Details:
Title  Sequential importance sampling for multiway tables.  Author(s)  YuFu Chen, Ian H. Dinwoodie, Seth Sullivant  Type  Article in Journal  Abstract  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.  ISSN  00905364; 21688966/e 
URL 
http://projecteuclid.org/euclid.aos/1146576273 
Language  English  Journal  Ann. Stat.  Volume  34  Number  1  Pages  523545  Publisher  Institute of Mathematical Statistics (IMS), Beachwood, OH/Bethesda, MD  Year  2006  Edition  0  Translation 
No  Refereed 
No 
