A note on accuracy of Bayesian LASSO regression in GWS

Abstract

Several genome wide selection (GWS) statistical methods have been proposed in the last years, and among these stands out the Bayesian LASSO (BL), which is a penalized regression method based on the regularization parameter (λ) estimates. In general, the posterior mean values for λ are those that minimize the residual sum of squares (RSS) while controlling the L1 norm (absolute values) of the regression coefficients. However, another option is to use fixed values of λ, which is independent of this minimization process. Nevertheless, the most important aim of GWS is to make predictions about genomic breeding values (GBV = u) for individuals that have not been measured directly for the trait, and for this reason the parameter to maximize should be the accuracy (). Thus, a question can arise as to whether such estimated λ values that minimize RSS are the same as that which maximize . In order to answer this question, this paper aims to provide methodological and computational resources in order to evaluate the influence of BL regularization parameter estimates on the correlation between true and estimated GBV (accuracy) depending on genetic structure of the target trait (few or many QTLs and low or medium heritability). In general, it is possible to report, on average, that GBV prediction is robust in relation to the λ estimation, since the different values for λ lead to similar accuracy values. Moreover, the fixed λ values grid request high computational costs, implying that the random λ method is more attractive, since it is much faster to use just one Gibbs sampler run, while the grid must to use one run for each fixed λ value.