This was just a thought that occurred to me, but technically, is it possible to redefine what I treat as latent variables and what I treat as data?
For example, lets assume I have a set of latent variables that can describe 2 datasets equally well (but datasets origin form 2 different distributions). Now I am interested what part of my latent variables is better associated with which distribution. Could I simply treat those latent variables as my dataset, and the distributions as my latent variables?
or in general, if I have a likelihood p(y|z) (described by some gaussian distribution) computed using some model. If I change my problem statement could I redefine this likelihood to be a posterior?