Minimal and minimal invariant Markov bases of decomposable models for contingency tables
Statistics Theory
2010-03-04 v3 Statistics Theory
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.
Keywords
Cite
@article{arxiv.math/0701429,
title = {Minimal and minimal invariant Markov bases of decomposable models for contingency tables},
author = {Hisayuki Hara and Satoshi Aoki and Akimichi Takemura},
journal= {arXiv preprint arXiv:math/0701429},
year = {2010}
}
Comments
Published in at http://dx.doi.org/10.3150/09-BEJ207 the Bernoulli (http://isi.cbs.nl/bernoulli/) by the International Statistical Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm)