I am currently working of Bayesian calibration of models and I can’t manage to explain myself the difference between defining my likelihood these 2 ways :
- pm.Normal(‘llk’, mu, sigma, observed) where both are nx1 vectors
- pm.MvNormal(‘llk’, mu, cov, observed) where cov is a diagonal matrix
Note that my and sigma are computed using a hierarchical model
My guess is if I don’t get the same result is because 1) is trying to minimise each likelihood points and 2) minimises only the product of my independent likelihoods but I am not sure because I can’t manage to understand how pm.MvNormal works.
Let me explain :
After sampling I’m interested in computing the marginal likelihood so I wanted to use the log likelihood computed for every sample. But instead of having a log likelihood for the pm.MvNormal likelihood with shape (chains, sample,1) I get a shape (chains, sample,n) where n is the number of observations and I don’t understand why.
I hope I am clear enough in my explanations, and hope someone has an answer
Thanx so much