Issue |
Genet. Sel. Evol.
Volume 34, Number 5, September-October 2002
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Page(s) | 537 - 555 | |
DOI | https://doi.org/10.1051/gse:2002022 |
DOI: 10.1051/gse:2002022
Irreducibility and efficiency of ESIP to sample marker genotypes in large pedigrees with loops
Soledad A. Fernándeza, Rohan L. Fernandob, Bernt Guldbrandtsenc, Christian Strickerd, Matthias Schellingd and Alicia L. Carriquiryea Department of Statistics, 317 Cockins Hall, Ohio State University, Columbus, OH 43210, USA
b Department of Animal Science, 225 Kildee Hall, Iowa State University, Ames, IA 50011, USA
c Danish Institute of Animal Science, Foulum, Denmark
d Institute of Animal Sciences, Swiss Federal Institute of Technology, ETH-Zentrum CLU, 8092 Zürich, Switzerland
e Department of Statistics, 219 Snedecor Hall, Iowa State University, Ames, IA 50011, USA
(Received 21 August 2001; accepted 6 May 2002)
Abstract
Markov chain Monte Carlo (MCMC) methods have been proposed to overcome
computational problems in linkage and segregation analyses. This
approach involves sampling genotypes at the marker and trait loci.
Among MCMC methods, scalar-Gibbs is the easiest to implement, and it
is used in genetics. However, the Markov chain that corresponds to
scalar-Gibbs may not be irreducible when the marker locus has more
than two alleles, and even when the chain is irreducible, mixing has
been observed to be slow. Joint sampling of genotypes has been
proposed as a strategy to overcome these problems. An algorithm that
combines the Elston-Stewart algorithm and iterative peeling (ESIP
sampler) to sample genotypes jointly from the entire pedigree is used
in this study. Here, it is shown that the ESIP sampler yields an
irreducible Markov chain, regardless of the number of alleles at a
locus. Further, results obtained by ESIP sampler are compared with
other methods in the literature. Of the methods that are guaranteed to
be irreducible, ESIP was the most efficient.
Key words: Metropolis-Hastings / irreducibility / Elston-Stewart algorithm / iterative peeling
Correspondence and reprints: Rohan L. Fernando
e-mail: rohan@iastate.edu
© INRA, EDP Sciences 2002