Open Access

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

  • Kathrin Friederike Stock1Email author,
  • Ottmar Distl1 and
  • Ina Hoeschele2
Genetics Selection Evolution200739:123

Received: 26 April 2006

Accepted: 24 October 2006

Published: 17 February 2007


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.


Gibbs sampling multivariate threshold model covariance estimates flat prior proper prior

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Authors’ Affiliations

Institute for Animal Breeding and Genetics, University of Veterinary Medicine Hannover (Foundation)
Virginia Bioinformatics Institute and Department of Statistics, Virginia Polytechnic Institute and State University


© INRA, EDP Sciences 2007