The main goal of this paper is to couple the Haseman-Elston method with a simple yet effective Bayesian factor-screening approach. This approach selects markers by considering a set of multigenic models that include epistasis effects. The markers are ranked based on their marginal posterior probability. A significant improvement over our previously proposed Bayesian variable selection methodology is a simple Metropolis-Hasting algorithm that requires minimum tuning on the prior settings. The algorithm, however, is also flexible enough for us to easily incorporate our hypotheses and avoid computational pitfalls. We apply our approach to the microsatellite data of Collaborative Studies on Genetics of Alcoholism using the coded values for the ALDX1 variable as our response.