Sequential Monte Carlo methods for statistical analysis of tables

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.