An inverse of Sanov's theorem

Let (X/sub k/)/sub k/spl ges/1/ be a sequence of independent, identically distributed random variables taking values in a finite set, and consider the problem of estimating the law of X/sub 1/ in a Bayesian framework. We prove that the sequence of posterior distributions satisfies a large deviation principle, and give an explicit expression for the rate function. We extend the result to Bayesian inference on compact metric spaces using Dirichlet process priors.