In this paper, we give an explicit and algorithmic description of Graver basis for the toric ideal associated with a simple undirected graph and apply the basis for testing the beta model of random graphs by Markov chain Monte Carlo method. Copyright The Institute of Statistical Mathematics,...

Markov basis for statistical model of contingency tables gives a useful tool for performing the conditional test of the model via the Markov chain Monte Carlo method. In this paper, we derive explicit forms of Markov bases for change point models and block diagonal effect models, which are...