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February 2010 Minimal and minimal invariant Markov bases of decomposable models for contingency tables
Hisayuki Hara, Satoshi Aoki, Akimichi Takemura
Bernoulli 16(1): 208-233 (February 2010). DOI: 10.3150/09-BEJ207

Abstract

We study Markov bases of decomposable graphical models consisting of primitive moves (i.e., square-free moves of degree two) by determining the structure of fibers of sample size two. We show that the number of elements of fibers of sample size two are powers of two and we characterize primitive moves in Markov bases in terms of connected components of induced subgraphs of the independence graph of a hierarchical model. This allows us to derive a complete description of minimal Markov bases and minimal invariant Markov bases for decomposable models.

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Hisayuki Hara. Satoshi Aoki. Akimichi Takemura. "Minimal and minimal invariant Markov bases of decomposable models for contingency tables." Bernoulli 16 (1) 208 - 233, February 2010. https://doi.org/10.3150/09-BEJ207

Information

Published: February 2010
First available in Project Euclid: 12 February 2010

zbMATH: 1203.62110
MathSciNet: MR2648755
Digital Object Identifier: 10.3150/09-BEJ207

Keywords: chordal graph , Gröbner bases , independence graph , Invariance , minimality , Symmetric group

Rights: Copyright © 2010 Bernoulli Society for Mathematical Statistics and Probability

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Vol.16 • No. 1 • February 2010
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