Parallel Computing to Speed up Whole-Genome Bayesian Regression Analyses Using Orthogonal Data Augmentation

1 AbstractBayesian multiple regression methods are widely used in whole-genome analyses to solve the problem that the number p of marker covariates is usually larger than the number n of observations. Inferences from most Bayesian methods are based on Markov chain Monte Carlo methods, where statistics are computed from a Markov chain constructed to have a stationary distribution equal to the posterior distribution of the unknown parameters. In practice, chains of about fifty thousand steps are typically used in whole-genome Bayesian regression analyses, which is computationally intensive. In this paper, we have shown how the sampling of marker effects can be made independent within each step of the chain. This is done by augmenting the marker covariate matrix by adding p new rows to it such that columns of the augmented marker covariate matrix are orthogonal. The phenotypes corresponding to the augmented rows of marker covariate matrix are considered missing. Ideally, the computations at each step of the MCMC chain, can be speeded up by the number k of computer processors up to the number p of markers. Addressing the heavy computational burden associated with Bayesian methods by parallel computing will lead to greater use of these methods.