Moment Matching Priors

There are various proposals for the selection of the so-called objective or default priors in Bayesian analysis. The paper introduces a new criterion, the moment matching criterion, which requires the matching of the posterior mean with the maximum likelihood estimator up to a high order of approximation. A complete characterization of such priors in the one or multi-parameter case is provided. In the process, many new priors are derived. One interesting finding is that even in the absence of nuisance parameters, it is possible to find priors different from Jeffreys' prior for a real valued parameter based on our criterion. AMS (2000) subject classification. Primary 62F15.