The Annals of Statistics

Exact sampling and counting for fixed-margin matrices

Jeffrey W. Miller and Matthew T. Harrison

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The uniform distribution on matrices with specified row and column sums is often a natural choice of null model when testing for structure in two-way tables (binary or nonnegative integer). Due to the difficulty of sampling from this distribution, many approximate methods have been developed. We will show that by exploiting certain symmetries, exact sampling and counting is in fact possible in many nontrivial real-world cases. We illustrate with real datasets including ecological co-occurrence matrices and contingency tables.

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Ann. Statist. Volume 41, Number 3 (2013), 1569-1592.

First available in Project Euclid: 1 August 2013

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Zentralblatt MATH identifier

Primary: 62H15: Hypothesis testing
Secondary: 62H17: Contingency tables 05A15: Exact enumeration problems, generating functions [See also 33Cxx, 33Dxx]

Exact sampling exact counting binary matrix contingency table integer points in polyhedra


Miller, Jeffrey W.; Harrison, Matthew T. Exact sampling and counting for fixed-margin matrices. Ann. Statist. 41 (2013), no. 3, 1569--1592. doi:10.1214/13-AOS1131.

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