Nonparametric Bayesian Clay for Robust Decision Bricks

This note discusses Watson and Holmes [Statist. Sci. (2016) 31 465-489] and their proposals towards more robust Bayesian decisions. While we acknowledge and commend the authors for setting new and all encompassing principles of Bayesian robustness, and while we appreciate the strong anchoring of these within a decision-theoretic framework, we remain uncertain as to what extent such principles can be applied outside binary decisions. We also wonder at the ultimate relevance of Kullback-Leibler neighbourhoods into characterising robustness and we instead favour extensions along nonparametric axes.