On Shrinkage Priors in High Dimensions

• Activity Number: 617
• Type: Invited
• Date/Time: Thursday, August 8, 2013 : 8:30 AM to 10:20 AM
• Sponsor: IMS
• Author(s): Debdeep Pati*+ and Anirban Bhattacharya and Natesh S. Pillai and David B. Dunson
• Companies: Florida State University and Duke University and Harvard University and Duke University
• Keywords: Bayesian ; covariance matrix ; high-dimensions ; posterior convergence ; shrinkage prior ; sub-optimality

Abstract

Shrinkage priors are routinely used as alternative to point-mass mixture priors for sparse modeling in high-dimensional applications. The question of statistical optimality in such settings is under-studied in a Bayesian framework. We provide theoretical understanding of such Bayesian procedures in terms of prior concentration around sparse vectors. In particular, we demonstrate that a large class of commonly used shrinkage priors lead to sub-optimal procedures in high-dimensional settings. We then go on to propose a shrinkage prior that improves the prior concentration around sparse vectors. A novel sampling algorithm for our proposed prior is devised and illustrations are provided through simulation examples.