  Gene-gene interactions are often regarded as playing significant roles in
influencing variabilities of complex traits. Although much research has been
devoted to this area, to date a comprehensive statistical model that addresses
the various sources of uncertainties, seem to be lacking. In this paper, we
propose and develop a novel Bayesian semiparametric approach composed of finite
mixtures based on Dirichlet processes and a hierarchical matrix-normal
distribution that can comprehensively account for the unknown number of
sub-populations and gene-gene interactions. Then, by formulating novel and
suitable Bayesian tests of hypotheses we attempt to single out the roles of the
genes, individually, and in interaction with other genes, in case-control
studies. We also attempt to identify the significant loci associated with the
disease. Our model facilitates a highly efficient parallel computing
methodology, combining Gibbs sampling and Transformation based MCMC (TMCMC).
Application of our ideas to biologically realistic data sets revealed quite
encouraging performance. We also applied our ideas to a real, myocardial
infarction dataset, and obtained interesting results that partly agree with,
and also complement, the existing works in this area, to reveal the importance
of sophisticated and realistic modeling of gene-gene interactions.
