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Estimating the number of zero-one multi-way tables via sequential importance sampling

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  • Jing Xi
  • Ruriko Yoshida
  • David Haws

Abstract

In 2005, Chen et al. introduced a sequential importance sampling (SIS) procedure to analyze zero-one two-way tables with given fixed marginal sums (row and column sums) via the conditional Poisson (CP) distribution. They showed that compared with Monte Carlo Markov chain (MCMC)-based approaches, their importance sampling method is more efficient in terms of running time and also provides an easy and accurate estimate of the total number of contingency tables with fixed marginal sums. In this paper, we extend their result to zero-one multi-way ( $$d$$ -way, $$d \ge 2$$ ) contingency tables under the no $$d$$ -way interaction model, i.e., with fixed $$d-1$$ marginal sums. Also, we show by simulations that the SIS procedure with CP distribution to estimate the number of zero-one three-way tables under the no three-way interaction model given marginal sums works very well even with some rejections. We also applied our method to Samson’s monks data set. Copyright The Institute of Statistical Mathematics, Tokyo 2013

Suggested Citation

  • Jing Xi & Ruriko Yoshida & David Haws, 2013. "Estimating the number of zero-one multi-way tables via sequential importance sampling," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 65(4), pages 763-783, August.
    • Handle: RePEc:spr:aistmt:v:65:y:2013:i:4:p:763-783
    DOI: 10.1007/s10463-012-0392-7
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    References listed on IDEAS

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    1. Yuguo Chen & Persi Diaconis & Susan P. Holmes & Jun S. Liu, 2005. "Sequential Monte Carlo Methods for Statistical Analysis of Tables," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 109-120, March.
    2. Tom Snijders, 1991. "Enumeration and simulation methods for 0–1 matrices with given marginals," Psychometrika, Springer;The Psychometric Society, vol. 56(3), pages 397-417, September.
    3. Ian Dinwoodie, 2010. "Polynomials for classification trees and applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(2), pages 171-192, June.
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