318 research outputs found
Sequential importance sampling for multiway tables
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.Comment: Published at http://dx.doi.org/10.1214/009053605000000822 in the
Annals of Statistics (http://www.imstat.org/aos/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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