*I explain the discretization trick that I mentioned in my previous post (Posterior consistency under possible misspecification). I think it was introduced by Walker (New approaches to Bayesian consistency (2004)).*

Let be a set of densities and let be a prior on . If follows some distribution having density , then the posterior distribution of can be written as

The discretization trick is to find densities in the convex hull of (taken in the space of all densities) such that