-In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.Bayesian methods / mixed linear model / Dirichlet process prior / correlated random effects / Gibbs sampler

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.

No abstract

-In the case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks. In this paper, the Dirichlet process prior was used to provide nonparametric Bayesian estimates for correlated random effects. This goal was achieved by providing a Gibbs sampler algorithm that allows these correlated random effects to have a nonparametric prior distribution. A sampling based method is illustrated. This method which is employed by transforming the genetic covariance matrix to an identity matrix so that the random effects are uncorrelated, is an extension of the theory and the results of previous researchers. Also by using Gibbs sampling and data augmentation a simulation procedure was derived for estimating the precision parameter M associated with the Dirichlet process prior. All needed conditional posterior distributions are given. To illustrate the application, data from the Elsenburg Dormer sheep stud were analysed. A total of 3325 weaning weight records from the progeny of 101 sires were used.Bayesian methods / mixed linear model / Dirichlet process prior / correlated random effects / Gibbs sampler

No abstract