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Monte Carlo methods have been used in exact inference for contingency tables for a long time; however, they suffer from ergodicity and the ability to achieve a desired proportion of valid tables. In this paper, we apply the stochastic approximation Monte Carlo(SAMC; Liang et al., 2007) algorithm, as an adaptive Markov chain Monte Carlo, to the exact test of mutual independence in a multiway contingency table. The performance of SAMC has been investigated on real datasets compared to with existing Markov chain Monte Carlo methods. The numerical results are in favor of the new method in terms of the quality of estimates.

Approximating Exact Test of Mutual Independence in Multiway Contingency Tables via Stochastic Approximation Monte Carlo