Bayesian Robustness and Bayesian Nonparametrics

Abstract

Bayesian robustness studies the sensitivity of Bayesian answers to user inputs, especially to the specification of the prior. Nonparametric Bayesian models, on the other hand, refrain from specifying a specific prior functional form P, but instead assume a second-level hyperprior on P with support on a suitable space of probability measures. Nonparametric Bayes thus appears to have the same goals as robust Bayes, and nonparametric Bayes models are typically presumed to be robust. We investigate this presumed robustness and prior flexibility of nonparametric Bayes models. In this context, we focus specifically on Dirichlet process mixture models. We argue that robustness should be an issue of concern in Dirichlet process mixture models and show how robustness measures can actually be evaluated in these models in a computationally feasible way.