2013
DOI: 10.1214/13-aos1131
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Exact sampling and counting for fixed-margin matrices

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 con… Show more

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Cited by 41 publications
(46 citation statements)
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References 36 publications
(58 reference statements)
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“…Until recently, there has been a dearth of methods for generating binary affiliation matrices with fixed margins, with the ones being used somewhat cumbersome and inefficient and too slow for application to large networks (Admiraal & Handcock, 2008; Chen, Diaconis, Holmes, & Liu, 2005). However, within the last few years, a pair of papers have appeared (Harrison & Miller, 2013; Miller & Harrison, 2013) that provide a computationally efficient method for generating affiliation matrices with fixed margins.…”
Section: Background For Proposed Testmentioning
confidence: 99%
“…Until recently, there has been a dearth of methods for generating binary affiliation matrices with fixed margins, with the ones being used somewhat cumbersome and inefficient and too slow for application to large networks (Admiraal & Handcock, 2008; Chen, Diaconis, Holmes, & Liu, 2005). However, within the last few years, a pair of papers have appeared (Harrison & Miller, 2013; Miller & Harrison, 2013) that provide a computationally efficient method for generating affiliation matrices with fixed margins.…”
Section: Background For Proposed Testmentioning
confidence: 99%
“…For some recent overview and results see e.g. Barvinok (2012), Miller et al (2013). In statistics this problem arises when evaluating tests for independence in contingency tables, for which the sampling needs to be done on the uniform distribution on all matrices.…”
Section: Introductionmentioning
confidence: 99%
“…Even for small k the enumeration problem is intractable: the number of 2 k tables with fixed margins grows exponentially in k. The work [64] presented an exhaustive algorithm to enumerate all 2 3 and 2 4 contingency tables with fixed margins, demonstrating for example that for n = 36, there are > 100 million 2 4 tables. Randomized and approximate counting methods for contingency tables have been developed (see, for example, [65,66] and references therein), although these generally do not provide a rigorous guarantee on the error in the approximation.…”
Section: Computing the Mutual Exclusivity Score (M)mentioning
confidence: 99%