Dr. Tod Kuffner

Department of Mathematics, Washington University in St.Louis

Title : "Objective Bayes and Conditional Frequentist Inference: Theory and Methodology".

Date and Time: February 13, 2014 - 4:15pm to 5:15pm
Location: Cupples I, Room 199

Abstract: The past two decades have witnessed a growth of interest in the study of probability matching priors (PMPs), that is, Bayesian priors chosen in such a way as to deliver posterior credible sets having the correct frequentist interpretation, to a high order of accuracy. What has largely been ignored in this literature is that in many cases, the appropriate frequentist inference to match is a conditional one. In an effort to extend the existing PMP analysis to the conditional frequentist setting, I propose new methods for the identification of PMPs (both conditional and unconditional) and present proofs of the theoretical validity of these methods. Connections with competing methods are discussed, and some relationships are established between conditional and unconditional PMPs. In one-parameter models, I will demonstrate a connection between Jeffreys' prior, conditional inference and the curvature of the statistical model. Ancillary statistic models are of particular interest. I will establish that the right-invariant Haar prior is exact probability matching in location-scale models. Finally, I will present the first simulation study of the conditional frequentist properties of Bayesian quantiles obtained from PMPs.