A0797
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 by utilizing dimension reduction techniques. It has been used in many contexts including linear regression, generalized linear models, matrix/tensor variate regression, reduced rank regression, and quantile regression, and has shown the potential to provide substantial efficiency gains. Most of these advances have been made from a frequentist perspective, and the literature addressing envelope models from a Bayesian point of view is still sparse. The Bayesian paradigm provides unique flexibility in terms of incorporating prior knowledge if available, and coherent quantification of all modeling uncertainties, including in envelope dimension selection. The objective is to propose a computationally feasible comprehensive Bayesian framework that is applicable across various envelope model contexts. We provide a simple block Metropolis-within-Gibbs MCMC sampler for efficient practical implementations of our method. Simulations and data examples are included for illustration.
