Bayesian Inference via the Blended Paradigm

• Activity Number: 364
• Type: Contributed
• Date/Time: Tuesday, August 6, 2013 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): John Lewis*+ and Steven MacEachern and Yoonkyung Lee
• Companies: The Ohio State University and Ohio State University and The Ohio State University

Abstract

The blended paradigm provides a means of achieving robust inference within the Bayesian framework. We seek to improve inference when the sampling distribution assumed for the data does not fully capture the data generating process. This paper focuses on the use of robust regression estimators (e.g., Huber estimators) in a Bayesian context. The distribution of the estimators is induced by an underlying model. This induced distribution yields a likelihood which is used to update from the prior distribution to the posterior distribution. We detail a data augmented MCMC algorithm used to fit such models. Empirical results show that good choices of robust estimators can produce posteriors that are more concentrated around the target value and less affected by model misspecification. Success of the method is also demonstrated with real data examples.