Genet. Sel. Evol. 39 (2007) 123-137
DOI: 10.1051/gse:2006038

Influence of priors in Bayesian estimation of genetic parameters for multivariate threshold models using Gibbs sampling

Kathrin Friederike Stock^a, Ottmar Distl^a and Ina Hoeschele<sup>b

a</sup>  Institute for Animal Breeding and Genetics, University of Veterinary Medicine Hannover (Foundation), Buenteweg 17p, D-30559 Hannover, Germany
^b  Virginia Bioinformatics Institute and Department of Statistics, Virginia Polytechnic Institute and State University, Blacksburg, Virginia, USA

(Received 26 April 2006; accepted 24 October 2006 ; published online 17 February 2007)

Abstract - Simulated data were used to investigate the influence of the choice of priors on estimation of genetic parameters in multivariate threshold models using Gibbs sampling. We simulated additive values, residuals and fixed effects for one continuous trait and liabilities of four binary traits, and QTL effects for one of the liabilities. Within each of four replicates six different datasets were generated which resembled different practical scenarios in horses with respect to number and distribution of animals with trait records and availability of QTL information. (Co)Variance components were estimated using a Bayesian threshold animal model via Gibbs sampling. The Gibbs sampler was implemented with both a flat and a proper prior for the genetic covariance matrix. Convergence problems were encountered in > 50% of flat prior analyses, with indications of potential or near posterior impropriety between about round 10 000 and 100 000. Terminations due to non-positive definite genetic covariance matrix occurred in flat prior analyses of the smallest datasets. Use of a proper prior resulted in improved mixing and convergence of the Gibbs chain. In order to avoid (near) impropriety of posteriors and extremely poorly mixing Gibbs chains, a proper prior should be used for the genetic covariance matrix when implementing the Gibbs sampler.

Key words: Gibbs sampling / multivariate threshold model / covariance estimates / flat prior / proper prior

Correspondence and reprints: Kathrin-Friederike.Stock@tiho-hannover.de

© INRA, EDP Sciences 2007