Robust Bayesian Inference via Coarsening

• Activity Number: 354
• Type: Contributed
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Jeffrey Miller* and David Dunson
• Companies: Duke University and Duke University
• Keywords: Model misspecification ; Robustness ; Tempering ; Mixture model ; Relative entropy ; Bayesian

Abstract

The standard approach to Bayesian inference is based on the assumption that the distribution of the data belongs to the chosen model class. However, even a small violation of this assumption can have a large impact on the outcome of a Bayesian procedure. We introduce a simple but coherent approach to Bayesian inference that improves robustness to perturbations of the model: rather than condition on the data exactly, one conditions on a neighborhood of the empirical distribution. In certain cases, inference is easily implemented using standard methods. We illustrate with real and simulated data, and provide theoretical results.