Structured Shrinkage Priors

Presented by Maryclare Griffin, Assistant Professor, Department of Mathematics and Statistics, University of Massachusetts Amherst

Wednesday, April 19, 2023
4:00 PM ET
AUST 163
Webex Meeting Link

In many regression settings the unknown coefficients may have some known structure, for instance they may be ordered in space or correspond to a vectorized matrix or tensor. At the same time, the unknown coefficients may be sparse, with many nearly or exactly equal to zero. However, many commonly used priors and corresponding penalties for coefficients do not encourage simultaneously structured and sparse estimates. In this paper we develop structured shrinkage priors that generalize multivariate normal, Laplace, exponential power and normal-gamma priors. These priors allow the regression coefficients to be correlated a priori without sacrificing elementwise sparsity or shrinkage. The primary challenges in working with these structured shrinkage priors are computational, as the corresponding penalties are intractable integrals and the full conditional distributions that are needed to approximate the posterior mode or simulate from the posterior distribution may be non-standard. We overcome these issues using a flexible elliptical slice sampling procedure, and demonstrate that these priors can be used to introduce structure while preserving sparsity.

Speaker Bio:

Maryclare Griffin is an assistant professor of statistics at UMass Amherst. She received a PhD in statistics from the University of Washington in Seattle in 2018. Her research interests include high dimensional regression problems, mixed models, and methods for spatio-temporal data.