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
Full-text: Open access
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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