In high-dimensional genome-wide (GWA) data, a key challenge is to detect genomic variants that interact in a nonlinear fashion in their association with disease. Identifying such genomic interactions is important for elucidating the inheritance of complex phenotypes and diseases. In this paper, we introduce a new computational method called Informative Bayesian Model Selection (IBMS) that leverages correlation among variants in GWA data due to the linkage disequilibrium to identify interactions accurately in a computationally efficient manner. IBMS combines several statistical methods including canonical correlation analysis, logistic regression analysis, and a Bayesians statistical measure of evaluating interactions. Compared to BOOST and BEAM that are two widely used methods for detecting genomic interactions, IBMS had significantly higher power when evaluated on synthetic data. Furthermore, when applied to Alzheimer's disease GWA data, IBMS identified previously reported interactions. IBMS is a useful method for identifying variants in GWA data, and software that implements IBMS is freely available online from http://lbb.ut.ac.ir/Download/LBBsoft/IBMS.