MCMC using Markov bases for computing <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$p$$</EquationSource> </InlineEquation>-values in decomposable log-linear models

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 <InlineEquation ID="IEq3"> <EquationSource Format="TEX">$$p$$</EquationSource> </InlineEquation>-values can be obtained from contingency tables generated from the proposed Markov chain Monte Carlo using the Markov basis. Copyright Springer-Verlag 2013