Maximum a posteriori estimators as a limit of Bayes estimators
成果类型：
Article
署名作者：
Bassett, Robert; Deride, Julio
署名单位：
University of California System; University of California Davis
刊物名称：
MATHEMATICAL PROGRAMMING
ISSN/ISSBN：
0025-5610
DOI：
10.1007/s10107-018-1241-0
发表日期：
2019
页码：
129-144
关键词：
摘要：
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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