Bayesian Inference on Variance and Covariance Components for Traits Influenced by Maternal and Direct Genetic Effects, Using the Gibbs Sampler

A method for analyzing traits influenced by both maternal and direct genetic effects is presented in a Bayesian setting. A Bayesian analysis requires full marginalization of the joint posterior density. The necessary multidimensional integrations were carried out using the Gibbs sampler. This gives the possibility of exact marginal inference on (co)variance components of interest as opposed to results of REML analysis, where only joint inferences are possible. The method is illustrated by an example on growth in sheep.