I am trying to do some experiments with Variational Inference. In the process, I want to make sure that the posterior of VI is consistent with MCMC. Currently, I take the samples from both VI and MCMC and make a density plot to check how close VI gets to MCMC. Is there a more standard or statistical way of doing this comparison?
P.S.: I have searched along these lines for the already open threads but please guide me to one if you find any.