Importance sampling on coalescent histories. II: Subdivided population models

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...

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Bibliographic Details
Published in:Advances in applied probability 2004-06, Vol.36 (2), p.434-454
Main Authors: De Iorio, Maria, Griffiths, Robert C.
Format: Article
Language:English
Subjects:
60G40
92D25
93E25
Alleles
Coalescent process
diffusion process
Founder effect
General Applied Probability
Genes
Genetic algorithms
Genetic mutation
importance sampling
Inference
Markov analysis
Markov chains
Mathematics
migration
Mutation
Population
Population distributions
Population migration
Probability
Probability distributions
Sampling distributions
Sampling techniques
subdivided population
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Summary: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-Tavaré method of likelihood calculation in gene trees of Bahlo and Griffiths (2000) is improved for subdivided populations.
ISSN:0001-8678
1475-6064
DOI:10.1239/aap/1086957580