Journal Article

Exact test of Hardy–Weinberg equilibrium by Markov chain Monte Carlo

Ao Yuan and George E. Bonney

in Mathematical Medicine and Biology: A Journal of the IMA

Published on behalf of Institute of Mathematics and its Applications

Volume 20, issue 4, pages 327-340
Published in print December 2003 | ISSN: 1477-8599
Published online December 2003 | e-ISSN: 1477-8602 | DOI:
Exact test of Hardy–Weinberg equilibrium by Markov chain Monte Carlo

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  • Applied Mathematics
  • Biomathematics and Statistics


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The assumption of Hardy–Weinberg equilibrium (HWE) among alleles is of fundamental importance in genetic studies. There are numerous testing methods for it using genotype counts data. The exact test is used when the sample size is not large enough for asymptotic approximations. There are several numerical methods to carry out this test, such as complete enumeration, Monte Carlo and Markov chain Monte Carlo simulations. Complete enumeration is impractical in many applications, especially when the table counts are large. The Monte Carlo method is simple to use but still difficult when the table counts become large. The Markov chain Monte Carlo method, by sampling a sub‐table each time, is suitable for this latter situation. Based on switches among a few (no more than four) cells, the existing Markov chain samplers are highly dependent and inefficient for large tables. Here we consider a new Markov chain sampling, in which a sub‐table of user‐specified size is updated at each iteration. The resulting chain is less dependent, and the sampling is flexible and efficient. The conventional test for HWE is based on a few test statistics, such as the likelihood and the chi‐squared statistic. To expand the family of test statistics, we consider a class of divergence measures for the departure of HWE. Examples are given as illustrations.

Keywords: allele; exact test; Hardy–Weinberg equilibrium; Markov chain Monte Carlo; Monte Carlo

Journal Article.  0 words. 

Subjects: Applied Mathematics ; Biomathematics and Statistics

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