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Bayesian High Dimensional Multivariate Regression with Shrinkage Priors

Banff International Research Station for Mathematical Innovation and Discovery

We consider sparse Bayesian estimation in the classical multivariate linear regression model with p regressors and q response variables. In univariate Bayesian linear regression with a single response y, shrinkage priors which can be expressed as scale-mixtures of normal densities are a popular approach for obtaining sparse estimates of the coefficients. In this paper, we extend the use of these priors to the multivariate case to estimate a p times q coefficients matrix B. Our method can be used for any sample size n and any dimension p. Moreover, we show that the posterior distribution can consistently estimate B even when p grows at nearly exponential rate with the sample size n. Concentration inequalities are proved and our results are illustrated through simulation and data analysis.

Mathematics; Statistics

video/mp4

Author affiliation: University of Florida

2019-10-06

Attribution-NonCommercial-NoDerivatives 4.0 International

http://hdl.handle.net/2429/71835

Unreviewed

http://creativecommons.org/licenses/by-nc-nd/4.0/