MCMC Estimation of Multi‐locus Genome Sharing and Multipoint Gene Location Scores

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Abstract
Summary: Effective linkage detection and gene mapping requires analysis of data jointly on members of extended pedigrees, jointly at multiple genetic markers. Exact likelihood computation is then often infeasible, but Markov chain Monte Carlo (MCMC) methods permit estimation of posterior probabilities of genome sharing among relatives, conditional upon marker data. In principle, MCMC also permits estimation of linkage analysis location score curves, but in practice effective MCMC samplers are hard to find. Although the whole‐meiosis Gibbs sampler (M‐sampler) performs well in some cases, for extended pedigrees and tightly linked markers better samplers are needed. However, using the M‐sampler as a proposal distribution in a Metropolis‐Hastings algorithm does allow genetic interference to be incorporated into the analysis.