Bayesian Inference with Half a Prior

• Activity Number: 291
• Type: Invited
• Date/Time: Tuesday, August 2, 2016 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Keli Liu* and Xiao-Li Meng
• Companies: Stanford University and Harvard
• Keywords: objective Bayes ; conformal prediction ; partial information ; uninformative prior

Abstract

Information about a quantity of interest is often not reliable enough to be encoded through a prior distribution. For example, an investigator may expect an odds ratio to lie between 1/3 and 3 with 90% probability but know nothing more definitive. A common approach in such situations is to use an uninformative or weakly informative prior. Such tactics do not address the fundamental problem: using any prior assumes complete knowledge of a population. To conduct Bayesian inference while genuinely acknowledging prior fallibility requires us to step away from the prior-likelihood setup. We will work with a knowledge representation that is intrinsically weaker than a distribution. To conduct posterior inference with such representations, we use the recent idea of conformal prediction. The resulting inference is robust to the fine-scale/local features of the prior distribution and allows for a quick and convenient assessment of prior influence.