Local Sensitivity of Inferences to Prior Marginals

The sensitivity of posterior expectations to perturbations of prior marginals is investigated, using a local method. This approach is particularly well suited to high-dimensional parameter spaces. Qualitative and quantitative results are obtained regarding the propagation of sensitivity in multiparameter settings. More specifically, a posterior expectation is treated as a functional of the prior marginal. The derivative of this functional is evaluated at the nominal prior marginal, yielding a measure of sensitivity. This is computationally more feasible than evaluating the range of a posterior quantity over a class of priors; hence sensitivity can be assessed in high-dimensional problems. The local technique is used to assess the influence of distributional assumptions at the various stages of a hierarchical model.