Criteria for posterior consistency

Understand

Frequentist 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 the flexibility in criteria for posterior consistency with i.i.d.
• data.
• We formulate a versatile posterior consistency theorem that applies both to well- and mis-specified models and which we use to re-derive Schwartz's theorem, consider Kullback-Leibler consistency and formulate consistency theorems in which priors charge metric balls.