CLT in HD Bayesian linear regression

SUMIT MUKHERJEE – COLUMBIA UNIVERSITY 

ABSTRACT

In this talk we study a CLT for linear statistics of the posterior in high dimensional Bayesian linear regression with an iid prior. In contrast to the existing literature which focuses on the high SNR regime where the prior washes away and one obtains Bernstein-von-Mises type results, our work focuses on the low SNR regime where the prior has a significant effect. As application of our result, we derive asymptotic coverage of posterior credible intervals when the prior is potentially misspecified.

This talk is based on joint work with Seunghyun Lee (Columbia) and Nabarun Deb (UChicago).