The space of compatible full conditionals is a unimodular toric variety
Abstract
The set of all mtuples 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.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 May 2004
 arXiv:
 arXiv:math/0405046
 Bibcode:
 2004math......5046S
 Keywords:

 Mathematics  Algebraic Geometry;
 Mathematics  Combinatorics;
 Mathematics  Statistics
 EPrint:
 15 pages