De Iorio, M and Griffiths, RC (2004) Importance sampling on coalescent histories. II: Subdivided population models. ADV APPL PROBAB , 36 (2) 434 - 454.
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De Iorio and Griffiths (2004) developed a new method of constructing sequential importance-sampling proposal distributions on coalescent histories of a sample of genes for computing the likelihood of a type configuration of genes in the sample by simulation. The method is based on approximating the diffusion-process generator describing the distribution of population gene frequencies, leading to an approximate sample distribution and finally to importance-sampling proposal distributions. This paper applies that method to construct an importance-sampling algorithm for computing the likelihood of samples of genes in subdivided population models. The importance-sampling technique of Stephens and Donnelly (2000) is thus extended to models with a Markov chain mutation mechanism between gene types and migration of genes between subpopulations. An algorithm for computing the likelihood of a sample configuration of genes from a subdivided population in an infinitely-many-alleles model of mutation is derived, extending Ewens's (1972) sampling formula in a single population. Likelihood calculation and ancestral inference in gene trees constructed from DNA sequences under the infinitely-many-sites model are also studied. The Griffiths-Tavare method of likelihood calculation in gene trees of Bahlo and Griffiths (2000) is improved for subdivided populations.
|Title:||Importance sampling on coalescent histories. II: Subdivided population models|
|Keywords:||coalescent process, diffusion process, importance sampling, migration, subdivided population, NEUTRAL ALLELES, GENE TREES, INFERENCE, RATES|
|UCL classification:||UCL > School of BEAMS > Faculty of Maths and Physical Sciences > Statistical Science|
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