Sequential importance sampling for multiway tables

Details Sequential importance sampling for multiway tables Sequential importance sampling for multiway tables

2006-05-23

arxiv.org/abs/math/0605615v1

Annals of Statistics 2006, Vol. 34, No. 1, 523-545

Mathematics

Statistics Theory

Published at http://dx.doi.org/10.1214/009053605000000822 in the Annals of Statistics (http://www.imstat.org/aos/) by the Inst

Scientific paper

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 Gr\"{o}bner 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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