Sampling high dimensional tables with applications to assessing linkage disequilibrium

We propose a sequential importance sampling strategy to sample high dimensional tables with fixed one way margins. The proposal distribution for the method is constructed by adapting an approximation to the total number of tables available in the literature. We apply the method to estimating the total number of tables and assessing linkage disequilibrium in multimarker genetic data with the table representing haplotype count data. We demonstrate efficient and accurate performance in these practical, real-world examples. The method may be applied in any situation in which uniformly sampling high dimensional tables with fixed one way margins is of interest. Detailed derivations are provided in the appendix.