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TitleSequential importance sampling for multiway tables.
Author(s) Yu-Fu Chen, Ian H. Dinwoodie, Seth Sullivant
TypeArticle in Journal
AbstractWe 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.
ISSN0090-5364; 2168-8966/e
URL http://projecteuclid.org/euclid.aos/1146576273
LanguageEnglish
JournalAnn. Stat.
Volume34
Number1
Pages523--545
PublisherInstitute of Mathematical Statistics (IMS), Beachwood, OH/Bethesda, MD
Year2006
Edition0
Translation No
Refereed No
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