Joint UConn/UMass
STATISTICS COLLOQUIUM
Maryclare Griffin, Assistant Professor
Department of Mathematics and Statistics
University of Massachusetts
Amherst
Structured Shrinkage Priors
ABSTRACT
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.
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.
DATE: Wednesday, April 19, 2023
TIME: 4:00 pm - 5:00 pm
PLACE: Philip E. Austin Bldg., Rm. 163
For more information, contact: Tracy Burke at tracy.burke@uconn.edu