Recent Development of Reference Priors Under a General Class of Divergence

• Activity Number: 339
• Type: Invited
• Date/Time: Tuesday, August 11, 2015 : 10:30 AM to 12:20 PM
• Sponsor: International Society for Bayesian Analysis (ISBA)
• Author(s): Dongchu Sun*
• Companies: University of Missouri - Columbia
• Keywords: Reference Priors ; Kullback-Leibler divergence ; f-divergence ; fidurial distribution

Abstract

Reference analysis produces objective Bayesian inference, that inferential statements depend only on the assumed model and the available data, and the prior distribution used to make an inference is least informative in a certain information-theoretic sense. A quick review of development of reference priors will be given. Recently, Berger, Bernardo and Sun (2009) derived reference priors rigorously in the contexts under Kullback-Leibler divergence. In special cases with common support and other regularity conditions, Ghosh, Mergel and Liu (2011) derived a general f-divergence criterion for prior selection. We generalize Ghosh, Mergel and Liu's (2011) results to the case without common support and show how an explicit expression for the reference prior can be obtained under posterior consistency. The explicit expression can be used to derive new reference priors both analytically and numerically. The connection between reference prior and fiducial distribution and recently developed general distribution theorem is explored.