Exact sampling and counting for fixed-margin matrices
Jeffrey W. Miller, Matthew T. Harrison
The Annals of Statistics · 2013 · Volume 41 · Issue 3
Abstract
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.
Keywords
05A15, 62H15, 62H17, binary matrix, Contingency table, exact counting, exact sampling, integer points in polyhedra
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