matrictint

function w=matrictint(S,XXi,T)
  S:  usually sample cross product matrix of LS residuals
 XXi:  inv(X'X) matrix for rhs variables
  T:  number of observations
  w:  log of integrated posterior for SUR or RF VAR with det(Sigma)^(-(m+1)/2) Jeffreys-like prior
  To get the log of the integral of the likelihood for a VAR with T observations, 
   k rhs variables in each equation, and m equations, set T=T-m-1 and subtract .5*m*(m+1)*log(2*pi).
 We are integrating the exponential of -.5*T*m*log(2*pi)-.5*(T+m+1)*log(det(Sigma))-.5*trace(Sigma\S(beta)).

0001 function w=matrictint(S,XXi,T)
0002 %function w=matrictint(S,XXi,T)
0003 %  S:  usually sample cross product matrix of LS residuals
0004 % XXi:  inv(X'X) matrix for rhs variables
0005 %  T:  number of observations
0006 %  w:  log of integrated posterior for SUR or RF VAR with det(Sigma)^(-(m+1)/2) Jeffreys-like prior
0007 %  To get the log of the integral of the likelihood for a VAR with T observations,
0008 %   k rhs variables in each equation, and m equations, set T=T-m-1 and subtract .5*m*(m+1)*log(2*pi).
0009 % We are integrating the exponential of -.5*T*m*log(2*pi)-.5*(T+m+1)*log(det(Sigma))-.5*trace(Sigma\S(beta)).
0010 k=size(XXi,1);
0011 m=size(S,1);
0012 [cx,p]=chol(XXi);
0013 [cs,q]=chol(S);
0014 %cx=cschol(XXi);
0015 %cs=cschol(S);
0016 if any(diag(cx)<100*eps)
0017     error('singular XXi')
0018 end
0019 if any(diag(cs<100*eps))
0020     error('singular S')
0021 end
0022 w=(-T+k+(m-1)/2)*m*.5*log(pi)-(T-k)*sum(log(diag(cs)))+m*sum(log(diag(cx)))+ggammaln(m,(T-k)/2);
0023 
0024 function lgg=ggammaln(m,ndf)
0025 %function gg=ggamma(m,ndf)
0026 % From 8.2.22 on p.427 of Box and Tiao, this is the log of generalized
0027 % gamma divided by gamma(.5)^(.5*m*(m-1))
0028 if ndf<=(m-1)/2
0029     error('too few df in ggammaln')
0030 else
0031     %lgg=.5*m*(m-1)*gammaln(.5); % normalizing factor not used in Wishart integral
0032     garg=ndf+.5*(0:-1:1-m);
0033     lgg=sum(gammaln(garg));
0034 end
0035