Characterization of the Bayes estimator and the MDL estimator forexponential families

摘要

We analyze the relationship between the MDL (minimum descriptionlength) estimator (posterior mode) and the PBE (projected Bayesestimator) for exponential families, where the PBE is obtained byprojecting the BE (Bayes estimator, i.e. posterior mixture) onto theoriginal exponential family and is equal to the BE under a certaincondition