An RV participates twice in defining the likelihood function

Hi all,

I am working on a problem that would require me to use the MatrixNormal distribution as a likelihood function. However, in order to avoid using large, sparse covariance matrices (which make inference practically infeasible), I have decided to break down my likelihood function into two components. The first component is focusing on identifying what would have been the row covariance, while the second one focuses on the column covariance. In addition, the mean of each RV is also updated.

My problem lies in the fact that one RV holds the most information for deciding the row covariance but must also contribute in determining the column covariance. Thus, its mean and standard deviation participate in both components of the likelihood function.

Am I allowed to formulate my problem like that? Can one RV participate in two components of the likelihood function?

Thank you in advance!

Sorry this went unanswered for so long. It’s hard to say exactly without the specifics of your problem, other than to say, I don’t see why an RV can’t be a component in multiple likelihood functions.

For your specific problem though you mention row and column coveriances in a MatrixNormal. You might try pm.KroneckerNormal instead.