Daniel@0: function p = student_t_pdf(X, mu, lambda, alpha)
Daniel@0: % STUDENT_T_PDF Evaluate the multivariate student-t distribution at a point
Daniel@0: % p = student_t_pdf(X, mu, lambda, alpha)
Daniel@0: %
Daniel@0: % Each column of X is evaluated.
Daniel@0: % See Bernardo and Smith p435.
Daniel@0: 
Daniel@0: k = length(mu);
Daniel@0: assert(size(X,1) == k);
Daniel@0: [k N] = size(X);
Daniel@0: numer = gamma(0.5*(alpha+k));
Daniel@0: denom = gamma(0.5*alpha) * (alpha*pi)^(k/2);
Daniel@0: c = (numer/denom) * det(lambda)^(0.5);
Daniel@0: p = c*(1 + (1/alpha)*(X-mu)'*lambda*(X-mu))^(-(alpha+k)/2); % scalar version
Daniel@0: %m = repmat(mu(:), 1, N);
Daniel@0: %exponent = sum((X-m)'*lambda*(X-m), 2); % column vector
Daniel@0: %p = c*(1 + (1/alpha)*exponent).^(-(alpha+k)/2);
Daniel@0: 
Daniel@0: keyboard