Importance sampling for Lambda-coalescents in the infinitely many sites model

TL;DR

This paper develops new importance sampling methods for genetic data analysis under Lambda-coalescents, extending classical models to more general genealogies and comparing their performance.

Contribution

It introduces importance sampling schemes based on compressed genetrees for Lambda-coalescents, generalizing previous methods and enhancing computational approaches in population genetics.

Findings

New schemes outperform classical methods in certain scenarios

Performance varies between Beta- and Kingman coalescents

Extensions enable analysis of more complex genealogical models

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 Tavar\'e (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.