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.

About the Speaker:

Dr. Xueying Tang is an Assistant Professor at the Department of Mathematics in the University of Arizona. She obtained her Ph.D in statistics from the University of Florida. Before joining the University of Arizona, she was a Postdoctoral Research Scientist in Columbia University. Her research interests include high dimensional Bayesian statistics, latent variable models, small area estimation, and statistical analysis of complex data in psychometrics.

**Statistics Seminar
WXLR A303 and Virtual via Zoom
Friday, Oct. 7
1:30 pm **

Meeting ID: 88521538236

Password: ASUSTATS

https://asu.zoom.us/j/88521538236?pwd=K1VscVlWTmFnN0tsRHlrWG8rT0Nhdz09

Xueying Tang

Assistant Professor

Department of Mathematics

University of Arizona