A Comprehensive Bayesian Framework for Envelope Models

Saptarshi Chakraborty and Zhihua Su

Journal of the American Statistical Association, 2024, vol. 119, issue 547, 2129-2139

Abstract: The envelope model aims to increase efficiency in multivariate analysis by using 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. 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 of this article is to propose a Bayesian framework that is applicable across various envelope model contexts. The proposed framework aids straightforward interpretation of model parameters and allows easy incorporation of prior information. We provide a simple block Metropolis-within-Gibbs MCMC sampler for practical implementations of our method. Simulations and data examples are included for illustration. Supplementary materials for this article are available online.

Date: 2024
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DOI: 10.1080/01621459.2023.2250096

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