riecovest.distance.wishart_log_likelihood

riecovest.distance.wishart_log_likelihood(mat_variable, cov, N, regularization=1000000.0)

Wishart log likelihood function.

It is not a true likelihood, since the mass is not 1. It is however proportional to true likelihood with regards to the covariance matrix. Anything constant with regards to the covariance is not taken into account. Therefore, the maximum likelihood estimator can be found by maximizing this function.

Parameters:

• mat_variable (ndarray of shape (M, M)) – positive definite matrix

• cov (ndarray of shape (M, M)) – positive definite matrix

• N (int) – the degree of freedom parameter for the wishart distribution

• regularization (float, optional) – regularization parameter for the covariance matrix. The default is 1e6. The matrix is regularized by adding a scaled identity matrix to the covariance matrix, such that the condition number becomes at most regularization.

Returns:

l – The log likelihood of the data given the covariance matrix

Return type:

float