Statistics Colloquium : Dr. Ryan Martin
Title: Empirical priors and posterior concentration rates.
Abstract: In high- and infinite-dimensional problems, Bayesian prior specification can be a challenge. For example, in high-dimensional regression, while sparsity considerations drive the choice of prior on the model, there is no genuine prior information available about the coefficients in a given model. Moreover, the choice of prior for the model-specific parameters impacts both the computational and theoretical performance of the posterior. As an alternative, one might consider a computationally simple "informative" empirical prior on the model-specific parameters, depending on data in a suitable way. In this talk, I will present a new approach for empirical prior specification in high-dimensional problems, based on the idea of data-driven prior centering. I will give (adaptive) concentration rate results for this new "empirical Bayes" posterior in several specific examples, with illustrations, and I will also say a few words about the general construction and corresponding theory.