A Bayesian Sparse Hierarchical Factor Model for Simultaneous Covariance Estimation

• Activity Number: 572 - Sparsity and Variable Selection in Posterior Inference
• Type: Contributed
• Date/Time: Wednesday, July 31, 2019 : 2:00 PM to 3:50 PM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Debamita Kundu* and Jeremy T. Gaskins and Riten Mitra
• Companies: University of Louisville and University of Louisville and University of Louisville
• Keywords: Simultaneous covarince estimation; sparse factor model; Multiple group

Abstract

Covariance estimation for multiple groups is a key feature for drawing an inference from a heterogeneous population. One should seek to share information about common features in the dependent structures across the various groups. In this paper, we introduce a novel approach for estimating the covariance matrices for multiple groups using a hierarchical latent factor model that shrinks the factor loadings across groups toward a global value. Using a sparse spike and slab model on these loading coefficients provides a level of sparsity to our approach. parameter estimation is accomplished through a Markov chain Monte Carlo scheme, and a model selection approach is used to select the number of factors to use. Finally, a simulation study and data application are shown to exhibit the performance of our methodology.