A Framework for Prediction of Breeding Value

Abstract

Inferences in a univariate normal linear model with two components of variance are discussed from a Bayesian perspective. When variances are known, three scenarios are considered: unknown “nuisance” parameters (β) and breeding values (u), unknown β and known u, and unknown u and known β. With unknown variances, several situations with corresponding predictors of breeding value are considered; the predictors differ in the degree of marginalization with respect to nuisance parameters and variance components, and in all these cases, inverted chi-square distributions are used as priors for the variance components. Prediction is discussed using the concept of a loss function, and it is argued that uniformly best predictors cannot be obtained in a classical framework, unless attention is restricted to the class of unbiased statistics. However, there is an unequivocal Bayesian solution. Model choice and prediction of future observations are also discussed.