Bayesian variable selection for linear regression with the κ-G priors
Zichen Ma, Ernest Fokoué · Mathematics for Applications · 2022
In this paper, we propose a method that balances between variable selection 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 g j , bounded between 0 and 1, on the diagonal serving as a stabilizer of the corresponding β j .Mathematically, a g j value close to 0 indicates that the β j is nonzero, and hence the corresponding variable should be selected, whereas the value of g j close to 1 indicates otherwise.We prove this property under orthogonality.Computationally, 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. MSC (2020): primary 65C20.