Gibbs Sampler‚ÆŽû‘©”»’è‚Ì—á
#include <oxstd.h> #include <oxprob.h> #include <oxfloat.h> #include <oxdraw.h> //Calculate variance of time series fTsvar(const x, const Bm){ decl n,sp; // Calculate Spectral density function using // Bandwidth=Bm at 2 points (0, pi) and Parzen Window n=rows(x);sp=periodogram(x,Bm,2,1)/n; return M_2PI*sp[0]; } fTsvar_batch(const x, const n){ // N=n*m decl i,m,N,y,xbar; N=rows(x);m=N/n;xbar=meanc(x);y=zeros(m,1); for(i=0;i<m;++i){y[i]=meanc(x[i*n:(i+1)*n-1]);} return n/(m-1)*sumsqrc(y-xbar); } // Calculate p-value for Convergence (Geweke's Method) // H0: Convergence, H1: No Convergence fGeweke(const x, const Bm){ decl n,n1,n2,sp1,sp2,var1,var2,x1,x2,x1bar,x2bar,z; n=rows(x);n1=floor(0.1*n);n2=floor(0.5*n); x1=x[:n1-1];x2=x[n-n2:]; x1bar=meanc(x1);x2bar=meanc(x2); var1=fTsvar(x1,Bm);var2=fTsvar(x2,Bm); z=(x1bar-x2bar)/sqrt(var1/n1+var2/n2); return 2*tailn(fabs(z)); } // main(){ decl a,b,Bm,burn,file,i,mu,mu_s,n,n_acf,n_x,sp,var,var_s,x,xbar; // true values mu=1;var=2; // generate x(1),...,x(n_x) n_x=100;x=mu+sqrt(var)*rann(n_x,1);xbar=meanc(x); //Burn-in & Samples burn=1000;n=10000; mu_s=var_s=zeros(n,1); for(i=-burn;i<n;++i){ mu=xbar+sqrt(var/n)*rann(1,1); // Generate var using Gamma(a,b) // mean=a/b, variaince=a/b^2 a=0.5*n_x;b=0.5*sumsqrc(x-mu);var=1.0/rangamma(1,1,a,b); if(i>=0){mu_s[i]=mu;var_s[i]=var;} } // println("XBAR=",xbar); Bm=100; println( "%r",{"Mu"}, "%c",{"Mean","Stdev","95%L","95%U","Geweke"}, meanc(mu_s)~varc(mu_s)^0.5~quantilec(mu_s,<0.025,0.975>)'~fGeweke(mu_s,Bm),"\n"); // println("Std Err of Estimated Posterior Mean of Mu:"); println(" (1)Parzen Window: ",sqrt(fTsvar(mu_s,Bm)/n)); println(" (2)Batch Mean Method:",sqrt(fTsvar_batch(mu_s,Bm)/n)); // println( "%r",{"Sigma^2"}, "%c",{"Mean","Stdev","95%L","95%U","Geweke"}, meanc(var_s)~varc(var_s)^0.5~quantilec(var_s,<0.025,0.975>)'~fGeweke(var_s,Bm),"\n"); // n_acf=50; //ACF DrawCorrelogram(0,mu_s',{"Mu"},n_acf); DrawTitle(0,"Sample ACF"); DrawCorrelogram(1,var_s',{"Sigma^2"},n_acf); DrawTitle(1,"Sample ACF"); //Path DrawTMatrix(2,mu_s',{"Mu"},1,1,1); DrawTitle(2,"Sample Path"); DrawTMatrix(3,var_s',{"Sigma^2"},1,1,1); DrawTitle(3,"Sample Path"); DrawDensity(4,mu_s',{"Mu"},1,0,0); //Posterior density DrawTitle(4,"Posterior Density"); DrawDensity(5,var_s',{"Sigma^2"},1,1,0); DrawTitle(5,"Posterior Density"); SaveDrawWindow("gibbs.ps"); CloseDrawWindow(); // QQ-plot decl t; t=(mu_s-xbar)/sqrt(varc(x)/n); DrawQQ(0,t',{"Mu"},QQ_T,n_x-1,0); DrawTitle(0,"QQ-plot vs T"); DrawQQ(1,t',{"Mu"},QQ_N,0,0); DrawTitle(1,"QQ-plot vs Normal"); SaveDrawWindow("qq.ps"); CloseDrawWindow(); // file = fopen("mu.txt","w");fprint(file,"mu","%15.10f",mu_s);fclose(file); file = fopen("var.txt","w");fprint(file,"var","%15.10f",var_s);fclose(file); }