Graduate Statistics Seminar
Ryan Martin
UIC
On pseudo-Bayesian inference via fractional likelihood
Abstract: Bayes's theorem provides the tool for combining prior beliefs with evidence from data, and there are general sufficient conditions
that guarantee the corresponding Bayesian posterior distribution will be consistent, i.e., will concentrate around the true parameter
asymptotically. Non-trivial examples of inconsistent posterior distributions are scarce, so it's not clear if the existing sufficient
conditions are the right things. Towards understanding what it takes for posterior consistency, I will show that by making a minor
adjustment to the formula of Bayes, namely, taking an arbitrary fractional power on the likelihood before combining with the prior, will avoid all
known non-trivial examples of inconsistency. That is, the corresponding pseudo-Bayes posterior based on the fractional likelihood is,
in a certain sense, always consistent. The key question is: how to make use of this interesting phenomenon? I will discuss some possible
answers.
Tuesday March 4, 2014 at 3:30 PM in SEO 1227