# Maximum a Posteriori Estimators as a Limit of Bayes Estimators

arXiv: https://arxiv.org/abs/1611.05917 · HTML: https://mlsanity.com/paper/1611.05917/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Nov 2016.

## Built on by (most cited first, 12 of 12)

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## Abstract (arXiv)

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.