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February 2006 Sequential importance sampling for multiway tables
Yuguo Chen, Ian H. Dinwoodie, Seth Sullivant
Ann. Statist. 34(1): 523-545 (February 2006). DOI: 10.1214/009053605000000822


We describe an algorithm for the sequential sampling of entries in multiway contingency tables with given constraints. The algorithm can be used for computations in exact conditional inference. To justify the algorithm, a theory relates sampling values at each step to properties of the associated toric ideal using computational commutative algebra. In particular, the property of interval cell counts at each step is related to exponents on lead indeterminates of a lexicographic Gröbner basis. Also, the approximation of integer programming by linear programming for sampling is related to initial terms of a toric ideal. We apply the algorithm to examples of contingency tables which appear in the social and medical sciences. The numerical results demonstrate that the theory is applicable and that the algorithm performs well.


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Yuguo Chen. Ian H. Dinwoodie. Seth Sullivant. "Sequential importance sampling for multiway tables." Ann. Statist. 34 (1) 523 - 545, February 2006.


Published: February 2006
First available in Project Euclid: 2 May 2006

zbMATH: 1091.62051
MathSciNet: MR2275252
Digital Object Identifier: 10.1214/009053605000000822

Primary: 62F03 , 62H17
Secondary: 13P10

Keywords: conditional inference , Contingency table , exact test , Monte Carlo , sequential importance sampling , toric ideal

Rights: Copyright © 2006 Institute of Mathematical Statistics


Vol.34 • No. 1 • February 2006
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