Estimating the number of 0-1 multi-way tables via sequential importance sampling

In 2005, Chen et al introduced a sequential importance sampling (SIS) procedure to analyze 0-1 two-way tables with given fixed marginal sums (row and column sums) via the conditional Poisson (CP) distribution. They showed that compared with Markov chain Monte Carlo (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 extended their result to 0-1 multi-way ($d$-way, $d \geq 2$) contingency tables under the no $d$-way interaction model, i.e., with fixed $d - 1$ marginal sums. Also we showed by simulations the SIS procedure with CP distribution to estimate the number of 0-1 three-way tables under no three-way interaction model given marginal sums works very well even with some rejection. We end this paper with further questions on the SIS procedure on 0-1 multi-way tables.