Issue |
Genet. Sel. Evol.
Volume 35, Number 2, March-April 2003
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|
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Page(s) | 137 - 158 | |
DOI | https://doi.org/10.1051/gse:2003001 |
DOI: 10.1051/gse:2003001
Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects
Abraham Johannes van der Merwe and Albertus Lodewikus PretoriusDepartment of Mathematical Statistics, Faculty of Science, University of the Free State, PO Box 339, Bloemfontein, 9300 Republic of South Africa
(Received 12 July 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.
Key words: Bayesian methods / mixed linear model / Dirichlet process prior / correlated random effects / Gibbs sampler
Correspondence and reprints: Abraham Johannes van der Merwe
e-mail: fay@wwg3.uovs.ac.za
© INRA, EDP Sciences 2003