A Two-Component G-Prior for Variable Selection

Abstract

We present a Bayesian variable selection method based on an extension of the Zellner’s $g$-prior in linear models. More specifically, we propose a two-component $G$-prior, wherein a tuning parameter, calibrated by use of pseudo-variables, is introduced to adjust the distance between the two components. We show that implementing the proposed prior in variable selection is more efficient than using the Zellner’s $g$-prior. Simulation results also indicate that models selected using the method with the two-component $G$-prior are generally more favorable with smaller losses compared to other methods considered in our work. The proposed method is further demonstrated using our motivating gene expression data from a lung disease study, and ozone data analyzed in earlier studies.