Computing p-values in conditional independence models for a contingency table (Q626252)

Conditional independence models are considered for four-ways contingency tables. The exact distributions of minimal sufficient statistics for these models are hypergeometric conditionally on the sets of marginal constraints. The authors propose a Markov chain Monte Carlo Metropolis-Hastings type algorithm for sampling from these distributions. It is used to compute the p-values for a Pearson chi-square type test for conditional independence. These p-values are compared to the exact p-values and p-values of the asymptotic \(\chi^2\) distribution in some numerical examples with real life data sets.