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Paper No. 14-12

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J Koskela, P Jenkins and D Spano

Computational inference beyond Kingman's coalescent

Abstract: Full likelihood inference under Kingman's coalescent is a computationally challenging problem. Importance sampling (IS) has been a successful means of solving this problem, and in recent decades much work has been done on designing good, and in some cases optimal IS algorithms. A parallel development in mathematical population genetics has been the emergence of more general coalescents and {coalescents, which provide better modelling its to some data sets. In this paper we aim to mitigate this cost by deriving an approximately optimal" IS algorithm by expressing the optimal proposal distribution in terms of certain intractable sampling distributions, and obtaining principled, tractable approximations to them. Results from {coalescents are also compared to existing methodology based on the Griffiths{Tavar recursion. Empirical tests suggest a noticeable improvement in accuracy, and an improvement in effciency of up to two orders of magnitude.