Markov Chain Monte Carlo Methods for Radiation Hybrid Mapping

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Abstract
The ordering of genetic loci is central to genetic mapping at all levels. Markov chain Monte Carlo (MCMC) techniques can provide estimates of the posterior density of orders while accounting naturally for missing data, data errors, and unknown parameters. MCMC sampling schemes have been proposed for mapping problems such as linkage mapping and radiation hybrid mapping. The sampling schemes tend, however, to suffer from poor mixing caused by strong correlations between the model parameters. The method described here investigates the effect of using a modified sampling scheme, simulated tempering, on the mixing characteristics of the Markov chain. The method is illustrated by the analysis of haploid radiation hybrid mapping data; the principles are, however, applicable to a range of mapping problems. The results demonstrate that simulated tempering greatly improves the performance of the MCMC sampling scheme. For the radiation hybrid problem, the approach is probably not suitable for simultaneously ordering very large number of loci (>100); it could, however, be useful for fine scale mapping of subsections of chromosomes. Key words: Markov chain Monte Carlo, simulated tempering, locus ordering, radiation hybrid mapping