Criteria for posterior consistency and convergence at a rate (Q2008624)

Dealing with Bayesian methods, a major problem is the limited availability of prior distributions, especially in infinite dimensional spaces. Moreover, the conditions for the priors arising from Bayesian limit theorems concerning lower bounds for prior mass in Kullback-Leibler neighborhoods of the data distribution are very crucial. Considering asymptotic aspects, the aim of the article is to extend the conditions on the priors for posterior consistency and convergence properties. Hence, the aim is to reach a larger flexibility in the choice of priors. Several examples are given.