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

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

2007-01-16

arxiv.org/abs/math/0701429v3

Bernoulli 2010, Vol. 16, No. 1, 208-233

Mathematics

Statistics Theory

Published in at http://dx.doi.org/10.3150/09-BEJ207 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statisti

Scientific paper

10.3150/09-BEJ207

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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