Characterization of the Bayes estimator and the MDL estimator for exponential families

摘要

We analyze the relationship between the MDL (minimum description length) estimator (posterior mode) and the PBE (projected Bayes estimator) for exponential families, where the PBE is obtained by projecting the BE (Bayes estimator, i.e. posterior mixture) onto the original exponential family and is equal to the BE under a certain condition.