Premium
On the Application of Markov Chain Monte Carlo Methods to Genetic Analyses on Complex Pedigrees
Author(s) -
Sheehan N. A.
Publication year - 2000
Publication title -
international statistical review
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.051
H-Index - 54
eISSN - 1751-5823
pISSN - 0306-7734
DOI - 10.1111/j.1751-5823.2000.tb00389.x
Subject(s) - pedigree chart , markov chain monte carlo , gibbs sampling , markov chain , monte carlo method , computer science , inheritance (genetic algorithm) , mathematics , statistics , bayesian probability , genetics , biology , gene
Summary Markov chain Monte Carlo methods are frequently used in the analyses of genetic data on pedigrees for the estimation of probabilities and likelihoods which cannot be calculated by existing exact methods. In the case of discrete data, the underlying Markov chain may be reducible and care must be taken to ensure that reliable estimates are obtained. Potential reducibility thus has implications for the analysis of the mixed inheritance model, for example, where genetic variation is assumed to be due to one single locus of large effect and many loci each with a small effect. Similarly, reducibility arises in the detection of quantitative trait loci from incomplete discrete marker data. This paper aims to describe the estimation problem in terms of simple discrete genetic models and the single‐site Gibbs sampler. Reducibility of the Gibbs sampler is discussed and some current methods for circumventing the problem outlined.