Consistency of Maximum Likelihood and Bayes Estimates

Abstract

It is proved in the paper that every possible set of conditions which implies consistency of the maximum likelihood method also implies consistency of Bayes estimates for a large class of prior distributions. The method of the proof is based on a necessary and sufficient condition for the consistency of maximum likelihood estimates which is due to Perlman (1972). Perlman's result is improved as far as certain questions of measurability are concerned.