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Möhle, M.

Simulation algorithms for integrals of a class of sampling distributions arising in population genetics. (English) Zbl 1080.62091

J. Stat. Comput. Simulation 75, No. 9, 731-749 (2005).
Summary: Efficient stochastic algorithms are presented in order to simulate allele configurations distributed according to a family \(\pi_A\), \(0<A< \infty\), of exchangeable sampling distributions arising in population genetics. Each distribution \(\pi_A\) has two parameters \(n\) and \(k\), the sample size and the number of alleles, respectively. For \(A\to 0\), the distribution \(\pi_A\) is induced from neutral sampling, whereas for \(A\to \infty\), it is induced from Maxwell-Boltzmann sampling.
Three different Monte Carlo methods (independent sampling procedures) are provided, based on conditioning, sequential methods and a generalization of Pitmans ‘Chinese restaurant process’. Moreover, an efficient Markov chain Monte Carlo method is provided. The algorithms are applied to the homozygosity test and to the Ewens-Watterson-Slatkin test in order to test the hypothesis of selective neutrality.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
65C05 Monte Carlo methods
92D10 Genetics and epigenetics
65C40 Numerical analysis or methods applied to Markov chains
62E17 Approximations to statistical distributions (nonasymptotic)
65D30 Numerical integration

Keywords:

Chinese restaurant process; Ewens sampling distribution; Independent sampling; Markov chain Monte Carlo; Neutrality tests; Neutral population genetics
PDFBibTeX XMLCite
\textit{M. Möhle}, J. Stat. Comput. Simulation 75, No. 9, 731--749 (2005; Zbl 1080.62091)
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