136 lines
8.9 KiB
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136 lines
8.9 KiB
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<title>Description of draw_prior_density</title>
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<div><a href="../index.html">Home</a> > <a href="index.html">.</a> > draw_prior_density.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>draw_prior_density
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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>stephane.adjemian@ens.fr [07-15-2004]</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 [x,f,abscissa,dens,binf,bsup] = draw_prior_density(indx); </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"> stephane.adjemian@ens.fr [07-15-2004]</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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<li><a href="lpdfgam.html" class="code" title="function ldens = lpdfgam(x,a,b);">lpdfgam</a> log GAMMA PDF</li><li><a href="mj_qgamma.html" class="code" title="function x = mj_qgamma(p,a)">mj_qgamma</a> MJ_QGAMMA The gamma inverse distribution function</li><li><a href="qbeta.html" class="code" title="function x = qbeta(p,a,b)">qbeta</a> QBETA The beta inverse distribution function</li><li><a href="qgamma.html" class="code" title="function x = qgamma(p,a)">qgamma</a> QGAMMA The gamma inverse distribution function</li><li><a href="qnorm.html" class="code" title="function x = qnorm(p,m,s)">qnorm</a> QNORM The normal inverse distribution function</li></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="PlotPosteriorDistributions.html" class="code" title="function PlotPosteriorDistributions()">PlotPosteriorDistributions</a> stephane.adjemian@ens.fr [09-09-2005]</li><li><a href="plot_priors.html" class="code" title="function plot_priors">plot_priors</a> stephane.adjemian@cepremap.cnrs.fr [07-31-2004]</li><li><a href="posterior_distribution.html" class="code" title="function [borneinf,bornesup,x1,x2,f1,f2,top,nam,texnam] =posterior_distribution(indx,number_of_mh_files,first_mh_file,first_line,number_of_blocks,number_of_simulations,number_of_simulations_per_file,TeX);">posterior_distribution</a> stephane.adjemian@cepremap.cnrs.fr [07-15-2004]</li></ul>
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<!-- crossreference -->
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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 [x,f,abscissa,dens,binf,bsup] = draw_prior_density(indx);</a>
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0002 <span class="comment">% stephane.adjemian@ens.fr [07-15-2004]</span>
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0003
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0004 <span class="keyword">global</span> bayestopt_
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0005
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0006 pmean = bayestopt_.pmean;
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0007 pshape = bayestopt_.pshape;
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0008 p1 = bayestopt_.p1;
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0009 p2 = bayestopt_.p2;
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0010 p3 = bayestopt_.p3;
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0011 p4 = bayestopt_.p4;
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0012
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0013 truncprior = 10^(-3);
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0014
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0015 <span class="keyword">if</span> pshape(indx) == 1 <span class="comment">%/* BETA Prior */</span>
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0016 density = inline(<span class="string">'((bb-x).^(b-1)).*(x-aa).^(a-1)./(beta(a,b)*(bb-aa)^(a+b-1))'</span>,<span class="string">'x'</span>,<span class="string">'a'</span>,<span class="string">'b'</span>,<span class="string">'aa'</span>,<span class="string">'bb'</span>);
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0017 mu = (p1(indx)-p3(indx))/(p4(indx)-p3(indx));
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0018 stdd = p2(indx)/(p4(indx)-p3(indx));
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0019 a = (1-mu)*mu^2/stdd^2 - mu;
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0020 b = a*(1/mu-1);
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0021 aa = p3(indx);
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0022 bb = p4(indx);
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0023 infbound = <a href="qbeta.html" class="code" title="function x = qbeta(p,a,b)">qbeta</a>(truncprior,a,b)*(bb-aa)+aa;
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0024 supbound = <a href="qbeta.html" class="code" title="function x = qbeta(p,a,b)">qbeta</a>(1-truncprior,a,b)*(bb-aa)+aa;
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0025 stepsize = (supbound-infbound)/200;
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0026 abscissa = infbound:stepsize:supbound;
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0027 dens = density(abscissa,a,b,aa,bb);
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0028 <span class="keyword">elseif</span> pshape(indx) == 2 <span class="comment">%/* GAMMA PRIOR */</span>
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0029 mu = p1(indx)-p3(indx);
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0030 b = p2(indx)^2/mu;
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0031 a = mu/b;
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0032 infbound = <a href="mj_qgamma.html" class="code" title="function x = mj_qgamma(p,a)">mj_qgamma</a>(truncprior,a)*b;
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0033 supbound = <a href="mj_qgamma.html" class="code" title="function x = mj_qgamma(p,a)">mj_qgamma</a>(1-truncprior,a)*b;
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0034 stepsize = (supbound-infbound)/200;
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0035 abscissa = infbound:stepsize:supbound;
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0036 dens = exp(<a href="lpdfgam.html" class="code" title="function ldens = lpdfgam(x,a,b);">lpdfgam</a>(abscissa,a,b));
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0037 abscissa = abscissa + p3(indx);
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0038 <span class="keyword">elseif</span> pshape(indx) == 3 <span class="comment">%/* GAUSSIAN PRIOR */</span>
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0039 density = inline(<span class="string">'inv(sqrt(2*pi)*b)*exp(-0.5*((x-a)/b).^2)'</span>,<span class="string">'x'</span>,<span class="string">'a'</span>,<span class="string">'b'</span>);
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0040 a = p1(indx);
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0041 b = p2(indx);
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0042 infbound = <a href="qnorm.html" class="code" title="function x = qnorm(p,m,s)">qnorm</a>(truncprior,a,b);
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0043 supbound = <a href="qnorm.html" class="code" title="function x = qnorm(p,m,s)">qnorm</a>(1-truncprior,a,b);
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0044 stepsize = (supbound-infbound)/200;
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0045 abscissa = infbound:stepsize:supbound;
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0046 dens = density(abscissa,a,b);
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0047 <span class="keyword">elseif</span> pshape(indx) == 4 <span class="comment">%/* INVGAMMA PRIOR type 1 */</span>
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0048 density = inline(<span class="string">'2*inv(gamma(nu/2))*(x.^(-nu-1))*((s/2)^(nu/2)).*exp(-s./(2*x.^2))'</span>,<span class="string">'x'</span>,<span class="string">'s'</span>,<span class="string">'nu'</span>);
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0049 nu = p2(indx);
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0050 s = p1(indx);
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0051 a = nu/2;
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0052 b = 2/s;
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0053 infbound = 1/sqrt(<a href="mj_qgamma.html" class="code" title="function x = mj_qgamma(p,a)">mj_qgamma</a>(1-10*truncprior,a)*b);
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0054 supbound = 1/sqrt(<a href="mj_qgamma.html" class="code" title="function x = mj_qgamma(p,a)">mj_qgamma</a>(10*truncprior,a)*b);
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0055 stepsize = (supbound-infbound)/200;
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0056 abscissa = infbound:stepsize:supbound;
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0057 dens = density(abscissa,s,nu);
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0058 <span class="keyword">elseif</span> pshape(indx) == 5 <span class="comment">%/* UNIFORM PRIOR */</span>
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0059 density = inline(<span class="string">'(x.^0)/(b-a)'</span>,<span class="string">'x'</span>,<span class="string">'a'</span>,<span class="string">'b'</span>);
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0060 a = p1(indx);
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0061 b = p2(indx);
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0062 infbound = a;
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0063 supbound = b;
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0064 stepsize = (supbound-infbound)/200;
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0065 abscissa = infbound:stepsize:supbound;
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0066 dens = density(abscissa,a,b);
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0067 <span class="keyword">elseif</span> pshape(indx) == 6 <span class="comment">%/* INVGAMMA PRIOR type 2 */</span>
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0068 density = inline(<span class="string">'inv(gamma(nu/2))*(x.^(-.5(nu+2)))*((s/2)^(nu/2)).*exp(-s./(2*x))'</span>,<span class="string">'x'</span>,<span class="string">'s'</span>,<span class="string">'nu'</span>);
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0069 nu = p2(indx);
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0070 s = p1(indx);
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0071 a = nu/2;
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0072 b = 2/s;
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0073 infbound = 1/(<a href="qgamma.html" class="code" title="function x = qgamma(p,a)">qgamma</a>(1-truncprior,a)*b);
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0074 supbound = 1/(<a href="qgamma.html" class="code" title="function x = qgamma(p,a)">qgamma</a>(truncprior,a)*b);
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0075 stepsize = (supbound-infbound)/200;
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0076 abscissa = infbound:stepsize:supbound;
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0077 dens = density(abscissa,s,nu);
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0078 <span class="keyword">end</span>
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0079
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0080 k = [1:length(dens)];
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0081 <span class="keyword">if</span> pshape(indx) ~= 5
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0082 [junk,k1] = max(dens);
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0083 <span class="keyword">if</span> k1 == 1 | k1 == length(dens)
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0084 k = find(dens < 10);
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0085 <span class="keyword">end</span>
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0086 <span class="keyword">end</span>
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0087 binf = abscissa(k(1));
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0088 bsup = abscissa(k(length(k)));
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0089 x = abscissa(k);
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0090 f = dens(k);</pre></div>
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