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Title: A Bayesian approach to envelope quantile regression Authors:  Zhihua Su - University of Florida (United States) [presenting]
Abstract: The envelope model is a nascent construct that aims to increase efficiency in multivariate analysis. It has been used in many contexts including linear regression, generalized linear models, matrix or tensor variate regression, reduced rank regression, and quantile regression, and has showed 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 Bayesian approach for envelope quantile regression. The proposed approach has straightforward interpretation of model parameters and allows easy incorporation of prior information. We provide a simple block Metropolis-within-Gibbs MCMC sampler for practical implementation of our method. Simulations and data examples are included for illustration.