In this paper, we propose a fast parallelized algorithm for Bayesian regression models called independent intensive Bayesian regression models (BayesXII, "X" stands for Bayesian alphabet methods and "II" stands for "parallel") and show how the sampling of each marker effect can be made independent of samples for other marker effects within each step of the chain.  We demonstrate the BayesXII algorithm using the prior for BayesC[Formula: see text], a Bayesian variable selection regression method, which is applied to simulated data with 50,000 individuals and a medium-density marker panel ([Formula: see text] 50,000 markers).  To reach about the same accuracy as the conventional samplers for BayesC[Formula: see text] required less than 30 min using the BayesXII algorithm on 24 nodes (computer used as a server) with 24 cores on each node.  In this case, the BayesXII algorithm required one tenth of the computation time of conventional samplers for BayesC[Formula: see text]. 
BayesXII
Fast parallelized sampling of Bayesian regression models for whole-genome prediction.BACKGROUND
 Bayesian regression models are widely used in genomic prediction, where the effects of all markers are estimated simultaneously by combining the information from the phenotypic data with priors for the marker effects and other parameters such as variance components or membership probabilities.  Inferences from most Bayesian regression models are based on Markov chain Monte Carlo methods, where statistics are computed from a Markov chain constructed to have a stationary distribution that is equal to the posterior distribution of the unknown parameters.  In this paper, we propose a fast parallelized algorithm for Bayesian regression models called independent intensive Bayesian regression models (BayesXII, "X" stands for Bayesian alphabet methods and "II" stands for "parallel") and show how the sampling of each marker effect can be made independent of samples for other marker effects within each step of the chain. 
Bayesian regression models
Inferences from most Bayesian regression models are based on Markov chain Monte Carlo methods, where statistics are computed from a Markov chain constructed to have a stationary distribution that is equal to the posterior distribution of the unknown parameters. 
Markov chain Monte Carlo methods
Ideally, the computations at each step of the MCMC chain can be accelerated by k times, where k is the number of computer processors, up to p times, where p is the number of markers.



MCMC
We demonstrate the BayesXII algorithm using the prior for BayesC[Formula: see text], a Bayesian variable selection regression method, which is applied to simulated data with 50,000 individuals and a medium-density marker panel ([Formula: see text] 50,000 markers).  To reach about the same accuracy as the conventional samplers for BayesC[Formula: see text] required less than 30 min using the BayesXII algorithm on 24 nodes (computer used as a server) with 24 cores on each node.  In this case, the BayesXII algorithm required one tenth of the computation time of conventional samplers for BayesC[Formula: see text]. 
BayesC[Formula: see text]
We demonstrate the BayesXII algorithm using the prior for BayesC[Formula: see text], a Bayesian variable selection regression method, which is applied to simulated data with 50,000 individuals and a medium-density marker panel ([Formula: see text] 50,000 markers). 
Bayesian variable selection regression method