Maximum a posteriori estimators as a limit of Bayes estimators

2016/11/30 by Robert Bassett, Julio Deride · 101 citations
Decision Sciences · Mathematics · #A priori and a posteriori #Advanced Statistical Methods and Models #Bayes estimator #Bayes' theorem #Bayesian probability #Counterexample #Estimator #Limit (mathematics) #Maximum a posteriori estimation #Point estimation #Risk and Portfolio Optimization #Statistical Methods and Inference #math.OC #math.ST #msc:62C10 #msc:62F10 #msc:62F15 #msc:65K10 #stat.TH

paper · pdf · doi:10.1007/s10107-018-1241-0

published in Mathematical Programming 174(1-2), 129-144 (Springer Science+Business Media)

openalex created_date 2016/11/30 · arxiv created 2018/01/21 · openalex publication_date 2018/01/30 · arxiv updated 2018/02/23 · openalex updated_date 2026/08/06

Abstract

Maximum a posteriori and Bayes estimators are two common methods of point estimation in Bayesian Statistics. It is commonly accepted that maximum a posteriori estimators are a limiting case of Bayes estimators with 0-1 loss. In this paper, we provide a counterexample which shows that in general this claim is false. We then correct the claim that by providing a level-set condition for posterior densities such that the result holds. Since both estimators are defined in terms of optimization problems, the tools of variational analysis find a natural application to Bayesian point estimation.

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