Not yet reviewed by Pith; the record is open.

Many complex diseases are known to be affected by the interactions between genetic variants and environmental exposures beyond the main genetic and environmental effects. Study of gene-environment (G$\times$E) interactions is important for elucidating the disease etiology. Existing Bayesian methods for G$\times$E interaction studies are challenged by the high-dimensional nature of the study and the complexity of environmental influences. Many studies have shown the advantages of penalization methods in detecting G$\times$E interactions in "large p, small n" settings. However, Bayesian variable selection, which can provide fresh insight into G$\times$E study, has not been widely examined. We propose a novel and powerful semi-parametric Bayesian variable selection model that can investigate linear and nonlinear G$\times$E interactions simultaneously. Furthermore, the proposed method can conduct structural identification by distinguishing nonlinear interactions from main-effects-only case within the Bayesian framework. Spike and slab priors are incorporated on both individual and group levels to identify the sparse main and interaction effects. The proposed method conducts Bayesian variable selection more efficiently than existing methods. Simulation shows that the proposed model outperforms competing alternatives in terms of both identification and prediction. The proposed Bayesian method leads to the identification of main and interaction effects with important implications in a high-throughput profiling study with high-dimensional SNP data.