The space of compatible full conditionals is a unimodular toric variety

Details The space of compatible full conditionals is a unimodular toric variety The space of compatible full conditionals is a unimodular toric variety

2004-05-04

arxiv.org/abs/math/0405046v1

Mathematics

Algebraic Geometry

15 pages

Scientific paper

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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