It is well known that estimation and prediction for multivariate models can be improved, in terms of mean squared error, by assuming that their effects come from a common underlying distribution. A common approach in quantitative genetics is to fit a mixed model in which genetic markers have random effects for which best linear unbiased predictors (BLUPs) are obtained [35]. This is one of several closely related formulations of multilevel models [36]. As these approaches tend to give similar results when the number of markers is large, a basic Bayesian estimation scheme is outlined here and will be assumed to give typical results for a shrinkage estimator.
