Seminar by Xueying Tang, University of Arizona

Abstract

Sparsity is often a desired structure for parameters in high-dimensional statistical problems. Within a Bayesian framework, sparsity is usually induced by spike-and-slab priors or global-local shrinkage priors. The latter choice is often expressed as a scale mixture of normal distributions. It marginally places a polynomial-tailed distribution on the parameter. In general, a heavy-tailed prior with significant probability mass around zero is preferred in estimating sparse parameters. In this talk, we consider a general class of priors, with the log Cauchy priors as a special case, in the normal mean estimation problem. This class of priors is proper while having a tail order arbitrarily close to one. The resulting posterior mean is a shrinkage estimator, and the posterior contraction rate is sharp minimax. We also demonstrate the performance of this class of priors on simulated and real datasets.

Bio

Xueying Tang is an assistant professor in the Department of mathematics at the University of Arizona. She got her Ph.D. in statistics from the University of Florida in 2017. Before joining the University of Arizona, she was a postdoctoral research scientist at Columbia University. Her research interests include high dimensional Bayesian statistics, small area estimation, and latent variable models with applications in education and psychology.