PAPER Special Issue on Foundations of Computer Science Approximate Counting Scheme

for m × n Contingency Tables ∗ SUMMARY In this paper, we propose a new counting scheme for m × n contingency tables. Our scheme is a modification of Dyer and Greenhill’s scheme for two rowed contingency tables [5]. We can estimate not only the sizes of error, but also the sizes of the bias of the number of tables obtained by our scheme, on the assumption that we have an approximate sampler. key words: counting, approximation, #P-completeness, fpras, MCMC method, contingency table 1