Statistical Modelling 22 (3) (2022), 199–220
A fully Bayesian approach to sparse reduced-rank
multivariate regression
Dunfu Yang,
Department of Statistics,
Kansas State University,
Manhattan, KS,
USA.
Gyuhyeong Goh,
Department of Statistics,
Kansas State University,
Manhattan, KS,
USA.
e-mail: ggoh@ksu.edu
Haiyan Wang,
Department of Statistics,
Kansas State University,
Manhattan, KS,
USA.
Abstract:
In the context of high-dimensional multivariate linear regression, sparse reduced-rank regression (SRRR) provides a way to handle both variable selection and low-rank estimation problems. Although there has been extensive research on SRRR, statistical inference procedures that deal with the uncertainty due to variable selection and rank reduction are still limited. To fill this research gap, we develop a fully Bayesian approach to SRRR. A major difficulty that occurs in a fully Bayesian framework is that the dimension of parameter space varies with the selected variables and the reduced-rank. Due to the varying-dimensional problems, traditional Markov chain Monte Carlo (MCMC) methods such as Gibbs sampler and Metropolis-Hastings algorithm are inapplicable in our Bayesian framework. To address this issue, we propose a new posterior computation procedure based on the Laplace approximation within the collapsed Gibbs sampler. A key feature of our fully Bayesian method is that the model uncertainty is automatically integrated out by the proposed MCMC computation. The proposed method is examined via simulation study and real data analysis.
Keywords:
bayesian reduced-rank regression, fully Bayesian inference, high-dimensional variable selection, low-rank matrix estimation, multivariate linear regression
Downloads:
Example code in
zipped archive.
back