I have a conceptual question. I use variational inference to fit my model to the data. But for different runnings, with same values of ELBO, I obtain different posterior distributions for parameters (regarding mean, std,...). I guess it is due to local optimums. Is it the reason?! if so, how should I know which one is the correct answer from different tries! (because I have same elbo). When I use HMC, the posterior of parameters are very wide and flat!
Thank you very much in advance for your comment.