Ryan Martin : Optimal Bayesian posterior concentration rates with empirical priors

Posted by Ryan Martin , part of the Statistics and Data Science Seminar.

At

Jan. 27, 2016, 4 p.m.

In

SEO 636

Abstract

A Bayesian approach provides a technically straightforward procedure to produce inference on high- and even infinite-dimensional parameters in complex models. Of course, the choice of a prior is always an issue and, especially in high-dimensional problems, the prior has a non-trivial effect. One attempt use data to help select an appropriate prior is <i>empirical Bayes</i> but, unfortunately, this approach does not lead to any theoretical guarantees that the posterior will behave properly. In this talk I will introduce a very simple strategy that incorporates data into the prior in such a way that the corresponding posterior distribution has optimal, even adaptive, concentration rates. Some illustrations of the general theory will also be presented. (This is joint work with Stephen Walker at University of Texas--Austin.)