Random generation of 2 times 2 times ... times 2 times J contingency tables

We propose two Markov chains for sampling (m + 1)-dimensional contingency tables indexed by {1, 2}m × {1, 2, . . . , n}. Stationary distributions of our chains are the uniform distribution and a conditional multinomial distribution (which is equivalent to the hypergeometric distribution ifm=1). Mixing times of our chains are bounded by ( 1 2 )n(n− 1) ln(N/(2m ))= ( 1 2 )n(n− 1) ln(dn/ ), where d is the average of the values in the cells and is a given error bound.We use the path coupling method for estimating the mixing times of our chains and showed that our chains mix rapidly. © 2004 Elsevier B.V. All rights reserved.