The space of compatible full conditionals is a unimodular toric variety
Algebraic Geometry
2007-06-13 v1 Combinatorics
Statistics Theory
Statistics Theory
Abstract
The set of all m-tuples of compatible full conditional distributions on discrete random variables is an algebraic set whose defining ideal is a unimodular toric ideal. We identify the defining polynomials of these ideals with closed walks on a bipartite graph. Our algebraic characterization provides a natural generalization of the requirement that compatible conditionals have identical odds ratios and holds regardless of the patterns of zeros in the conditional arrays.
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Cite
@article{arxiv.math/0405046,
title = {The space of compatible full conditionals is a unimodular toric variety},
author = {Aleksandra B Slavkovic and Seth Sullivant},
journal= {arXiv preprint arXiv:math/0405046},
year = {2007}
}
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15 pages