Robust Bayes Analysis with Hierarchical Classes of Priors

• Activity Number: 503
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Xiaomu Wang*+ and Mark Berliner
• Companies: Ohio State University and Ohio State University
• Keywords: robust bayes ; contaminated prior ; hierarchical priors ; unimodal contamination ; posterior measure

Abstract

We do robust bayes and empirical bayes analysis with hierarchical classes of priors with the second stage prior having uncertainty being epsilon-contaminated.

This study is motivated by a situation that we want to study the robustness of a large number of parameters associated with big data. With those many parameters depending on a much smaller number of hyperparameters which have contaminated priors.

We derive ranges of posterior measures, such as posterior mean, variance, and probability of a set, for a family of priors with unimodal contaminations.