Bayesian model diagnostics using functional Bregman divergence

It is crucial to check validation of any statistical model after fitting it for a given set of data. In Bayesian statistics, a researcher can check the fit of the model using a variety of strategies. In this paper we consider two major aspects, first checking that the posterior inferences are reasonable, given the substantive context of the model; and then examining the sensitivity of inferences to reasonable changes in the prior distribution and the likelihood. Here we consider functional Bregman divergence between posterior distributions for model diagnostics, which produce methods for outlier detection as well as for prior sensitivity analysis. The methodology is exemplified through a logistic regression and a circular data model.