Department of Statistics Seminar
North Carolina State University

presents

Elizabeth A. Thompson

University of Washington

"Monte Carlo Likelihood for Multipoint Linkage Analysis"

ABSTRACT

There are two dimensions to the conditional independence structure underlying multilocus data on related individuals. One is the pedigree structure; individuals receive copies of their parents' genes, and in turn pass copies to their offspring. The other is the linear structure of a chromosome: under simple models for meiosis the inheritance of genes follows a first-order Markov process along a chromosome. These two dimensions to structure have facilitated algorithms for exact computations on pedigrees, but exact computations are limited either to small pedigrees or to small numbers of loci.

Monte Carlo methods, including MCMC methods, allow estimation of conditional probabilities and likelihoods. In particular, MCMC methods allow estimation of multilocus location score curves --- the log-likelihood-ratio for linkage as a function of trait locus position against a fixed map of genetic markers. However, effective MCMC samplers have proved elusive for data at tightly linked loci, sparsely observed on extended complex pedigrees. Recently several different block updating schemes have been proposed. The current talk will focus on one of these, the M-sampler. This is a Gibbs sampler in which joint updates are made for the inheritance of all genes at linked loci, in a single meiosis. The sampler has proven effective in some cases in which other samplers show poor mixing: it can be further improved, by updating several meioses jointly. By incorporating a etropolis-Hastings step into the sampler, it can also accommodate more general meiosis models.

Examples will be discussed.

Monday, May 3, 1999

9:00 - 10:00 am

Stephens Room, 3353 Gardner Hall

Coffee and Doughnuts will be served before the seminar.