Appropriate and Inappropriate Estimation Techniques

TL;DR

This paper analyzes when mode, mean, and median estimation techniques are appropriate for deriving cost-minimizing Bayesian estimates, highlighting their limitations based on different cost functions.

Contribution

It clarifies the conditions under which each estimation method yields optimal Bayesian estimates, especially regarding various cost functions.

Findings

Modal estimation is optimal only with 0-1 cost functions.

Mean estimation is optimal with squared distance cost functions.

Median estimation is optimal with absolute distance cost functions.

Abstract

Mode {also called MAP} estimation, mean estimation and median estimation are examined here to determine when they can be safely used to derive {posterior) cost minimizing estimates. (These are all Bayes procedures, using the mode. mean. or median of the posterior distribution). It is found that modal estimation only returns cost minimizing estimates when the cost function is 0-t. If the cost function is a function of distance then mean estimation only returns cost minimizing estimates when the cost function is squared distance from the true value and median estimation only returns cost minimizing estimates when the cost function ts the distance from the true value. Results are presented on the goodness or modal estimation with non 0-t cost functions