A Method for Robust Bayesian Inference in the Presence of a Hypothesized Mean-Variance Relationship

• Activity Number: 452
• Type: Contributed
• Date/Time: Thursday, August 7, 2003 : 8:30 AM to 10:20 AM
• Sponsor: Biopharmaceutical Section
• Author(s): Kent M. Koprowicz*+ and Peter Hoff and Scott S. Emerson
• Companies: University of Washington and University of Washington and University of Washington
• Keywords: approximate likelihood ; Bayesian analysis ; interval estimation ; nonparametric ; robust

Abstract

We consider an approach to Bayesian inference where interest lies in a specific functional. Instead of specifying a sampling distribution for the data we specify an approximate distribution of a summary statistic or "coarsening" of the data. The approach is robust in that it provides some protection against model misspecification and allows one to account for the possibility of a specified mean-variance relationship. Notably, the method allows one to place prior mass directly on the quantity of interest or, alternatively, to employ a noninformative prior--a counterpart to the standard frequentist approach. We explore interval estimation of a population location parameter in the presence of a mean-variance relationship--a problem that is not well-addressed by standard nonparametric frequentist methods. We find the method has performance comparable to the correct parametric model, and performs notably better than some plausible yet incorrect models. Finally, we apply the method to real data and compare ours to previously reported results and to those from a more complicated nonparametric Bayesian analysis with a prior having support equal to the space of distribution functions.