Bayesian estimation in animal breeding using the Dirichlet process prior for correlated random effects

Abraham Johannes Van Der Merwe,Albertus Lodewikus Pretorius

doi:10.1051/gse:2003001

Abraham Johannes Van Der Merwe, Albertus Lodewikus Pretorius

Open Access

https://doi.org/10.1051/gse:2003001

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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.

Highlights

In animal breeding applications, it is usually assumed that the data follows a mixed linear model
And II, it is clear that the point estimates and 95% credibility intervals of σε2 using restricted maximum likelihood (REML) or Bayesian methods are for all practical purposes the same. This comes as no surprise since the posterior density of the error variance is not directly influenced by the Dirichlet process prior
We extended the results of Ibrahim and Kleinman [13] by placing a vague prior on M and simulating its posterior distribution

Summary

Introduction

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 case of the mixed linear model the random effects are usually assumed to be normally distributed in both the Bayesian and classical frameworks.

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