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Importance sampling on coalescent histories. I. (English) Zbl 1045.62111
Summary: M. Stephens and P. Donnelly [J. R. Stat. Soc., Ser. B, Stat. Methodol. 62, 605–655 (2000; Zbl 0962.62107)] constructed an efficient sequential importance-sampling proposal distribution on coalescent histories of a sample of genes for computing the likelihood of a type configuration of genes in the sample. In the current paper, a characterization of their importance-sampling proposal distribution is given in terms of the diffusion-process generator describing the distribution of the population gene frequencies. This characterization leads to a new technique for constructing importance-sampling algorithms in a much more general framework when the distribution of population gene frequencies follows a diffusion process, by approximating the generator of the process.

62P10 Applications of statistics to biology and medical sciences; meta analysis
92D10 Genetics and epigenetics
60J70 Applications of Brownian motions and diffusion theory (population genetics, absorption problems, etc.)
62L99 Sequential statistical methods
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