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Title: A comprehensive Bayesian framework for envelope models Authors:  Saptarshi Chakraborty - State University of New York at Buffalo (United States) [presenting]
Zhihua Su - University of Florida (United States)
Abstract: The envelope model aims to increase efficiency in multivariate analysis. It has been used in many contexts, including linear regression, generalized linear models, matrix/tensor variate regression, reduced rank regression, and quantile regression. It has shown the potential to provide substantial efficiency gains. Virtually all of these advances, however, have been made from a frequentist perspective, and the literature addressing envelope models from a Bayesian point of view is sparse. The objective is to propose a comprehensive Bayesian framework that is applicable across various envelope model contexts. The proposed framework aids the straightforward interpretation of model parameters and allows easy incorporation of prior information. We provide a simple block Metropolis-within-Gibbs MCMC sampler for the practical implementation of our method. Simulations and data examples show impressive efficiency gains over standard Bayesian regression methods.