Computational inference beyond Kingman's coalescent

Abstract

Full likelihood inference under Kingman's coalescent is a computationally challenging problem to which importance sampling (IS) and the product of approximate conditionals (PAC) method have been applied successfully. Both methods can be expressed in terms of families of intractable conditional sampling distributions (CSDs), and rely on principled approximations for accurate inference. Recently, more general $\Lambda$- and $\Xi$-coalescents have been observed to provide better modelling fits to some genetic data sets. We derive families of approximate CSDs for finite sites $\Lambda$- and $\Xi$-coalescents, and use them to obtain "approximately optimal" IS and PAC algorithms for $\Lambda$-coalescents, yielding substantial gains in efficiency over existing methods.

20 pages, 5 figures

References in corpus (3)

• A modified lookdown construction for the Xi-Fleming-Viot process with mutation and populations with recurrent bottlenecks
• A sequentially Markov conditional sampling distribution for structured populations with migration and recombination
• Importance sampling for Lambda-coalescents in the infinitely many sites model

Cited by in corpus (5)

• Multi-locus data distinguishes between population growth and multiple merger coalescents
• Bayesian non-parametric inference for $\Lambda$-coalescents: consistency and a parametric method
• Asymptotic behaviour of sampling and transition probabilities in coalescent models under selection and parent dependent mutations
• Weak convergence of the scaled jump chain and number of mutations of the Kingman coalescent
• Large-sample analysis of cost functionals for inference under the coalescent