A fast algorithm for BayesB type of prediction of genome-wide estimates of genetic value

Genomic selection uses genome-wide dense SNP marker genotyping for the prediction of genetic values, and consists of two steps: (1) estimation of SNP effects, and (2) prediction of genetic value based on SNP genotypes and estimates of their effects. For the former step, BayesB type of estimators have been proposed, which assume a priori that many markers have no effects, and some have an effect coming from a gamma or exponential distribution, i.e. a fat-tailed distribution. Whilst such estimators have been developed using Monte Carlo Markov chain (MCMC), here we derive a much faster non-MCMC based estimator by analytically performing the required integrations. The accuracy of the genome-wide breeding value estimates was 0.011 (s.e. 0.005) lower than that of the MCMC based BayesB predictor, which may be because the integrations were performed one-by-one instead of for all SNPs simultaneously. The bias of the new method was opposite to that of the MCMC based BayesB, in that the new method underestimates the breeding values of the best selection candidates, whereas MCMC-BayesB overestimated their breeding values. The new method was computationally several orders of magnitude faster than MCMC based BayesB, which will mainly be advantageous in computer simulations of entire breeding schemes, in cross-validation testing, and practical schemes with frequent re-estimation of breeding values.