LOG PDF.rar_Log pdf_Log核密度_Log核密度估计_imageujb_log-pdf

function y = logSt(X, mu, sigma, v) % Compute log pdf of a Student's t distribution. % Input: % X: d x n data matrix % mu: mean % sigma: variance % v: degree of freedom % Output: % y: probability density in logrithm scale y=log p(x) % Written by mo Chen (sth4nth@gmail.com). [d,k] = size(mu); if size(sigma,1)==d && size(sigma,2)==d && k==1 [R,p]= chol(sigma); if p ~= 0 error('ERROR: sigma is not SPD.'); end X = bsxfun(@minus,X,mu); Q = R'\X; q = dot(Q,Q,1); % quadratic term (M distance) o = -log(1+q/v)*((v+d)/2); c = gammaln((v+d)/2)-gammaln(v/2)-(d*log(v*pi)+2*sum(log(diag(R))))/2; y = c+o; elseif size(sigma,1)==d && size(sigma,2)==k lambda = 1./sigma; ml = mu.*lambda; q = bsxfun(@plus,X'.^2*lambda-2*X'*ml,dot(mu,ml,1)); % M distance o = bsxfun(@times,log(1+bsxfun(@times,q,1./v)),-(v+d)/2); c = gammaln((v+d)/2)-gammaln(v/2)-(d*log(pi*v)+sum(log(sigma),1))/2; y = bsxfun(@plus,o,c); elseif size(sigma,1)==1 && size(sigma,2)==k X2 = repmat(dot(X,X,1)',1,k); D = bsxfun(@plus,X2-2*X'*mu,dot(mu,mu,1)); q = bsxfun(@times,D,1./sigma); % M distance o = bsxfun(@times,log(1+bsxfun(@times,q,1./v)),-(v+d)/2); c = gammaln((v+d)/2)-gammaln(v/2)-d*log(pi*v.*sigma)/2; y = bsxfun(@plus,o,c); else error('Parameters are mismatched.'); end