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arXiv · 1611.05917

Maximum a Posteriori Estimators as a Limit of Bayes Estimators

Robert Bassett·Julio Deride
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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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Robert Bassett, Julio Deride. 2016-11-17. Maximum a Posteriori Estimators as a Limit of Bayes Estimators. https://doi.org/10.1007/s10107-018-1241-0

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