Robust Bayesian Analysis for a Simply Elicitable Class of Prior Distributions

摘要

Suppose that the lower or upper prior probability p of a measurable subset K in the parameter space Omega is given. Instead of eliciting just one prior density function, consider the class Gamma(sub p,K) of all the density functions compatible with the bound p. Under mild regularity conditions about the likelihood function, find the upper and lower bounds for the posterior probability of any measurable set A contained in Omega, as the density varies in Gamma(sub p,K). Such a scheme agrees with a robust Bayesian viewpoint. Conditions are found in order to check the robustness in the inferences, and then they are applied to some examples. The importance of the likelihood sets in ensuring robustness is shown.