Bayesian Inference for Mixed Model-Based Genome-Wide Analysis of Expression Quantitative Trait Loci by Gibbs Sampling

The importance of expression quantitative trait locus (eQTL) has been emphasized in understanding the genetic basis of cellular activities and complex phenotypes. Mixed models can be employed to effectively identify eQTLs by explaining polygenic effects. In these mixed models, the polygenic effects are considered as random variables, and their variability is explained by the polygenic variance component. The polygenic and residual variance components are first estimated, and then eQTL effects are estimated depending on the variance component estimates within the frequentist mixed model framework. The Bayesian approach to the mixed model-based genome-wide eQTL analysis can also be applied to estimate the parameters that exhibit various benefits. Bayesian inferences on unknown parameters are based on their marginal posterior distributions, and the marginalization of the joint posterior distribution is a challenging task. This problem can be solved by employing a numerical algorithm of integrals called Gibbs sampling as a Markov chain Monte Carlo. This article reviews the mixed model-based Bayesian eQTL analysis by Gibbs sampling. Theoretical and practical issues of Bayesian inference are discussed using a concise description of Bayesian modeling and the corresponding Gibbs sampling. The strengths of Bayesian inference are also discussed. Posterior probability distribution in the Bayesian inference reflects uncertainty in unknown parameters. This factor is useful in the context of eQTL analysis where a sample size is too small to apply the frequentist approach. Bayesian inference based on the posterior that reflects prior knowledge, will be increasingly preferred with the accumulation of eQTL data. Extensive use of the mixed model-based Bayesian eQTL analysis will accelerate understanding of eQTLs exhibiting various regulatory functions.