Empirical Bayes methods are often thought of as a bridge between classical and Bayesian inference. In fact, in the literature the term empirical Bayes is used in quite diverse contexts and with different motivations. In this article, we provide a brief overview of empirical Bayes methods...

In this paper we discuss consistency of the posterior distribution in cases where the Kullback-Leibler condition is not verified. This condition is stated as : for all $\epsilon 0$ the prior probability of sets in the form $\{f ; KL(f0 , f ) \leq \epsilon\}$ where KL(f0 , f ) denotes the...

Bayesian inference is attractive for its coherence and good frequentist properties. However, eliciting a honest prior may be difficult and a common practice is to take an empirical Bayes approach, using some empirical estimate of the prior hyperparameters. Despite not rigorous, the underlying...