  In high-throughput genetics studies, an important aim is to identify
gene-environment interactions associated with the clinical outcomes. Recently,
multiple marginal penalization methods have been developed and shown to be
effective in G$\times$E studies. However, within the Bayesian framework,
marginal variable selection has not received much attention. In this study, we
propose a novel marginal Bayesian variable selection method for G$\times$E
studies. In particular, our marginal Bayesian method is robust to data
contamination and outliers in the outcome variables. With the incorporation of
spike-and-slab priors, we have implemented the Gibbs sampler based on MCMC. The
proposed method outperforms a number of alternatives in extensive simulation
studies. The utility of the marginal robust Bayesian variable selection method
has been further demonstrated in the case studies using data from the Nurse
Health Study (NHS). Some of the identified main and interaction effects from
the real data analysis have important biological implications.
