG5c+dgdFMoJjDdunVTK+zGNHv1mVc0BMRUS9ynSgAmCXq1YuMuXJbIqY3aoGUng3eboumZrZZ2AlTc3eATcOSfTdix/k+c9L8M/6NtlDs3PZtj3GBqHCIJkEAxE/j3v/+N41pQzRlffoiczKu27BJJ9M0334Qo7hR9BMS+fsnqv/H4i2/h3P6tCPHORmhUFYQ37ojOvQZAlDtrIsq4bACeNGmStewCaeIzXq6P2OvKI3/ZlEtxDQJyEyWvF2dswekEwxM+Ly9v1xgcR+GRBKi4u/BlFc8C8iW9du1a0yjXzP9Ruat65513lEswUwYPSKCQBFIzsjF30wm7tZpVi0Dz6iXrQi4tMweHztkP3165XBAiQwwmJHYnxExF4I677kNmtfZIO/kP+jQMQ4UKFSDeOPR41CDC/AQqVa6KloNGq8Txd92IZTtO48/9cZq3m4LKW3Z2tlqhFRObkydPIiXF/ufa2JOsrMuqrtjqUkiABEo3ASruLnr9xVuBROWTXfGWIo9WJfiGPDIdPdrwg2FZhuck4IiA2Ef/+s9Vt3PWygf6eZe44i526u8tth/98r4OddCliWMXbdbmWFrTJFJozRtvxcN3tymtCIp83vJdLb7F5ftczCpmzZql/OgbOxZFXE+wq969e1NpN0LjOwmUcgJU3F30AyBR+awp7ebDfemll5Rv38jISPNkHpOALgLeXmUQExagysqj+7gUg61tqLbJMcjP8NXgrm4TdQFgIRIoAgKnjuzHmq8/xKy9G/F2VqZSuMWPtJg3il95c4mJicGpU6dsbm4Ve3lvb2+1gdW8Ho9dk0Ba4nmc3L4Ge5LP4c1D9dXim3g+opCAMwlQcXcmTSe2NWPGDIf+ltPS0lRUvlGjRjmxZzZVWghEBPvjw5Gt1HRz8y7jni/XquNBrWu41Op1jagQvD/8JjW2hNRM/GeBYfX9vg610ahKuEovG5hfIVKJ/OMUAhKx8+uvv1avf3Zp7Mt4o3zNRlhS9S307dPbKX14SiPLlizEO4/fg9ycHNOUZLVdXhJFU9w2mpu7BAQEQFwTHjp0yFTeeCCBsMQ15+eff15kvuiNffH9+glsWDgZa3/6Enm5hmu/bTlUVE4xQZMou3KTRiEBZxDwckYjbMP5BPRG5Tt69KjzO2eLJOBCBPx8vFAxPEi9osMCTSOTGw9jepA/1yBMYJx4IKYeEgRIoo/u2LFDKaS52Zk4d3A7+vXtA3GJSDEQSI0/hycfvi+f0m7OJkdT5vfu3auUcWO6rKaLO8dhT7+lNrUa0+W9Vq1ayrzm4YcfNk/msQsSEBera2Z+ZlLazYf4xx9/QHz5u0NQM/Nx89h1CfDXzkWvjfjtlVUaR6InKp+jNphPAiRAAtYISJAacXcnks9X+RWf4++9955yHWkMbmKtjdKQln72ALbO/J/y621vvuLz/eLFi6jd/00bAABAAElEQVRatSp69eqlopzKSuzHv+yBV91OiEIC7mxcVpnVSOAliusTEFedr732mt2B7tKeVMmTkzFjxtgtx0wS0EOAK+56KJVAGYnKp0ccReXT0wbLkAAJkIAlgaSkJEyYMMEyOd+5mHOIe8nSKLKCvmLFCrw55gnE/TEZ8bEndGGoUqWK8v/+9NNPFzCfKF+5Bjp27KiipepqjIVKnIBsOnbki1/2KsjGZAoJOIMAV9ydQbEI2pCNp9OnT1dfCPlWusz6Gjp0qN2ofGZFeUgCJEAChSKwYcMGiHJqT8QGe/fu3UhMTER4uGG/gb3ynpCXlZmBOXPmQPYhxcXFmaYkLPRIzZo1S7XbzUsXY3H4ryUYMy8W5UICcNNNN+H+++9H5cqV9eBzuTJi1upI5Df88OHDjooxnwR0EaDirgtT8ReqW7cufvrpJwwePFiF1DaOwBiVT3aqy4YxCgmQAAkUBQE9pnrGfiVAkKcr7rkZqUjc9xe+WLABGWkFzRglQJI4DHAkDRo0cFTEY/N/nDwJi8aNVrbg8lsmrwULFmD8+PEqGNXw4cPdbu56zVXFsxCFBJxBwG0V9+TkZBWYSDZOWYqsfMgmINnF37JlS7f9QRHfvTKPYU+8jL1bNwA56WjRtJHazHTPPfcoN2GWc+c5CZBAyRP4YMkuZGTbXoGtWyEUQ26uWfIDtTMCvTbWEh1UAjh5qkggvNmzZ+PY/AW4fMVjiLW5RkdH48KFC9ayVJooqb6+viqons1CHpyxZMkSPP2vx7QZllGzlFVo49PkrKwsiHc0cZnZuXNnt6Kg11xVoqtSSMAZBNxWcX/33XchGz4sFXdRdMeNG4eBAweiTp06eOONN9CoUSM88sgjzuBV7G3UqFEDfR5+GbVPJ+GmmpF45o5GxT4GdkgCJFA4AvvPJiM9K9dmpQDfglE1bRYuoYwmTZqgWbNm6nvWnhmIrJJKMDhPk4MHDypzmJUrV+bzBGNrnuXKRaJBw0bYt3dPgSLGJ6Xvv/8+xMa9NMozzzxj08WxUYF/7rnnsHXrVrfC07x5c/Tv3x8///yz1XHLPhBx+/nCCy9YzWciCRSWgFt+2y5evBhbtmxREenMJyyrHeIFoV+/fsrERPKqV6+ulHixn5MVbAoJkAAJFDUBucnO1CLTivxzMlFbfc9FVKg/xCe9SM3oUPXu6n++/fZbtG/fXtm6W1PeoytUxKAHn8HmI1dXmhtWDkewG7vn3LZtG6ZNm4aNGzfqujw+2ip6QLXmCGvYAZPv6YTHn34eK376Hpfzrt64iZewDz/8UNly62rUwwodOHAAciNkT0R5F/byhKNSpUr2irpc3vfff4+Nuw7jzMGd2gMF7YnCFa9LMtDAwEC1GVkW4Sgk4AwCbqe4nzx5Ut2Rt2rVCv/8808+BpMnT1abpERxN4rYld12222YOHEiunfvrh5VGvP4TgIkYJvA+eQMJKdn2y6g5dSKDlGraHYLlcLMR7vUN836xRlbcDohDU2rReD+jnVN6e5wIN+zq1atUmYMR44cyTfkqNrN0Pbesfhh03ktXV4GGTewOWrHuMeNiXHMly/nIe3UHrz+/Pc4eti+gmmsExoaqhaJbuzQA5+uMniUkScPAx4ag9Ab++Jy7B7cXi8M1apVU+YfYgNfWiU2Nlb31MXE1d0Ud7kxG/7611izdC6Obf4NaRdPo3rFKHTt2hXPPvuscv+pGwALkoADAm6luIuHA/GFKh5XZPXCXCS63+rVq9U/iOUmkMaNGytfxH/99RcYfticGo9JwDaB+VtOYPXec7YLaDmTH2kHH29thYnisQTatm2L/fv3QwLJTJyzEicTMrTIqY0RWe3qzYm7Tl7c+K3+bRnOLJ6OnEvxuPrcwPaMQsPLYdTwoUppF2V835kkrXB+V5ABoeGoWasbHht8o+2GSlFOYfZAiJ27O4qXtw/qtu+jXtFhAfjflajU7jgXjtm1CbiV4i6Po8SWzJr3Anm8Ji7JxJ7dUox37+K2jIq7JR2ekwAJkIB9ArKSLJvwcqIaYuo6w8r7fR1q4/s1h1XFfw9qjrJBfuo4LNDXfmMukJubmY6pU6eqTacJCQm6RuRbNhphDW7FfUPvRL+WNXTVYSEDAdnoLHvOxCWi0Z7dko3YgsueCuPvtWU+z0mABAwE3EZx3759u3KL2KZNG6vXLj4+XqVbexwpG0NEzH3uqoQrfySIxvPPP2+epI7lESeFBEorgX43aY/4Gxm8hazaE6tW34P8vPFCnyYmJN5eXG03wSgFB77eV2P2hQRcVdDDg/0QEezv8gRSEi8iYdtSpBz6GwdysnSNVzbpygbc73Zrjr00R0He2soqpfAE/ve//6Fv375WKxo3737wwQdW85lIAiRwlYBbfAOlpKSozUJvv/321ZFbHBl9Dvv5GVZ9zLPFBZeIrehmskr/+uuvm1dRx/fddx/ExReFBEojAXncG66tombl5CLkymZD2XdVoWygCUdqZg6CtDwvyaCQgIsSOHr0KGbOnIlly5ZrHmKubhq1N1wxERo5ciSaNm2qik3as1Z7v2yvCvPsEOjTpw/+9+nneO7pJ9XGXVHW5SWbnuU3+rvvvkOXLl3stMAsEiABIeAWivunn36q3Dn6+9te0Slfvry6ouIP1lKMCrutFXTxODNgwADLaibPNAUymEACpYTA4m0nMW/TVfvd1MxcPDpJiylgJnW1jYh+Pt7odWMVNNM2YHqiZGumFbnZl+HtW3BhwBPn6ylzEpfB4iFGnqpK7A8x0xAvH2FhYVY3VXtrJkFdNZOgESNGoEaNGp6CwWXmce/9D2J1QiQOrV+C8MxYRIT4q8ipDzzwQKE2cMp1lACFP/zwA7Zs/wcZl30QU+cGHOxaARK8kEICnkzA5RV3+eIVF1GWdnHir11W4mUVXkxhHnroIXWdrEWuM6bxi9iTP8qcW0kROHguRXXdrr5nPZ2SRQDZBP/VV1/h+PHjao7hlWqhYZchqHXzHSWFm/06ICC/Feln9uPJ0dOwQzOxFDeERlNKY1X5zRC7a1HgRcr4+CGkdiu8PeZRtGhQQ6XxT9EQCClfCc37PoQnuzdE69qGBbfC9CT/l3fddZeKuGo0sZH6SWePonHjJZgyZUqpDXJVGI4s674EXF5xly/Yhg0bFjBzMSryxtV0ccckm1pkk6qlGG3ba9asaZnFcxIgASsEjsSlYNLqQ8pMprzmfzwlI1vzS64Z+FpIjGZOUyE8EGLrHqmtnnmKyM2+RDpct25dvpXZxDNH8deUd3Du4HaM7v6Dp0zXI+YhftNTj+1A0t7VyEk+j7OaF7KdO3ciPT29wPwyMjKUO+F27dqh/9BR2JxdA15+gSgXWXhFskDjLphw6tQpfPzxx1g0awGy0lOxR1uVjnvkPuXm09vb9YOBmSMdM2aMUtolzagHGPPF85w8LZGbshtvpEcfIxe+exYBpyvuS5cuxfr16yEr4sHBwdodcGPlNqtBgwbXRE52ov/73/8uUFeio8pKvHnekCFD8Mknn0D8wJq7lNq3b596DMdHaAUwMoEErBKQqJ/Hzl+ymmeeeF/HOmhS1fPMY2SzuijtIvmVA4ON85ENv2D+zB/R5tXnzHHwuAQIyE3Wr4vnY9f3E3Hu9HHlxEC84IiLYGtKu/kQL168iF7978LW+fljgpiXcffjX3/9VZmCGveByXy2x8fivg1rILFPFi1aBPFJ7w4iC3PiEtqWyP+q2MyLXjBv3jxbxZhOAm5NwGmK++nTp5W5yi+//FIAyNixY/Hkk0+qfyaxLywq6dmzJ+bPn4/p06dDQieLyCNS+QEW3+/ibopCAiTgmIBsSr31iulLWlYOthw1eG1yXNP9S4hb2a+//trBRMrghy8/xTtU3B1wurZsUTJl4ceeyHf73LlzMWfOHBWUTyJnF0ZEyZMFpl07t2vV3GvVWe88jx07plwoW97AGG9GJfaJmJnKxl13EAkGZi2Cr/nYZW7Lly83T7J6/Pb8nbiYkqHyEtIMe+N2nEjAkz9uVGnVIkMwpldjq3WZSAIlScApirusbMjmzr///lvN5YYbboCssEvQBVnt3rBhg7IVldUN8cVeVCJmNZ999hnGjx+P1157TZnYbN68Wd003HrrrUXVLdslAY8jULlcEB65Ev3zjBb1U4/iHpeUjj/3x9ll0bJWJKqXD7FbpqQzN23aBHnkbl8u4+ypE8rFLD1P2SelN/fi6SP4c9aXmL1nA+7JzFCrwJ269YLXDf0REnk1KI+YfYiiKYtEYu8sNuyFVdrNx3Tk0AHAq6F5ksccv/vuuzDu8bI1qVmzZqnfS3F76eqi1+e+zDk7O9tupPTE1CzkXXESpOn6SrJz8xB/yaDEhwcZ3l2dCcdX+gg4RXGXR1eitIv7xBdeeEEp7eYo5Q5Ygh89+uijanVk0KBB5tnXdPzGG29YrSebjeTLSmwY5Z982LBhXGm3SoqJJOBcAueSM/Dz5qseaKy1Li4mXV1xl+8OvVKYsnrbLI3lli1bhqmvjUJuTrZp+uJ8YNHcmfBdsgi3/etDHDoQiomL5qkIrsYVY1HQzp07Z6pzLQfqKXDmtdR0/Tp6Vp5lFuJ1xx0Ud70OJmTR0OgG2tZV6qTFqFioRYdO08wCa0RpZr2Vw/MVLedBe3byTYwnbk/AKYq7fDm89957VoMYCSHZ+S1fCmJLJ4q9MxR3R+Rl9d3czt1ReeaTAAlcHwEfbYOq0d97nraUlZZt8Jcd4OsFnytmar4+rm+uZi36sjUyQcEhjPJoDUwh08R5wODBgzWbdOtPObIz0rDqs2eQvK65Fvwov0mLpbeYQnatfpua39QaG9bbf1JU2HZdpbw85dYjeley9bRVlGVuu+02FTk9KSnJYu9J/l5lwc6R9Nbc167cfVYp7g0qlsWwtrUcVWE+CbgEAaco7hLcQs9GkIiICKteX1yCBAdBAiRwXQQaaitWXz5wi2rjdHwaXpy5RR0/c0djNK6SfzXrujoq4sq1a9dG+/bt1d4Y48qutS7v0DY1yiZIyvUR+OKLL3Dpkr2N0JeRlZGO8+fPK/NL897EHOJ65J577kF0jEQH9kzFXTypiWcde59j4Ve9evXrwVhsdSUyujigkOtm7grSOABJkwW7V155xZjEdxLwOAJO+dWpUqWKw8dSQk42AlkLkORxVDkhEigkgaOa+8W3ft5ht9aIdrVwe5NKdssw0zkEZHNqmzZtlEJpTekRX9SPPPOSczor5a2I8wBxHOBo06EEUBITCHOxFinbPN/ecevWrTFhwgScSdEXSdVeW66aN3ToUOzYYf97RQIbSlRTd5G7775bmcI+/fTTBbwGSZRb2bBsDMjoLnPiOEmgMASc8txavkzFRtGeHD58GAMHDlRR0uyVYx4JlEYCskkqO/ey3VeucSdVaQRUzHOW2BHi1taaL+jKTdqi+5gvEFbWfZ4iFDO+QnUn+wSs3RxZNmKp2MuTkVdffTWfn33LOsbzqlWrmsxsZKNrq/6PYs2aNQgJce2N0sbxX+v76NGjC+w5s2xLXCe62wbrhx9+GOIxZ+LEieg77H406jYCnR97V7mIFhfSFOBSZjaMvxmZmtliouY5R16pmdZN0sjMfQg4ZcVdNp326NEDL774oopoJo/dZCVE3KpJ5NOpU6cqF43yWPmJJ55wHzocKQkUE4FILcjR0FsMAcLSNfeLC7acVD23qxeNqpEGt3j1NDtMSvERkH05W7ZsUcrAc5//jKxcLchUjYYIjapcfIPw8J5iY2OVBx89irvRlbB4LZMgO7fcYjDL2rp1q1LgrKES04nKlSurYEviq/ynDYexaHssgvx9ICvNni7iUnPlypXqd9kYl8A4Z/k9fuutt2zuTTOWc9V3udl47LHHULPtaUxddwRltIHS5fPVqzVh+T7Tyep95yAvEfHs9XSPRqY8HrgfAaco7m3btlWbTsUFo7zkn0e+ZM0DPsgOb3HhJSsfFBIggfwExG+6bJYSSUjNNCnuLWtGotU1hAXP3zrProeArLrXb5uhRY/lStX1cDSve+jQIfV78Ntvv+X7nTAvY3l8e/ceeP7ZZ5SbX/O8jz76CGfOJ2D+TzMMyZqyri3hq2NZfV28eDEksraIr6+fei9NfySi+Nq1a5UC/8wHPyIz/RI6tmqKsU8+wN/j0vRB4Fw9hoBTFHehIQp78+bN8a9//QvHjx/P92Usiv1XX33lFu6mPObKciIkQAIk4GIEtm/fjmnTpqnYHsahiQtf2VAoEa9tSZNuw/GfDz5BhbKBBYrI093/fvIFUqu2x/EtK3Hpwln4BYXglYeH4p67R6qnvwUqlcKELl264MaD/sp84s62NTWl3bBQUApRlIop39myqulprfmEywV7/pMm8/l64rHTFHeB07t3b/Tq1QviZUb8tsujSXnczI0invjR4ZxIgARIwDEBsU2XFV8xmRQHBdakVq1aSsE+ceJEPnt3cbnZuPfDqNfhTmvV8qVF124KeRnl7nvaws83v/tIYx7fScBTCBw+l4If/jykppOVk2ea1sZDF7BTiwQrMrBVddxQvZwpjwfuTcCpirugkGh2sqlLvqDFvq5x48bo16+fww0y7o2RoycBEiABEjAnIB7Efv31V7XCLtFO7YnYoosZZZWadRFZsTq6tm0OcWUYWbsZPvv9mL2qzCOBUk0gTdsTdSSuoDvVs4npJi4pGdfnNtXUEA9cgoDTFPfTp0/joYceUoq75czGjh2LJ598ErJ73bjByLIMz0mABPQR2HL0Iv7cbz9a5EjNdWT50AB9DbIUCTiRgPhkX7BgAWbPng29AZKqVasG75o3IzemCbo3r4a7b62tRrTjRLwTR8amSMDzCEQE+6F9/Wi7E4sOK2hiZrcCM12agFMU99zcXAwYMAB///23mqzs+m/QoIHyubtv3z5lz/jhhx9Corh9//33Lg2EgyMBVycQq62kbD5iPyLigJbVgFBXnwnH50kELly4gJ9++gnz589HWlqarqlJlFrxEHPrrbdizLTNOJecoaseC5EACRgIVCkXjEe71CeOUkTAKYr7559/rpT2++67T3mXEaXdXMTVl9i8i9vIOXPmYNCgQebZPCYBEigEAXEd2bCSwUtGkuaX98yVR6J1K4TCR/PoJBJA295CEC1c0Ysn9uPw+sV4ZFIsIkIDVaAmcUvnLtEnCzdbx6Wzk+Mw4eMPseq3Fcq1o+MawM0334xRo0ahWbNmeoqzDAmQAAmQwBUCTlHcly9fjvfee8+mP1ixX5RNqosWLVKKPRV3fv5I4NoJ3FwnCvISWX8wDhNX7FfHz/ZsjNAAX3XMP0VDYMeib7Fr2Y+qcfleE/njjz8gLgnlaeLw4cNVWmH+nDx5EuPHj8dPc+chXlu1DgiNgP+2gRj3xuuQqNSuKscO7Ufcn1ORfmoPzugYpLe3N26//Xa1wi726xQScHcCYsqVnGawHxdbc6NkaAGP/tT8pgf4eaNVrfLGZJd7l82seVdcpxqDNeVpgf5k/CJe2lecnw83eLvahXOK4i5eZObNm+dwbhEREThzRs9XvMOmWIAESIAEipXAwT8XmJR26dg8aFB2drZaQRZb7fbt2+se18aNG9G9e3ckJSWZ6mSkxGPSt99g7k+z1ebO1q1bm/JK+kDmnH5mP5L2rMZn54/pGo7saxJvY0OHDkVMTIyuOixEAu5AYP7mEzgYm1JgqMnp2fjq9wOICgtwacX9vwv/wYHY5HzjPxyXgge/Wa/SymtPdz8e5TrfP/kGWopPnKK4y6qQBFhyJOJpRjwNUEiABEjAnQjk5uRg+8KvbQ7ZqMS/8sorWLNmjc1y5hkpKSno06cP5N2aSHrfvn0hwYpCQkKsFSm2tBxt/hIs6etJP+D82VO6+g0PD8fAgQPVS1wDU0iABEiABK6fgFMU9woVKmDZsmXo2bOnzREdPnxYfYHLDxGFBEiABNyJwPlje5CVZl3BNs5DlPc///xTKeJ6FNVJkybh/PnzxuoF3sX/+blz5zB58mQV2K5AgWJIkE2mS5YsUVFO4+LidPUokTqHDBmiVtn9/Qsf7CUzI10F7JMbIImIeu5yOGq27qb13VJX/yxEAsVF4KU+TZF7xdRk0daTWLTVcFMbpa1Ujx/SQjM1MZjTFdd4CttPv5uqIkl7OmBLuFfKFpmSTXeK4i6bTnv06IEXX3wRd911l9qkJdHsEhMTsWvXLhV4Y/r06fDx8cETTzxRsjNm7yRAAiRQSALpyYZAJnqqiXcVPYq7KKZiJ29crbfWtuRLOYlIXZySkJCAuXPnKhNIW08ELMdTv359ZQ7TuXNniD37tYhs/H3h9VeReDFOsQGETx72/jYDb13agc8//t+V9GtpnXVIwLkE/M2cAPh6GxwDSA/yfxvk5xT1yrkDtmiNQZksgLjJqVM+WW3btlWbTl977TXIy0vzbCF2jampqSYMYkozc+ZMFWTDlMgDEiABEnADAsERhs3AjoYqCqteO275ftSjuItf9OISiccxa9Ystcqu16wxIKY2Xn7qYdx2a9vrGmZKfBx+n/AsstMN8zXc0Fw2tfnFpx+jSkwUxByJQgIkQAKllYBTFHeBJwp78+bN1crQ8ePH8yntoth/9dVXyrNMaQXNeZNAcRFYqwVnOnHx6k2zZb/e2mrQkFvo1cOSi73zqOoNEBgehfSkC7Ir1WpRUcK7deuGoKAgq/mWifXq1YN45LInYi4jK9lFLfv378eMGTOwatUqSJ8ORZvrDS1vQVy5FvArVwk3trjJYRVHBTYumOTQHOmtt97CI488gsjISEfNMZ8ESIAEPJKA0xR3odO7d29l1yheZsRvuzwuFjeQ5cu7rjskj7yqnFSpJrD1aDz+PqIpmDbER/PxRcXdBhyL5NjYWGzfvh0nd+9Fs573YuP09y1KGE7lKaOYB7777rtW860ljhw5EhMmTLCWlS9NyhWVpJw+iGeemYnNmzfr6sLH1w8B1ZsjrGEHjBrQFhN+3aernp5Ch7b84bBYZmYmVqxYoUxyHBZmARIgARLwQAJOVdyFj6w61apVS72s8dqzZw8kWh6FBEigaAiEBvoiMsSwKTA1M0f55BV/vBHBhjQfb9feMFU0VArXqmzElP04EjDOXCKq1EXS2aPIy80x2VqLSYd4UJGooU2bNjUvbvdY3DyK7fpnn31ms9xTTz2Fm266/tVs8w4k0vWhHRtxZtnPyE44a55l81gWYfr374+YJh0we5u+Tao2G7OSIQzTkuKt5BRMokvhgkyKIkX8ecelFIxkK64OY5PSVZfB/j6MHVEU8NkmCdgh4HTF3U5fkB9D+SF8/fXX7RVjHgmQwHUQuK9jHVPtqWsPY9nOM4gMDcBHI1uZ0nlgm4BsLm3Tpg2OHTtWoFDCqYMILFsetW7picq+l1AhIkSVlVXxsLCwAuUdJXzyySfK7OM///kPxBe8UWT1Xmy5nfldKavVv/zyizKJ0av8RkdHK4cD4g1M9i2t3CWKvvMVd1nwCQwNR3pKohGBzXfxYkYpegLibWTMtIJPYhZsOQl5ifS6sQqG0eyu6C8GeyABMwKFUtwXLFiAdevWmVXXfyieCX7//XcMGzZMfyWWJAESIIFiJvD8889bVdqNwxA799SLZ/HWjGloU1vfplVjXct3MbF588038fjjj2PilLlYuG6XdmMQiSnjHkGtapUti1/TeXJyMn7++We1aCKevvSIRDaV7+quXbsqb2B66lxvmdotOmDX6oV2mxEnBxJ9lUICJEACpZVAoRR3+QF4/33rNp6lFSDnTQKuQuCjpXs0N3z5zWDOJRoeaSemZkFCWnuLzQzFJgHx4DJt2jSb+caM41t+R6oKnHR9iruxPVnZ7tFvEA4FNlFJ5aOuv13xAS/mO7LgkpFR0OTB2Lf5u5j6jBgxAuJQQFbBi1Pa9Lsf+zasQG5Whk0XmeJyWFhRip5AaIAPXuht+Dza6i0qzGB+Zyuf6SRAAs4nUCjF/Y477lCuHmUVRuzUC+OrV/wCS5AmCgmQQNEQsAxdbd5Ldm7eFWWoeJUx8zG4w/GBAwfymazYGvPlvFwcO3IQaF7LVpEiTz95ZD/WTf4Isfs2Y3ZmGj6sU1sp3f369cP8+fPVJk6xZ9cj7du3h5j7NG7cWE/xIilTNqoSOj/+PtZ/9xpSkxPVb43YvhvcQgJ33/cgxo0bVyR9s9GCBHw0v+TNqkUUzGAKCZBAiRIolOIu3mEGDBigbCQlmFJh5ciRI5gyZUphq7E8CZCADgI3VI+Ar2Z6cTohDWe1lXbxHlNO26Qal5wBPx+vYl9B1TFklytSmO81b+/Cfwc6a8KzZ8/GK/eOQK62SdYoe/fuxauvvoq3335bbZIVO3m74uWNcnVaYMIbT6NatWp2ixZXZnSdZnh/hvY0Y89KFXgq9mIiEr3KoWabbnh37H1KmS+usbAfEiABEnBFAv9v7zzgo6i2P37SE1JICCGUEEpC701AqqjAQ3pvPuuzPBVFEfX9n2J9iKiI3YfY6b0XBUEevfdOQgkhPSG98p9zw2w22TZJNrs7s7/zYZnZe+/MnPu9k+TMnXPPKfdfnpdeeqnCPo8cbYZDRkJAAASsT+CZ+5uJCA8rDlylVYeukbenG3VsWEMsTq1ezRNuMgqQN2/enPz8/MhS0iM3Dy9q1KSpgjNav8m5c+fE7HihNOuvL/LMdHZ2NnFcdlMRbjjOfNPOfSihRjuqFVLTYYx2uS++/gH07LRpNE36HL+WTLPXn5arbLrNKygUP0fyRdnVjIV1yswtXkjctHZ18pF+ziAgAAIgYCsCJTl6FV6xR48eBi15hkdR0g7pSGuHNjNQBgUgAAIgUEECPEvNIRotSdPeI8jLy9tSsyqp53VGIgKNiURQfNG0tDTiNUn6wkmLOHnRihUr6N6HxpO7T/mj4OifT+v7eQVFtO7IDd3nrt1OZ2PSdGWnbqRoHQP6BwIg4GAEyj3jbkx/jjTToUMH8Qdv3LhxFQqLZuy8KAMBEAABWxPgKC979uwRrhrGrh3SuA21G/KEsaoqL8vMzKS1a81HXpGVYOOdQ1TWr19fJCwaOHCgSBJVXG/9kI7ydbWy5cW5gdKbKnNSzdMqf0LNXQJ1IAACIFCKgFV+69SpU4d4QdTOnTuFjyWn/X7ssceoX79+8KsthRtfQAAEHJ2Al5eXWNg5c+ZM+uqrryghIUGo7OVbnZr0Hk6tBzxMblIGUVsKx5bnHBi86FRpSMcaNWrQe++9R71794ZveAUGi5MLffloV4tHnruZZrENGoAACICAtQhYxXDnDIPsAvPMM88QzwjxH5ePP/6YnnrqKRHl4NFHHzWZSdVaHdHyeTj7JUuCtMiwOAGKYW/7tqwNH2ZDLCgBgQoRYJeZGTNm0JtvvkmcrOiNxYepyDuQXKTFv7aUa9eu0ZIlS0TiJDlBEydC4rwYlmTKlCnUt29fS81QDwIgAAIgoCICVjHc9f3WfX19hbHOsYA5jvDixYtpwIABVLduXTELP2bMGOI2EOUEOMU0y7WkTPrxr0tGD+zRrJZkuGORlFE4KASBChLgBElhYWHkV+M6peeURHCp4OkUH3ZOihCzduUy4a4jLzqVD+Y45uYMd3bx4AWonO0UAgIgAAIgoC0CVTp9xCnD2f89KipK/AFi9xlOV/3ss8/SmTNntEUSvQEBEACBShLIvnmBbm37nl558XnheljWaOfTh4aGkr+/v9ErsdHOx8yZM4fYVQYCAiAAAiCgLQJWMdwPHz6so8LRZdhVplevXtStWzeRuY9nrR555BE6ceIEXb9+XbjVjBo1SsSE51fBEPMEalcvjl7Bof1GdWkgGnt7uNEvz/TUffg7BARAQH0ECgoKhE/9J2++RPE7f6Lc+CtmO8G/T7t3705NW7UzaMehLOfPn0//+Mc/DOpQAAIgAAIgoH4CVnGV4T8UgYGBtHXrVjHTc/GilFFQEv4jwn7uU6dOFa+bZVxPPvmkMORffPFFEWv4r7/+onbtDP8Iye2dfSunHuet9E8Ib1yRvt7Zbw30X8UEON76hg0bREK7+HhlUV44EMDYsWNpyJAhtPJwDC3cvJtunT9C9f1daNyDXYkjx1SvXl3FVKA6CIAACICAOQJWMdzZFSYyMlJ3HX6Vywuj/vnPfwqDXleht+Ph4UFPPPEEffPNN8QG/I4dO/RqsQsCIAAC2iTAUWFWrlwposSY81XX7z3/fp04caKI1OXmVvJ2rXrthsSfftLi9HF9m+gfgn0QAAEQAAENErCK4S5zadKkCb3yyitiNt3b23JyEp5pZ+EsfxAQAAEQ0DKB9OQE+uyzDbRu3TrKy8tT1FXOj8EL/bt2tRyWUNEJ0QgEQAAEQEDVBKxiuLu7u9Pnn38uZtj1Z4MskZGjywwePNhSU9SDAAiAgCoJZCbeoIT9v9OKayfEwlHLnXChHtIaocce+Ts1a9bMcnO0KDcBXsCbmVMcrSs7ryRaEO/L5V7SuiF3N6ssAyu3fjgABEAABEwRsIrhzj7rnICpvML+7z179qSWLVuW91C0BwEQKEPgVlo2/fOHfXTnbnmGFL5w84mb4hvnAHj46100pmtDGtqpfpkj8bUqCBw5coQWLlxIx/fvV3R6d3cP8m7QngJa9KZ/TRlEAT62TfKkSEmNNCosukNPSz8rZeWDNSd1Ra8MakkdGgbrvmMHBEAABByBgFUM94oY7XLnYbTLJLAFgUoSkCx22Wg3diauu2O2hbGjUFYeAhxVi10Af/vtN8UugLyIf/jw4RTRpR/9tO9WeS6HtiAAAiAAAk5GwCqGu5MxQ3dBwCEJ+Pt40MM9G9Oxq8l08npqKR39vN1pROdwalI7oFQ5vliHQG5uLm3ZskXMsMfExCg6aUhIiIgQw4mSOGHSvksJ0nEw3BXBq2Qjjsj17APm3ZAa1PSr5FVwOAiAAAhYnwAMd+szxRlBwC4EfL3caUDbesQuMmUNdx/P4jq7KGaHi27bto1mffoVHTtxitw8vGh69N/o+eefp/DwcKtqw1FhOG/FsmXLKCUlRdG5GzZsSOPHjxcZpXl9EMT2BFyluLo9mtay/YVxRRAAARCoJAH81agkQBwOAiDgOATYVYXXznBuCSLOdlDsPDR79imxgJ59zkeOHFlphQuy0mjd4p/pzZ1bieOxK5Fa4RE09dknqUePHlI+hrsJGZQciDZmCaRl5VGctL6jrNxIziRP9+LQmXUCfbDQtCwgDX8vktYw8JqfssL3ys2ULFHs7+1RthrfNUqAfz+culH8FvpWasl9sf9yIl2MSxe9bh9eg4L9vVRBAIa7KoYJSoIACCgh8O6779412rl1aY9/DsE4btw4OnDgAHGYxYpIXloc3T67izKjj1HMnSJFpwhq2Io8I3vSoL5dpcX41om1Hh0dTT98/Bbt+2s75Wal066wcEr6x6PirYKPj48ivbTSaPuZW7TiwFWD7sxYcVxXNntiJ6oTWE33HTvaJpCWnUfTF5VkdJd7u/bIDeIPS49mtSi/sPhnmA36K/HFBpyf9OayVnXn+hmS+Wh1e1ka2x93XjLo3prD13Vl0x5qBcNdRwM7IAACIGADApzYaObMmSavxCEACwsL6e2336Y1a9aYbGesIjMumuKPb6fsmHPGqg3K2AXmgQceEDHYv9mbRDF3Z/kMGlaggH3p+a1BVlbxzCGf4vqlszR9+nT6+eef6Y8//qDatWtX4Mw4BASch8Du8yXZivdeSiT+sNwTUZOmDGjhPCDQU9URwIy76oYMCoMACBgjsHPnTouJjdh437x5s4inbsldhdvu2bNHRIiJOnXK2CUNyni2mxeb8sw+Lz4VIhnu1pLr16/TqFGjKCcnp9QpWVeW06dPi2szC2eRXtLMqa+nG/3yvyuiy0/2jaTQMjOmwX7qeAXuLGNW1f1kN5jXh7Q2epnZG04ThwO1lizYfUW4YfCsvSxJGbn0xpIj4qu7tBD6vTEVe8Mnnw/byhHoHhlCXSPu/j42cSppmFQjMNxVM1RQFARAwByBxMTiGTNzbbiOXWYyMjLI39/faNOCggL6/fffacGCBXT1qqELhrGDgoKCaPTo0TRixAiT5zV2XHnLPv30U8rMzDR7GIejZMO9T58+ZttppbKmvzc1CCmJANOolj8hIoxWRrdi/eDEWa3rBxk9+K0R7ajo7oOusQbl9X1PSs+l60mlfyb5wUAuY8MdYl8CPEnjpqFhgOFu3/sJVwcBELASgfr1lSWWYoPdmNHOridr166lJUuWkNKHgLCwMDHDPWjQIPL0rPqESRwtR4ls377dwHD/61wcRSdkiMMvxKaJbWZuAf2y67LY5/WyD/eMUHJ6p2+Tm18oojcxCP2Z1lRp1jU3v9hv2oxt6PT87AkgItT4A3tFdWpVP5CqSX7x/LMVnZghLYJ2oZ5NQ3Wn4+8QELAmARju1qSJc4EACNiNQO/evYlnvtnXXXYdMaYMz4zrS3JyMq1YsYJWrlwpZuL160zte9aoR+PGT6Anxw0hV1dXU82sXs59UyJpacWGuX7bk9dSJD9ejhVfImxkbj1ZnF2XzQsY7iVszO0diU6ir34/b9Bk9vrTurLs/ALdPna0S+D+VnWIWhGtPHhVGO7eUiSjJ++zziJ07VJDzypDAIZ7ZejhWBAAAYch4O3tTXPmzKFHH31UhFssa7yzgR0QEEDvvPOO0PnGjRu0ePFi2rRpk0XfeLmT3rUjKaBFb/KRtu3uaW5To511aNKkCbHeZfsm6ydvIyIMZ84DfT0l329vuYnBlmObQ0AABEAABBybAAx3xx4faAcCVU6As34mJCZRUWEBubo55q+E27dvC7/tS1dvUMzZDApt0t4ol0ceeYS47bRp0wyMcXalWbVqlfARf+utt2jHjh0WDWC+iJubG/mFt6ZqzXqTZ5A0u2ZHmTBhArEbjDnx8PAwGqt+Uo/GxB9I5Qk0q1Odpv6tpdETbTkRQ2di0sjrbgx5o41QCAIgAAIVJOCYf6Ur2BkcBgIgoJwAxzP/v//7P/rzzz9FmEQ22uu16UEP1H+PqLV9DVS5FzyzPGvWLOL47PqJjjy8q1HjjHeo47+nyU112xdeeIGGDx9O78z5jv7ce0TKnOpJM54eQw0aNBDhEg8fNozvrDtYb8fLy4vYd52N5Xc3RVO6lJHW3sJvE3766SfavXu3SVXee+89qlevnsl6VFSeQA0pSg1/jMmhK8WLpN2wKNEYHpSBAAhUkgAM90oCxOEgoEYCy5YtEwYpZxqV3S54xv36sZ307LgBFCHFCu/Vq5fduzZ16lSaO3eugR75OVk0881Xyc81j/71r38Z1PPs+phHn6Xsxpco6/pJESXm8uXiRZgGjcsUsDsNx0nnsIuBgYF3a6PLtLLPV44Pv3HjRnr88ceFX76+Fvyg8f7774u3Dfrl2HdMApuPx1CiFJGERY5AEidldfztbljLgGoeNLRjfcdUHlqBAAjYjQAMd7uhx4VBwD4EOBb4ww8/TPpGu74muVKMcDZar1y5Qn5+JWH29NvYYn/fvn1GjXb9a7PLy5gxY4Tvt345xzk/uHMLxWxYRYWZqaQkUGRoaKiIEDNkyBBif3lHFX6wWL58OX348wZaumYj5UmZUzu3aUazpj1J3AeIOgjsuRgvZessjvIja5ycmUebJVcbltpSLHoY7jIZbEEABGQCMNxlEtiCgJMQ+Prrr4n92k0Jz8AnJCTQwoUL6amnnjLVrMrL2SXEknAm1F9//VW40nBbjqbCfuxs2BqLrGLsfLyQk91h7r//fuIZbbVIgyYtqOUDAULd3i1rw2hXy8Dd1bOGrxel++eb1BpJo0yiQQUIODUB9fyVcuphQudBwHoEeCabE1LILjKmzrx37167Gu5nz561qCf3g9vdunVLxF9ft26d2YcS/b62b9+eJk2aRN26ddMvxj4I2ITASyYWt9rk4rgICICAagnAcFft0EFxEKgYAc4caknYIFbSztJ5KlPv4+Nj0XDn81+4cIHGjx8vFthauh73q2fPnjR58mRq2dJ4VBBL50A9CIAACIAACNiLAAx3e5G3cN3DUUmUnVccxYKz8bFwamU5UEEh0vJZIIhqUwRatWpFe/bsMVUtynk2vnXr1mbbVHXlvffeS1ukRbLmhPXMzMwU8dnNteMQiQMGDKCJEyeS0gyr5s6HOhAAARAAARCwBwEY7vagruCai/dGUawUYUBfOJ0yf1jyC4vTauvXYx8ElBB44oknaN68eWaaupCHh7twIzHTqMqrnnnmGZo9ezZlZWWJhbTGLsgGea1atYxViTIXDy/yj+xKv8x8mYKDg022QwUIgAAIgAAIqIEADHc1jBJ0BAErEujatasIGfjxxx8bcUXh7Jl3RAbS8PBwK161/Kdig3zp0qU0YsQIo37rnBipRYsWIkFS2bOzkd6u1wC66N5EiuPuZRejPTU1lX755Rdav3QTZWbnUVbHdvRg46mY8S87WBr4zrHbkzKKF3zHpGSJHqVJY87JmFi8PNyob4vaYh//aYfAwj1XaM+FeNGhnPxCsc3MLaDnf9qn6+Sch+8hDzdX3XfsgEBlCcBwryzBKjr+vTEdpFnGOwZn33DsBq05fB1Z+QzIoKA8BHgmm5P0cDjF9PR03aFeftXplTc/oOee+6euzF47GRkZlJycTN27d6eTJ09SSkqKmHl3dXUVhjgnVCobtpEfNjhCDLvFbD8bT5fvxsS2dR/YxYf97tl4J+KHIaKrR7bThl++oi+++MKui36FMuX473xsGl28VXyPXLp1W3cku/PJkp1XSEG+8jfn2/5+MpZOx/BYl0hyRh79evf+q+7jAcO9BI1m9rIkIz01q3RkIP6rrV8Gr1bNDLfDdASGu8MMRWlFvKUZGmMiP7kXmwLGWqAMBJQReOmll4jdUTgLZ1xcPP10KJlqNmpJ/e5rbnCC2HOH6Pyfyynp6lkpGk0R1ajfjJr0GkY0xPp+8ImJicQJolavXi3cZFgZnllnf3YO/2gsZCP77bP/OieN4gWo9pRjx47R0KFDqaBAzrRa8gCen59PTz/9NNWsWVMkebKnnkqvfeJaipgskNtnpcRT7NmDdHpLCvkEhlDdlvfo1uPIbZxua+GWs/Mt6XTDYasOt29QgwJ8PM1eDhl0zeJBZQUIwHCvADQcAgJaIcAz1hy/vFB6u7Mx9X9Gu/XBO2/S9i8+lerYOik2QmPPHZSMtwP0VuoZWrH4V6sYy1evXqVFixaJBaklRm+JSmyQlzXaeTaeDXYO7egoMn36dGID3Vi4TS7jfvBD0/Dhw4nfHji6sOHBEwacWffQyq/p7Pbl4uFN1tvVzYPCU6bTJzPfs8p9IJ9XTds3hrZRk7o21TU+LZuW7IsW18zTW5u1SXp7vP9Sgijv3SKU2oXXsKle1rhY58Y1iT8QELAlARjutqSNa4GAyghwcqOv57LRzlIycyxZbqJk1dIF9EmX9sJnXhRU4L9Tp06JZE+7du1SdrSLK/k2aEsvPPU4PdSrg7JjbNSK3Xu2bdtm1GiXVWDjnbPX8sx8x44d5WKH3Y7s0oD4w9l2z2xbaqBnUWE+zZn1AXlSAX344YcG9ShwbgIZkjvJ/suGuYsvxknuV/yRpGmdAMlwd25O6D0IKCUAw10pKbQDASckMGPGDDGLamz2WMbxwQcf0IsvvihFovGQiyxu+XycCGrBggV0/Phxi+25Acd1v7//3+jonUhy9w2kOmGO95eeE0EVFSmL+BQTE6MKw53Z88PIb7/9xrsm5aOPPhLGPbstQUBAJsBun01rF2f4lcvKbgN9zbublG2P7yDgzARUZbjzIrr9+/eLVOaNGzemDh2Mz7bxH07OphgbG0udO3emwMBAZx5j9B0EKkTg2rVrFBUVZfFYXoDJxjf/rFkSdoH5448/hMEeHR1tqbmo55/fUaNGiU8uedBLvx5UdJw9GoWEhCi+rLkwlopPYqOGlox2VoMfxhYuXEj8IAcBAZlA3aBq9NbIdvJXbEEABCpJQDWGOy+g4z8I+hEw2FCYOXNmqcgSbLC/88474o98ZGQk8YwhZ0jkBWEQEAAB5QRu3y6JIGLpKI74Yk44Fvv69etpyZIlFB9fHD7NXHuuq1u3Lo0bN44eeugh8vLyEs1z03MsHWbX+urVq1OPHj1EgitTbynYx50Xp3bq1Mmuupbn4hcvXrT45oX7xe0gIAACIAACVUdAFYb7jRs36McffxT+k2yMsxHP8ZEPHTpE33//PT3//POCEEejeOONN2jYsGE0ZswYUcYh43i2jkPfDR48uOpI4swgoDECHFqRY6VzJBdLwtFpLl26ZLA4sTAng9Yu/Y12/bGx1EO3ufM1bdpULDjt27ev0Rjt5o51hDqeTGDdWYwZ71zGvuBlF9qKAxz0Pz8/P4uGO/eL20FAAARAAASqjoDjhzSQ+r5p0yZ6++23qW3btlStWjV68MEHpTjTzwkqbMTL8tNPP4m4yWy4y1KjRg3q168fff311yLSg1yOLQg4IgF28+LZaUeQgIAA6tatmyJVrly5Ivyb5cZxt2Ip6eAailn7EW1ctUSR0c5v0D799FOaP3++iHTDDw1qFA5JyYt6dT7/0ky0HMudZ6Xfffddevzxx1XVtT59+ijy3ZcfWFTVOSgLAiAAAioioArDvU2bNhQWFlYKa5cuXYTvenZ2tijnWcGdO3eKrIRsrOsLL5ZiF5u9e/fqF2MfBByGAD+ActIgDs8YVqsGLX9tCB1a9jmlpiTbTcfz58/T4cOHFV+fQzmyrzs/ZL/07OOUcWk/3ZFCCJoTDod43333CWN9zpw5xD/XWhAOUcluI/wGsEHLzlQrsi31GzGZjh49Sm+++abqushvVIKCgkyGr+QHkkaNGgnXJtV1DgqDAAiAgIoIqMJVxtisH8/GeXp6UkREhMB98+ZNMdvO/uxlhX1lWU6fPk29e/cuW43vIGBXAvPmzdOtwZBdK3Iz0uj8juU0ecge2rfnf8IosrWSbGDm5Cj3Kee3BZMnT1a0GJx/dgcNGiSynMo/n7buX1Vfj12N/vOf/1Bhm1EUk5JF/VrVpnbtmlT1Zavk/Gy0r127VoyZ/joj+WI1a4aIenktglyOLQiAAAiAgHUJqMJwN9Zl9mfnRW7y7BWnRmdhV5qyIqdFN7UojuNHv//++2UPE37xBoUoAAErEuBY3jybySIb7fqnj4+LFes1Dh48aOA/rt/O2vtshLOhVl7hxEPmxN/fn0aMGEGjR48WM7jm2qLOsQj07NmTOOY+P4ysW7eO4qTfv94BNal++960dv4n1KRh6beijqU9tAEBEAABbRBQreH+888/i7TicsbEzMxMMSI8k1dWZF/T3NzcslXiO8/4cRbDssLGEgQEqpLAJ598Igx2Y0a7uK604I/dVf7880+xVqMqddE/N4d4NPXzot/O2D6HeeSfR3afYEM9NDRUuLqNHTtW/MxyPHaIOgnwW4Rvv/1WfA5eSaS5m8+KjtQsRxhMdfYcWoMACICAYxBQpeHOsz7sGjNr1iwdRQ6vxpKXl6crk3dkA4T/6BgTdrd59tlnDarkaDUGFSgAASsR4Lc9Jo12vWuwDzwvsraVcOx0fgg29vNkSgc21NkvXl/4TVhs7C2aPn26iO6kX4d9EAABEAABEACB8hFQxeJU/S7FxcXRDz/8IBbA6YdT41k9FmMROeSyhg0bijb4DwQchYC8uNqSPuXxNbd0LiX1vGiU46ezMa5UTD2A5OfniUWLBw4cUHoqtAMBEAABEAABEDBCQFUz7myAf/XVV8KvnV/B6wsnPmGXF56JLyuybztHPYCAgCMR4IhHCQkJFmfdmzdvbnO1n3rqKeHnriSOOxv67BdvTNig57rXXntNuPwYa4MyEKgqAj//dYl2nosTpy8suiO2WbkF9Ph/S0IJf/t4d/J0V908VlUhc/jzno9No6j4DKHn2ZtpYssju/l4jE73+1rWJi8PdYaU1XUCOyBghIBqflOxuwuHi+P47RzhQF84zjsLZ1nkNO2xsbH61XTu3DkRJrJJE3VGdCjVGXzRFIHHHnvMrNHOM978UDp06FCb9fvqpXPCyOZMxfzAYCqeOi/65rdYrVu3Nmm0y0qz8c7hWsuTjVU+FlsQqAyBAslYzysoEh/ZcOfzyWW8lZaGV+YSONbGBI5EJdFvu6+Iz2FpXxa5jLfZ+ZYTx8nHYQsCaiKgihn3goICeuutt0Ta89WrV+v48kwgG+rNmjUTZRxejusXLlxIr7zyiihjH1v2D3799ddNxiDWnRA7IGBjApMmTaLFixfTxo0bDa8sGe1s8H733XfCeDdsYL0Svk7WjTOUdmYn/Zh0XXdifkjmxEi3bt0SRje348Wl7JrmHxhMDwwcRBFhoSIMpO4gEzt8LLu6cWInRxfW9en5JXkfsvIMjYAdZ25R14gQR++KZvW7EHtbN8OanlMSzWjhnijy9Sz+0zakU33q0rgmhQZ4m+XgJr0x0qJk5RXQl1vP6bomP7j8Kd27p26kivIujYPpvpZ1dG3UsMMTGtI/s2Kh2uyxqAQBRyagCsP9o48+oj179hjlyK/oX375ZVHHM4Bffvkl8Uzhv//9b2rRogUdOnSIpkyZQpzNEAICjkaA79+VK1fStGnT6JtvviF9txRv/yB698M5VZrUhsM3bt26VTzsJkgPwcaEozLVr19fV+Xm7U/+zbqTf2Q3GjmqM+XEXdbVmdvhP7byWhRz7RyhjudfjRnr+rrlFxp3DdJvg/2qI5CckUsHpMg2ZeX0XYOUy3s1D6UODWtQ2/DSb2nLHqPV7wXSPXriWopB92JTs4k/LHUDDUMoGxzgYAXjuzci/kBAwBkJqMJw/9e//kX8USI8m8fRZngxX0pKikjwwsYRBAQclQAnrfniiy/Ewya7k9yMT6T1F/IoRMq22bd/2ypRm8M1cpz2JUuWUFJSyatmcxdz9w+mgOa9yK9RR3JxK/nV0bFjR6pdu7aYTeeZamPCRjsnP1PDbDvr7yrpO+qeBrquZEszlxuPlfjPckVELcd/c6DrgIPuzFx7kti4ZEnOLA7Xe+ByIl1NLPZfruHnZVLzAB8PalbH/Bj4eZfcpyZPpOEKdzdXamfhoaVeDfUZ7hoeMnQNBCwS0OxvNZ59r1NHXa//LI4WGmiaAM9Gc6zzFMmAOfRz1URgYSN92bJlwqVMzn1gCWpk02aUWqsTVQtrKb2eNnwI5gfjTz/9lCZOnGj0VGy0cxv98K1GGzpY4YjO4TqNeEzKGu6NQ/109dipGAF2dyn75iI1K4/4w9K0dukgBPpXaRkWSPyBmCZQTXIZenVwa9MNUAMCIKA6Apo13FU3ElAYBKqQQE5qPLHL2ebNm8lSdlNZja5duxL74Ic2bEbTFx2Wi41uJ0yYIPzgX331VeHu4yIZ6mL2XZqB95IeohcuWEB8PggI6BO4J6KmbsZdv1zer+blRhdupctfsQUBEAABpycAw93pbwEA0DKBXGmh6e0zf9FVaeHpKSWRM6QZ9Tad76VXnnuSODEZy82ULEWIpk6dSoMHDxZ5Fg4ePkbn4zIouEFzmvvOq9SnQ1NF50Aj5yLw7APFgQVM9fr4tWT680xxKEdTbVAOAiAAAs5EAIa7M402+qoZAryGg1PP//jbYrp0JYp4IesHMaNp+ivFC7Wzb16gtLM7KTc+SlGf2bXMI7yD8GEf9bfOktFeMTczDrk6c+ZMiknOotcWF8/S1wyppUgHNAIBEAABEAABEDBPAIa7eT6oBQGHIxATE0P9+/enM2fOiMym7JKSlZJAs/7zAX371ZfUoUs3KsjJVKQ3x4gfOXIkjRg5il5YeELRMWgEAiAAAiAAAiBgHwIwy76ebwAALsdJREFU3O3DHVcFgQoRYCN9xIgRwmjnE5REcSmO5pKWlka7d26nTp06kbu76R9vXrjNCcvYtYWj2sjxnSukFA4CARAAARAAARCwCQHTf9ltcnlcBARAoDwE1q9fTwcPHjR7CC8+5YRJYWFhBu0iIyNF9Jd+/fqZzIhqcBAKQAAEQAAEQAAEHIIADHeHGAYoAQLKCPz++++KGnIOA33D3b9uJM14+RlEdlFED41AAARAAARAwDEJwHB3zHGBViBgQODixYvECZqUSEFBgdTMharVb0UBLXpTWKNIyWjvouRQtAEBEAABEAABEHBQAjDcHXRgoBYIyASOHDlCC6Q46AcOHBDZgOVyc1u/4DpUd/DL5CFlO4WAAAiAAAiAAAhogwAMd22MI3qhMQJ37hRR1vXT9Onb8+lG9GVd74KDg+n69eu676Z2Ih+YBKPdFByUgwAIgAAIgIBKCcBwV+nAQW1tEsjNzaXNG9fTzfW/UEFGskEn/fz8iCPCxMbGGtTJBa2lBEruXj60f+Fsyk5LlGK816AW9/ShO5M6i/CRcjtsQQAEQAAEQAAE1EUAhru6xgvaapRAeno6rV69mpYtW2bRHaZx48bCAL9586YBDQ7vGBWbRDu/eb24zsWFY0bS5b0bqNehNbRq1SoKCQkxOA4FpgmkZObRhqM3DBrsu5RAN5KKs8q2DQ+iJrUDDNqgAARAAARAAASsSQCGuzVp4lwgUE4C8fHxtHTpUlq7di1lZ2crOrpNmzb04YcfCgP88/kL6Y8Dp8jbL5Dmvv4kzXzvbTp9eG/JeSSjXZbdu3fTkCFDaM+ePeTq6ioXY2uBQGqm9BbkhOFD0sHLSXSQksTRvl7uFTLcT15PIX4AYIm/nSO2/N9v/7tCHu7FYzSycwMK9vfS1WEHBEAABEDAeQnAcHfesUfP7UggKiqKFi9eTFu2bKHCwkJFmtx77700efJkYsNdlkn/eI7SGp4XX5OTk2jr1q1yldHt/v37xYPC+PHjjdaj0JCAq6sLsWGemcuReoi8PdzI3U16k6EnnneNbL0iRbvXkzJp59k4g7Z7LhYb81zxYOu6MNwNCKEABEAABJyTAAx35xx39NpOBE6ePCkixPDstxJxdXOjAf37i6RJDRs2NHvIhnVrzdZzpYvkOrNmzRqC4W4Rla5Bg5p+9OH4jvTCzwdE2dP9mlKXiJq6+srsBPh4UHiwr9lTVPShwOxJUQkCIAACIKBKAjDcVTlsUFpNBO5I7irsnsIhHdlwVyIu7p7kF9GFpj7zGD3YuZmSQ0S2VHaBKSoqMtvemG+82QNQWWUEejYLJf5AQAAEQAAEQEAJARjuSiihDQhUgAAnQeJMpwsXLqTo6GhFZwgKCqKHho6gnRn1yNXThwKDlMdhr1Ur1KLRzkrUrl1bkS5oBAL2ILD3Yjwt2B0lLp1fWPIQ+u7K4+TKi60leXFgiwqtKRAH4z8QAAEQUDEBGO4qHjyo7pgEsrKyxGLTJUuWUGJioiIl69WrRxMmTKCBAwdSluRKveuuW4aig+82GjhoEP30w/dmD+HZf448AwEBRyWQm19EqVl5Burdzs7XlRXoGfS6QuyAAAiAgBMQgOHuBIOMLtqGQHJyMi1fvlyEXMzIyFB00WbNmtGkSZOoT58+ukgvWQW5io4t26j/gIEUGBhIqampZat03/l6/IAAAQFHJRBe05eGdAgzq16wv7fZelSCAAiAgFYJwHDX6siiXzYjcOPGDREhZtOmTZSXZzhTaEyRLl26CIO9U6dOxqorVPb9f78za7TzSXlxqpu04BVimQDP6qbnFEeSSdObAc7MzSeO7c5SzdONvKQoMxDrEWhcy5/4AwEBEAABEDAkAMPdkIlDlfDM7aeffkqLFi0iDiHo4xtAQZEdqdNDj0h63utQujqbMufOnRP+6zt27JByHJXESzfFgReO9uvXTxjskZGRpppVuPyH7/8rDHNzurDOHBKyW7duFb6Osxx4NTGTZqw4ZtDd73dcksr4Q/Rwz8Y0oG09sY//QAAEQAAEQKCqCcBwr2rClTh/TEyMMPQuXLigM8hycxMo9cAWunp4O61u60PDhw+vxBVwaEUIHDhwQESIOXLkiKLDvby8aJDkf84uKnXq1FF0THkbFRUW0HnJKDdntMvnPHHiBAx3GQa2IAACIAACIKAiAjDcHXiwxo0bR2y0s5Q1yNhQ41jcZ86cocaNGztwL7ShGidJ2r59u5hhv3SpeLbVUs8CAgJo5MiRNGrUKOF7bql9ZepdXFyFj7ySZE5wlVFGunZ1b5oyoIXZxg0kf2xby8EriVLSrjt0M6Uk025cWjbtu5u0KdDXk5rXrW5rtXA9EAABEAABGxCA4W4DyBW5BLtfmE/Sc4dyc3Ppk08+oa+++qoil8AxCgjk5OTQxo0bhavSrVu3FBxBFBoaSvzQNWTIEPL2ts0iOhfJDadd+w509Mhhg4e8skqzfz3EMgFfbw+6x0qJlixfTXmLedsvUFZe6Wy7p2PSiD8s7RsEwXBXjhMtQQAEQEBVBGC4O+hwseGuRHgWGGJ9AmlpabRy5UpasWIF8b4SiYiIEO4w999/P7m72/5H67kXptATj/7dpKq8MJWj17Rt29ZkG1SAAAiAAAiAAAg4LgHbWxeOy8KhNEtPT1ekj9J2ik6GRiL7KMdfX7dunXijoQRJ+/btxYJTey/4HDNuPO3bvYvmzZsnqc2JakovmGX/+l9++UVJl9DGgQl8MrmLeKuy8uA1+uNULAVJrjEfjO2g09jdzVW3jx0QAAEQAAFtEYDh7qDj2aRJE4ua8Qxq06ZNLbZDA8sE2G+dI/ds27ZN8h8u7YZg7Ghm36tXL2Gwt2zZ0lgTu5T997//JdfgRvTbf+dSZnKc0MHVXfJ5vrc/bV/6vXDjsYtiuKjVCPhLLjwsXu7FBrp0K1KAj6fVzo8TgQAIgAAIOC4BGO4OOjYjRoygqVOnilnfsgtTZZW5fPLkyfJXbCtA4OjRoyJCDIdIVCIeHh40YMAA4RITHh6u5BCbt3lwxETKqN+TslITqCAvh3yDQql2cACMdpuPBC4IAiAAAiAAAtYlAMPdujytdjZe4PjRRx/RlClTdKEgy568b9++9MgjHM8dUh4CRUVFtGvXLmGwnz17VtGhvr6+IvTmmDFjKDg4WNExtm5UUFBAGzZspaWr/6CzN1MpKKwJ1W3Zldw8MBtr67HA9UAABEAABECgKgjAcK8KqlY65wsvvEA8w/vqq68SJ2LSl4h7+kt+2CuQBVMfioV9zmq6ZcsW4RJz/fp1C62Lq9lIHzt2LA0bNozYeHdUSb52njq1e5SirlwppWK1wFrU47E3KaRj11Ll+AICIAACIAACIKA+AjDcHXzMnnnmGRGvfdOmTSJz6tW0Ior1bkShYY3Iz8/PwbV3DPX4oWfNmjW0dOlSSk5OVqQUu8FwwiR2i+GHJ0eW23HX6ffPplCh5BZTVrLSEmjbFy9TyIz5UhXCQJblg+8gAAIgAAIgoCYCMNxVMFqBgYHCiGRVVx+6RssPXFWB1vZXMTExkZYtW0arV6+mrKwsRQq1atWKJk6cKBae8gJUNcjhFV9QQW5JMp5SOkvrIDhZ158/zyb698OlqvAFBEAABEAABEBAXQRguKtrvKCtAgJXr14V7jDsFsN+30qke/fuIkJMu3btlDR3mDbpt9Po5hkLC2sl4z320km6du0aOeqCWocBCkVAAARAAARAwIEJwHB34MGBauUjcOrUKVq4cKFYeKrkSDc3N3rggQeEwd6oUSMlhzhcm1sxN6Rw7aXjtZtS8ork/w7D3RQdlIMACIAACICA4xOA4e74YwQNzRDgkJh79+4VBvvx48fNtCyp8vHxocGDB9O4ceNUHyLRz9+/pGMW9qpXr26hBapBAARAAARAAAQcmQAMd0ceHehmkgC7wPzxxx/CYI+KijLZTr+C1wqMHj2aRo4cSf7lMHj1z+Fo+3XCwsm3RihlpsSbmXl3IS9ff2rbtq2jqQ99QAAEQAAEQAAEykEAhns5YKGp/QnwItP169fTkiVLKD5eMlYVSN26dcXs+kMPPUReXl4KjlBXk7YPPU57f51pRuk71G3EkwgdaoYQqkAABEAABEBADQRguKthlKAjpaSk0PLly2nVqlWUnp6uiEjTpk1FhBhOVMX+7FqVxt3+Rmmx0XTmj0Wlk3VxVBzJlSiy51Bq33+cVruPfoEACIAACICA0xCA4e40Q63Ojt68eZMWL14sZQTdQJxASYl07txZLDjlrbNIhxHP0sypf6f5331Df+3eSzl5BVSjflNq0ns4hbXpIQx6Z2CxQgqVuuVEjOhqfmHxol3+/6nv9+i6P3tiZ6peDdlkdUCwAwIgAAIgoBoCMNxVM1TOpej58+eF//qOHTuoqKjIYuddXV2JZ9Y5BnuzZs0sttdig/v63U9DBw0kNl5XSfH+nVHyCgopK6/QoOv6ZUXKgvAYnAMFIAACIAACIGBvAjDc7T0CuH4pAocOHaIFCxYQb5WIp6cnDRo0SCSoYl92iHMTaBMeRN6e5n+t+Xhq123KuUcfvQcBEAAB7RMw/xdO+/1HDx2AQGFhIe3cuVMY7BcuXFCkEUeFGTFihIgSExQUpOgYNNI+gdZhQcQfrUpUfDolZxa7jN1KK86Wm1dQRIejknRd7tQoWLePHRAAARAAAW0RgOGurfFUVW9yc3Np48aNwoedfdmVSK1atWjs2LE0dOhQ4njsEBBwJgIbj8fQ3osJpbqckVNAczadEWXScmT69Z+9StXjCwiAAAiAgHYIwHDXzliqpiccFWblypUiSkxqaqoivTmzKfuvc6ZTd3fctoqgoREIgAAIgAAIgICmCMAC0tRwOnZn4uLiaOnSpbRu3TrKzi5+zW9JY04aNGnSJOrevbvTREaxxAT1zkvgkV4RNL5bI9MAeModAgIgAAIgoFkCMNw1O7SO07ErV66ICDGc6ZT92ZVIr169hMHeqlUrJc3RBgScgoCftwf5eTtFV9FJEAABEAABIwRguBuBgiLrEDh+/Lgw2PfsKYmhbe7M7ALTv39/YbCHh4eba4o6EAABEAABEAABEHA6AjDcnW7Iq7bDd6RMnf/73/9EhJjTp08ruli1atVo2LBhYtFpzZo1FR2DRiAAAiAAAiAAAiDgbARguDvbiFdRf/Pz82nr1q1ihv3aNWXJf4KDg2nMmDHCaPfz86sizXBaEAABEAABEAABENAGARju2hhHu/UiMzOT1qxZIxadJiWVxJI2p1D9+vVp/PjxNHDgQOIEShAQAAEQAAEQAAEQAAHLBGC4W2aEFkYIsJG+bNkyWr16NbHxrkRatmwpQjrywlNXV1clh6ANCIAACIAACIAACIDAXQIw3HErlIsAu8EsXryYNm/eTOweo0S6du0qFpx26NBBSXO0AYFSBFKz8mj/peKkQ5m5Bbq6o9HJlJCeI763rBdI9YN9dXXYAQEQAAEQAAEtEoDhrsVRrYI+nTlzRiw43bVrF/ECVEvi5uZG/fr1EwZ7RESEpeaotwOBjJx8Wrb/qriy/pjuuRhP15KK36K0Cw+i2oH2zVAbn5ZDv/7vigGhP8/e0pU91jsShruOBnZAAARAAAS0SgCGu1ZH1kr92rdvnzDYjx07puiM3t7eNHjwYOHDHhoaqugYNLIPgZz8Qtp2Otbg4udjbxN/WPy83e1uuBsoiAIQAAEQAAEQcFICMNyddODNdbugoIC2b98uIsRcvnzZXFNdXfXq1WnUqFE0cuRI4n2I4xNwc3WhukHmZ9MDfDzs3pGmdQLot3/2srseUAAEQAAEQAAE7E0Ahru9R8CBrp+dnU3r16+nJUuWUFxcnCLN6tSpQ+PGjROz7F5eXoqOQSPHIBDk60UfTehsUZmbKVkW26ABCIAACIAACIBA1ROA4V71jB3+CqmpqbRy5UpasWIF3b5d7CJhSenIyEgRIYb92NmfHQICIAACIAACIAACIFC1BGC4Vy1fhz57bGysiBCzYcMGys3NVaRrx44dhcHOkWIgIAACIAACIAACIAACtiMAw912rB3mShcvXhT+6+zHXlRUZFEvFxcX6tOnj4gQ07x5c4vt0QAEQAAEQAAEQAAEQMD6BGC4W5+pw57x8OHDwmA/cOCAIh05qylnN50wYQKFhYUpOgaNQAAEQAAEQAAEQAAEqoYADPeq4eowZ+UZ9Z07d4qQjufPn1ekl5+fH40YMYJGjx5NNWrUUHQMGmmPwF/n4ujczTTK0kt6VLaXRQpi+pc9xhm+z9t+gXILit9mJWcUu6Gdup5KX249J7rfMMSPBnfAw7Az3AvoIwiAAAhYkwAMd2vSdKBzsc86ZzddtGgRxcTEKNIsJCSExo4dS0OHDqVq1aopOgaNtEvgfGwasfFuTvQTN5lr52x1B64kUnZeYalux9/OIf6wcAx9GO6l8OALCIAACICAAgIw3BVAUlOT9PR0Wr16NS1btoxSUlIUqd6wYUPhDtO/f39yd8ctoQialRsVFt2hzNx8cdZ0KaOpLFl5BXQ7O0989fZwJ093V7mqyrfBfl7UoKYv5RcW0c2UbKPXcyEXo+XOXhgZ6i+Mc1Mc6lmIn2/qOHuXX5Ae5g5eSRJqxKWV3BOrDl4jL4/i6FID29ajYH+EhrX3WOH6IAAC2iQAK00j45qQkCDir69du5Y4HrsSadOmjVhweu+99xIvQIXYj0B0QgbNWGGYnXbenxd1Sj3cszENkIwiW8nILg2IPxzHffqiw0Yv6yolcYIYEnhtSBvDQg2UREn36abjhm/wtp+5petdt8gQGO46GtgBARAAAesS0KThzn7dZ8+eJQ532LlzZwoMDLQuNQc6W1RUlHCH2bp1KxUWln41b0pNNtQnTZpEbdu2NdUE5SAAAiBgQMDH0534TYw5cXfDw5w5PqgDARAAgcoQ0Jzhzgb7O++8Q6NGjSJOEjRjxgxq2bIlPf3005Xh5HDHZsVH0+uvr6Xdu3cr0o2TJLErzMSJE4ldYyCORSC0ujc9/6D5UJu8oNHWcjkunY5GF7tGGLv24agkaiy5hVSTDDqI9gn0bh5K/IGAAAiAAAjYh4Cm/tomJibSG2+8QcOGDaMxY8YIog0aNBBGfL169Wjw4MH2oWylq/JCwMunjtCt35dTbuJVuqbgvD4+PmKx6bhx44gXn0Ick4Cftwd1a+I44xObmkWbj9+kK/HpxO4RpuT3U7F0IfY2eUi+98M7h1P7BohCZIoVykEABEAABECgsgQ0Zbj/9NNPlJqaKgx3GQyHM+zXrx99/fXXNGDAAPLw8JCrVLMtKCggdoXhCDHR0dGK9A4KChLhHDmso7+/v6Jj0AgEZALJGXm07XSs/NXs9mpSpqi/nV2yqNbsAagEARAAARAAARCoEAHNGO7s383xyuvXr28Qe7xVq1bC8N27dy/17t27QqDscVBWVhbxYtMlS5YQv01QIvxmgRMmceIkLy/zvqhKzoc2zknAy8OV6t6NfMJvejiyTEZOQSkY4cG+VEPyd5YXNtcK8C5Vjy8gAAIgAAIgAALWJaAZw/3mzZtitp392ctK3bp1RdHp06dVYbgnJyfT8uXLadWqVZSRYdpNQb+fzZo1EwtO+/TpQ66utgsZqK8D9rVDIDI0gD6a0Fk7HUJPQAAEQAAEQEADBDRjuLOxy2IscZC3d/FMYHx8vNEhO3jwIH3++ecGdbVr1zYoq8qCGzduCHcYTpyUl1ccu9vS9e655x6x4LRTp06WmqIeBEAABEAABEAABEBAxQQ0Y7hnZhb72Xp6ehoMh+zXztlEjYmvr6+IQFO2jg1oW8i5c+do4cKFtGPHDlKUiVKKue7foC3NfetFatKkiS1UxDVAAARAAARAAARAAATsTEAzhnvNmjUFSmMz1bLBHh4ebhQ3u9dw2Miy8u6771Ljxo3LFlvt+4EDB2jBggV05MgRRedkn/UWXXpTQlB78g+qCaNdETU0AgEQAAEQAAEQAAFtENCM4R4aWhxbmBd0lhW5zBHil/Mi2u3bt4sZ9kuXLpVV1ej3gIAAGjlypAhruePSbVp+4KrRdigEAXsSOHU9hWatO2Wgwsy1J0lOyfP0/U2pZzPEATeAhAIQAAEQAAEQUEBAM4Z79erViReh8iLVsiL7tjdq1Khslc2+5+Tk0IYNG2jx4sV061ZJenBzCvDDCMdfHzJkCMl++kS3zR2COhCwG4E70pX5Y0zkcilADQQEQAAEQAAEQKCCBDRjuHP/2cidO3cuxcbGUp06dXRI2Iecw0Tawx88LS2NVq5cSStWrCDeVyIRERFiwSnHn3d319QQKek+2qiUQJ1AH5rcw7xrWYSUZRUCAiAAAiAAAiBQMQKasgoHDRpEq1evFm4or7zyiiDC0WZ2795Nr7/+uk3DJPKsOsdfX79+PfFsuxJp3769COnYrVs3Jc3RBgQcikBNf28a2K6eQ+kEZUAABEAABEBASwQ0ZbizO8mXX35JH3zwAf373/+mFi1a0KFDh2jKlCnUq1cvm4wb+61zhtNt27YR+7NbEk5ew7pNmjSJjMWgt3Q86kEABEAABEAABEAABJyDgKYMdx4yXsg5a9YsMcudkpIisojaIiHR0aNHRYSY/fv3K7pzOEQlZzcdP348mYp2o+hEaAQCIAACIAACIAACIOAUBDRnuMujxrPv+n7ucrk1t0VFRbRr1y5hsJ89e1bRqTlm/PDhw2nMmDEUHBys6Bg0AgEQAAEQAAEQAAEQAAHNGu5VObQcK56TM3GEmOvXryu6FBvpY8eOpWHDhhEb7xAQAAEQAAEQAAEQAAEQKA8BGO7loJWRkUFr1qyhpUuXEi96VSLsBjNx4kTq378/yRlclRyHNiAAAiAAAiAAAiAAAiCgTwCGuz4NE/uJiYnCWGejXU7mZKKprrhVq1bCYOeFp7wAFQICIAACIAACIAACIAAClSEAw90MvTtSthhO6MT+6AUFBWZallR1795dRIhp165dSSH2QAAEQAAEQAAEQAAEQKCSBGC4WwCYmppq0Wh3c3OjBx54QBjs9szOaqErqNYIgY3HbtCivVHFvdHLRPrPH/eJMmQn1chAoxsgAAIgAAIgUIYADPcyQMrz1cfHh4YMGSIWnYaGhpbnULQFgQoTYMPcmHFurKzCF8GBIAACIAACIAACDkcAhnsFhiQwMJBGjx5NI0eOJH9/pHCvAEIcUgkCLcMCaVKPxibPcPxaMp26nmqyHhUgAAIgAAIgAALqJADDvRzjVrduXZEwadCgQeTl5VWOI9EUBKxHoFGIH/HHlGTlFsBwNwUH5SAAAiAAAiCgYgIw3BUMXtOmTUWEmL59+xL7s0NAAARAAARAAARAAARAwNYEYLhbIM5x2OfPn2+hFapBAARAAARAAARAAARAoGoJuFbt6dV9do6/7udn2iVB3b2D9iAAAiAAAiAAAiAAAmoigBl3NY0WdAUBBQSORicZtEpKz6EXft4vyt3dXGnO5C4GbVAAAiAAAiAAAiDg2ARguDv2+EA7ECg3gbyCIoNjiqQQkimZeaLc3RWZfA0AoQAEQAAEQAAEVEAAhrsKBgkqgkB5CNQJqkY3U7N1h7QLD6L6wb66724w3HUssAMCIAACIAACaiIAw11NowVdQUABgXDJSD8cVeIu0zUyhHo3R4IwBejQBARAAARAAAQcmgAWpzr08EA5EAABEAABEAABEAABECgmAMMddwIIgAAIgAAIgAAIgAAIqIAADHcVDBJUBAEQAAEQAAEQAAEQAAH4uKvgHmB/5ctx6ULTC7FpYptfWERL90XrtB/ZJZw4zB8EBEAABEAABEAABEBAmwRguKtgXE9cS6Ftp2NLaVogxfdbe+S6rmxop/qS4a77ih0nI7BOuheORCeLXidl5JTq/ZrD1+jPM7fo38PbEiLKlEKDLyAAAiAAAiCgKgIw3FUwXNU83SiwmodZTRGZ2ywezVfeSsumi7duG+1nXFoO8efOHSmYO+FOMQoJhSAAAiAAAiCgAgIw3FUwSOO6NyL+QEDAFIGIWv6Uk1+oqy6U3sgculIcErJxLT8KCfAmVxcY7TpA2AEBEAABEAABFRKA4a7CQYPKIFCWQL9WdYg/smTnFUiG+17x9YHWdRHHXQaDLQiAAAiAAAiomABWM6p48KA6CIAACIAACIAACICA8xCA4e48Y42eggAIgAAIgAAIgAAIqJgADHcVDx5UBwEQAAEQAAEQAAEQcB4CMNydZ6zRUxAAARAAARAAARAAARUTwOJUFQ8eVAcBfQJFUiSZzNwCUZSdX7zlLzl5hZSenS/KvTxcyRMB/wUL/AcCIAACIAACaiPgIsV25uDOECME3NzcqHPnzrR//34jtSgCAccicDMli6YvOmxWqTFdG9CwTuFm26ASBEAABEAABEDAMQnAVcYxxwVagQAIgAAIgAAIgAAIgEApAnCVKYUDX0BAvQSCfD3p+Qebm+1A/WBfs/WoBAEQAAEQAAEQcFwCMNwdd2ygGQiUi4CPpzt1axJSrmPQGARAAARAAARAQD0E4CqjnrGCpiAAAiAAAiAAAiAAAk5MAIa7Ew8+ug4CIAACIAACIAACIKAeAjDc1TNW0BQEQAAEQAAEQAAEQMCJCcBwd+LBR9dBAARAAARAAARAAATUQwCGu3rGCpqCAAiAAAiAAAiAAAg4MQEY7k48+Og6CIAACIAACIAACICAegjAcFfPWEFTEAABEAABEAABEAABJyYAw92JBx9dBwEQAAEQAAEQAAEQUA8BGO7qGStoCgIgAAIgAAIgAAIg4MQEYLg78eCj6yAAAiAAAiAAAiAAAuohAMNdPWMFTUEABEAABEAABEAABJyYAAx3Jx58dB0EQAAEQAAEQAAEQEA9BGC4q2esoCkIgAAIgAAIgAAIgIATE3B34r5b7PqdO3coPj6evv/+e4tt0QAEQAAEQAAEQAAEQAAElBJo27Yt3XPPPUqbi3YuknF6p1xHOFHjV199lT7++GO79zgoKIiysrIoNzfX7rpAARCwRMDV1ZX4nk1NTaXCwkJLzVEPAnYn4OXlRb6+vpScnGx3XaAACCghwPcr/65NT09X0hxtHJTAtGnTaPbs2eXSDoa7GVzZ2dm0aNEiMy1sU/XZZ59R3759qX379ra5IK4CApUgkJiYSPPnz6fHH3+cQkJCKnEmHAoCtiFw/Phx+vPPP+mll16yzQVxFRCoJIENGzaICb0xY8ZU8kw43J4E2rRpQ126dCmXCjDcy4XLPo07d+5MPPs/btw4+yiAq4JAOQhcvnyZBg0aROvXr6cmTZqU40g0BQH7EFi6dCnNmjWLDh8+bB8FcFUQKCeB119/nZKSkmjevHnlPBLN1U4Ai1PVPoLQHwRAAARAAARAAARAwCkIwHB3imFGJ0EABEAABEAABEAABNROAIa72kcQ+oMACIAACIAACIAACDgFAYSDVMEwd+/enWrXrq0CTaEiCBBVq1aNevbsKbbgAQJqIMC/X/n3LAQE1EKgadOmiCijlsGysp5YnGploDgdCIAACIAACIAACIAACFQFAbjKVAVVnBMEQAAEQAAEQAAEQAAErEwAhruVgeJ0IAACIAACIAACIAACIFAVBGC4VwVVnBMEQAAEQAAEQAAEQAAErEwAi1OtDNSapysqKqKzZ89SbGwscRKmwMBAa54e5wKBShHgVNv79++ntLQ0aty4MXXo0MHo+XAfG8WCQjsT2LdvH4WGhlKjRo0MNElJSRHJmOrUqUMtWrQQqeUNGqEABGxIoKCggE6fPk1XrlwhX19f6t+/f6mr454thUPTXzDj7qDDywb7xIkT6cyZMxQcHEwzZsyg7777zkG1hVrORmD37t0ik+8777xDn332GU2ZMoWmTp1KOTk5pVDgPi6FA18chMD58+eJM0+eOHGilEZ37tyh999/n2bOnEm1atWiY8eO0eTJk+nmzZul2uELCNiSwNGjR+kf//gHHTp0iO67775SRjvuWVuOhGNcCzPujjEOpbRITEykN954g4YNG0ZjxowRdQ0aNKBRo0ZRvXr1aPDgwaXa4wsI2JLAjRs36Mcff6QPP/yQIiMjiY34X375RfxR+f777+n5558X6uA+tuWo4FpKCfDD5SeffEKFhYUGh/B9vWvXLlq1apUIZ9q2bVvi+/i1116jb7/9Vsx0GhyEAhCoQgJ8r27cuFFMkLRp08bgSrhnDZBovgAz7g44xD/99BOlpqYKw11Wr0aNGtSvXz/6+uuvKT8/Xy7GFgRsTmDTpk309ttvExs1HLP9wQcfpOeee07owUa8LLiPZRLYOhIB/h06fPhwoZKLi4tONTbQ+Z4dNGhQqRwEo0ePpujoaFq7dq2uLXZAwBYEVq5cSatXrxZvNI0Z7bhnbTEKjncNGO4ONiY8C7Rz506qX78+sbGuL61atRIJF/bu3atfjH0QsCkB/gMSFhZW6ppdunQRazCys7NFOe7jUnjwxUEI/PXXX1SzZk3ht15WpR07dhC7HfADqb7wW05eX7Rlyxb9YuyDQJUSYHeuL7/8Utyr/PbdmOCeNUZF+2Uw3B1sjNmXkmfb69ata6CZXMYLVCAgYC8C3bp1M7i0m5sbeXp6EmfzY8F9bIAIBXYmwLOTmzdvpkmTJhnVRP69Kv+e1W/Ei1QvX75ssIZDvw32QcCaBObNmyfervMi1D/++EO4ai1btozi4+N1l8E9q0PhVDsw3B1suJOTk4VG7IJQVry9vUWR/g9u2Tb4DgL2IMBGEd+XvKCaBfexPUYB1zRFgGfS586dSy+88ALxQ6Yxke9ZHx8fg2r5d29CQoJBHQpAoCoIcGAKlosXL4oHRnbr+vXXX+nvf/+7WE/EdbhnmYLzCRanOtiYZ2ZmCo149rKseHh4iKLc3NyyVfgOAnYl8PPPP9PQoUOpffv2Qg/cx3YdDly8DIGlS5dSr169iGfOTYl8z3p5eRk0kX8f43evARoUVAEBDgDA4XabNWsmAlXIl7j33nvFw+esWbNowYIFhHtWJuNcW8y4O9h4s/8lS15enoFm8h+N8PBwgzoUgIC9CJw6dUq4xnA4SFlwH8sksLU3gUuXLgk3l7Jxr8vqZe6e5Ug0POPJa48gIFDVBDh3C0uTJk1KXYrXF/Hn1q1bFBUVJdZrcANj9gLu2VLoNPUFM+4ONpycEIQlKyvLQDO5rGHDhgZ1KAABexCIi4ujH374gTieu7t7ya8T3Mf2GA1c0xgBjiLDs+gcn12WjIwMsbthwwYRy50jI1m6Z3m23thsvHxObEHAWgTkN0PyZJ3+eTnZHecX4N+9uGf1yTjPPmbcHWysq1evLhamGkv4Ifu2G8v052DdgDpOQIAfJL/66it68803yd/fv1SPcR+XwoEvdiTAmU/5oZKNIPkjh9TlbJRcxltux2Lsdy/7tmPCxI6D6GSXrl27tljsLy8+1e++nEGdjXbcs/pknGe/ZIrMefrs8D0dN26cWEjFr8vkJ29W+ty5c+JVbdnXZw7fISioOQJs7MyZM0fEbw8KCirVP47z/re//U1kVuUFgbiPS+HBFxsT4IyTZeXatWsiugyH2eO1GSxszHOSpf3794vslPIx7JbAkb44jwYEBGxBgB80Ofki+7HzvScb63xttgNCQkKIZ975g3vWFiPiWNfAjLtjjYfQhhOAcKbUhQsX6rTj1eOc3ObZZ58lV1cMmw4MdmxOgGcn33rrLTFTyclBvvvuO/FhlwROI8+GDgvuY5sPDS5YCQK8+P/pp5+mrVu3CjcE+VSceIlnNu+//365CFsQqHICHD2GcwjwwmpZ+C3nyZMnhR3A9yvuWZmMc21dpDBZd5yry+ro7e3bt+mDDz4QP5j8R+PQoUM0cOBAGjBggDo6AC01S+A///kP8ay6MeGHSo41XKtWLVGN+9gYJZTZm4A84/7qq6/qZtxlnTjWO2es5HwFPGGSlpZGL7/8MpV9syS3xxYEqooA//6cOXMm+fn5UUREBB08eFDYAGUXWuOeraoRcMzzwnB3zHHRacUrw1NSUsQiFMy067BgR2UEcB+rbMCgrnhzxGs3fH19QQME7EqAZ9r5IZJn4Dm6kSnht524Z03R0U45DHftjCV6AgIgAAIgAAIgAAIgoGECcJbW8OCiayAAAiAAAiAAAiAAAtohAMNdO2OJnoAACIAACIAACIAACGiYAAx3DQ8uugYCIAACIAACIAACIKAdAjDctTOW6AkIgAAIgAAIgAAIgICGCcBw1/DgomsgAAIgAAIgAAIgAALaIQDDXTtjiZ6AAAiAAAiAAAiAAAhomAAMdw0PLroGAiAAAiAAAiAAAiCgHQIw3LUzlugJCIAACIAACIAACICAhgnAcNfw4KJrIAACIAACIAACIAAC2iEAw107Y4megAAIgAAIgAAIgAAIaJgADHcNDy66BgIgAAIgAAIgAAIgoB0CMNy1M5boCQiAAAiAAAiAAAiAgIYJwHDX8OCiayAAAiAAAiAAAiAAAtohAMNdO2OJnoAACIAACIAACIAACGiYgLuG+4augQAIgAAIVAGBS5cuUVJSUqkzh4WFUb169UTZjRs3KCYmRux7e3tTu3btSrXFFxAAARAAgYoRwIx7xbjhKBAAARBwWgK5ubk0depU6tatm/js2rWL3NzcdDw8PDxo/vz51KdPH4qOjtaVYwcEQAAEQKByBFzuSFK5U+BoEAABEAABZyNw4cIFatWqFRUUFNDBgwepc+fOpRC8//77xDPv3377balyfAEBEAABEKg4Acy4V5wdjgQBEAABpyXQtGlTmjBhguj/3LlzDTgsW7aMnnjiCYNyFIAACIAACFScAAz3irPDkSAAAiDg1ASmT58u+r9kyRIxuy7DOHnyJBUWFlKXLl3kImxBAARAAASsQACGuxUg4hQgAAIg4IwEWrduTYMGDaL8/Hz6/PPPdQh+++03evTRR3XfsQMCIAACIGAdAvBxtw5HnAUEQAAEnJLAzp07qW/fvlS9enW6fv06+fr6UkREBO3bt49CQ0Odkgk6DQIgAAJVRQAz7lVFFucFARAAAScgwJFjunbtSmlpaSKSDBvybdq0gdHuBGOPLoIACNieAGbcbc8cVwQBEAABTRFYuXIljRo1iho0aCBCQA4bNoxGjhypqT6iMyAAAiDgCARguDvCKEAHEAABEFAxgaKiImrRogVxiMiQkBCRfIljuUNAAARAAASsSwCuMtblibOBAAiAgNMRcHV1pWnTpol+T5w4kWC0O90tgA6DAAjYiABm3G0EGpcBARAAAS0TyMzMJD8/Pzp69Ci1b99ey11F30AABEDAbgQw42439LgwCIAACGiHwLlz56hjx44w2rUzpOgJCICAAxKA4e6AgwKVQAAEQEBtBL755ht64YUX1KY29AUBEAABVRGAq4yqhgvKggAIgIBjEOAFqSzs3378+HF66KGH6PLly+Tl5eUYCkILEAABENAgAXcN9gldAgEQAAEQqEICCQkJ1KFDB8rKyqIePXrQ3r17afbs2TDaq5A5Tg0CIAACTAAz7rgPQAAEQAAEykUgPj5eZEfNyMgQxz3yyCP0448/kouLS7nOg8YgAAIgAALlIwDDvXy80BoEQAAEQEAiwItROUtqs2bNqG/fvmACAiAAAiBgAwIw3G0AGZcAARAAARAAARAAARAAgcoSQFSZyhLE8SAAAiAAAiAAAiAAAiBgAwIw3G0AGZcAARAAARAAARAAARAAgcoSgOFeWYI4HgRAAARAAARAAARAAARsQACGuw0g4xIgAAIgAAIgAAIgAAIgUFkCMNwrSxDHgwAIgAAIgAAIgAAIgIANCMBwtwFkXAIEQAAEQAAEQAAEQAAEKksAhntlCeJ4EAABEAABEAABEAABELABARjuNoCMS4AACIAACIAACIAACIBAZQnAcK8sQRwPAiAAAiAAAiAAAiAAAjYgAMPdBpBxCRAAARAAARAAARAAARCoLIH/Bw/KJsKQbNLUAAAAAElFTkSuQmCC" width="60%" style="display: block; margin: auto;" /></p>
<p>Finally, we use PSIS-LOO to approximate the expected log predictive density (ELPD) for new data, which we will validate using exact LOO-CV in the upcoming section.</p>
<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>(psis_loo <span class="ot">&lt;-</span> <span class="fu">loo</span>(loglik))</span></code></pre></div>
<pre><code>
Computed from 4000 by 49 log-likelihood matrix.

         Estimate   SE
elpd_loo   -186.8 10.7
p_loo         8.0  5.0
looic       373.7 21.4
------
MCSE of elpd_loo is NA.
MCSE and ESS estimates assume independent draws (r_eff=1).

Pareto k diagnostic values:
                         Count Pct.    Min. ESS
(-Inf, 0.7]   (good)     48    98.0%   651     
   (0.7, 1]   (bad)       0     0.0%   &lt;NA&gt;    
   (1, Inf)   (very bad)  1     2.0%   &lt;NA&gt;    
See help(&#39;pareto-k-diagnostic&#39;) for details.</code></pre>
</div>
<div id="exact-loo-cv" class="section level3">
<h3>Exact LOO-CV</h3>
<p>Exact LOO-CV for the above example is somewhat more involved, as we need to re-fit the model <span class="math inline">\(N\)</span> times and each time model the held-out data point as a parameter. First, we create an empty dummy model that we will update below as we loop over the observations.</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><span class="co"># see help(&quot;mi&quot;, &quot;brms&quot;) for details on the mi() usage</span></span>
<span id="cb12-2"><a href="#cb12-2" aria-hidden="true" tabindex="-1"></a>fit_dummy <span class="ot">&lt;-</span> <span class="fu">brm</span>(</span>
<span id="cb12-3"><a href="#cb12-3" aria-hidden="true" tabindex="-1"></a>  CRIME <span class="sc">|</span> <span class="fu">mi</span>() <span class="sc">~</span> INC <span class="sc">+</span> HOVAL <span class="sc">+</span> <span class="fu">sar</span>(COL.nb, <span class="at">type =</span> <span class="st">&quot;lag&quot;</span>), </span>
<span id="cb12-4"><a href="#cb12-4" aria-hidden="true" tabindex="-1"></a>  <span class="at">data =</span> COL.OLD,</span>
<span id="cb12-5"><a href="#cb12-5" aria-hidden="true" tabindex="-1"></a>  <span class="at">data2 =</span> <span class="fu">list</span>(<span class="at">COL.nb =</span> COL.nb),</span>
<span id="cb12-6"><a href="#cb12-6" aria-hidden="true" tabindex="-1"></a>  <span class="at">chains =</span> <span class="dv">0</span></span>
<span id="cb12-7"><a href="#cb12-7" aria-hidden="true" tabindex="-1"></a>)</span></code></pre></div>
<p>Next, we fit the model <span class="math inline">\(N\)</span> times, each time leaving out a single observation and then computing the log predictive density for that observation. For obvious reasons, this takes much longer than the approximation we computed above, but it is necessary in order to validate the approximate LOO-CV method. Thanks to the PSIS-LOO approximation, in general doing these slow exact computations can be avoided.</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>S <span class="ot">&lt;-</span> <span class="dv">500</span></span>
<span id="cb13-2"><a href="#cb13-2" aria-hidden="true" tabindex="-1"></a>res <span class="ot">&lt;-</span> <span class="fu">vector</span>(<span class="st">&quot;list&quot;</span>, N)</span>
<span id="cb13-3"><a href="#cb13-3" aria-hidden="true" tabindex="-1"></a>loglik <span class="ot">&lt;-</span> <span class="fu">matrix</span>(<span class="at">nrow =</span> S, <span class="at">ncol =</span> N)</span>
<span id="cb13-4"><a href="#cb13-4" aria-hidden="true" tabindex="-1"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="fu">seq_len</span>(N)) {</span>
<span id="cb13-5"><a href="#cb13-5" aria-hidden="true" tabindex="-1"></a>  dat_mi <span class="ot">&lt;-</span> COL.OLD</span>
<span id="cb13-6"><a href="#cb13-6" aria-hidden="true" tabindex="-1"></a>  dat_mi<span class="sc">$</span>CRIME[i] <span class="ot">&lt;-</span> <span class="cn">NA</span></span>
<span id="cb13-7"><a href="#cb13-7" aria-hidden="true" tabindex="-1"></a>  fit_i <span class="ot">&lt;-</span> <span class="fu">update</span>(fit_dummy, <span class="at">newdata =</span> dat_mi, </span>
<span id="cb13-8"><a href="#cb13-8" aria-hidden="true" tabindex="-1"></a>                  <span class="co"># just for vignette</span></span>
<span id="cb13-9"><a href="#cb13-9" aria-hidden="true" tabindex="-1"></a>                  <span class="at">chains =</span> <span class="dv">1</span>, <span class="at">iter =</span> S <span class="sc">*</span> <span class="dv">2</span>)</span>
<span id="cb13-10"><a href="#cb13-10" aria-hidden="true" tabindex="-1"></a>  posterior <span class="ot">&lt;-</span> <span class="fu">as.data.frame</span>(fit_i)</span>
<span id="cb13-11"><a href="#cb13-11" aria-hidden="true" tabindex="-1"></a>  yloo <span class="ot">&lt;-</span> sdloo <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="cn">NA</span>, S)</span>
<span id="cb13-12"><a href="#cb13-12" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> (s <span class="cf">in</span> <span class="fu">seq_len</span>(S)) {</span>
<span id="cb13-13"><a href="#cb13-13" aria-hidden="true" tabindex="-1"></a>    p <span class="ot">&lt;-</span> posterior[s, ]</span>
<span id="cb13-14"><a href="#cb13-14" aria-hidden="true" tabindex="-1"></a>    y_miss_i <span class="ot">&lt;-</span> y</span>
<span id="cb13-15"><a href="#cb13-15" aria-hidden="true" tabindex="-1"></a>    y_miss_i[i] <span class="ot">&lt;-</span> p<span class="sc">$</span>Ymi</span>
<span id="cb13-16"><a href="#cb13-16" aria-hidden="true" tabindex="-1"></a>    eta <span class="ot">&lt;-</span> p<span class="sc">$</span>b_Intercept <span class="sc">+</span> p<span class="sc">$</span>b_INC <span class="sc">*</span> fit_i<span class="sc">$</span>data<span class="sc">$</span>INC <span class="sc">+</span> p<span class="sc">$</span>b_HOVAL <span class="sc">*</span> fit_i<span class="sc">$</span>data<span class="sc">$</span>HOVAL</span>
<span id="cb13-17"><a href="#cb13-17" aria-hidden="true" tabindex="-1"></a>    W_tilde <span class="ot">&lt;-</span> <span class="fu">diag</span>(N) <span class="sc">-</span> p<span class="sc">$</span>lagsar <span class="sc">*</span> spdep<span class="sc">::</span><span class="fu">nb2mat</span>(COL.nb)</span>
<span id="cb13-18"><a href="#cb13-18" aria-hidden="true" tabindex="-1"></a>    Cinv <span class="ot">&lt;-</span> <span class="fu">t</span>(W_tilde) <span class="sc">%*%</span> W_tilde <span class="sc">/</span> p<span class="sc">$</span>sigma<span class="sc">^</span><span class="dv">2</span></span>
<span id="cb13-19"><a href="#cb13-19" aria-hidden="true" tabindex="-1"></a>    g <span class="ot">&lt;-</span> Cinv <span class="sc">%*%</span> (y_miss_i <span class="sc">-</span> <span class="fu">solve</span>(W_tilde, eta))</span>
<span id="cb13-20"><a href="#cb13-20" aria-hidden="true" tabindex="-1"></a>    cbar <span class="ot">&lt;-</span> <span class="fu">diag</span>(Cinv);</span>
<span id="cb13-21"><a href="#cb13-21" aria-hidden="true" tabindex="-1"></a>    yloo[s] <span class="ot">&lt;-</span> y_miss_i[i] <span class="sc">-</span> g[i] <span class="sc">/</span> cbar[i]</span>
<span id="cb13-22"><a href="#cb13-22" aria-hidden="true" tabindex="-1"></a>    sdloo[s] <span class="ot">&lt;-</span> <span class="fu">sqrt</span>(<span class="dv">1</span> <span class="sc">/</span> cbar[i])</span>
<span id="cb13-23"><a href="#cb13-23" aria-hidden="true" tabindex="-1"></a>    loglik[s, i] <span class="ot">&lt;-</span> <span class="fu">dnorm</span>(y[i], yloo[s], sdloo[s], <span class="at">log =</span> <span class="cn">TRUE</span>)</span>
<span id="cb13-24"><a href="#cb13-24" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb13-25"><a href="#cb13-25" aria-hidden="true" tabindex="-1"></a>  ypred <span class="ot">&lt;-</span> <span class="fu">rnorm</span>(S, yloo, sdloo)</span>
<span id="cb13-26"><a href="#cb13-26" aria-hidden="true" tabindex="-1"></a>  res[[i]] <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(<span class="at">y =</span> <span class="fu">c</span>(posterior<span class="sc">$</span>Ymi, ypred))</span>
<span id="cb13-27"><a href="#cb13-27" aria-hidden="true" tabindex="-1"></a>  res[[i]]<span class="sc">$</span>type <span class="ot">&lt;-</span> <span class="fu">rep</span>(<span class="fu">c</span>(<span class="st">&quot;pp&quot;</span>, <span class="st">&quot;loo&quot;</span>), <span class="at">each =</span> S)</span>
<span id="cb13-28"><a href="#cb13-28" aria-hidden="true" tabindex="-1"></a>  res[[i]]<span class="sc">$</span>obs <span class="ot">&lt;-</span> i</span>
<span id="cb13-29"><a href="#cb13-29" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb13-30"><a href="#cb13-30" aria-hidden="true" tabindex="-1"></a>res <span class="ot">&lt;-</span> <span class="fu">do.call</span>(rbind, res)</span></code></pre></div>
<p>A first step in the validation of the pointwise predictive density is to compare the distribution of the implied response values for the left-out observation to the distribution of the <span class="math inline">\(y_i^{\mathrm{mis}}\)</span> posterior-predictive values estimated as part of the model. If the pointwise predictive density is correct, the two distributions should match very closely (up to sampling error). In the plot below, we overlay these two distributions for the first four observations and see that they match very closely (as is the case for all <span class="math inline">\(49\)</span> observations of in this example).</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>res_sub <span class="ot">&lt;-</span> res[res<span class="sc">$</span>obs <span class="sc">%in%</span> <span class="dv">1</span><span class="sc">:</span><span class="dv">4</span>, ]</span>
<span id="cb14-2"><a href="#cb14-2" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(res_sub, <span class="fu">aes</span>(y, <span class="at">fill =</span> type)) <span class="sc">+</span></span>
<span id="cb14-3"><a href="#cb14-3" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_density</span>(<span class="at">alpha =</span> <span class="fl">0.6</span>) <span class="sc">+</span></span>
<span id="cb14-4"><a href="#cb14-4" aria-hidden="true" tabindex="-1"></a>  <span class="fu">facet_wrap</span>(<span class="st">&quot;obs&quot;</span>, <span class="at">scales =</span> <span class="st">&quot;fixed&quot;</span>, <span class="at">ncol =</span> <span class="dv">4</span>)</span></code></pre></div>
<p><img src="data:image/png;base64,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" width="95%" style="display: block; margin: auto;" /></p>
<p>In the final step, we compute the ELPD based on the exact LOO-CV and compare it to the approximate PSIS-LOO result computed earlier.</p>
<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>log_mean_exp <span class="ot">&lt;-</span> <span class="cf">function</span>(x) {</span>
<span id="cb15-2"><a href="#cb15-2" aria-hidden="true" tabindex="-1"></a>  <span class="co"># more stable than log(mean(exp(x)))</span></span>
<span id="cb15-3"><a href="#cb15-3" aria-hidden="true" tabindex="-1"></a>  max_x <span class="ot">&lt;-</span> <span class="fu">max</span>(x)</span>
<span id="cb15-4"><a href="#cb15-4" 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 class="sc">-</span> <span class="fu">log</span>(<span class="fu">length</span>(x))</span>
<span id="cb15-5"><a href="#cb15-5" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb15-6"><a href="#cb15-6" aria-hidden="true" tabindex="-1"></a>exact_elpds <span class="ot">&lt;-</span> <span class="fu">apply</span>(loglik, <span class="dv">2</span>, log_mean_exp)</span>
<span id="cb15-7"><a href="#cb15-7" aria-hidden="true" tabindex="-1"></a>exact_elpd <span class="ot">&lt;-</span> <span class="fu">sum</span>(exact_elpds)</span>
<span id="cb15-8"><a href="#cb15-8" aria-hidden="true" tabindex="-1"></a><span class="fu">round</span>(exact_elpd, <span class="dv">1</span>)</span></code></pre></div>
<pre><code>[1] -188.9</code></pre>
<p>The results of the approximate and exact LOO-CV are similar but not as close as we would expect if there were no problematic observations. We can investigate this issue more closely by plotting the approximate against the exact pointwise ELPD values.</p>
<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>df <span class="ot">&lt;-</span> <span class="fu">data.frame</span>(</span>
<span id="cb17-2"><a href="#cb17-2" aria-hidden="true" tabindex="-1"></a>  <span class="at">approx_elpd =</span> psis_loo<span class="sc">$</span>pointwise[, <span class="st">&quot;elpd_loo&quot;</span>],</span>
<span id="cb17-3"><a href="#cb17-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">exact_elpd =</span> exact_elpds</span>
<span id="cb17-4"><a href="#cb17-4" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb17-5"><a href="#cb17-5" aria-hidden="true" tabindex="-1"></a><span class="fu">ggplot</span>(df, <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="cb17-6"><a href="#cb17-6" 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="cb17-7"><a href="#cb17-7" 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="cb17-8"><a href="#cb17-8" aria-hidden="true" tabindex="-1"></a>  <span class="fu">geom_point</span>(<span class="at">data =</span> df[<span class="dv">4</span>, ], <span class="at">size =</span> <span class="dv">3</span>, <span class="at">color =</span> <span class="st">&quot;red3&quot;</span>) <span class="sc">+</span></span>
<span id="cb17-9"><a href="#cb17-9" aria-hidden="true" tabindex="-1"></a>  <span class="fu">xlab</span>(<span class="st">&quot;Approximate elpds&quot;</span>) <span class="sc">+</span></span>
<span id="cb17-10"><a href="#cb17-10" aria-hidden="true" tabindex="-1"></a>  <span class="fu">ylab</span>(<span class="st">&quot;Exact elpds&quot;</span>) <span class="sc">+</span></span>
<span id="cb17-11"><a href="#cb17-11" aria-hidden="true" tabindex="-1"></a>  <span class="fu">coord_fixed</span>(<span class="at">xlim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">16</span>, <span class="sc">-</span><span class="dv">3</span>), <span class="at">ylim =</span> <span class="fu">c</span>(<span class="sc">-</span><span class="dv">16</span>, <span class="sc">-</span><span class="dv">3</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>In the plot above the fourth data point —the observation flagged as problematic by the PSIS-LOO approximation— is colored in red and is the clear outlier. Otherwise, the correspondence between the exact and approximate values is strong. In fact, summing over the pointwise ELPD values and leaving out the fourth observation yields practically equivalent results for approximate and exact LOO-CV:</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>without_pt_4 <span class="ot">&lt;-</span> <span class="fu">c</span>(</span>
<span id="cb18-2"><a href="#cb18-2" aria-hidden="true" tabindex="-1"></a>  <span class="at">approx =</span> <span class="fu">sum</span>(psis_loo<span class="sc">$</span>pointwise[<span class="sc">-</span><span class="dv">4</span>, <span class="st">&quot;elpd_loo&quot;</span>]),</span>
<span id="cb18-3"><a href="#cb18-3" aria-hidden="true" tabindex="-1"></a>  <span class="at">exact =</span> <span class="fu">sum</span>(exact_elpds[<span class="sc">-</span><span class="dv">4</span>])  </span>
<span id="cb18-4"><a href="#cb18-4" aria-hidden="true" tabindex="-1"></a>)</span>
<span id="cb18-5"><a href="#cb18-5" aria-hidden="true" tabindex="-1"></a><span class="fu">round</span>(without_pt_4, <span class="dv">1</span>)</span></code></pre></div>
<pre><code>approx  exact 
-173.2 -173.1 </code></pre>
<p>From this we can conclude that the difference we found when including <em>all</em> observations does not indicate a bug in our implementation of the approximate LOO-CV but rather a violation of its assumptions.</p>
</div>
</div>
</div>
<div id="working-with-stan-directly" class="section level1">
<h1>Working with Stan directly</h1>
<p>So far, we have specified the models in brms and only used Stan implicitely behind the scenes. This allowed us to focus on the primary purpose of validating approximate LOO-CV for non-factorized models. However, we would also like to show how everything can be set up in Stan directly. The Stan code brms generates is human readable and so we can use it to learn some of the essential aspects of Stan and the particular model we are implementing. The Stan program below is a slightly modified version of the code extracted via <code>stancode(fit_dummy)</code>:</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><span class="sc">/</span><span class="er">/</span> generated with brms <span class="dv">2</span>.<span class="fl">2.0</span></span>
<span id="cb20-2"><a href="#cb20-2" aria-hidden="true" tabindex="-1"></a>functions {</span>
<span id="cb20-3"><a href="#cb20-3" aria-hidden="true" tabindex="-1"></a><span class="sc">/</span><span class="er">**</span> </span>
<span id="cb20-4"><a href="#cb20-4" aria-hidden="true" tabindex="-1"></a> <span class="er">*</span> Normal log<span class="sc">-</span>pdf <span class="cf">for</span> spatially lagged responses</span>
<span id="cb20-5"><a href="#cb20-5" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> </span>
<span id="cb20-6"><a href="#cb20-6" aria-hidden="true" tabindex="-1"></a> <span class="er">*</span> <span class="er">@</span>param y Vector of response values.</span>
<span id="cb20-7"><a href="#cb20-7" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param mu Mean parameter vector.</span>
<span id="cb20-8"><a href="#cb20-8" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param sigma Positive scalar residual standard deviation.</span>
<span id="cb20-9"><a href="#cb20-9" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param rho Positive scalar autoregressive parameter.</span>
<span id="cb20-10"><a href="#cb20-10" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span> <span class="er">@</span>param W Spatial weight matrix.</span>
<span id="cb20-11"><a href="#cb20-11" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span></span>
<span id="cb20-12"><a href="#cb20-12" aria-hidden="true" tabindex="-1"></a> <span class="er">*</span> <span class="er">@</span>return A scalar to be added to the log posterior.</span>
<span id="cb20-13"><a href="#cb20-13" aria-hidden="true" tabindex="-1"></a> <span class="sc">*</span><span class="er">/</span></span>
<span id="cb20-14"><a href="#cb20-14" aria-hidden="true" tabindex="-1"></a>  real <span class="fu">normal_lagsar_lpdf</span>(vector y, vector mu, real sigma,</span>
<span id="cb20-15"><a href="#cb20-15" aria-hidden="true" tabindex="-1"></a>                          real rho, matrix W) {</span>
<span id="cb20-16"><a href="#cb20-16" aria-hidden="true" tabindex="-1"></a>    int N <span class="ot">=</span> <span class="fu">rows</span>(y);</span>
<span id="cb20-17"><a href="#cb20-17" aria-hidden="true" tabindex="-1"></a>    real inv_sigma2 <span class="ot">=</span> <span class="dv">1</span> <span class="sc">/</span> <span class="fu">square</span>(sigma);</span>
<span id="cb20-18"><a href="#cb20-18" aria-hidden="true" tabindex="-1"></a>    matrix[N, N] W_tilde <span class="ot">=</span> <span class="sc">-</span>rho <span class="sc">*</span> W;</span>
<span id="cb20-19"><a href="#cb20-19" aria-hidden="true" tabindex="-1"></a>    vector[N] half_pred;</span>
<span id="cb20-20"><a href="#cb20-20" aria-hidden="true" tabindex="-1"></a>    <span class="cf">for</span> (n <span class="cf">in</span> <span class="dv">1</span><span class="sc">:</span>N) W_tilde[n, n] <span class="sc">+</span><span class="er">=</span> <span class="dv">1</span>;</span>
<span id="cb20-21"><a href="#cb20-21" aria-hidden="true" tabindex="-1"></a>    half_pred <span class="ot">=</span> W_tilde <span class="sc">*</span> (y <span class="sc">-</span> <span class="fu">mdivide_left</span>(W_tilde, mu));</span>
<span id="cb20-22"><a href="#cb20-22" aria-hidden="true" tabindex="-1"></a>    return <span class="fl">0.5</span> <span class="sc">*</span> <span class="fu">log_determinant</span>(<span class="fu">crossprod</span>(W_tilde) <span class="sc">*</span> inv_sigma2) <span class="sc">-</span></span>
<span id="cb20-23"><a href="#cb20-23" aria-hidden="true" tabindex="-1"></a>           <span class="fl">0.5</span> <span class="sc">*</span> <span class="fu">dot_self</span>(half_pred) <span class="sc">*</span> inv_sigma2;</span>
<span id="cb20-24"><a href="#cb20-24" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb20-25"><a href="#cb20-25" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb20-26"><a href="#cb20-26" aria-hidden="true" tabindex="-1"></a>data {</span>
<span id="cb20-27"><a href="#cb20-27" aria-hidden="true" tabindex="-1"></a>  int<span class="sc">&lt;</span>lower<span class="ot">=</span><span class="dv">1</span><span class="sc">&gt;</span> N;  <span class="sc">/</span><span class="er">/</span> total number of observations</span>
<span id="cb20-28"><a href="#cb20-28" aria-hidden="true" tabindex="-1"></a>  vector[N] Y;  <span class="sc">/</span><span class="er">/</span> response variable</span>
<span id="cb20-29"><a href="#cb20-29" aria-hidden="true" tabindex="-1"></a>  int<span class="sc">&lt;</span>lower<span class="ot">=</span><span class="dv">0</span><span class="sc">&gt;</span> Nmi;  <span class="sc">/</span><span class="er">/</span> number of missings</span>
<span id="cb20-30"><a href="#cb20-30" aria-hidden="true" tabindex="-1"></a>  int<span class="sc">&lt;</span>lower<span class="ot">=</span><span class="dv">1</span><span class="sc">&gt;</span> Jmi[Nmi];  <span class="sc">/</span><span class="er">/</span> positions of missings</span>
<span id="cb20-31"><a href="#cb20-31" aria-hidden="true" tabindex="-1"></a>  int<span class="sc">&lt;</span>lower<span class="ot">=</span><span class="dv">1</span><span class="sc">&gt;</span> K;  <span class="sc">/</span><span class="er">/</span> number of population<span class="sc">-</span>level effects</span>
<span id="cb20-32"><a href="#cb20-32" aria-hidden="true" tabindex="-1"></a>  matrix[N, K] X;  <span class="sc">/</span><span class="er">/</span> population<span class="sc">-</span>level design matrix</span>
<span id="cb20-33"><a href="#cb20-33" aria-hidden="true" tabindex="-1"></a>  matrix[N, N] W;  <span class="sc">/</span><span class="er">/</span> spatial weight matrix</span>
<span id="cb20-34"><a href="#cb20-34" aria-hidden="true" tabindex="-1"></a>  int prior_only;  <span class="sc">/</span><span class="er">/</span> should the likelihood be ignored?</span>
<span id="cb20-35"><a href="#cb20-35" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb20-36"><a href="#cb20-36" aria-hidden="true" tabindex="-1"></a>transformed data {</span>
<span id="cb20-37"><a href="#cb20-37" aria-hidden="true" tabindex="-1"></a>  int Kc <span class="ot">=</span> K <span class="sc">-</span> <span class="dv">1</span>;</span>
<span id="cb20-38"><a href="#cb20-38" aria-hidden="true" tabindex="-1"></a>  matrix[N, K <span class="sc">-</span> <span class="dv">1</span>] Xc;  <span class="sc">/</span><span class="er">/</span> centered version of X</span>
<span id="cb20-39"><a href="#cb20-39" aria-hidden="true" tabindex="-1"></a>  vector[K <span class="sc">-</span> <span class="dv">1</span>] means_X;  <span class="sc">/</span><span class="er">/</span> column means of X before centering</span>
<span id="cb20-40"><a href="#cb20-40" aria-hidden="true" tabindex="-1"></a>  <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">2</span><span class="sc">:</span>K) {</span>
<span id="cb20-41"><a href="#cb20-41" aria-hidden="true" tabindex="-1"></a>    means_X[i <span class="sc">-</span> <span class="dv">1</span>] <span class="ot">=</span> <span class="fu">mean</span>(X[, i]);</span>
<span id="cb20-42"><a href="#cb20-42" aria-hidden="true" tabindex="-1"></a>    Xc[, i <span class="sc">-</span> <span class="dv">1</span>] <span class="ot">=</span> X[, i] <span class="sc">-</span> means_X[i <span class="sc">-</span> <span class="dv">1</span>];</span>
<span id="cb20-43"><a href="#cb20-43" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb20-44"><a href="#cb20-44" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb20-45"><a href="#cb20-45" aria-hidden="true" tabindex="-1"></a>parameters {</span>
<span id="cb20-46"><a href="#cb20-46" aria-hidden="true" tabindex="-1"></a>  vector[Nmi] Ymi;  <span class="sc">/</span><span class="er">/</span> estimated missings</span>
<span id="cb20-47"><a href="#cb20-47" aria-hidden="true" tabindex="-1"></a>  vector[Kc] b;  <span class="sc">/</span><span class="er">/</span> population<span class="sc">-</span>level effects</span>
<span id="cb20-48"><a href="#cb20-48" aria-hidden="true" tabindex="-1"></a>  real temp_Intercept;  <span class="sc">/</span><span class="er">/</span> temporary intercept</span>
<span id="cb20-49"><a href="#cb20-49" aria-hidden="true" tabindex="-1"></a>  real<span class="sc">&lt;</span>lower<span class="ot">=</span><span class="dv">0</span><span class="sc">&gt;</span> sigma;  <span class="sc">/</span><span class="er">/</span> residual SD</span>
<span id="cb20-50"><a href="#cb20-50" aria-hidden="true" tabindex="-1"></a>  real<span class="sc">&lt;</span>lower<span class="ot">=</span><span class="dv">0</span>,upper<span class="ot">=</span><span class="dv">1</span><span class="sc">&gt;</span> lagsar;  <span class="sc">/</span><span class="er">/</span> SAR parameter</span>
<span id="cb20-51"><a href="#cb20-51" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb20-52"><a href="#cb20-52" aria-hidden="true" tabindex="-1"></a>transformed parameters {</span>
<span id="cb20-53"><a href="#cb20-53" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb20-54"><a href="#cb20-54" aria-hidden="true" tabindex="-1"></a>model {</span>
<span id="cb20-55"><a href="#cb20-55" aria-hidden="true" tabindex="-1"></a>  vector[N] Yl <span class="ot">=</span> Y;</span>
<span id="cb20-56"><a href="#cb20-56" aria-hidden="true" tabindex="-1"></a>  vector[N] mu <span class="ot">=</span> Xc <span class="sc">*</span> b <span class="sc">+</span> temp_Intercept;</span>
<span id="cb20-57"><a href="#cb20-57" aria-hidden="true" tabindex="-1"></a>  Yl[Jmi] <span class="ot">=</span> Ymi;</span>
<span id="cb20-58"><a href="#cb20-58" aria-hidden="true" tabindex="-1"></a>  <span class="sc">/</span><span class="er">/</span> priors including all constants</span>
<span id="cb20-59"><a href="#cb20-59" aria-hidden="true" tabindex="-1"></a>  target <span class="sc">+</span><span class="er">=</span> <span class="fu">student_t_lpdf</span>(temp_Intercept <span class="sc">|</span> <span class="dv">3</span>, <span class="dv">34</span>, <span class="dv">17</span>);</span>
<span id="cb20-60"><a href="#cb20-60" aria-hidden="true" tabindex="-1"></a>  target <span class="sc">+</span><span class="er">=</span> <span class="fu">student_t_lpdf</span>(sigma <span class="sc">|</span> <span class="dv">3</span>, <span class="dv">0</span>, <span class="dv">17</span>)</span>
<span id="cb20-61"><a href="#cb20-61" aria-hidden="true" tabindex="-1"></a>    <span class="sc">-</span> <span class="dv">1</span> <span class="sc">*</span> <span class="fu">student_t_lccdf</span>(<span class="dv">0</span> <span class="sc">|</span> <span class="dv">3</span>, <span class="dv">0</span>, <span class="dv">17</span>);</span>
<span id="cb20-62"><a href="#cb20-62" aria-hidden="true" tabindex="-1"></a>  <span class="sc">/</span><span class="er">/</span> likelihood including all constants</span>
<span id="cb20-63"><a href="#cb20-63" aria-hidden="true" tabindex="-1"></a>  <span class="cf">if</span> (<span class="sc">!</span>prior_only) {</span>
<span id="cb20-64"><a href="#cb20-64" aria-hidden="true" tabindex="-1"></a>    target <span class="sc">+</span><span class="er">=</span> <span class="fu">normal_lagsar_lpdf</span>(Yl <span class="sc">|</span> mu, sigma, lagsar, W);</span>
<span id="cb20-65"><a href="#cb20-65" aria-hidden="true" tabindex="-1"></a>  }</span>
<span id="cb20-66"><a href="#cb20-66" aria-hidden="true" tabindex="-1"></a>}</span>
<span id="cb20-67"><a href="#cb20-67" aria-hidden="true" tabindex="-1"></a>generated quantities {</span>
<span id="cb20-68"><a href="#cb20-68" aria-hidden="true" tabindex="-1"></a>  <span class="sc">/</span><span class="er">/</span> actual population<span class="sc">-</span>level intercept</span>
<span id="cb20-69"><a href="#cb20-69" aria-hidden="true" tabindex="-1"></a>  real b_Intercept <span class="ot">=</span> temp_Intercept <span class="sc">-</span> <span class="fu">dot_product</span>(means_X, b);</span>
<span id="cb20-70"><a href="#cb20-70" aria-hidden="true" tabindex="-1"></a>}</span></code></pre></div>
<p>Here we want to focus on two aspects of the Stan code. First, because there is no built-in function in Stan that calculates the log-likelihood for the lag-SAR model, we define a new <code>normal_lagsar_lpdf</code> function in the <code>functions</code> block of the Stan program. This is the same function we showed earlier in the vignette and it can be used to compute the log-likelihood in an efficient and numerically stable way. The <code>_lpdf</code> suffix used in the function name informs Stan that this is a log probability density function.</p>
<p>Second, this Stan program nicely illustrates how to set up missing value imputation. Instead of just computing the log-likelihood for the observed responses <code>Y</code>, we define a new variable <code>Yl</code> which is equal to <code>Y</code> if the reponse is observed and equal to <code>Ymi</code> if the response is missing. The latter is in turn defined as a parameter and thus estimated along with all other paramters of the model. More details about missing value imputation in Stan can be found in the <em>Missing Data &amp; Partially Known Parameters</em> section of the <a href="https://mc-stan.org/users/documentation/index.html">Stan manual</a>.</p>
<p>The Stan code extracted from brms is not only helpful when learning Stan, but can also drastically speed up the specification of models that are not support by brms. If brms can fit a model similar but not identical to the desired model, we can let brms generate the Stan program for the similar model and then mold it into the program that implements the model we actually want to fit. Rather than calling <code>stancode()</code>, which requires an existing fitted model object, we recommend using <code>make_stancode()</code> and specifying the <code>save_model</code> argument to write the Stan program to a file. The corresponding data can be prepared with <code>make_standata()</code> and then manually amended if needed. Once the code and data have been edited, they can be passed to RStan’s <code>stan()</code> function via the <code>file</code> and <code>data</code> arguments.</p>
</div>
<div id="conclusion" class="section level1">
<h1>Conclusion</h1>
<p>In summary, we have shown how to set up and validate approximate and exact LOO-CV for non-factorized multivariate normal models using Stan with the <strong>brms</strong> and <strong>loo</strong> packages. Although we focused on the particular example of a spatial SAR model, the presented recipe applies more generally to models that can be expressed in terms of a multivariate normal likelihood.</p>
<p><br /></p>
</div>
<div id="references" class="section level1">
<h1>References</h1>
<p>Anselin L. (1988). <em>Spatial econometrics: methods and models</em>. Dordrecht: Kluwer Academic.</p>
<p>Bürkner P. C., Gabry J., &amp; Vehtari A. (2020). Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-t models. <em>Computational Statistics</em>, :10.1007/s00180-020-01045-4. <a href="https://arxiv.org/abs/1810.10559">ArXiv preprint</a>.</p>
<p>Sundararajan S. &amp; Keerthi S. S. (2001). Predictive approaches for choosing hyperparameters in Gaussian processes. <em>Neural Computation</em>, 13(5), 1103–1118.</p>
<p>Vehtari A., Mononen T., Tolvanen V., Sivula T., &amp; Winther O. (2016). Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models. <em>Journal of Machine Learning Research</em>, 17(103), 1–38. <a href="https://jmlr.org/papers/v17/14-540.html">Online</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>
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