comments on Watson and Holmes
“The world is full of obvious things which nobody by any chance ever observes.” The Hound of the Baskervilles
In connection with the incoming publication of James Watson’s and Chris Holmes’ Approximating models and robust decisions in Statistical Science, Judith Rousseau and I wrote a discussion on the paper that has been arXived yesterday.
“Overall, we consider that the calibration of the Kullback-Leibler divergence remains an open problem.” (p.18)
While the paper connects with earlier ones by Chris and coauthors, and possibly despite the overall critical tone of the comments!, I really appreciate the renewed interest in robustness advocated in this paper. I was going to write Bayesian robustness but to differ from the perspective adopted in the 90’s where robustness was mostly about the prior, I would say this is rather a Bayesian approach to model robustness from a decisional perspective. With definitive innovations like considering the impact of posterior uncertainty over the decision space, uncertainty being defined e.g. in terms of Kullback-Leibler neighbourhoods. Or with a Dirichlet process distribution on the posterior. This may step out of the standard Bayesian approach but it remains of definite interest! (And note that this discussion of ours [reluctantly!] refrained from capitalising on the names of the authors to build easy puns linked with the most Bayesian of all detectives!)