Bayesian Analysis with Orthogonal Matrix Parameters

• Activity Number: 666 - Bayesian Penalized Regression Models
• Type: Contributed
• Date/Time: Thursday, August 2, 2018 : 10:30 AM to 12:20 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Michael Jauch* and Peter Hoff and David B Dunson
• Companies: Duke University and Duke University and Duke University
• Keywords: Bayesian analysis; Data augmentation; Sparsity; Markov Chain Monte Carlo; Matrix decompositions; Multivariate data

Abstract

Models for multivariate data based on matrix decompositions naturally involve orthogonal matrix parameters. Bayesian analysis with orthogonal matrix parameters presents two major challenges: posterior sampling on the constrained parameter space and incorporation of prior information such as sparsity. We propose methodology to address both of these challenges. To sample from posterior distributions defined on the set of orthogonal matrices, we introduce a data augmentation scheme based on the polar decomposition. To incorporate sparsity information, we construct prior distributions having element-wise marginal distributions approximately matching conventional sparsity-inducing priors. We illustrate these techniques in simulation studies and applications to data.