MCMC using Markov bases for computing $$p$$-values in decomposable log-linear models

Abstract We derive an explicit form of a Markov basis on the junction tree for a decomposable log-linear model. Then we give a description of a Markov basis characterized by global Markov properties associated with the graph of a decomposable log-linear model and show how to use the Markov basis for generating contingency tables of a Markov chain. The estimates of exact $$p$$-values can be obtained from contingency tables generated from the proposed Markov chain Monte Carlo using the Markov basis.

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