Genet. Sel. Evol. 39 (2007) 27-38
DOI: 10.1051/gse:2006032

Improved techniques for sampling complex pedigrees with the Gibbs sampler

K. Joseph Abraham^a, Liviu R. Totir^b and Rohan L. Fernando<sup>b, c

a</sup>  1301 Agronomy Hall, Iowa State University, Ames, IA 50011, USA
^b  Department of Animal Science, Iowa State University, Ames, IA 50011, USA
^c  Lawrence H. Baker Center for Bioinformatics and Biological Statistics, Iowa State University, Ames, IA 50011, USA

(Received 5 January 2006; accepted 3 September 2006; published online 11 January 2007)

Abstract - Markov chain Monte Carlo (MCMC) methods have been widely used to overcome computational problems in linkage and segregation analyses. Many variants of this approach exist and are practiced; among the most popular is the Gibbs sampler. The Gibbs sampler is simple to implement but has (in its simplest form) mixing and reducibility problems; furthermore in order to initiate a Gibbs sampling chain we need a starting genotypic or allelic configuration which is consistent with the marker data in the pedigree and which has suitable weight in the joint distribution. We outline a procedure for finding such a configuration in pedigrees which have too many loci to allow for exact peeling. We also explain how this technique could be used to implement a blocking Gibbs sampler.

Key words: Gibbs sampler / Markov chain Monte Carlo / pedigree peeling / Elston Stewart algorithm

Correspondence and reprints: abraham@iastate.edu

© INRA, EDP Sciences 2006