## The Annals of Statistics

### 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 contingency tables.

#### Article information

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

Dates
First available in Project Euclid: 1 August 2013

https://projecteuclid.org/euclid.aos/1375362560

Digital Object Identifier
doi:10.1214/13-AOS1131

Mathematical Reviews number (MathSciNet)
MR3113822

Zentralblatt MATH identifier
1292.62083

#### Citation

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. https://projecteuclid.org/euclid.aos/1375362560

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