Some comments about James Watson's and Chris Holmes' "Approximate Models and Robust Decisions": Nonparametric Bayesian clay for robust decision bricks

TL;DR

This paper discusses the principles of Bayesian robustness proposed by Watson and Holmes, questioning their applicability beyond binary decisions and suggesting non-parametric extensions for better robustness characterization.

Contribution

It critically evaluates existing Bayesian robustness principles and advocates for non-parametric approaches to enhance decision-making robustness.

Findings

Acknowledges the robustness principles but questions their general applicability.

Highlights the potential of non-parametric methods for robustness.

Suggests extensions beyond Kullback-Leibler neighborhoods for better robustness modeling.

Abstract

This note discusses Watson and Holmes (2016) and their pro- posals towards more robust Bayesian decisions. While we acknowledge and commend the authors for setting new and all-encompassing prin- ciples of Bayesian robustness, and we appreciate the strong anchoring of those within a decision-theoretic referential, we remain uncertain as to which extent such principles can be applied outside binary de- cisions. We also wonder at the ultimate relevance of Kullback-Leibler neighbourhoods to characterise robustness and favour extensions along non-parametric axes.