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mBICV.html
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mBICV.html
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<h1>Modified vine copula Bayesian information criterion (mBICv)</h1>
<small class="dont-index">Source: <a href='https://github.com/vinecopulib/rvinecopulib/blob/master/R/vinecop_methods.R'><code>R/vinecop_methods.R</code></a></small>
<div class="hidden name"><code>mBICV.Rd</code></div>
</div>
<div class="ref-description">
<p>Calculates the modified vine copula Bayesian information criterion.</p>
</div>
<pre class="usage"><span class='fu'>mBICV</span><span class='op'>(</span><span class='va'>object</span>, psi0 <span class='op'>=</span> <span class='fl'>0.9</span>, newdata <span class='op'>=</span> <span class='cn'>NULL</span><span class='op'>)</span></pre>
<h2 class="hasAnchor" id="arguments"><a class="anchor" href="#arguments"></a>Arguments</h2>
<table class="ref-arguments">
<colgroup><col class="name" /><col class="desc" /></colgroup>
<tr>
<th>object</th>
<td><p>a fitted <code>vinecop</code> object.</p></td>
</tr>
<tr>
<th>psi0</th>
<td><p>baseline prior probability of a non-independence copula.</p></td>
</tr>
<tr>
<th>newdata</th>
<td><p>optional; a new data set.</p></td>
</tr>
</table>
<h2 class="hasAnchor" id="details"><a class="anchor" href="#details"></a>Details</h2>
<p>The modified vine copula Bayesian information criterion (mBICv) is defined as</p>
<p>$$BIC = -2 loglik + \nu log(n) - 2 \sum_{t=1}^{d - 1} (q_t log(\psi_0^t)
- (d - t - q_t) log(1 - \psi_0^t)) $$</p>
<p>where \(\mathrm{loglik}\) is the log-likelihood and \(\nu\) is the
(effective) number of parameters of the model, \(t\) is the tree level
\(\psi_0\) is the prior probability of having a non-independence copula and
\(q_t\) is the number of non-independence copulas in tree \(t\). The
mBICv is a consistent model selection criterion for parametric sparse vine
copula models.</p>
<h2 class="hasAnchor" id="references"><a class="anchor" href="#references"></a>References</h2>
<p>Nagler, T., Bumann, C., Czado, C. (2019). Model selection for
sparse high-dimensional vine copulas with application to portfolio risk.
<em>Journal of Multivariate Analysis, in press</em>
(<a href='https://arxiv.org/pdf/1801.09739.pdf'>https://arxiv.org/pdf/1801.09739.pdf</a>)</p>
<h2 class="hasAnchor" id="examples"><a class="anchor" href="#examples"></a>Examples</h2>
<pre class="examples"><div class='input'><span class='va'>u</span> <span class='op'><-</span> <span class='fu'><a href='https://rdrr.io/r/base/lapply.html'>sapply</a></span><span class='op'>(</span><span class='fl'>1</span><span class='op'>:</span><span class='fl'>5</span>, <span class='kw'>function</span><span class='op'>(</span><span class='va'>i</span><span class='op'>)</span> <span class='fu'><a href='https://rdrr.io/r/stats/Uniform.html'>runif</a></span><span class='op'>(</span><span class='fl'>50</span><span class='op'>)</span><span class='op'>)</span>
<span class='va'>fit</span> <span class='op'><-</span> <span class='fu'><a href='vinecop.html'>vinecop</a></span><span class='op'>(</span><span class='va'>u</span>, family <span class='op'>=</span> <span class='st'>"par"</span>, keep_data <span class='op'>=</span> <span class='cn'>TRUE</span><span class='op'>)</span>
<span class='fu'>mBICV</span><span class='op'>(</span><span class='va'>fit</span>, <span class='fl'>0.9</span><span class='op'>)</span> <span class='co'># with a 0.9 prior probability of a non-independence copula</span>
</div><div class='output co'>#> [1] 26.75294</div><div class='input'><span class='fu'>mBICV</span><span class='op'>(</span><span class='va'>fit</span>, <span class='fl'>0.1</span><span class='op'>)</span> <span class='co'># with a 0.1 prior probability of a non-independence copula</span>
</div><div class='output co'>#> [1] 76.18497</div></pre>
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