On the application of Markov chain Monte Carlo methods to genetic analyseson complex pedigrees

Markov chain Monte Carlo methods are frequently used in the analyses of gen etic data on pedigrees for the estimation of probabilities and likelihoods which cannot be calculated by existing exact methods. In the case of discre te data, the underlying Markov chain may be reducible and care must be take n to ensure that reliable estimates are obtained. Potential reducibility th us has implications for the analysis of the mixed inheritance model, for ex ample, where genetic variation is assumed to be due to one single locus of large effect and many loci each with a small effect. Similarly, reducibilit y arises in the detection of quantitative trait loci from incomplete discre te marker data. This paper aims to describe the estimation problem in terms of simple discrete genetic models and the single-site Gibbs sampler. Reduc ibility of the Gibbs sampler is discussed and some current methods for circ umventing the problem outlined.