Criteria for Bayesian consistency

Conditions for asymptotic suitability of Bayesian procedures focus on lower bounds for prior mass in Kullback-Leibler neighbourhoods of the data distribution. The goal of this paper is to investigate whether there is more flexibility in asymptotic criteria for posterior consistency, with the ultimate goal of formulating new, alternative consistency theorems based on a wider variety of prior suitability conditions. We formulate a versatile Bayesian consistency theorem, re-derive Schwartz' theorem (Schwartz (1965)), sharpen it to Kullback-Leibler consistency and formulate several other consistency theorems in which priors charge metric (e.g. Hellinger) balls. Results also apply to marginal, semi-parametric consistency; support boundary estimation is considered explicitly and posterior consistency is proved in a model where Schwartz' theorem fails.