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Journal of the American Statistical Association
Sequential Monte Carlo Methods for Statistical Analysis of Tables
To cite this paper:
Yuguo Chen, Persi Diaconis, Susan P Holmes, Jun S Liu.
Journal of the American Statistical Association.
March 1, 2005,
100(469): 109-120.
doi:10.1198/016214504000001303.
Yuguo Chen, Persi Diaconis, Susan P. Holmes, and Jun S. LiuYuguo Chen is Assistant Professor, Institute of Statistics and Decision Sciences, Duke University, Durham, NC 27708 (E-mail: yuguo@stat.duke.edu). Persi Diaconis is Mary V. Sunseri Professor and Susan P. Holmes is Associate Professor (E-mail: susan@stat.stanford.edu), Department of Statistics, Stanford University, Stanford, CA 94305. Jun S. Liu is Professor, Department of Statistics and Department of Biostatistics, Harvard University, Cambridge, MA 02138 (E-mail: jliu@stat.harvard.edu). This work was supported in part by National Science Foundation grants DMS-02-03762, DMS-02-04674, and DMS-02-44638. The authors thank Arnab Chakraborty, Dylan Small, Charles Stein, the associate editor, and two referees for helpful discussions and valuable suggestions.
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.
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