The space of compatible full conditionals is a unimodular toric variety

• Autores: Aleksandra B. Slavkovic, Seth Sullivant
• Localización: Journal of symbolic computation, ISSN 0747-7171, Vol. 41, Nº 2, 2006, págs. 196-209
• Idioma: inglés
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• Resumen

  • 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.