Approximate methods for assessing influence and sensitivity in Bayesian analysis

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.