Markov chains on the reference set of contingency tables with upper bounds

This paper presents the computation of Markov bases for contingency tables when the cell entries are bounded. Markov bases allow a connected random walk on the reference set of the table. Using some theory in Commutative Algebra, we show that a Markov basis for bounded contingency tables is in general different from the Markov basis for unbounded contingency tables. In addition, we give a simple method to compute Markov bases in this case and we provide some practical examples both in one-dimensional and in multi-dimensional settings.