A finiteness theorem for Markov bases of hierarchical models |
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| Authors: | Serkan Ho?ten |
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| Affiliation: | a Department of Mathematics, San Francisco State University, San Francisco, USA
b Society of Fellows, Harvard University, USA |
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| Abstract: | We show that the complexity of the Markov bases of multidimensional tables stabilizes eventually if a single table dimension is allowed to vary. In particular, if this table dimension is greater than a computable bound, the Markov bases consist of elements from Markov bases of smaller tables. We give an explicit formula for this bound in terms of Graver bases. We also compute these Markov and Graver complexities for all K×2×2×2 tables. |
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| Keywords: | Contingency tables Markov bases Hierarchical models Graver complexity |
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