An Algorithm for Sampling Descent Graphs in Large Complex Pedigrees Efficiently

No exact method for determining genotypic and identity-by-descent probabilities is available for large, complex pedigrees. Approximate methods for such pedigrees cannot be guaranteed to be unbiased. Anew method is proposed that uses the Metropolis-Hastings algorithm to sample a Markov Chain of descent graphs which fit the pedigree and known genotypes. Unknown genotypes are determined from each descent graph. Genotypic probabilities are estimated as their means. The algorithm is shown to be unbiased for small, complex pedigrees and feasible and consistent for large complex pedigrees.