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Markov Bases

Part of the Oberwolfach Seminars book series (OWS, volume 39)

Abstract

This chapter introduces the fundamental notion of a Markov basis, which represents one of the first connections between commutative algebra and statistics. This connection was made in the paper by Diaconis and the second author [33] on contingency table analysis. Statistical hypotheses about contingency tables can be tested in an exact approach by performing random walks on a constrained set of tables with non-negative integer entries. Markov bases are of key importance to this statistical methodology because they comprise moves between tables that ensure that the random walk connects every pair of tables in the considered set.

Keywords

Contingency Table Hierarchical Model Simplicial Complex Independence Model Integer Lattice 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Birkhäuser Verlag AG 2009

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