title: Importance sampling for Lambda-coalescents in the infinitely many sites model.
abstract: We present and discuss new importance sampling schemes for the approximate computation of the sample probability of observed genetic types in the infinitely many sites model from population genetics. More specifically, we extend the 'classical framework', where genealogies are assumed to be governed by Kingman's coalescent, to the more general class of Lambda-coalescents and develop further Hobolth et al.'s (2008) idea of deriving importance sampling schemes based on 'compressed genetrees'. The resulting schemes extend earlier work by Griffiths and Tavaré (1994), Stephens and Donnelly (2000), Birkner and Blath (2008) and Hobolth et al. (2008). We conclude with a performance comparison of classical and new schemes for Beta- and Kingman coalescents.
authors.affiliation: Johannes-Gutenberg-Universität Mainz, Institut für Mathematik, Staudingerweg 9, 55099 Mainz, Germany. birkner@mathematik.uni-mainz.de
authors.forename: Matthias
authors.initials: M
authors.lastname: Birkner
authors.forename: Jochen
authors.initials: J
authors.lastname: Blath
authors.forename: Matthias
authors.initials: M
authors.lastname: Steinrücken
mesh_terms: D000818:Animals; D019143:Evolution, Molecular; D005787:Gene Frequency / Q000235:genetics*; D005828:Genetics, Population / Q000379:methods*; D008390:Markov Chains; D008957:Models, Genetic; D009010:Monte Carlo Method; D009154:Mutation / Q000235:genetics*; D012494:Sampling Studies