Bayesian analysis of calving ease scores and birth weights

Abstract

In a typical two stage procedure, breeding value prediction for calving ease in a threshold model is conditioned on estimated genetic and residual covariance matrices. These covariance matrices are traditionally estimated using analytical approximations. A Gibbs sampler for making full Bayesian inferences about fixed effects, breeding values, thresholds and genetic and residual covariance matrices to analyze jointly a discrete trait with multiple ordered categories (calving ease scores) and a continuously Gaussian distributed trait (birth weights) is described. The Gibbs sampler is implemented by drawing from a set of densities - (truncated) normal, uniform and inverted Wishart - making implementation of Gibbs sampling straightforward. The method should be useful for estimating genetic parameters based on features of their marginal posterior densities taking into full account uncertainties in estimating other parameters. For routine, large-scale estimation of location parameters (breeding values), Gibbs sampling is impractical. The joint posterior mode given the posterior mean estimates of thresholds and dispersion parameters is suggested. An analysis of simulated calving ease scores and birth weights is described.