Bayesian brittleness, again
“With the advent of high-performance computing, Bayesian methods are increasingly popular tools for the quantification of uncertainty throughout science and industry. Since these methods impact the making of sometimes critical decisions in increasingly complicated contexts, the sensitivity of their posterior conclusions with respect to the underlying models and prior beliefs is becoming a pressing question.”
A second paper by Owhadi, Scovel and Sullivan on Bayesian brittleness has just been arXived. This one has the dramatic title `When Bayesian inference shatters‘..! If you remember (or simply check) my earlier post, the topic of this work is the robustness of Bayesian inference under model mispsecification, robustness which is completely lacking from the authors’ perspective. This paper is much shorter than the earlier one (and sounds like a commentary on it), but it concludes in a similar manner, namely that Bayesian inference suffers from `maximal brittleness under local mis-specication’ (p.6), which means that `the range of posterior predictions among all admissible priors is as wide as the deterministic range of the quantity of interest’ when the true model is not within the range of the parametric models covered by the prior distribution. The novelty in the paper appears to be in the extension that, even when we consider only the k first moments of the unknown distribution, Bayesian inference is not robust (this is called the Brittleness Theorem, p.9). As stated earlier, while I appreciate this sort of theoretical derivation, I am somehow dubious as to whether or not this impacts the practice of Bayesian statistics to the amount mentioned in the above quote. In particular, I do not see how those results cast more doubts on the impact of the prior modelling on the posterior outcome. While we all (?) agree on the fact that “any given prior and model can be slightly perturbed to achieve any desired posterior conclusion”, the repeatability or falsifiability of the Bayesian experiment (change your prior and run the experiment afresh) allows for an assessment of the posterior outcome that prevents under-the-carpet effects.