Bayesian variable selection for linear regression with the κ-G priors

Abstract

In this paper, we propose a method that balances between variable se- lection and variable shrinkage in linear regression. A diagonal matrix G is injected to the covariance matrix of prior distribution of the coefficient vector β, with each gj , bounded between 0 and 1, on the diagonal serving as a stabilizer of the corre- sponding βj . Mathematically, a gj value close to 0 indicates that the βj is nonzero, and hence the corresponding variable should be selected, whereas the value of gj close to 1 indicates otherwise. We prove this property under orthogonality. Com- putationally, the proposed method is easy to fit using automated programs such as JAGS. We provide three examples to verify the capability of this methodology in variable selection and shrinkage.