Tuyển tập các báo cáo nghiên cứu về sinh học được đăng trên tạp chí sinh học thế giới đề tài: Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects | 137 Genet Sei. Evol. 35 2003 137-158 INRA EDP Sciences 2003 DOI gse 2003001 Original article BaYesian estimation in animal breeding using the Dirichlet process prior for correlated random effects Abraham Johannes van der Merwe Albertus Lodewikus Pretorius Department of Mathematical Statistics FacultY of Science UniversitY of the Free State PO Box 339 Bloemfontein 9300 Republic of South Africa Received 12 JuIy 2001 accepted 23 August 2002 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 1. introduction In animal breeding applications it is usually assumed that the data follows a mixed linear model. Mixed linear models are naturally modelled within the Bayesian framework. The main advantage of a Bayesian approach is that it allows explicit use of prior information thereby giving new insights in problems where classical statistics fail. In the
