Statistics and Data Science Seminar
Ryan Martin
UIC
Optimal Bayesian posterior concentration rates with empirical priors
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 empirical Bayes 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.)
Wednesday January 27, 2016 at 4:00 PM in SEO 636