Joint Sensitivity in Bayesian Decision Theory

Research in Bayesian robustness has mainly concentrated on sensitivity to the prior, although it is well-known that joint changes in both the prior and the utility (and likelihood, as well) may be very influential. We provide some tools to detect changes in the ranking of decisions under perturbations of the prior and the utility, as well as relevant changes in expected utility. The methods allow us to detect also the most critical judgements in determining choices and they may guide additional modeling efforts.