Maximum a posteriori estimators as a limit of Bayes estimators
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.
Mathematics Subject Classification62C10 62F10 62F15 65K10
Both authors express their gratitude to Roger J.-B. Wets for his guidance and supervision. This paper is dedicated to him, in honor of his 80th birthday.
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