• Bernoulli
  • Volume 16, Number 1 (2010), 208-233.

Minimal and minimal invariant Markov bases of decomposable models for contingency tables

Hisayuki Hara, Satoshi Aoki, and Akimichi Takemura

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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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Bernoulli, Volume 16, Number 1 (2010), 208-233.

First available in Project Euclid: 12 February 2010

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chordal graph Gröbner bases independence graph invariance minimality symmetric group


Hara, Hisayuki; Aoki, Satoshi; Takemura, Akimichi. Minimal and minimal invariant Markov bases of decomposable models for contingency tables. Bernoulli 16 (2010), no. 1, 208--233. doi:10.3150/09-BEJ207.

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