AN ALGORITHM FOR MONTE-CARLO ESTIMATION OF GENOTYPE PROBABILITIES ON COMPLEX PEDIGREES

Exact probability and likelihood computation on complex pedigrees is often infeasible, since exact methods are too computationally intensive even with today's computing technology. A statistical tool, Markov chain Monte Carlo (MCMC), is increasingly being explored as a technique for estimating probabilities of genotypic configurations on pedigrees conditional on phenotypic data. However, this conditional probability distribution on a complex pedigree is, in general, multimodal, and multimodality is one of the major difficulties in MCMC exploration of a probability surface. In this paper, a new member of the MCMC Metropolis-Hastings class of algorithms is proposed; the heated-Metropolis algorithm. The algorithm achieves passage through low probability states to other local modes of the probability distribution, and so provides much improved estimates of probabilities of interest. The example considered is the estimation of the probabilities of carrier genotype for the founders of a complex pedigree in which a very rare lethal recessive trait is segregating.