Koko Kayibi

Sampling Contingency Tables

Let Ω be the set of all m×n matrices where ri and cj are the sums of entries in row i and column j, respectively. Sampling efficiently uniformly at random elements of Ω is a problem with interesting applications in Combinatorics and Statistics. To calibrate the statistics χ2 for testing independence, Diaconis and Gangolli in [1] propose a Markov Chain on Ω that samples uniformly at random contingency tables of fixed row and column sums. Although the scheme works well for practical purposes, no formal proof is available on its rate of convergence. By using a canonical path argument, we prove that this Markov chain is fast mixing and provide an expression for the mixing time.