Bayesian Inference on Multilocus Genotypic Effects Using a Gibbs Sampler

Simultaneous analysis of multiple genetic variants is an essential strategy for understanding genetic dissection of complex traits, focusing epistasis along with additive and dominance effects of individual genes. Although phenotypic variation for complex traits might be largely explained by epistasis, most analyses have excluded the possibility of epistasis, especially with lack of individual locus effects. The conventional models for estimating all the possible epistatic effects have a decisively vulnerable point of potentially low power or often nonestimable statistics due to a large number of parameters. Restricted partition method (RPM), a recently developed nonparametric approach for estimating epistasis, overcame the drawback but has both biologically and statistically undesirable properties caused by grouping genotypes. A Bayesian method using a Gibbs sampler for estimating epistasis for complex continuous traits was developed to overcome such problems. This method was devised to draw inferences on multilocus genotypic effects by a Bayesian approach based on their marginal posterior distributions and to attain the marginalization of the joint posterior distribution through Gibbs sampler as a Markov chain Monte Carlo. A simulation study revealed that the Bayesian method using a Gibbs sampler was superior to the currently utilized MDR. Especially, prediction errors substantially decreased under various environmental exposures by the Bayesian method using a Gibbs sampler. The programs would be available for both Gamma and Chi-square prior distributions.