Maximum a Posteriori Estimators as a Limit of Bayes Estimators
Statistics Theory
2018-02-23 v2 Optimization and Control
Statistics Theory
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.
Keywords
Cite
@article{arxiv.1611.05917,
title = {Maximum a Posteriori Estimators as a Limit of Bayes Estimators},
author = {Robert Bassett and Julio Deride},
journal= {arXiv preprint arXiv:1611.05917},
year = {2018}
}