This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 235
Type: Contributed
Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
Sponsor: Biometrics Section
Abstract - #308125
Title: Exact Test of Hardy-Weinberg Equilibrium in Multi-Allelic Case via Markov Base
Author(s): Marepalli B. Rao*+ and Subramaniam Venkatesan and Subramanyam Kasala
Companies: University of Cincinnati and University of Cincinnati and University of North Carolina Wilmington
Address: Department of Environmental Health, Cincinnati, OH, 45267,
Keywords: Hardy-Weinberg ; Exact Test ; Algebraic Statistics ; Markov Base ; MCMC ; Alleles
Abstract:

If one wants to adapt Fisher's exact test module to test Hardy-Weinberg Equilibrium in multi-allelic cases, one faces the unenviable task of enumerating all possible matrices with non-negative entries, even diagonals, and prescribed row sums. The row sums come from the allelic frequencies computed from the given genotype data. The number of possible matrices under focus could be in the stratosphere. We invoke ideas from 'algebraic statistics' to manage the number. We describe a Markov Base for the fiber of all possible matrices of interest. Typically, the cardinality of the Markov Base is a manageable number. Knowing the fiber is equivalent to knowing its Markov Base. We demonstrate how the Markov Base can be used in tandem with MCMC algorithm to calculate the p-value of the given genotype data. There is no need to know the Fiber.


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