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Activity Number: 638
Type: Topic Contributed
Date/Time: Thursday, August 4, 2016 : 8:30 AM to 10:20 AM
Sponsor: Section on Nonparametric Statistics
Abstract #319722
Title: A Bayesian Approach for Envelope Models
Author(s): Zhihua Su* and Kshitij Khare and Subhadip Pal
Companies: and University of Florida and Emory University
Keywords: sufficient dimension reduction ; envelope model ; Gibbs sampling ; Stiefel manifold ; matrix Bingham distribution

The envelope model is a new paradigm to address estimation and prediction in multivariate analysis. Using sufficient dimension reduction techniques, it has the potential to achieve substantial efficiency gains compared to standard models. This model was first introduced for multivariate linear regression, and has since been adapted to many other contexts. However, a Bayesian approach for analyzing envelope models has not yet been investigated in the literature. In this paper, we develop a comprehensive Bayesian framework for estimation and model selection in envelope models in the context of multivariate linear regression. We use the matrix Bingham distribution to construct a prior on the orthogonal basis matrix of the envelope subspace. This prior respects the manifold structure of the envelope model, and can directly incorporate prior information about the envelope subspace through the specification of hyperparamaters. This feature has potential applications in the broader Bayesian sufficient dimension reduction area.

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