function bvar_density(maxnlags)

    for nlags = 1:maxnlags
        [ny, nx, posterior, prior] = bvar_toolbox(nlags);
        
        posterior_int = matrictint(posterior.S, posterior.df, posterior.XXi);
        prior_int = matrictint(prior.S, prior.df, prior.XXi);
        
        lik_nobs = posterior.df - prior.df;
        
        log_dnsty = posterior_int - prior_int - 0.5*ny*lik_nobs*log(2*pi);
        
        disp(' ')
        fprintf('The marginal log density of the BVAR(%g) model is equal to %10.4f\n', ...
                nlags, log_dnsty);
        disp(' ')
    end


function w = matrictint(S, df, XXi)
% Computes the log of the integral of the kernel of the PDF of a
% normal-inverse-Wishart distribution.
%
% S:   parameter of inverse-Wishart distribution
% df:  number of degrees of freedom of inverse-Wishart distribution
% XXi: first component of VCV matrix of matrix-normal distribution
% 
% Computes the integral over (Phi, Sigma) of:
%
% det(Sigma)^(-k/2)*exp(-0.5*Tr((Phi-PhiHat)'*(XXi)^(-1)*(Phi-PhiHat)*Sigma^(-1)))*
% det(Sigma)^((df+ny+1)/2)*exp(-0.5*Tr(Sigma^(-1)*S))
%
% (where k is the dimension of XXi and ny is the dimension of S and
% Sigma)
    
    k=size(XXi,1);
    ny=size(S,1);
    [cx,p]=chol(XXi);
    [cs,q]=chol(S);

    if any(diag(cx)<100*eps)
        error('singular XXi')
    end
    if any(diag(cs<100*eps))
        error('singular S')
    end

    % Matrix-normal component
    w1 = 0.5*k*ny*log(2*pi)+ny*sum(log(diag(cx)));
    
    % Inverse-Wishart component
    w2 = -df*sum(log(diag(cs))) + 0.5*df*ny*log(2) + ny*(ny-1)*0.25*log(pi) + ggammaln(ny, df);
    
    w = w1 + w2;

function lgg = ggammaln(m, df)
    if df <= (m-1)
        error('too few df in ggammaln')
    else
        garg = 0.5*(df+(0:-1:1-m));
        lgg = sum(gammaln(garg));
    end