Approximate methods for assessing influence and sensitivity in Bayesian analysis

Abstract

We use asymptotic approximations to posterior expectations in deriving diagnostics for case influence and prior sensitivity. We obtain an easily-interpreted expression for the change in posterior expectation following perturbation of the problem, which also produces a useful interpretation of the likelihood displacement discussed by Cook & Weisberg (1982). In addition, we propose two simple diagnostics of posterior nonnor mality. The leukaemia data analysed by Feigl & Zelen (1965) are used to illustrate the diagnostic measures we discuss.