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Appendix-B.html
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<body>
<h1 class="title toc-ignore">Appendix-B</h1>
<h4 class="author">Afra Kilic, Supervisor: dr. ir. Joris Mulder</h4>
<h4 class="date">2023-07-30</h4>
<div id="mcmc-model-search-method" class="section level2">
<h2>MCMC Model Search Method</h2>
<p>In this part of the simulation, we will apply the Bayes factor presented for the variable selection for linear and nonlinear regression models. In Appendix-A, the consistency of the Bayes factor approximated via BIC is checked. However, when the number of candidate variables is large, exhaustive calculation of the posterior model probabilities for all possible models becomes infeasible. For instance, given <span class="math inline">\(J=20\)</span>, there are more than three billions (<span class="math inline">\(3^{20}\)</span>) possible models under consideration. This problem can be addressed by using MCMC model search method in the selection algorithm with different prior model probability setting.</p>
<p><br />
<br />
</p>
<p>A popular MCMC model search method was proposed by George and McCulloch (1993) for cases where the model space is large. The basic idea of the MCMC algorithm for Bayesian variable selection is to sequentially sample <span class="math inline">\(\gamma\)</span> from its posterior distribution, <span class="math inline">\(\pi(\gamma|Y)\)</span>, and select the best model which appears most often in the sample of <span class="math inline">\(\gamma\)</span>. When using conjugate priors the marginal posterior distribution of <span class="math inline">\(\gamma\)</span> has an analytical form:</p>
<p><span class="math display">\[\begin{equation}
\tag{1}
\pi(\gamma|Y) = P(M_\gamma|Y) \propto BF_{\gamma0}P(M_\gamma)
\end{equation}\]</span></p>
<p>where <span class="math inline">\(BF_{\gamma0}\)</span> is given in and <span class="math inline">\(P(M_\gamma) = \frac{1}{3^J}\)</span>.</p>
<p>Gibbs sampler algorithm is only applied to <span class="math inline">\(\gamma\)</span>, i.e.i to sequentially sample along <span class="math inline">\(\gamma_p^t\)</span> for <span class="math inline">\(p=1, ..., J\)</span> and <span class="math inline">\(t= 1,...,T\)</span> with T the iteration number:</p>
<p><span class="math display">\[\begin{equation}
\tag{2}
\gamma_{1}^{0},...,\gamma_{J}^{0}, \gamma_{1}^{1},...,\gamma_{J}^{1}, ..., \gamma_{1}^{t},...,\gamma_{J}^{t},...,
\end{equation}\]</span></p>
<p>where <span class="math inline">\(\gamma_{1}^{0},...,\gamma_{P}^{0}\)</span> denote the initial values, which can be set as zero. In the Gibbs algorithm the subsequent values of <span class="math inline">\(\gamma_j^t\)</span> can be sample from its conditional posterior distribution given the latest values of all other <span class="math inline">\(\gamma\)</span>s.</p>
<p>The conditional distribution of <span class="math inline">\(\gamma_j\)</span> given all other <span class="math inline">\(\gamma\)</span>s is Bernoulli. The three probabilities of sampling <span class="math inline">\(\gamma_j^{t} = r\)</span> for <span class="math inline">\(r=0,1,2\)</span> at iteration rate <span class="math inline">\(t\)</span> are</p>
<p><span class="math display">\[\begin{equation}
\tag{3}
P(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, y) = \frac{\pi(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, y)}{\sum_{r}\pi(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, y)}
\end{equation}\]</span></p>
<p><br />
</p>
<p>where <span class="math inline">\(\gamma^{t}_{-j} = (\gamma^t_1, ..., \gamma^{t}_{j-1},\gamma^{t-1}_{j+1},...,\gamma^{t-1}_{J})\)</span> denotes the latest values of <span class="math inline">\(\gamma\)</span> except <span class="math inline">\(\gamma_j\)</span>. Note that when sampling <span class="math inline">\(\gamma_j^t, (\gamma_{t+1} + ... + \gamma_{J})\)</span> have not been sampled at iteration <span class="math inline">\(t\)</span>, and thus their values at the <span class="math inline">\(t-1\)</span> iteration are used. <span class="math inline">\(\pi(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, y)\)</span> can be computed using Equation (1). However, regardless of the number of variables <span class="math inline">\(J\)</span>, a fixed <span class="math inline">\(P(M_\gamma)\)</span> causes the algorithm to include more variables as <span class="math inline">\(J\)</span> increases. This phenomenon, called multiplicity, arises from multiple tests or comparison in variable selection. This is most obvious in orthogonal situation where <span class="math inline">\(J\)</span> independent tests on the effect type of the variable <span class="math inline">\(x_j\)</span> are performed. Therefore, for instance, at iteration rate <span class="math inline">\(t\)</span>, three independent models are compared to test the effect type of variable <span class="math inline">\(x_j\)</span> on the outcome variable, and the prior model probabilities for each model will be <span class="math inline">\(P(M_{\gamma_j}^t) = 1/3\)</span>. Regardless of <span class="math inline">\(J\)</span>, <span class="math inline">\(P(M_{\gamma_j}^t)\)</span> remains the same at every iteration for each variable. However, <span class="math inline">\(P(M_{\gamma_j}^t) = 1/3\)</span> suggests a model size of <span class="math inline">\(2J/3\)</span> a priori since each variable has a probability of <span class="math inline">\(2/3\)</span> of being included (either as linear or nonlinear), and there are <span class="math inline">\(J\)</span> total number of variables. This problem remains in case of other fixed prior choices, therefore no fixed choice of prior which is independent from the total number of variables can adjust for multiplicity.</p>
<p><br />
</p>
<p><br />
</p>
<p>To correct for the multiplicity, we specify a Dirichlet distribution, (<span class="math inline">\(\alpha_0\)</span>, <span class="math inline">\(\alpha_1\)</span>, <span class="math inline">\(\alpha_2\)</span>), for the prior probabilities of effect types. For variable <span class="math inline">\(x_j\)</span>, prior probabilities of having nonlinear, linear and zero effects respectively are denoted by <span class="math inline">\(p_{2}\)</span>, <span class="math inline">\(p_{1}\)</span> and <span class="math inline">\(p_{0}\)</span>. <span class="math inline">\(p_{2}+p_{1}+p_{0}=1\)</span> and <span class="math inline">\(\alpha_0\)</span>, <span class="math inline">\(\alpha_1\)</span>, <span class="math inline">\(\alpha_2\)</span> are the corresponding parameters for the Dirichlet distribution. Hence, Equation (12) can be rewritten by correcting multiplicity via multiplying each <span class="math inline">\(\pi(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, y)\)</span> with <span class="math inline">\(p_r^t\)</span>:</p>
<p><span class="math display">\[\begin{equation}
\tag{4}
P(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, p_r^t, Y) = \frac{\pi(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, Y) p_r^t}{\sum_{r}(\pi(\gamma^{t}_{j}= r|\gamma^{t}_{-j}, Y)p_r^t)}
\end{equation}\]</span></p>
<p>where <span class="math inline">\(p_r^t\)</span> can be written as:</p>
<p><span class="math display">\[\begin{equation}
\tag{5}
p_r^t \sim dirichlet (\alpha_0^{t-1} + |G_0 ^{t-1}|, \alpha_1^{t-1} + |G_1^{t-1}|, \alpha_2^{t-1} + |G_2^{t-1}|)
\end{equation}\]</span></p>
<p><span class="math inline">\(G_0\)</span>, <span class="math inline">\(G_1\)</span>, and <span class="math inline">\(G_2\)</span> are the numbers of variables of which the effect types are zero, linear and nonlinear respectively, and they are set to zero at <span class="math inline">\(t=0\)</span>. Note that <span class="math inline">\(G_0+G_1+G_2 = J\)</span>. First, three sampling probabilities, either <span class="math inline">\(\gamma^{t}_{j} = 0\)</span>, <span class="math inline">\(\gamma^{t}_{j} = 1\)</span> or <span class="math inline">\(\gamma^{t}_{j} = 2\)</span> will be sampled using Equation (4). Thereafter, the algorithm visits the next <span class="math inline">\(\gamma^{t}_{j+1}\)</span>. Once all <span class="math inline">\(\gamma^t\)</span> have been sampled, at the end of iteration <span class="math inline">\(t\)</span>, the algorithm samples for <span class="math inline">\(p_r^{t+1}\)</span> using the resulted <span class="math inline">\(\gamma^t\)</span>. Then, the algorithm proceeds to the <span class="math inline">\(t+1\)</span> iteration and sample for the next <span class="math inline">\(\gamma^{t+1}\)</span> with updated prior probabilities, <span class="math inline">\(p_r^{t+1}\)</span>, until the Gibbs chain converges to obtain the samples shown in (2). After obtaining the Gibbs samples and discarding the burn-in phase (e.g., the first 1000 iterations), the best model will be the one with the highest frequency in the useful samples.</p>
<p><br />
</p>
<p><strong>Gibbs Sampler Algorithm:</strong> in total <span class="math inline">\(3 \times P \times T\)</span> model fit<br />
</p>
<p>Initialize <span class="math inline">\(\gamma^{0} = 0\)</span> and <span class="math inline">\(p_r^0= 1/3\)</span> at <span class="math inline">\(t=0\)</span><br />
</p>
<p><strong>repeat</strong><br />
</p>
<p><span class="math inline">\(\qquad\)</span>for <span class="math inline">\(p = 1,..., J\)</span> do<br />
</p>
<p><span class="math inline">\(\qquad\)</span> <span class="math inline">\(\qquad\)</span> Sample <span class="math inline">\(\gamma^{t} = 0\)</span> with probability <span class="math inline">\(P(\gamma^{t}_{j}= 0|\gamma^{t}_{-j}, p_r^t,Y)\)</span><br />
</p>
<p><span class="math inline">\(\qquad\)</span> <span class="math inline">\(\qquad\)</span> Sample <span class="math inline">\(\gamma^{t} = 1\)</span> with probability <span class="math inline">\(P(\gamma^{t}_{j}= 1|\gamma^{t}_{-j},p_r^t, Y)\)</span><br />
</p>
<p><span class="math inline">\(\qquad\)</span> <span class="math inline">\(\qquad\)</span> Sample <span class="math inline">\(\gamma^{t} = 2\)</span> with probability <span class="math inline">\(P(\gamma^{t}_{j}= 2|\gamma^{t}_{-j},p_r^t, Y)\)</span><br />
</p>
<p><strong>end for</strong><br />
</p>
<p><span class="math inline">\(\qquad\)</span> Sample <span class="math inline">\(p_r^{t+1}\)</span> with probability <span class="math inline">\(dirichlet(\alpha_0^t + |G_0^t|, \alpha_1^t + |G_1^t|, \alpha_2^t + |G_2^t|)\)</span><br />
</p>
<p><strong>set</strong> <span class="math inline">\(t=t+1\)</span><br />
</p>
<p><strong>until</strong> Gibbs chain converges.</p>
</div>
<div id="performance-of-the-model-search-method" class="section level2">
<h2>Performance of the Model Search Method</h2>
<p>In this subsection, we conducted a simulation study to assess the performance of the MCMC model search method. We considered four levels of number of variables <span class="math inline">\(\{J \in 6, 10, 15, 20 \}\)</span>, and four levels of sample sizes <span class="math inline">\(\{ n \in 50, 100, 250, 500 \}\)</span>, and seven levels of effect sizes <span class="math inline">\(\{ \beta \in .1, .5, 1, 1.5, 2, 2.5, 3 \}\)</span>. For each scenario, 100 data sets were generated. The candidate variables <span class="math inline">\(x_{1},..., x_{J}\)</span> of length <span class="math inline">\(n\)</span> were independently simulated from a standard normal distribution <span class="math inline">\(N(0,1)\)</span>. The nonlinear relationship is defined with the exponential function. Therefore, the outcome variable, <span class="math inline">\(y\)</span>, was calculated with a zero intercept as follows:</p>
<p><span class="math display">\[\begin{equation}
\tag{6}
y = \beta exp(x_1) + \beta exp(x_2) + \beta x_3 + \beta x_4 + \beta^0 X_{J-4} + \epsilon
\end{equation}\]</span></p>
<p>where <span class="math inline">\(\beta^0 = 0\)</span>, <span class="math inline">\(\epsilon \sim N(0, \sigma^2)\)</span> and <span class="math inline">\(\sigma^2 = .1\)</span>. Thus, the first two variables exhibit a nonlinear effect, the next two variables have a linear effect, and the remaining variables have no effect on the outcome variable.</p>
<p><br />
</p>
<p> </p>
<p>The following function function <code>bayesian_selection</code> generates the model in (6) using the specified parameters as input variables. Then it applies the variable selection algorithm using MCMC model search method with the specified number of iteration which is 1000 in this simulation.</p>
<p><br />
</p>
<p>It returns a list including the following values:</p>
<ul>
<li>Is the selected model the same with the true model. 1: Yes and 0: No</li>
<li>Posterior probability of the true model</li>
<li>Posterior probability of the selected model</li>
<li>Selected model</li>
<li>True model</li>
<li><span class="math inline">\(\gamma\)</span> draws in (2)</li>
<li><span class="math inline">\(p_r\)</span> draws in (5)</li>
</ul>
<p><br />
</p>
<p>Input variables:</p>
<ul>
<li><code>beta</code>: <span class="math inline">\(\beta\)</span></li>
<li><code>n</code>: sample size <span class="math inline">\(n\)</span></li>
<li><code>knots</code>: k (number of basis function = k-1)</li>
<li><code>n_var</code>: total number of variables <span class="math inline">\(J\)</span></li>
<li><code>iteration</code>: burn-in</li>
<li><code>gamma_prior</code>: initial <span class="math inline">\(\gamma\)</span> values (<span class="math inline">\(\gamma_{1}^{0},...,\gamma_{P}^{0}\)</span>)</li>
<li><code>prior_p</code>: initial <span class="math inline">\(p_r\)</span> values (<span class="math inline">\(p_r^0\)</span>)</li>
</ul>
<p><br />
</p>
<div class="sourceCode" id="cb1"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb1-1"><a href="#cb1-1"></a>bayesian_selection<-<span class="st"> </span><span class="cf">function</span>(<span class="dt">beta =</span> <span class="fl">0.8</span>, <span class="dt">n =</span> <span class="dv">100</span>, </span>
<span id="cb1-2"><a href="#cb1-2"></a> <span class="dt">sigma2 =</span> <span class="fl">0.1</span>, <span class="dt">n_var =</span> <span class="dv">10</span>, </span>
<span id="cb1-3"><a href="#cb1-3"></a> <span class="dt">knots=</span> <span class="dv">4</span>,</span>
<span id="cb1-4"><a href="#cb1-4"></a> <span class="dt">iteration=</span><span class="dv">1000</span>,</span>
<span id="cb1-5"><a href="#cb1-5"></a> <span class="dt">gamma_prior =</span> <span class="kw">c</span>(<span class="kw">rep</span>(<span class="dv">0</span>, n_var)),</span>
<span id="cb1-6"><a href="#cb1-6"></a> <span class="dt">prior_p=</span><span class="kw">c</span>(<span class="dv">1</span><span class="op">/</span><span class="dv">3</span>, <span class="dv">1</span><span class="op">/</span><span class="dv">3</span>, <span class="dv">1</span><span class="op">/</span><span class="dv">3</span>)){</span>
<span id="cb1-7"><a href="#cb1-7"></a> </span>
<span id="cb1-8"><a href="#cb1-8"></a> <span class="co">#penalty is calculated as max edf - df(lm) for each variable swhere max edf = k-1 and df(lm)=1 </span></span>
<span id="cb1-9"><a href="#cb1-9"></a> penalty=knots<span class="dv">-2</span></span>
<span id="cb1-10"><a href="#cb1-10"></a> <span class="co">#Data Generation</span></span>
<span id="cb1-11"><a href="#cb1-11"></a> <span class="co">#independent predictor variables </span></span>
<span id="cb1-12"><a href="#cb1-12"></a> variables <-<span class="st"> </span><span class="kw">matrix</span>(<span class="ot">NA</span>, <span class="dt">nrow=</span>n, <span class="dt">ncol=</span>n_var)</span>
<span id="cb1-13"><a href="#cb1-13"></a> <span class="kw">colnames</span>(variables) <-<span class="kw">c</span>(<span class="kw">paste0</span>(<span class="st">"x"</span>, <span class="dv">1</span><span class="op">:</span>n_var))</span>
<span id="cb1-14"><a href="#cb1-14"></a> <span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span>n_var){</span>
<span id="cb1-15"><a href="#cb1-15"></a> variables[,i] =<span class="st"> </span><span class="kw">rnorm</span>(n)</span>
<span id="cb1-16"><a href="#cb1-16"></a> }</span>
<span id="cb1-17"><a href="#cb1-17"></a> <span class="co">#outcome variable</span></span>
<span id="cb1-18"><a href="#cb1-18"></a> error <-<span class="st"> </span><span class="kw">rnorm</span>(n,<span class="dt">sd=</span><span class="kw">sqrt</span>(sigma2)); y=error</span>
<span id="cb1-19"><a href="#cb1-19"></a> </span>
<span id="cb1-20"><a href="#cb1-20"></a> <span class="co">#randomly selecting the nonlinears and the zero relationships </span></span>
<span id="cb1-21"><a href="#cb1-21"></a> nonlinear_true <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"x1"</span>, <span class="st">"x2"</span>)</span>
<span id="cb1-22"><a href="#cb1-22"></a> linear_true <-<span class="st"> </span><span class="kw">c</span>(<span class="st">"x3"</span>, <span class="st">"x4"</span>)</span>
<span id="cb1-23"><a href="#cb1-23"></a> zero_true <-<span class="st"> </span><span class="kw">setdiff</span>(<span class="kw">colnames</span>(variables), <span class="kw">c</span>(nonlinear_true, linear_true))</span>
<span id="cb1-24"><a href="#cb1-24"></a> </span>
<span id="cb1-25"><a href="#cb1-25"></a> <span class="co"># relationship definitions and creating the true model</span></span>
<span id="cb1-26"><a href="#cb1-26"></a> <span class="co">#nonlinear effects</span></span>
<span id="cb1-27"><a href="#cb1-27"></a> nonlinear_indices <-<span class="st"> </span><span class="kw">match</span>(nonlinear_true, <span class="kw">colnames</span>(variables))</span>
<span id="cb1-28"><a href="#cb1-28"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="kw">length</span>(nonlinear_indices)){y=y<span class="op">+</span>beta<span class="op">*</span><span class="kw">exp</span>(variables[, nonlinear_indices][,i])}</span>
<span id="cb1-29"><a href="#cb1-29"></a> </span>
<span id="cb1-30"><a href="#cb1-30"></a> <span class="co">#zero effects</span></span>
<span id="cb1-31"><a href="#cb1-31"></a> zero_indices <-<span class="st"> </span><span class="kw">match</span>(zero_true, <span class="kw">colnames</span>(variables))</span>
<span id="cb1-32"><a href="#cb1-32"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="kw">length</span>(zero_indices)){y=y<span class="op">+</span><span class="dv">0</span><span class="op">*</span>variables[,zero_indices][,i]}</span>
<span id="cb1-33"><a href="#cb1-33"></a> </span>
<span id="cb1-34"><a href="#cb1-34"></a> <span class="co">#linear effects</span></span>
<span id="cb1-35"><a href="#cb1-35"></a> linear_indices<-<span class="st"> </span><span class="kw">match</span>(linear_true, <span class="kw">colnames</span>(variables))</span>
<span id="cb1-36"><a href="#cb1-36"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="st"> </span><span class="kw">length</span>(linear_indices)){y=y<span class="op">+</span>beta<span class="op">*</span>variables[,linear_indices][,i]}</span>
<span id="cb1-37"><a href="#cb1-37"></a> </span>
<span id="cb1-38"><a href="#cb1-38"></a> y =<span class="st"> </span>y <span class="op">-</span><span class="st"> </span><span class="kw">mean</span>(y) <span class="co">#not considering the intercept </span></span>
<span id="cb1-39"><a href="#cb1-39"></a> </span>
<span id="cb1-40"><a href="#cb1-40"></a> <span class="co">#true model gamma sequence </span></span>
<span id="cb1-41"><a href="#cb1-41"></a> true_gamma =<span class="st"> </span><span class="kw">c</span>(<span class="kw">rep</span>(<span class="ot">NA</span>, n_var))</span>
<span id="cb1-42"><a href="#cb1-42"></a> true_gamma[nonlinear_indices]=<span class="dv">2</span>; true_gamma[zero_indices]=<span class="dv">0</span>; true_gamma[linear_indices]=<span class="dv">1</span></span>
<span id="cb1-43"><a href="#cb1-43"></a> data_original<-<span class="st"> </span><span class="kw">as.data.frame</span>(variables) <span class="co">#transforming the matrix into a dataframe</span></span>
<span id="cb1-44"><a href="#cb1-44"></a> </span>
<span id="cb1-45"><a href="#cb1-45"></a> gamma_update_k <-gamma_prior <span class="co">#initial gamma specification</span></span>
<span id="cb1-46"><a href="#cb1-46"></a> gamma_draws <-<span class="st"> </span><span class="kw">matrix</span>(<span class="ot">NA</span>, <span class="dt">nrow=</span> iteration, <span class="dt">ncol =</span> n_var) <span class="co">#matrix for gamma draws</span></span>
<span id="cb1-47"><a href="#cb1-47"></a> ps<-<span class="st"> </span><span class="kw">matrix</span>(<span class="ot">NA</span>, <span class="dt">nrow =</span> iteration<span class="op">+</span><span class="dv">1</span>, <span class="dt">ncol =</span> <span class="dv">3</span>) <span class="co">#matrix for p_draws</span></span>
<span id="cb1-48"><a href="#cb1-48"></a> </span>
<span id="cb1-49"><a href="#cb1-49"></a> pb<-progress_bar<span class="op">$</span><span class="kw">new</span>(<span class="dt">format =</span> <span class="st">"(:spin) [:bar] :percent [Elapsed time: :elapsedfull || Estimated time remaining: :eta]"</span>,</span>
<span id="cb1-50"><a href="#cb1-50"></a> <span class="dt">total =</span> iteration,</span>
<span id="cb1-51"><a href="#cb1-51"></a> <span class="dt">complete =</span> <span class="st">"="</span>, <span class="co"># Completion bar character</span></span>
<span id="cb1-52"><a href="#cb1-52"></a> <span class="dt">incomplete =</span> <span class="st">"-"</span>, <span class="co"># Incomplete bar character</span></span>
<span id="cb1-53"><a href="#cb1-53"></a> <span class="dt">current =</span> <span class="st">">"</span>, <span class="co"># Current bar character</span></span>
<span id="cb1-54"><a href="#cb1-54"></a> <span class="dt">clear =</span> <span class="ot">FALSE</span>, <span class="co"># If TRUE, clears the bar when finish</span></span>
<span id="cb1-55"><a href="#cb1-55"></a> <span class="dt">width =</span> <span class="dv">100</span>) <span class="co"># Width of the progress bar</span></span>
<span id="cb1-56"><a href="#cb1-56"></a> <span class="cf">for</span>(s <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span>iteration){</span>
<span id="cb1-57"><a href="#cb1-57"></a> pb<span class="op">$</span><span class="kw">tick</span>()</span>
<span id="cb1-58"><a href="#cb1-58"></a> <span class="cf">for</span>(k <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span>n_var){</span>
<span id="cb1-59"><a href="#cb1-59"></a> data =<span class="st"> </span>data_original</span>
<span id="cb1-60"><a href="#cb1-60"></a> gamma_update_k1 <-<span class="st"> </span>gamma_update_k[<span class="op">-</span><span class="kw">c</span>(k)]</span>
<span id="cb1-61"><a href="#cb1-61"></a> </span>
<span id="cb1-62"><a href="#cb1-62"></a> a <-<span class="st"> </span>data[, k] <span class="co">#the variable of interest </span></span>
<span id="cb1-63"><a href="#cb1-63"></a> data <-<span class="st"> </span>data[, <span class="op">-</span>k] <span class="co">#the remaining variables </span></span>
<span id="cb1-64"><a href="#cb1-64"></a> </span>
<span id="cb1-65"><a href="#cb1-65"></a> <span class="co"># for linear effects</span></span>
<span id="cb1-66"><a href="#cb1-66"></a> linears <-<span class="st"> </span><span class="kw">c</span>()</span>
<span id="cb1-67"><a href="#cb1-67"></a> <span class="cf">if</span>(<span class="kw">length</span>(gamma_update_k1[gamma_update_k1 <span class="op">==</span><span class="st"> </span><span class="dv">1</span>]) <span class="op">!=</span><span class="st"> </span><span class="dv">0</span>){</span>
<span id="cb1-68"><a href="#cb1-68"></a> </span>
<span id="cb1-69"><a href="#cb1-69"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="kw">ncol</span>(data[<span class="kw">which</span>(gamma_update_k1 <span class="op">==</span><span class="st"> </span><span class="dv">1</span>)])){</span>
<span id="cb1-70"><a href="#cb1-70"></a> linears <-<span class="st"> </span><span class="kw">c</span>(linears, <span class="kw">paste</span>(<span class="kw">c</span>(<span class="kw">colnames</span>(data[<span class="kw">which</span>(gamma_update_k1 <span class="op">==</span><span class="st"> </span><span class="dv">1</span>)][i])), <span class="dt">collapse=</span> <span class="st">""</span>))</span>
<span id="cb1-71"><a href="#cb1-71"></a> } </span>
<span id="cb1-72"><a href="#cb1-72"></a> }</span>
<span id="cb1-73"><a href="#cb1-73"></a> </span>
<span id="cb1-74"><a href="#cb1-74"></a> <span class="co">#for nonlinear effects</span></span>
<span id="cb1-75"><a href="#cb1-75"></a> non_linears <-<span class="st"> </span><span class="kw">c</span>()</span>
<span id="cb1-76"><a href="#cb1-76"></a> <span class="cf">if</span>(<span class="kw">length</span>(gamma_update_k1[gamma_update_k1 <span class="op">==</span><span class="st"> </span><span class="dv">2</span>]) <span class="op">!=</span><span class="st"> </span><span class="dv">0</span>) {</span>
<span id="cb1-77"><a href="#cb1-77"></a> <span class="cf">for</span>(i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="kw">ncol</span>(data[<span class="kw">which</span>(gamma_update_k1 <span class="op">==</span><span class="st"> </span><span class="dv">2</span>)])){</span>
<span id="cb1-78"><a href="#cb1-78"></a> non_linears <-<span class="st"> </span><span class="kw">c</span>(non_linears, <span class="kw">paste</span>(<span class="kw">c</span>(<span class="st">'s('</span>, <span class="kw">colnames</span>(data[<span class="kw">which</span>(gamma_update_k1 <span class="op">==</span><span class="st"> </span><span class="dv">2</span>)][i]), <span class="st">',k='</span>,knots,<span class="st">')'</span>), <span class="dt">collapse=</span> <span class="st">""</span>))</span>
<span id="cb1-79"><a href="#cb1-79"></a> } </span>
<span id="cb1-80"><a href="#cb1-80"></a> }</span>
<span id="cb1-81"><a href="#cb1-81"></a> </span>
<span id="cb1-82"><a href="#cb1-82"></a> vars <-<span class="st"> </span><span class="kw">c</span>(linears, non_linears) <span class="co">#vector for non-zero effects to include to the models below</span></span>
<span id="cb1-83"><a href="#cb1-83"></a> </span>
<span id="cb1-84"><a href="#cb1-84"></a> <span class="co">#model fitting</span></span>
<span id="cb1-85"><a href="#cb1-85"></a> <span class="cf">if</span>(<span class="kw">length</span>(vars) <span class="op">!=</span><span class="st"> </span><span class="dv">0</span>){ <span class="co">#remaining variables contain non-zero effect</span></span>
<span id="cb1-86"><a href="#cb1-86"></a> M1 <-<span class="st"> </span><span class="kw">gam</span>(<span class="kw">as.formula</span>(<span class="kw">paste</span>(<span class="st">'y'</span>, <span class="st">'~'</span>, <span class="kw">paste</span>(vars, <span class="dt">collapse =</span> <span class="st">"+"</span>))), <span class="dt">data =</span> data)</span>
<span id="cb1-87"><a href="#cb1-87"></a> M2 <-<span class="st"> </span><span class="kw">gam</span>(<span class="kw">as.formula</span>(<span class="kw">paste</span>(<span class="st">'y'</span>, <span class="st">'~'</span>, <span class="st">'a +'</span>, <span class="kw">paste</span>(vars, <span class="dt">collapse =</span> <span class="st">"+"</span>))), <span class="dt">data =</span> data) <span class="co">#1</span></span>
<span id="cb1-88"><a href="#cb1-88"></a> M3 <-<span class="st"> </span><span class="kw">gam</span>(<span class="kw">as.formula</span>(<span class="kw">paste</span>(<span class="st">'y'</span>, <span class="st">'~'</span>, <span class="st">'s(a, k='</span>,knots, <span class="st">') +'</span>, <span class="kw">paste</span>(vars, <span class="dt">collapse =</span> <span class="st">"+"</span>))), <span class="dt">data =</span> data) <span class="co">#2</span></span>
<span id="cb1-89"><a href="#cb1-89"></a> } <span class="cf">else</span>{ <span class="co">#remaining variables do not contain non-zero effect</span></span>
<span id="cb1-90"><a href="#cb1-90"></a> M1 <-<span class="st"> </span><span class="kw">gam</span>(y <span class="op">~</span><span class="st"> </span><span class="dv">1</span>, <span class="dt">data =</span> data)</span>
<span id="cb1-91"><a href="#cb1-91"></a> M2 <-<span class="st"> </span><span class="kw">gam</span>(y <span class="op">~</span><span class="st"> </span>a, <span class="dt">data =</span> data) <span class="co">#1</span></span>
<span id="cb1-92"><a href="#cb1-92"></a> M3 <-<span class="st"> </span><span class="kw">gam</span>(y <span class="op">~</span><span class="st"> </span><span class="kw">s</span>(a, <span class="dt">k=</span>knots), <span class="dt">data =</span> data)</span>
<span id="cb1-93"><a href="#cb1-93"></a> }</span>
<span id="cb1-94"><a href="#cb1-94"></a> </span>
<span id="cb1-95"><a href="#cb1-95"></a> <span class="co">#BIC scores </span></span>
<span id="cb1-96"><a href="#cb1-96"></a> bic_M1 <-<span class="st"> </span>(<span class="op">-</span><span class="dv">2</span>) <span class="op">*</span><span class="st"> </span><span class="kw">head</span>(<span class="kw">logLik</span>(M1)) <span class="op">+</span><span class="st"> </span><span class="kw">attr</span>(<span class="kw">logLik</span>(M1), <span class="st">"df"</span>)<span class="op">*</span><span class="st"> </span><span class="kw">log</span>(n)</span>
<span id="cb1-97"><a href="#cb1-97"></a> bic_M2 <-<span class="st"> </span>(<span class="op">-</span><span class="dv">2</span>) <span class="op">*</span><span class="st"> </span><span class="kw">head</span>(<span class="kw">logLik</span>(M2)) <span class="op">+</span><span class="st"> </span><span class="kw">attr</span>(<span class="kw">logLik</span>(M2), <span class="st">"df"</span>)<span class="op">*</span><span class="st"> </span><span class="kw">log</span>(n)</span>
<span id="cb1-98"><a href="#cb1-98"></a> bic_M3 <-<span class="st"> </span>(<span class="op">-</span><span class="dv">2</span>) <span class="op">*</span><span class="st"> </span><span class="kw">head</span>(<span class="kw">logLik</span>(M3)) <span class="op">+</span><span class="st"> </span>(<span class="kw">attr</span>(<span class="kw">logLik</span>(M2), <span class="st">"df"</span>) <span class="op">+</span><span class="st"> </span>penalty)<span class="op">*</span><span class="st"> </span><span class="kw">log</span>(n) <span class="co">#penalty depends on the #of knots</span></span>
<span id="cb1-99"><a href="#cb1-99"></a> </span>
<span id="cb1-100"><a href="#cb1-100"></a> </span>
<span id="cb1-101"><a href="#cb1-101"></a> <span class="co">#Bayes Factors </span></span>
<span id="cb1-102"><a href="#cb1-102"></a> BF11 <-<span class="st"> </span><span class="kw">exp</span>((bic_M1 <span class="op">-</span><span class="st"> </span>bic_M1) <span class="op">/</span><span class="dv">2</span>) <span class="co">#null against the null</span></span>
<span id="cb1-103"><a href="#cb1-103"></a> BF21_ <-<span class="st"> </span><span class="kw">exp</span>((bic_M1 <span class="op">-</span><span class="st"> </span>bic_M2) <span class="op">/</span><span class="dv">2</span>) <span class="co">#linear against the null</span></span>
<span id="cb1-104"><a href="#cb1-104"></a> BF31_ <-<span class="st"> </span><span class="kw">exp</span>((bic_M1 <span class="op">-</span><span class="st"> </span>bic_M3) <span class="op">/</span><span class="dv">2</span>) <span class="co">#nonlinear against the null </span></span>
<span id="cb1-105"><a href="#cb1-105"></a> </span>
<span id="cb1-106"><a href="#cb1-106"></a> </span>
<span id="cb1-107"><a href="#cb1-107"></a> <span class="co">#infinity BFs</span></span>
<span id="cb1-108"><a href="#cb1-108"></a> <span class="cf">if</span>(BF21_ <span class="op">==</span><span class="st"> "-Inf"</span>){BF21 =<span class="st"> </span><span class="fl">-1e5</span>} <span class="cf">else</span> <span class="cf">if</span>(BF21_<span class="op">==</span><span class="st"> "Inf"</span>) {BF21 =<span class="st"> </span><span class="fl">1e5</span>} <span class="cf">else</span>{BF21=BF21_}</span>
<span id="cb1-109"><a href="#cb1-109"></a> <span class="cf">if</span>(BF31_ <span class="op">==</span><span class="st"> "-Inf"</span>){BF31 =<span class="st"> </span><span class="fl">-1e5</span>} <span class="cf">else</span> <span class="cf">if</span>(BF31_ <span class="op">==</span><span class="st"> "Inf"</span>) {BF31 =<span class="st"> </span><span class="fl">1e5</span>} <span class="cf">else</span>{BF31=BF31_}</span>
<span id="cb1-110"><a href="#cb1-110"></a> </span>
<span id="cb1-111"><a href="#cb1-111"></a> <span class="co">#Posterior Probabilities</span></span>
<span id="cb1-112"><a href="#cb1-112"></a> zero <-<span class="st"> </span>(prior_p[<span class="dv">1</span>] <span class="op">*</span><span class="st"> </span>BF11) <span class="op">/</span><span class="st"> </span><span class="kw">sum</span>(prior_p[<span class="dv">1</span>] <span class="op">*</span><span class="st"> </span>BF11, prior_p[<span class="dv">2</span>]<span class="op">*</span>BF21, prior_p[<span class="dv">3</span>]<span class="op">*</span><span class="st"> </span>BF31)</span>
<span id="cb1-113"><a href="#cb1-113"></a> one <-<span class="st"> </span>(prior_p[<span class="dv">2</span>] <span class="op">*</span><span class="st"> </span>BF21) <span class="op">/</span><span class="st"> </span><span class="kw">sum</span>(prior_p[<span class="dv">1</span>] <span class="op">*</span><span class="st"> </span>BF11, prior_p[<span class="dv">2</span>]<span class="op">*</span>BF21, prior_p[<span class="dv">3</span>]<span class="op">*</span><span class="st"> </span>BF31)</span>
<span id="cb1-114"><a href="#cb1-114"></a> two <-<span class="st"> </span>(prior_p[<span class="dv">3</span>] <span class="op">*</span><span class="st"> </span>BF31) <span class="op">/</span><span class="st"> </span><span class="kw">sum</span>(prior_p[<span class="dv">1</span>] <span class="op">*</span><span class="st"> </span>BF11, prior_p[<span class="dv">2</span>]<span class="op">*</span>BF21, prior_p[<span class="dv">3</span>]<span class="op">*</span><span class="st"> </span>BF31)</span>
<span id="cb1-115"><a href="#cb1-115"></a> </span>
<span id="cb1-116"><a href="#cb1-116"></a> </span>
<span id="cb1-117"><a href="#cb1-117"></a> </span>
<span id="cb1-118"><a href="#cb1-118"></a> <span class="co">#sampling the effect type of the variable of interest </span></span>
<span id="cb1-119"><a href="#cb1-119"></a> gamma_update_k[k] <-<span class="st"> </span><span class="kw">sample</span>(<span class="kw">c</span>(<span class="dv">0</span>,<span class="dv">1</span>,<span class="dv">2</span>), <span class="dt">size=</span><span class="dv">1</span>, <span class="dt">prob =</span> <span class="kw">c</span>(zero, one, two)) </span>
<span id="cb1-120"><a href="#cb1-120"></a> }</span>
<span id="cb1-121"><a href="#cb1-121"></a> </span>
<span id="cb1-122"><a href="#cb1-122"></a> <span class="co">#multiplicity correction for the next chain </span></span>
<span id="cb1-123"><a href="#cb1-123"></a> prior_p <-<span class="st"> </span><span class="kw">rdirichlet</span>(<span class="dv">1</span>, <span class="kw">c</span>(<span class="dv">1</span><span class="op">+</span><span class="kw">length</span>(gamma_update_k[<span class="kw">which</span>(gamma_update_k <span class="op">==</span><span class="st"> </span><span class="dv">0</span>)]), <span class="co">#alpha1 = 1</span></span>
<span id="cb1-124"><a href="#cb1-124"></a> <span class="dv">1</span><span class="op">+</span><span class="kw">length</span>(gamma_update_k[<span class="kw">which</span>(gamma_update_k <span class="op">==</span><span class="st"> </span><span class="dv">1</span>)]), <span class="co">#alpha2 = 1</span></span>
<span id="cb1-125"><a href="#cb1-125"></a> <span class="dv">1</span><span class="op">+</span><span class="kw">length</span>(gamma_update_k[<span class="kw">which</span>(gamma_update_k <span class="op">==</span><span class="st"> </span><span class="dv">2</span>)])))</span>
<span id="cb1-126"><a href="#cb1-126"></a> ps[s<span class="op">+</span><span class="dv">1</span>, ] <-<span class="st"> </span>prior_p</span>
<span id="cb1-127"><a href="#cb1-127"></a> gamma_draws[s,] <-<span class="st"> </span>gamma_update_k</span>
<span id="cb1-128"><a href="#cb1-128"></a> }</span>
<span id="cb1-129"><a href="#cb1-129"></a> <span class="co">#posterior probability calculation of the true model </span></span>
<span id="cb1-130"><a href="#cb1-130"></a> posterior <-<span class="st"> </span><span class="kw">data.table</span>(gamma_draws)</span>
<span id="cb1-131"><a href="#cb1-131"></a> frequency <-<span class="st"> </span><span class="kw">as.matrix</span>(posterior[,<span class="kw">list</span>(<span class="dt">posterior=</span>.N),<span class="dt">by=</span><span class="kw">names</span>(posterior)][<span class="kw">order</span>(posterior,<span class="dt">decreasing=</span>T)])</span>
<span id="cb1-132"><a href="#cb1-132"></a> t=<span class="kw">apply</span>(frequency[,<span class="op">-</span>(n_var<span class="op">+</span><span class="dv">1</span>)], <span class="dv">1</span>, <span class="cf">function</span>(x) <span class="kw">return</span>(<span class="kw">all</span>(x <span class="op">==</span><span class="st"> </span>true_gamma))) <span class="co">#checking any true model among the draws</span></span>
<span id="cb1-133"><a href="#cb1-133"></a> pp_t<-<span class="st"> </span><span class="cf">if</span> (<span class="kw">any</span>(t)<span class="op">==</span><span class="ot">FALSE</span>) <span class="dv">0</span> <span class="cf">else</span> <span class="kw">as.numeric</span>(frequency[<span class="kw">which</span>(t),(n_var<span class="op">+</span><span class="dv">1</span>)])<span class="op">/</span>iteration <span class="co">##posterior prob calculation of the true</span></span>
<span id="cb1-134"><a href="#cb1-134"></a> pp_s <-<span class="st"> </span><span class="kw">as.numeric</span>(frequency[<span class="dv">1</span>,(n_var<span class="op">+</span><span class="dv">1</span>)])<span class="op">/</span>iteration <span class="co">##posterior prob calculation of the selected</span></span>
<span id="cb1-135"><a href="#cb1-135"></a> results <-<span class="st"> </span><span class="kw">list</span>(<span class="st">"is true"</span> =<span class="st"> </span><span class="cf">if</span>(<span class="kw">identical</span>(<span class="kw">as.vector</span>(frequency[<span class="dv">1</span>,<span class="dv">1</span><span class="op">:</span>n_var]),true_gamma) <span class="op">==</span><span class="st"> </span><span class="ot">TRUE</span>) <span class="dv">1</span> <span class="cf">else</span> <span class="dv">0</span>,</span>
<span id="cb1-136"><a href="#cb1-136"></a> <span class="st">"posterior probability_true"</span> =<span class="st"> </span>pp_t,</span>
<span id="cb1-137"><a href="#cb1-137"></a> <span class="st">"posterior probability_selected"</span> =<span class="st"> </span>pp_s,</span>
<span id="cb1-138"><a href="#cb1-138"></a> <span class="st">"selected model"</span> =<span class="st"> </span><span class="kw">as.vector</span>(frequency[<span class="dv">1</span>,<span class="dv">1</span><span class="op">:</span>n_var]),</span>
<span id="cb1-139"><a href="#cb1-139"></a> <span class="st">"true model"</span> =<span class="st"> </span>true_gamma,</span>
<span id="cb1-140"><a href="#cb1-140"></a> <span class="st">"gamma draws"</span> =<span class="st"> </span>gamma_draws,</span>
<span id="cb1-141"><a href="#cb1-141"></a> <span class="st">"p draws"</span> =<span class="st"> </span>ps)</span>
<span id="cb1-142"><a href="#cb1-142"></a> <span class="kw">return</span>(results)</span>
<span id="cb1-143"><a href="#cb1-143"></a>}</span></code></pre></div>
<div id="convergence-of-gibbs-sampler-chain" class="section level3">
<h3>Convergence of Gibbs sampler chain</h3>
<p>To start, we need to discard the initial burn-in phase and ensure the convergence of the chain. Monitoring the sample of <span class="math inline">\(\gamma\)</span>, which is a vector of discrete variables that fluctuates in the chain, is not recommended. Instead, we monitor the largest posterior probability among all possible models given the current sample since it serves as the criterion for selecting the best model. To check the Gibbs sampler chain, we examine every 100 samples. For instance, if in the first 100 samples, <span class="math inline">\(M_\gamma\)</span> appears most frequently, say 40 times, then the probability is 0.4. Subsequently, if for the first 200 samples, M0c0 (which is often the same as <span class="math inline">\(M_\gamma\)</span>) has the largest count, say 100, then the probability becomes 0.5. As the number of iterations in the Gibbs sampler increases, the largest posterior probability should converge to a certain value, allowing us to confidently select the best model.<br />
</p>
</div>
<div id="j6" class="section level3">
<h3>J=6</h3>
<div class="sourceCode" id="cb2"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb2-1"><a href="#cb2-1"></a>chain_<span class="dv">6</span> <-<span class="st"> </span><span class="kw">bayesian_selection_m</span>(<span class="dt">iteration =</span> <span class="dv">10000</span>, <span class="dt">n_var =</span> <span class="dv">6</span>) <span class="co">#fit</span></span>
<span id="cb2-2"><a href="#cb2-2"></a></span>
<span id="cb2-3"><a href="#cb2-3"></a>chain_<span class="dv">6</span>_pp <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">rep</span>(<span class="ot">NA</span>, <span class="dv">100</span>))<span class="co">#matrix to store the posterior probabilities at every 100 iteration</span></span>
<span id="cb2-4"><a href="#cb2-4"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">100</span>){</span>
<span id="cb2-5"><a href="#cb2-5"></a> gamma_draws <-<span class="st"> </span>chain_<span class="dv">6</span><span class="op">$</span><span class="st">`</span><span class="dt">gamma draws</span><span class="st">`</span></span>
<span id="cb2-6"><a href="#cb2-6"></a> posterior <-<span class="st"> </span><span class="kw">data.table</span>(gamma_draws[<span class="dv">1</span><span class="op">:</span>(i<span class="op">*</span><span class="dv">100</span>),])</span>
<span id="cb2-7"><a href="#cb2-7"></a> frequency <-<span class="st"> </span><span class="kw">as.matrix</span>(posterior[,<span class="kw">list</span>(<span class="dt">posterior=</span>.N),<span class="dt">by=</span><span class="kw">names</span>(posterior)][<span class="kw">order</span>(posterior,<span class="dt">decreasing=</span>T)])</span>
<span id="cb2-8"><a href="#cb2-8"></a> pp_s <-<span class="st"> </span><span class="kw">as.numeric</span>(frequency[<span class="dv">1</span>,(<span class="dv">6</span><span class="op">+</span><span class="dv">1</span>)])<span class="op">/</span>(i<span class="op">*</span><span class="dv">100</span>) <span class="co">##posterior prob calculation of the selected</span></span>
<span id="cb2-9"><a href="#cb2-9"></a> chain_<span class="dv">6</span>_pp[i] =<span class="st"> </span>pp_s</span>
<span id="cb2-10"><a href="#cb2-10"></a>}</span></code></pre></div>
<div class="sourceCode" id="cb3"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb3-1"><a href="#cb3-1"></a><span class="kw">plot</span>(<span class="kw">c</span>(<span class="dv">100</span><span class="op">*</span><span class="kw">c</span>(<span class="dv">1</span><span class="op">:</span><span class="dv">100</span>)), chain_<span class="dv">6</span>_pp, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), </span>
<span id="cb3-2"><a href="#cb3-2"></a> <span class="dt">ylab =</span> <span class="st">"Posterior probability of the selected model"</span>, <span class="dt">xlab =</span> <span class="st">"T"</span>, <span class="dt">main =</span> <span class="st">"J=6"</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
</div>
<div id="j20" class="section level3">
<h3>J=20</h3>
<div class="sourceCode" id="cb4"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb4-1"><a href="#cb4-1"></a>chain_<span class="dv">20</span> <-<span class="st"> </span><span class="kw">bayesian_selection_m</span>(<span class="dt">iteration =</span> <span class="dv">10000</span>, <span class="dt">n_var =</span> <span class="dv">20</span>) <span class="co">#fit</span></span>
<span id="cb4-2"><a href="#cb4-2"></a></span>
<span id="cb4-3"><a href="#cb4-3"></a>chain_<span class="dv">20</span>_pp <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">rep</span>(<span class="ot">NA</span>, <span class="dv">100</span>))<span class="co">#matrix to store the posterior probabilities at every 100 iteration</span></span>
<span id="cb4-4"><a href="#cb4-4"></a><span class="cf">for</span> (i <span class="cf">in</span> <span class="dv">1</span><span class="op">:</span><span class="dv">100</span>){</span>
<span id="cb4-5"><a href="#cb4-5"></a> gamma_draws <-<span class="st"> </span>chain_<span class="dv">20</span><span class="op">$</span><span class="st">`</span><span class="dt">gamma draws</span><span class="st">`</span></span>
<span id="cb4-6"><a href="#cb4-6"></a> posterior <-<span class="st"> </span><span class="kw">data.table</span>(gamma_draws[<span class="dv">1</span><span class="op">:</span>(i<span class="op">*</span><span class="dv">100</span>),])</span>
<span id="cb4-7"><a href="#cb4-7"></a> frequency <-<span class="st"> </span><span class="kw">as.matrix</span>(posterior[,<span class="kw">list</span>(<span class="dt">posterior=</span>.N),<span class="dt">by=</span><span class="kw">names</span>(posterior)][<span class="kw">order</span>(posterior,<span class="dt">decreasing=</span>T)])</span>
<span id="cb4-8"><a href="#cb4-8"></a> pp_s <-<span class="st"> </span><span class="kw">as.numeric</span>(frequency[<span class="dv">1</span>,(<span class="dv">20</span><span class="op">+</span><span class="dv">1</span>)])<span class="op">/</span>(i<span class="op">*</span><span class="dv">100</span>) <span class="co">##posterior prob calculation of the selected</span></span>
<span id="cb4-9"><a href="#cb4-9"></a> chain_<span class="dv">20</span>_pp[i] =<span class="st"> </span>pp_s</span>
<span id="cb4-10"><a href="#cb4-10"></a>}</span></code></pre></div>
<div class="sourceCode" id="cb5"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb5-1"><a href="#cb5-1"></a><span class="kw">plot</span>(<span class="kw">c</span>(<span class="dv">100</span><span class="op">*</span><span class="kw">c</span>(<span class="dv">1</span><span class="op">:</span><span class="dv">100</span>)), chain_<span class="dv">20</span>_pp, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), </span>
<span id="cb5-2"><a href="#cb5-2"></a> <span class="dt">ylab =</span> <span class="st">"Posterior probability of the selected model"</span>, <span class="dt">xlab =</span> <span class="st">"T"</span>, <span class="dt">main =</span> <span class="st">"J=20"</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
<p><br />
</p>
<ul>
<li>The posterior probability of the selected model against the iteration number for <span class="math inline">\(\gamma\)</span> given <span class="math inline">\(J=6\)</span> and <span class="math inline">\(J=20\)</span> under fixed prior probabilities. The chain starts with the null model <span class="math inline">\(\gamma = 0\)</span>. Both, when <span class="math inline">\(J=6\)</span> and <span class="math inline">\(J=20\)</span>, the chain converges rapidly, stabilizing after around 2,000 iterations. However, due to the time limitations of the study, we decided to discard the first 1,000 iterations for the variable selection, despite the Gibbs sampler chain suggesting the need for more iterations.</li>
</ul>
<p><br />
<br />
</p>
<div class="sourceCode" id="cb6"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb6-1"><a href="#cb6-1"></a><span class="co"># Run the loop in parallel</span></span>
<span id="cb6-2"><a href="#cb6-2"></a><span class="kw">detectCores</span>()</span>
<span id="cb6-3"><a href="#cb6-3"></a><span class="kw">registerDoParallel</span>(<span class="dv">30</span>)</span>
<span id="cb6-4"><a href="#cb6-4"></a>trials=<span class="dv">100</span></span></code></pre></div>
</div>
<div id="sample-size-n" class="section level3">
<h3>Sample Size <span class="math inline">\(n\)</span></h3>
<ul>
<li>The sample size varied from <span class="math inline">\(n=50\)</span> to <span class="math inline">\(n=500\)</span> given <span class="math inline">\(\beta = .5\)</span> and <span class="math inline">\(\beta = 2\)</span> for <span class="math inline">\(J=10\)</span></li>
</ul>
<div class="sourceCode" id="cb7"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb7-1"><a href="#cb7-1"></a><span class="co">####SAMPLE SIZES </span></span>
<span id="cb7-2"><a href="#cb7-2"></a>xresults_n50 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb7-3"><a href="#cb7-3"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb7-4"><a href="#cb7-4"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb7-5"><a href="#cb7-5"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb7-6"><a href="#cb7-6"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">5</span>, <span class="dt">n=</span><span class="dv">50</span>)</span>
<span id="cb7-7"><a href="#cb7-7"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">2</span>, <span class="dt">n=</span><span class="dv">50</span>)</span>
<span id="cb7-8"><a href="#cb7-8"></a> </span>
<span id="cb7-9"><a href="#cb7-9"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-10"><a href="#cb7-10"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb7-11"><a href="#cb7-11"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-12"><a href="#cb7-12"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb7-13"><a href="#cb7-13"></a> }</span>
<span id="cb7-14"><a href="#cb7-14"></a></span>
<span id="cb7-15"><a href="#cb7-15"></a>xresults_n100 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb7-16"><a href="#cb7-16"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb7-17"><a href="#cb7-17"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb7-18"><a href="#cb7-18"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb7-19"><a href="#cb7-19"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">5</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb7-20"><a href="#cb7-20"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">2</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb7-21"><a href="#cb7-21"></a> </span>
<span id="cb7-22"><a href="#cb7-22"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-23"><a href="#cb7-23"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb7-24"><a href="#cb7-24"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-25"><a href="#cb7-25"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb7-26"><a href="#cb7-26"></a> }</span>
<span id="cb7-27"><a href="#cb7-27"></a></span>
<span id="cb7-28"><a href="#cb7-28"></a>xresults_n250 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb7-29"><a href="#cb7-29"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb7-30"><a href="#cb7-30"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb7-31"><a href="#cb7-31"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb7-32"><a href="#cb7-32"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">5</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb7-33"><a href="#cb7-33"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">2</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb7-34"><a href="#cb7-34"></a> </span>
<span id="cb7-35"><a href="#cb7-35"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-36"><a href="#cb7-36"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb7-37"><a href="#cb7-37"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-38"><a href="#cb7-38"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb7-39"><a href="#cb7-39"></a> }</span>
<span id="cb7-40"><a href="#cb7-40"></a></span>
<span id="cb7-41"><a href="#cb7-41"></a>xresults_n500 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb7-42"><a href="#cb7-42"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb7-43"><a href="#cb7-43"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb7-44"><a href="#cb7-44"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb7-45"><a href="#cb7-45"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">5</span>, <span class="dt">n=</span><span class="dv">500</span>)</span>
<span id="cb7-46"><a href="#cb7-46"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">2</span>, <span class="dt">n=</span><span class="dv">500</span>)</span>
<span id="cb7-47"><a href="#cb7-47"></a> </span>
<span id="cb7-48"><a href="#cb7-48"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-49"><a href="#cb7-49"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb7-50"><a href="#cb7-50"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb7-51"><a href="#cb7-51"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb7-52"><a href="#cb7-52"></a> }</span></code></pre></div>
<div id="plots" class="section level4">
<h4>Plots</h4>
<div class="sourceCode" id="cb8"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb8-1"><a href="#cb8-1"></a><span class="co">#proportion of correct selection </span></span>
<span id="cb8-2"><a href="#cb8-2"></a></span>
<span id="cb8-3"><a href="#cb8-3"></a><span class="co">#beta=.5</span></span>
<span id="cb8-4"><a href="#cb8-4"></a>cs_n_.<span class="dv">5</span> <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">length</span>(n50[,<span class="dv">1</span>][n50[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]), </span>
<span id="cb8-5"><a href="#cb8-5"></a> <span class="kw">length</span>(n100[,<span class="dv">1</span>][n100[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]), </span>
<span id="cb8-6"><a href="#cb8-6"></a> <span class="kw">length</span>(n250[,<span class="dv">1</span>][n250[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb8-7"><a href="#cb8-7"></a> <span class="kw">length</span>(n500[,<span class="dv">1</span>][n500[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]))</span>
<span id="cb8-8"><a href="#cb8-8"></a></span>
<span id="cb8-9"><a href="#cb8-9"></a><span class="co">#beta=2</span></span>
<span id="cb8-10"><a href="#cb8-10"></a>cs_n_<span class="dv">2</span> <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">length</span>(n50[,<span class="dv">14</span>][n50[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]), </span>
<span id="cb8-11"><a href="#cb8-11"></a> <span class="kw">length</span>(n100[,<span class="dv">14</span>][n100[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]), </span>
<span id="cb8-12"><a href="#cb8-12"></a> <span class="kw">length</span>(n250[,<span class="dv">14</span>][n250[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb8-13"><a href="#cb8-13"></a> <span class="kw">length</span>(n500[,<span class="dv">14</span>][n500[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]))</span>
<span id="cb8-14"><a href="#cb8-14"></a></span>
<span id="cb8-15"><a href="#cb8-15"></a><span class="co">#plot</span></span>
<span id="cb8-16"><a href="#cb8-16"></a><span class="kw">plot</span>(<span class="kw">c</span>( <span class="dv">50</span>, <span class="dv">100</span>, <span class="dv">250</span>, <span class="dv">500</span>), cs_n_.<span class="dv">5</span><span class="op">/</span><span class="dv">100</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), </span>
<span id="cb8-17"><a href="#cb8-17"></a> <span class="dt">ylab =</span> <span class="st">"Proportion of correct selection"</span>, <span class="dt">xlab =</span> <span class="st">"n"</span>)</span>
<span id="cb8-18"><a href="#cb8-18"></a><span class="kw">legend</span>(<span class="dv">400</span>, <span class="fl">0.5</span>, <span class="dt">legend=</span><span class="kw">c</span>(<span class="kw">expression</span>(<span class="kw">paste</span>(beta, <span class="st">"=.5"</span>)), <span class="kw">expression</span>(<span class="kw">paste</span>(beta, <span class="st">"=2"</span>))),</span>
<span id="cb8-19"><a href="#cb8-19"></a> <span class="dt">lty=</span><span class="dv">1</span><span class="op">:</span><span class="dv">2</span>, <span class="dt">cex=</span><span class="dv">1</span>)</span>
<span id="cb8-20"><a href="#cb8-20"></a><span class="kw">lines</span>(<span class="kw">c</span>( <span class="dv">50</span>, <span class="dv">100</span>, <span class="dv">250</span>, <span class="dv">500</span>), cs_n_<span class="dv">2</span><span class="op">/</span><span class="dv">100</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">2</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb9"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb9-1"><a href="#cb9-1"></a><span class="co">#posterior probability of the true model </span></span>
<span id="cb9-2"><a href="#cb9-2"></a></span>
<span id="cb9-3"><a href="#cb9-3"></a><span class="co">#beta=.5</span></span>
<span id="cb9-4"><a href="#cb9-4"></a>pp_n_.<span class="dv">5</span> <-<span class="kw">c</span>(<span class="kw">mean</span>(n50[,<span class="dv">2</span>]),</span>
<span id="cb9-5"><a href="#cb9-5"></a> <span class="kw">mean</span>(n100[,<span class="dv">2</span>]),</span>
<span id="cb9-6"><a href="#cb9-6"></a> <span class="kw">mean</span>(n250[,<span class="dv">2</span>]),</span>
<span id="cb9-7"><a href="#cb9-7"></a> <span class="kw">mean</span>(n500[,<span class="dv">2</span>])) <span class="co">#</span></span>
<span id="cb9-8"><a href="#cb9-8"></a><span class="co">#beta=2</span></span>
<span id="cb9-9"><a href="#cb9-9"></a>pp_n_<span class="dv">2</span> <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">mean</span>(n50[,<span class="dv">15</span>]),</span>
<span id="cb9-10"><a href="#cb9-10"></a> <span class="kw">mean</span>(n100[,<span class="dv">15</span>]),</span>
<span id="cb9-11"><a href="#cb9-11"></a> <span class="kw">mean</span>(n250[,<span class="dv">15</span>]),</span>
<span id="cb9-12"><a href="#cb9-12"></a> <span class="kw">mean</span>(n500[,<span class="dv">15</span>]))</span>
<span id="cb9-13"><a href="#cb9-13"></a></span>
<span id="cb9-14"><a href="#cb9-14"></a><span class="co">#plot</span></span>
<span id="cb9-15"><a href="#cb9-15"></a><span class="kw">plot</span>(<span class="kw">c</span>( <span class="dv">50</span>, <span class="dv">100</span>, <span class="dv">250</span>, <span class="dv">500</span>), pp_n_.<span class="dv">5</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), </span>
<span id="cb9-16"><a href="#cb9-16"></a> <span class="dt">ylab =</span> <span class="st">"Posterior Probability of the true model"</span>, <span class="dt">xlab =</span> <span class="st">"n"</span>)</span>
<span id="cb9-17"><a href="#cb9-17"></a><span class="kw">legend</span>(<span class="dv">400</span>, <span class="fl">0.5</span>, <span class="dt">legend=</span><span class="kw">c</span>(<span class="kw">expression</span>(<span class="kw">paste</span>(beta, <span class="st">"=.5"</span>)), <span class="kw">expression</span>(<span class="kw">paste</span>(beta, <span class="st">"=2"</span>))),</span>
<span id="cb9-18"><a href="#cb9-18"></a> <span class="dt">lty=</span><span class="dv">1</span><span class="op">:</span><span class="dv">2</span>, <span class="dt">cex=</span><span class="dv">1</span>)</span>
<span id="cb9-19"><a href="#cb9-19"></a><span class="kw">lines</span>(<span class="kw">c</span>( <span class="dv">50</span>, <span class="dv">100</span>, <span class="dv">250</span>, <span class="dv">500</span>), pp_n_<span class="dv">2</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">2</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
</div>
</div>
<div id="effect-size-beta" class="section level3">
<h3>Effect Size <span class="math inline">\(\beta\)</span></h3>
<ul>
<li>The effect size varied from <span class="math inline">\(\beta = .1\)</span> to <span class="math inline">\(\beta = 3\)</span> given <span class="math inline">\(n=100\)</span> and <span class="math inline">\(n=250\)</span> for <span class="math inline">\(J=10\)</span>.</li>
</ul>
<div class="sourceCode" id="cb10"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb10-1"><a href="#cb10-1"></a><span class="co">#beta=0.1</span></span>
<span id="cb10-2"><a href="#cb10-2"></a>xresults_beta_.<span class="dv">1</span> <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb10-3"><a href="#cb10-3"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb10-4"><a href="#cb10-4"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb10-5"><a href="#cb10-5"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb10-6"><a href="#cb10-6"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">1</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb10-7"><a href="#cb10-7"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">1</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb10-8"><a href="#cb10-8"></a> </span>
<span id="cb10-9"><a href="#cb10-9"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-10"><a href="#cb10-10"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb10-11"><a href="#cb10-11"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-12"><a href="#cb10-12"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb10-13"><a href="#cb10-13"></a> }</span>
<span id="cb10-14"><a href="#cb10-14"></a></span>
<span id="cb10-15"><a href="#cb10-15"></a></span>
<span id="cb10-16"><a href="#cb10-16"></a></span>
<span id="cb10-17"><a href="#cb10-17"></a><span class="co">#beta=0.5</span></span>
<span id="cb10-18"><a href="#cb10-18"></a>xresults_beta_.<span class="dv">5</span> <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb10-19"><a href="#cb10-19"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb10-20"><a href="#cb10-20"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb10-21"><a href="#cb10-21"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb10-22"><a href="#cb10-22"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">5</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb10-23"><a href="#cb10-23"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span>.<span class="dv">5</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb10-24"><a href="#cb10-24"></a> </span>
<span id="cb10-25"><a href="#cb10-25"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-26"><a href="#cb10-26"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb10-27"><a href="#cb10-27"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-28"><a href="#cb10-28"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb10-29"><a href="#cb10-29"></a> }</span>
<span id="cb10-30"><a href="#cb10-30"></a></span>
<span id="cb10-31"><a href="#cb10-31"></a></span>
<span id="cb10-32"><a href="#cb10-32"></a></span>
<span id="cb10-33"><a href="#cb10-33"></a><span class="co">#beta=0.1</span></span>
<span id="cb10-34"><a href="#cb10-34"></a>xresults_beta_<span class="dv">1</span> <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb10-35"><a href="#cb10-35"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb10-36"><a href="#cb10-36"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb10-37"><a href="#cb10-37"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb10-38"><a href="#cb10-38"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">1</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb10-39"><a href="#cb10-39"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">1</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb10-40"><a href="#cb10-40"></a> </span>
<span id="cb10-41"><a href="#cb10-41"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-42"><a href="#cb10-42"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb10-43"><a href="#cb10-43"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-44"><a href="#cb10-44"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb10-45"><a href="#cb10-45"></a> }</span>
<span id="cb10-46"><a href="#cb10-46"></a></span>
<span id="cb10-47"><a href="#cb10-47"></a></span>
<span id="cb10-48"><a href="#cb10-48"></a></span>
<span id="cb10-49"><a href="#cb10-49"></a><span class="co">#beta=0.1</span></span>
<span id="cb10-50"><a href="#cb10-50"></a>xresults_beta_<span class="fl">1.5</span> <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb10-51"><a href="#cb10-51"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb10-52"><a href="#cb10-52"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb10-53"><a href="#cb10-53"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb10-54"><a href="#cb10-54"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="fl">1.5</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb10-55"><a href="#cb10-55"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="fl">1.5</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb10-56"><a href="#cb10-56"></a> </span>
<span id="cb10-57"><a href="#cb10-57"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-58"><a href="#cb10-58"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb10-59"><a href="#cb10-59"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-60"><a href="#cb10-60"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb10-61"><a href="#cb10-61"></a> }</span>
<span id="cb10-62"><a href="#cb10-62"></a></span>
<span id="cb10-63"><a href="#cb10-63"></a></span>
<span id="cb10-64"><a href="#cb10-64"></a></span>
<span id="cb10-65"><a href="#cb10-65"></a></span>
<span id="cb10-66"><a href="#cb10-66"></a><span class="co">#beta=0.1</span></span>
<span id="cb10-67"><a href="#cb10-67"></a>xresults_beta_<span class="dv">2</span> <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb10-68"><a href="#cb10-68"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb10-69"><a href="#cb10-69"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb10-70"><a href="#cb10-70"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb10-71"><a href="#cb10-71"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">2</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb10-72"><a href="#cb10-72"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">2</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb10-73"><a href="#cb10-73"></a> </span>
<span id="cb10-74"><a href="#cb10-74"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-75"><a href="#cb10-75"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb10-76"><a href="#cb10-76"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-77"><a href="#cb10-77"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb10-78"><a href="#cb10-78"></a> }</span>
<span id="cb10-79"><a href="#cb10-79"></a></span>
<span id="cb10-80"><a href="#cb10-80"></a></span>
<span id="cb10-81"><a href="#cb10-81"></a></span>
<span id="cb10-82"><a href="#cb10-82"></a>xresults_beta_<span class="fl">2.5</span> <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb10-83"><a href="#cb10-83"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb10-84"><a href="#cb10-84"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb10-85"><a href="#cb10-85"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb10-86"><a href="#cb10-86"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="fl">2.5</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb10-87"><a href="#cb10-87"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="fl">2.5</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb10-88"><a href="#cb10-88"></a> </span>
<span id="cb10-89"><a href="#cb10-89"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-90"><a href="#cb10-90"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb10-91"><a href="#cb10-91"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-92"><a href="#cb10-92"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb10-93"><a href="#cb10-93"></a> }</span>
<span id="cb10-94"><a href="#cb10-94"></a></span>
<span id="cb10-95"><a href="#cb10-95"></a></span>
<span id="cb10-96"><a href="#cb10-96"></a>xresults_beta_<span class="dv">3</span> <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(trials),</span>
<span id="cb10-97"><a href="#cb10-97"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb10-98"><a href="#cb10-98"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb10-99"><a href="#cb10-99"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb10-100"><a href="#cb10-100"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">3</span>, <span class="dt">n=</span><span class="dv">100</span>)</span>
<span id="cb10-101"><a href="#cb10-101"></a> b =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">beta=</span><span class="dv">3</span>, <span class="dt">n=</span><span class="dv">250</span>)</span>
<span id="cb10-102"><a href="#cb10-102"></a> </span>
<span id="cb10-103"><a href="#cb10-103"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-104"><a href="#cb10-104"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>,</span>
<span id="cb10-105"><a href="#cb10-105"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,b<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb10-106"><a href="#cb10-106"></a> b<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb10-107"><a href="#cb10-107"></a> }</span></code></pre></div>
<div id="plots-1" class="section level4">
<h4>Plots</h4>
<div class="sourceCode" id="cb11"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb11-1"><a href="#cb11-1"></a><span class="co">#proportion of correct selection</span></span>
<span id="cb11-2"><a href="#cb11-2"></a></span>
<span id="cb11-3"><a href="#cb11-3"></a><span class="co">#n=100</span></span>
<span id="cb11-4"><a href="#cb11-4"></a>cs_beta_<span class="dv">100</span> <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">length</span>(beta<span class="fl">.1</span>[,<span class="dv">1</span>][beta<span class="fl">.1</span>[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]), </span>
<span id="cb11-5"><a href="#cb11-5"></a> <span class="kw">length</span>(beta<span class="fl">.5</span>[,<span class="dv">1</span>][beta<span class="fl">.5</span>[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]), </span>
<span id="cb11-6"><a href="#cb11-6"></a> <span class="kw">length</span>(beta1[,<span class="dv">1</span>][beta1[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-7"><a href="#cb11-7"></a> <span class="kw">length</span>(beta1<span class="fl">.5</span>[,<span class="dv">1</span>][beta1<span class="fl">.5</span>[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-8"><a href="#cb11-8"></a> <span class="kw">length</span>(beta2[,<span class="dv">1</span>][beta2[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-9"><a href="#cb11-9"></a> <span class="kw">length</span>(beta2<span class="fl">.5</span>[,<span class="dv">1</span>][beta2<span class="fl">.5</span>[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]), </span>
<span id="cb11-10"><a href="#cb11-10"></a> <span class="kw">length</span>(beta3[,<span class="dv">1</span>][beta3[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]))</span>
<span id="cb11-11"><a href="#cb11-11"></a></span>
<span id="cb11-12"><a href="#cb11-12"></a><span class="co">#n=250</span></span>
<span id="cb11-13"><a href="#cb11-13"></a>cs_beta_<span class="dv">250</span> <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">length</span>(beta<span class="fl">.1</span>[,<span class="dv">14</span>][beta<span class="fl">.1</span>[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-14"><a href="#cb11-14"></a> <span class="kw">length</span>(beta<span class="fl">.5</span>[,<span class="dv">14</span>][beta<span class="fl">.5</span>[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-15"><a href="#cb11-15"></a> <span class="kw">length</span>(beta1[,<span class="dv">14</span>][beta1[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-16"><a href="#cb11-16"></a> <span class="kw">length</span>(beta1<span class="fl">.5</span>[,<span class="dv">14</span>][beta1<span class="fl">.5</span>[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-17"><a href="#cb11-17"></a> <span class="kw">length</span>(beta2[,<span class="dv">14</span>][beta2[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-18"><a href="#cb11-18"></a> <span class="kw">length</span>(beta2<span class="fl">.5</span>[,<span class="dv">14</span>][beta2<span class="fl">.5</span>[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]),</span>
<span id="cb11-19"><a href="#cb11-19"></a> <span class="kw">length</span>(beta3[,<span class="dv">14</span>][beta3[,<span class="dv">14</span>]<span class="op">==</span><span class="dv">1</span>]))</span>
<span id="cb11-20"><a href="#cb11-20"></a></span>
<span id="cb11-21"><a href="#cb11-21"></a></span>
<span id="cb11-22"><a href="#cb11-22"></a></span>
<span id="cb11-23"><a href="#cb11-23"></a><span class="co">#plot</span></span>
<span id="cb11-24"><a href="#cb11-24"></a><span class="kw">plot</span>(<span class="kw">c</span>( <span class="fl">.1</span>,.<span class="dv">5</span>,<span class="dv">1</span>, <span class="fl">1.5</span>, <span class="dv">2</span>, <span class="fl">2.5</span>, <span class="dv">3</span>), cs_beta_<span class="dv">100</span><span class="op">/</span><span class="dv">100</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), </span>
<span id="cb11-25"><a href="#cb11-25"></a> <span class="dt">ylab =</span> <span class="st">"Proportion of correct selection"</span>, <span class="dt">xlab =</span> <span class="kw">expression</span>(beta))</span>
<span id="cb11-26"><a href="#cb11-26"></a><span class="kw">legend</span>(<span class="dv">2</span>, <span class="fl">0.3</span>, <span class="dt">legend=</span><span class="kw">c</span>(<span class="st">"n=100"</span>, <span class="st">"n=250"</span>),</span>
<span id="cb11-27"><a href="#cb11-27"></a> <span class="dt">lty=</span><span class="dv">1</span><span class="op">:</span><span class="dv">2</span>, <span class="dt">cex=</span><span class="dv">1</span>)</span>
<span id="cb11-28"><a href="#cb11-28"></a><span class="kw">lines</span>(<span class="kw">c</span>( <span class="fl">.1</span>,.<span class="dv">5</span>,<span class="dv">1</span>, <span class="fl">1.5</span>, <span class="dv">2</span>, <span class="fl">2.5</span>, <span class="dv">3</span>), cs_beta_<span class="dv">250</span><span class="op">/</span><span class="dv">100</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">2</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
<div class="sourceCode" id="cb12"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb12-1"><a href="#cb12-1"></a><span class="co">#posterior probability of the true model </span></span>
<span id="cb12-2"><a href="#cb12-2"></a></span>
<span id="cb12-3"><a href="#cb12-3"></a><span class="co">#n=100</span></span>
<span id="cb12-4"><a href="#cb12-4"></a>pp_beta_<span class="dv">100</span> <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">mean</span>(beta<span class="fl">.1</span>[,<span class="dv">2</span>]),</span>
<span id="cb12-5"><a href="#cb12-5"></a> <span class="kw">mean</span>(beta<span class="fl">.5</span>[,<span class="dv">2</span>]), </span>
<span id="cb12-6"><a href="#cb12-6"></a> <span class="kw">mean</span>(beta1[,<span class="dv">2</span>]), </span>
<span id="cb12-7"><a href="#cb12-7"></a> <span class="kw">mean</span>(beta1<span class="fl">.5</span>[,<span class="dv">2</span>]),</span>
<span id="cb12-8"><a href="#cb12-8"></a> <span class="kw">mean</span>(beta2[,<span class="dv">2</span>]),</span>
<span id="cb12-9"><a href="#cb12-9"></a> <span class="kw">mean</span>(beta2<span class="fl">.5</span>[,<span class="dv">2</span>]), </span>
<span id="cb12-10"><a href="#cb12-10"></a> <span class="kw">mean</span>(beta3[,<span class="dv">2</span>]))</span>
<span id="cb12-11"><a href="#cb12-11"></a></span>
<span id="cb12-12"><a href="#cb12-12"></a><span class="co">#n=250</span></span>
<span id="cb12-13"><a href="#cb12-13"></a>pp_beta_<span class="dv">250</span> <-<span class="st"> </span><span class="kw">c</span>(<span class="kw">mean</span>(beta<span class="fl">.1</span>[,<span class="dv">15</span>]),</span>
<span id="cb12-14"><a href="#cb12-14"></a> <span class="kw">mean</span>(beta<span class="fl">.5</span>[,<span class="dv">15</span>]),</span>
<span id="cb12-15"><a href="#cb12-15"></a> <span class="kw">mean</span>(beta1[,<span class="dv">15</span>]),</span>
<span id="cb12-16"><a href="#cb12-16"></a> <span class="kw">mean</span>(beta1<span class="fl">.5</span>[,<span class="dv">15</span>]),</span>
<span id="cb12-17"><a href="#cb12-17"></a> <span class="kw">mean</span>(beta2[,<span class="dv">15</span>]),</span>
<span id="cb12-18"><a href="#cb12-18"></a> <span class="kw">mean</span>(beta2<span class="fl">.5</span>[,<span class="dv">15</span>]),</span>
<span id="cb12-19"><a href="#cb12-19"></a> <span class="kw">mean</span>(beta3[,<span class="dv">15</span>]))</span>
<span id="cb12-20"><a href="#cb12-20"></a></span>
<span id="cb12-21"><a href="#cb12-21"></a><span class="co">#plot</span></span>
<span id="cb12-22"><a href="#cb12-22"></a><span class="kw">plot</span>(<span class="kw">c</span>( <span class="fl">.1</span>,.<span class="dv">5</span>,<span class="dv">1</span>, <span class="fl">1.5</span>, <span class="dv">2</span>, <span class="fl">2.5</span>, <span class="dv">3</span>), pp_beta_<span class="dv">100</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">ylim=</span><span class="kw">c</span>(<span class="dv">0</span>, <span class="dv">1</span>), </span>
<span id="cb12-23"><a href="#cb12-23"></a> <span class="dt">ylab =</span> <span class="st">"Posterior Probability of the true model"</span>, <span class="dt">xlab =</span> <span class="kw">expression</span>(beta))</span>
<span id="cb12-24"><a href="#cb12-24"></a><span class="kw">legend</span>(<span class="dv">2</span>, <span class="fl">0.3</span>, <span class="dt">legend=</span><span class="kw">c</span>(<span class="st">"n=100"</span>, <span class="st">"n=250"</span>),</span>
<span id="cb12-25"><a href="#cb12-25"></a> <span class="dt">lty=</span><span class="dv">1</span><span class="op">:</span><span class="dv">2</span>, <span class="dt">cex=</span><span class="dv">1</span>)</span>
<span id="cb12-26"><a href="#cb12-26"></a><span class="kw">lines</span>(<span class="kw">c</span>( <span class="fl">.1</span>,.<span class="dv">5</span>,<span class="dv">1</span>, <span class="fl">1.5</span>, <span class="dv">2</span>, <span class="fl">2.5</span>, <span class="dv">3</span>), pp_beta_<span class="dv">250</span>, <span class="dt">type=</span><span class="st">"l"</span>, <span class="dt">lty=</span><span class="dv">2</span>)</span></code></pre></div>
<p><img 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" /><!-- --></p>
</div>
</div>
<div id="number-of-variables-j" class="section level3">
<h3>Number of variables (J)</h3>
<ul>
<li><span class="math inline">\(J\)</span> varied from <span class="math inline">\(J=6\)</span> to <span class="math inline">\(J=30\)</span> given <code>k=4</code>.</li>
</ul>
<p><br />
</p>
<div class="sourceCode" id="cb13"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb13-1"><a href="#cb13-1"></a>start <-<span class="st"> </span><span class="kw">proc.time</span>()</span>
<span id="cb13-2"><a href="#cb13-2"></a>mj6 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(<span class="dv">100</span>),</span>
<span id="cb13-3"><a href="#cb13-3"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb13-4"><a href="#cb13-4"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb13-5"><a href="#cb13-5"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb13-6"><a href="#cb13-6"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">n_var=</span><span class="dv">6</span>)</span>
<span id="cb13-7"><a href="#cb13-7"></a> </span>
<span id="cb13-8"><a href="#cb13-8"></a> </span>
<span id="cb13-9"><a href="#cb13-9"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb13-10"><a href="#cb13-10"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb13-11"><a href="#cb13-11"></a> }</span>
<span id="cb13-12"><a href="#cb13-12"></a></span>
<span id="cb13-13"><a href="#cb13-13"></a>mj6_CPU <-<span class="st"> </span><span class="kw">proc.time</span>()<span class="op">-</span>start</span>
<span id="cb13-14"><a href="#cb13-14"></a></span>
<span id="cb13-15"><a href="#cb13-15"></a><span class="co">######################################################################################################</span></span>
<span id="cb13-16"><a href="#cb13-16"></a></span>
<span id="cb13-17"><a href="#cb13-17"></a>start <-<span class="st"> </span><span class="kw">proc.time</span>()</span>
<span id="cb13-18"><a href="#cb13-18"></a>mj10 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(<span class="dv">100</span>),</span>
<span id="cb13-19"><a href="#cb13-19"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb13-20"><a href="#cb13-20"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb13-21"><a href="#cb13-21"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb13-22"><a href="#cb13-22"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">n_var=</span><span class="dv">10</span>)</span>
<span id="cb13-23"><a href="#cb13-23"></a> </span>
<span id="cb13-24"><a href="#cb13-24"></a> </span>
<span id="cb13-25"><a href="#cb13-25"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb13-26"><a href="#cb13-26"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb13-27"><a href="#cb13-27"></a> }</span>
<span id="cb13-28"><a href="#cb13-28"></a></span>
<span id="cb13-29"><a href="#cb13-29"></a>mj10_CPU <-<span class="st"> </span><span class="kw">proc.time</span>()<span class="op">-</span>start</span>
<span id="cb13-30"><a href="#cb13-30"></a></span>
<span id="cb13-31"><a href="#cb13-31"></a></span>
<span id="cb13-32"><a href="#cb13-32"></a><span class="co">######################################################################################################</span></span>
<span id="cb13-33"><a href="#cb13-33"></a>start <-<span class="st"> </span><span class="kw">proc.time</span>()</span>
<span id="cb13-34"><a href="#cb13-34"></a>mj20 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(<span class="dv">100</span>),</span>
<span id="cb13-35"><a href="#cb13-35"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb13-36"><a href="#cb13-36"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb13-37"><a href="#cb13-37"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb13-38"><a href="#cb13-38"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">n_var=</span><span class="dv">20</span>)</span>
<span id="cb13-39"><a href="#cb13-39"></a> </span>
<span id="cb13-40"><a href="#cb13-40"></a> </span>
<span id="cb13-41"><a href="#cb13-41"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb13-42"><a href="#cb13-42"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb13-43"><a href="#cb13-43"></a> }</span>
<span id="cb13-44"><a href="#cb13-44"></a></span>
<span id="cb13-45"><a href="#cb13-45"></a>mj20_CPU <-<span class="st"> </span><span class="kw">proc.time</span>()<span class="op">-</span>start</span>
<span id="cb13-46"><a href="#cb13-46"></a></span>
<span id="cb13-47"><a href="#cb13-47"></a><span class="co">######################################################################################################</span></span>
<span id="cb13-48"><a href="#cb13-48"></a></span>
<span id="cb13-49"><a href="#cb13-49"></a>start <-<span class="st"> </span><span class="kw">proc.time</span>()</span>
<span id="cb13-50"><a href="#cb13-50"></a>mj15 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(<span class="dv">100</span>),</span>
<span id="cb13-51"><a href="#cb13-51"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb13-52"><a href="#cb13-52"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb13-53"><a href="#cb13-53"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb13-54"><a href="#cb13-54"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">n_var=</span><span class="dv">15</span>)</span>
<span id="cb13-55"><a href="#cb13-55"></a> </span>
<span id="cb13-56"><a href="#cb13-56"></a> </span>
<span id="cb13-57"><a href="#cb13-57"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb13-58"><a href="#cb13-58"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb13-59"><a href="#cb13-59"></a> }</span>
<span id="cb13-60"><a href="#cb13-60"></a></span>
<span id="cb13-61"><a href="#cb13-61"></a>mj15_CPU <-<span class="st"> </span><span class="kw">proc.time</span>()<span class="op">-</span>start</span>
<span id="cb13-62"><a href="#cb13-62"></a></span>
<span id="cb13-63"><a href="#cb13-63"></a><span class="co">######################################################################################################</span></span>
<span id="cb13-64"><a href="#cb13-64"></a></span>
<span id="cb13-65"><a href="#cb13-65"></a>start <-<span class="st"> </span><span class="kw">proc.time</span>()</span>
<span id="cb13-66"><a href="#cb13-66"></a>mj30 <-<span class="st"> </span><span class="kw">foreach</span>(<span class="kw">icount</span>(<span class="dv">100</span>),</span>
<span id="cb13-67"><a href="#cb13-67"></a> <span class="dt">.packages =</span> <span class="kw">c</span>(<span class="st">"mgcv"</span>, <span class="st">"data.table"</span>, <span class="st">"MCMCprecision"</span>, <span class="st">"lubridate"</span>, <span class="st">"progress"</span>),</span>
<span id="cb13-68"><a href="#cb13-68"></a> <span class="dt">.combine =</span> rbind) <span class="op">%dopar%</span>{</span>
<span id="cb13-69"><a href="#cb13-69"></a> <span class="co"># set the specific values of the parameters </span></span>
<span id="cb13-70"><a href="#cb13-70"></a> a =<span class="st"> </span><span class="kw">bayesian_selection</span>(<span class="dt">n_var=</span><span class="dv">30</span>)</span>
<span id="cb13-71"><a href="#cb13-71"></a> </span>
<span id="cb13-72"><a href="#cb13-72"></a> </span>
<span id="cb13-73"><a href="#cb13-73"></a> <span class="kw">c</span>(a<span class="op">$</span><span class="st">`</span><span class="dt">is true</span><span class="st">`</span>, a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_true</span><span class="st">`</span>,a<span class="op">$</span><span class="st">`</span><span class="dt">posterior probability_selected</span><span class="st">`</span>,</span>
<span id="cb13-74"><a href="#cb13-74"></a> a<span class="op">$</span><span class="st">`</span><span class="dt">selected model</span><span class="st">`</span>)</span>
<span id="cb13-75"><a href="#cb13-75"></a> }</span>
<span id="cb13-76"><a href="#cb13-76"></a></span>
<span id="cb13-77"><a href="#cb13-77"></a>mj30_CPU <-<span class="st"> </span><span class="kw">proc.time</span>()<span class="op">-</span>start</span></code></pre></div>
<div class="sourceCode" id="cb14"><pre class="sourceCode r"><code class="sourceCode r"><span id="cb14-1"><a href="#cb14-1"></a><span class="co">#proportion of correct selection & posterior probability of the true model</span></span>
<span id="cb14-2"><a href="#cb14-2"></a>J <-<span class="st"> </span><span class="kw">cbind</span>(<span class="kw">c</span>(<span class="kw">length</span>(mj6[,<span class="dv">1</span>][mj6[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]), <span class="kw">length</span>(mj10[,<span class="dv">1</span>][mj10[,<span class="dv">1</span>]<span class="op">==</span><span class="dv">1</span>]),</span>