A nonparametric Bayesian approach for genetic evaluation in animal breeding

This article proposes the Bayesian approach to solve problems arising in animal breeding theory. General elements of Bayesian inferences, e.g. prior and posterior distributions, likelihood functions, and the solving of the random effects in the case of the mixed linear model are discussed. Since the random effects are typically assumed to be normally distributed in both the Bayesian and Classical models, a Bayesian procedure is provided which allows these random effects to have a nonparametric Dirichlet process prior distribution. In the case of the Dirichlet process, the Gibbs sampler is introduced to overcome some computational difficulties in solving the genetic parameters of the mixed linear model. To illustrate the application of these techniques, data from the Elsenburg Dormer sheep stud and data from a simulation experiment are utilized.