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.
Markov chains on the reference set of contingency tables with upper bounds
F. RAPALLO;ROGANTIN, MARIA PIERA
2007-01-01
Abstract
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.
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