TY - JOUR
T1 - A fully Bayesian approach to sparse reduced-rank multivariate regression
AU - Yang, Dunfu
AU - Goh, Gyuhyeong
AU - Wang, Haiyan
N1 - Publisher Copyright:
© 2020 Statistical Modeling Society.
PY - 2022/6
Y1 - 2022/6
N2 - 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.
AB - 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.
KW - bayesian reduced-rank regression
KW - fully Bayesian inference
KW - high-dimensional variable selection
KW - low-rank matrix estimation
KW - multivariate linear regression
UR - http://www.scopus.com/inward/record.url?scp=85091437969&partnerID=8YFLogxK
U2 - 10.1177/1471082X20948697
DO - 10.1177/1471082X20948697
M3 - Article
AN - SCOPUS:85091437969
SN - 1471-082X
VL - 22
SP - 199
EP - 200
JO - Statistical Modelling
JF - Statistical Modelling
IS - 3
ER -