Title
An Algorithm to Sample Genotypes in Complex Pedigrees
Speaker
Soledad Fernandez, The Ohio State University
Abstract
Markov chain Monte Carlo (MCMC) methods have been proposed to overcome computational problems in linkage and segregation analyses. This approach involves sampling genotypes at the marker and trait loci. Scalar-Gibbs is easy to implement, and it is widely used in genetics. However, the Markov chain that corresponds to scalar-Gibbs may not be irreducible when the marker locus has more than two alleles, and even when the chain is irreducible, mixing has been observed to be slow. These problems do not arise if the genotypes are sampled jointly from the entire pedigree. Here, a method to jointly sample genotypes is proposed. The method combines the Elston-Stewart algorithm and iterative peeling, and is called the ESIP sampler. The ESIP sampler yields an irreducible Markov chain, regardless of the number of alleles at a locus. For a hypothetical pedigree, genotype probabilities of biallelic disease locus are estimated from samples obtained using ESIP and also scalar-Gibbs. Approximate probabilities were also obtained by iterative peeling. Comparisons of these with exact genotypic probabilities obtained by the Elston-Stewart algorithm showed that ESIP and iterative peeling yielded genotypic probabilities that were very close to the exact values. On the other hand, estimated probabilities from scalar-Gibbs with a chain of length 235,000, including a burn-in of 200,000 steps, were less accurate than probabilities estimated using ESIP with a chain of length 10,000, with a burn-in of 5,000 steps. Genotype probabilities were also estimated for a large real pedigree consisting of 3,223 individuals. For this pedigree, it is not feasible to obtain exact genotype probabilities by the Elston-Stewart algorithm. ESIP and iterative peeling yielded very similar results. However, results from scalar-Gibbs were less accurate. Further, for loci with more than two alleles, results obtained by ESIP sampler are compared with other methods in the literature. Of the methods that are guaranteed to be irreducible, ESIP was the most efficient.
Meet the speaker in Room 212 Cockins Hall at 4:30 p.m. Refreshments will be served.
