Bayesian Estimation of Sufficient Dimension-Reduction Space

• Activity Number: 41
• Type: Contributed
• Date/Time: Sunday, August 9, 2015 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Moumita Karmakar* and Kofi Placid Adragni
• Companies: University of Maryland, Baltimore County and University of Maryland, Baltimore County
• Keywords: Principal fitted components ; Sufficient Dimension Reduction ; Inverse regression ; Gibbs sampling ; Bayesian Estimation ; Manifold

Abstract

We develop a Bayesian model based on principal fitted components (PFC) to estimate the Sufficient Dimension Reduction (SDR) subspace. The key component of the model is the reduction matrix, an element in the Grassman manifold, which spans the SDR subspace. Using a uniform prior distribution on the Grassmannian, we develop a fully Bayesian specification for the PFC model. Efficient posterior computation methods are developed based on a Gibbs sampler. Consistency of the Bayes estimators are established under reasonable assumptions on the data generating process. In addition, a method for variable selection is proposed based on the posterior samples of the reduction subspace. The efficacy of the Bayesian procedure is demonstrated via numerous simulation studies and a real data exam