Question

I am not sure if this is a programming or statistics question, but I am %99 sure that there should be a numerical problem. So maybe a programmatic solution can be proposed.

I am using MATLAB’s mvnpdf function to calculate multi-variate Gaussian PDF of some observations. Frequently I get “SIGMA must be symmetric and positive definite” errors.

However, I am obtaining the covarince matrix from the data, so the data should be legal. A code to regenerate the problem is:

err_cnt = 0;
for i = 1:1000
    try 
        a = rand(3); 
        c = cov(a); 
        m = mean(a); 
        mvnpdf(a, m, c);
    catch me
        err_cnt = err_cnt + 1;
    end
end

I get ~500-600 errors each time I run.

P.S. I do not generate random data in my case, just generated here to demonstrate.

Answer 1

This happens if the diagonal values of the covariance matrix are (very close to) zero. A simple fix is add a very small constant number to c.

err_cnt = 0;
for i = 1:1000
    try 
        a = rand(3); 
        c = cov(a) + .0001 * eye(3); 
        m = mean(a); 
        mvnpdf(a, m, c);
    catch me
        err_cnt = err_cnt + 1;
    end
end

Results in 0 errors.