Sequential Monte Carlo methods for statistical analysis of tables

Yuguo Chen, Persi Diaconis, Susan P. Holmes, Jun S. Liu

Research output: Contribution to journalArticlepeer-review


We describe a sequential importance sampling (SIS) procedure for analyzing two-way zero-one or contingency tables with fixed marginal sums. An essential feature of the new method is that it samples the columns of the table progressively according to certain special distributions. Our method produces Monte Carlo samples that are remarkably close to the uniform distribution, enabling one to approximate closely the null distributions of various test statistics about these tables. Our method compares favorably with other existing Monte Carlo-based algorithms, and sometimes is a few orders of magnitude more efficient. In particular, compared with Markov chain Monte Carlo (MCMC)-based approaches, our importance sampling method not only is more efficient in terms of absolute running time and frees one from pondering over the mixing issue, but also provides an easy and accurate estimate of the total number of tables with fixed marginal sums, which is far more difficult for an MCMC method to achieve.

Original languageEnglish (US)
Pages (from-to)109-120
Number of pages12
JournalJournal of the American Statistical Association
Issue number469
StatePublished - Mar 2005
Externally publishedYes


  • Conditional inference
  • Contingency table
  • Counting problem
  • Exact test
  • Sequential importance sampling
  • Zero-one table

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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