Local and global robustness in conjugate Bayesian analysis

Abstract

This paper studies the influence of perturbations of conjugate priors in Bayesian inference. A perturbed prior is defined inside a larger family, local mixture models, and the effect on posterior inference is studied. The perturbation, in some sense, generalizes the linear perturbation studied in \cite{Gustafson1996}. It is intuitive, naturally normalized and is flexible for statistical applications. Both global and local sensitivity analyses are considered. A geometric approach is employed for optimizing the sensitivity direction function, the difference between posterior means and the divergence function between posterior predictive models. All the sensitivity measure functions are defined on a convex space with non-trivial boundary which is shown to be a smooth manifold.