Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7546490 | Journal of Multivariate Analysis | 2018 | 18 Pages |
Abstract
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 popular for obtaining sparse estimates of the coefficients. In this paper, we extend the use of these priors to the multivariate case to estimate a pÃq coefficients matrix B. We derive sufficient conditions for posterior consistency under the Bayesian multivariate linear regression framework and prove that our method achieves posterior consistency even when p>n
and even when p grows at nearly exponential rate with the sample size. We derive an efficient Gibbs sampling algorithm and provide the implementation in a comprehensive R package called MBSP. Finally, we demonstrate through simulations and data analysis that our model has excellent finite sample performance.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Numerical Analysis
Authors
Ray Bai, Malay Ghosh,