I have a number of multivariate observations and would like to evaluate the probability density across all variables. It is assumed that the data is normally distributed. At low numbers of variables everything works as I would expect, but moving to greater numbers results in the covariance matrix becoming non positive definite.
I have reduced the problem in Matlab to:
load raw_data.mat; % matrix number-of-values x number of variables Sigma = cov(data); [R,err] = cholcov(Sigma, 0); % Test for pos-def done in mvnpdf.
If err>0 then Sigma is not positive definite.
Is there anything that I can do in order to evaluate my experimental data at higher dimensions? Does it tell me anything useful about my data?
I'm somewhat of a beginner in this area so apologies if I've missed out something obvious.