90 lines
5.4 KiB
HTML
90 lines
5.4 KiB
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<title>Description of matrictint</title>
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > matrictint.m</div>
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<!--<table width="100%"><tr><td align="left"><a href="../index.html"><img alt="<" border="0" src="../left.png"> Master index</a></td>
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<td align="right"><a href="index.html">Index for . <img alt=">" border="0" src="../right.png"></a></td></tr></table>-->
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<h1>matrictint
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</h1>
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<h2><a name="_name"></a>PURPOSE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function w=matrictint(S,XXi,T)</strong></div>
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<h2><a name="_synopsis"></a>SYNOPSIS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="box"><strong>function w=matrictint(S,XXi,T) </strong></div>
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<h2><a name="_description"></a>DESCRIPTION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre class="comment">function w=matrictint(S,XXi,T)
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S: usually sample cross product matrix of LS residuals
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XXi: inv(X'X) matrix for rhs variables
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T: number of observations
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w: log of integrated posterior for SUR or RF VAR with det(Sigma)^(-(m+1)/2) Jeffreys-like prior
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To get the log of the integral of the likelihood for a VAR with T observations,
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k rhs variables in each equation, and m equations, set T=T-m-1 and subtract .5*m*(m+1)*log(2*pi).
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We are integrating the exponential of -.5*T*m*log(2*pi)-.5*(T+m+1)*log(det(Sigma))-.5*trace(Sigma\S(beta)).</pre></div>
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<!-- crossreference -->
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<h2><a name="_cross"></a>CROSS-REFERENCE INFORMATION <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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This function calls:
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<ul style="list-style-image:url(../matlabicon.gif)">
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</ul>
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This function is called by:
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="mgnldnsty.html" class="code" title="function w=mgnldnsty(ydata,lags,xdata,breaks,lambda,mu,mnprior,vprior,train,flat)">mgnldnsty</a> function w=mgnldnsty(ydata,lags,xdata,breaks,lambda,mu,mnprior,vprior,train,flat)</li></ul>
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<!-- crossreference -->
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<h2><a name="_subfunctions"></a>SUBFUNCTIONS <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<ul style="list-style-image:url(../matlabicon.gif)">
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<li><a href="#_sub1" class="code">function lgg=ggammaln(m,ndf)</a></li></ul>
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<h2><a name="_source"></a>SOURCE CODE <a href="#_top"><img alt="^" border="0" src="../up.png"></a></h2>
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<div class="fragment"><pre>0001 <a name="_sub0" href="#_subfunctions" class="code">function w=matrictint(S,XXi,T)</a>
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0002 <span class="comment">%function w=matrictint(S,XXi,T)</span>
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0003 <span class="comment">% S: usually sample cross product matrix of LS residuals</span>
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0004 <span class="comment">% XXi: inv(X'X) matrix for rhs variables</span>
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0005 <span class="comment">% T: number of observations</span>
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0006 <span class="comment">% w: log of integrated posterior for SUR or RF VAR with det(Sigma)^(-(m+1)/2) Jeffreys-like prior</span>
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0007 <span class="comment">% To get the log of the integral of the likelihood for a VAR with T observations,</span>
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0008 <span class="comment">% k rhs variables in each equation, and m equations, set T=T-m-1 and subtract .5*m*(m+1)*log(2*pi).</span>
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0009 <span class="comment">% We are integrating the exponential of -.5*T*m*log(2*pi)-.5*(T+m+1)*log(det(Sigma))-.5*trace(Sigma\S(beta)).</span>
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0010 k=size(XXi,1);
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0011 m=size(S,1);
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0012 [cx,p]=chol(XXi);
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0013 [cs,q]=chol(S);
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0014 <span class="comment">%cx=cschol(XXi);</span>
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0015 <span class="comment">%cs=cschol(S);</span>
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0016 <span class="keyword">if</span> any(diag(cx)<100*eps)
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0017 error(<span class="string">'singular XXi'</span>)
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0018 <span class="keyword">end</span>
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0019 <span class="keyword">if</span> any(diag(cs<100*eps))
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0020 error(<span class="string">'singular S'</span>)
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0021 <span class="keyword">end</span>
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0022 w=(-T+k+(m-1)/2)*m*.5*log(pi)-(T-k)*sum(log(diag(cs)))+m*sum(log(diag(cx)))+<a href="#_sub1" class="code" title="subfunction lgg=ggammaln(m,ndf)">ggammaln</a>(m,(T-k)/2);
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0023
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0024 <a name="_sub1" href="#_subfunctions" class="code">function lgg=ggammaln(m,ndf)</a>
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0025 <span class="comment">%function gg=ggamma(m,ndf)</span>
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0026 <span class="comment">% From 8.2.22 on p.427 of Box and Tiao, this is the log of generalized</span>
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0027 <span class="comment">% gamma divided by gamma(.5)^(.5*m*(m-1))</span>
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0028 <span class="keyword">if</span> ndf<=(m-1)/2
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0029 error(<span class="string">'too few df in ggammaln'</span>)
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0030 <span class="keyword">else</span>
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0031 <span class="comment">%lgg=.5*m*(m-1)*gammaln(.5); % normalizing factor not used in Wishart integral</span>
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0032 garg=ndf+.5*(0:-1:1-m);
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0033 lgg=sum(gammaln(garg));
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0034 <span class="keyword">end</span>
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0035</pre></div>
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<hr><address>Generated on Fri 16-Jun-2006 09:09:06 by <strong><a href="http://www.artefact.tk/software/matlab/m2html/">m2html</a></strong> © 2003</address>
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