Bernoulli

  • 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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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.

Article information

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

Dates
First available in Project Euclid: 12 February 2010

Permanent link to this document
https://projecteuclid.org/euclid.bj/1265984709

Digital Object Identifier
doi:10.3150/09-BEJ207

Mathematical Reviews number (MathSciNet)
MR2648755

Zentralblatt MATH identifier
1203.62110

Keywords
chordal graph Gröbner bases independence graph invariance minimality symmetric group

Citation

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. https://projecteuclid.org/euclid.bj/1265984709


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