Sampling for Conditional Inference on Contingency Tables

ABSTRACT

We propose new sequential importance sampling methods for sampling contingency tables with given margins. The proposal for each method is based on asymptotic approximations to the number of tables with fixed margins. These methods generate tables that are very close to the uniform distribution. The tables, along with their importance weights, can be used to approximate the null distribution of test statistics and calculate the total number of tables. We apply the methods to a number of examples and demonstrate an improvement over other methods in a variety of real problems. Supplementary materials are available online.

KEYWORDS:

• Counting problem
• Monte Carlo method
• Sequential importance sampling

Supplementary Materials

• C code: The supplemental files for this article include C programs, which can be used to replicate the simulation study included in the article. Please read file README contained in the zip file for more details. (SamplingTables.zip, zip archive)

• Appendix: The supplemental files include the Appendix, which gives the proofs of Proposal 1, Proposal 2, and Theorem 2. (SamplingTables.Appendix.pdf)

Acknowledgments

The authors are very grateful to the editor, the associate editor, and two referees for helpful suggestions. This research was partly supported by the National Science Foundation grant DMS-1406455.