The space of compatible full conditionals is a unimodular toric variety

Aleksandra B. Slavkovic; Seth Sullivant

doi:10.1016/j.jsc.2005.04.006

The space of compatible full conditionals is a unimodular toric variety

Aleksandra B. Slavkovic, Seth Sullivant

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8 Scopus citations

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.

Original language	English (US)
Pages (from-to)	196-209
Number of pages	14
Journal	Journal of Symbolic Computation
Volume	41
Issue number	2
DOIs	https://doi.org/10.1016/j.jsc.2005.04.006
State	Published - Feb 2006

All Science Journal Classification (ASJC) codes

Algebra and Number Theory
Computational Mathematics

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10.1016/j.jsc.2005.04.006

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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.",

author = "Slavkovic, {Aleksandra B.} and Seth Sullivant",

note = "Funding Information: The authors wish to thank the referees whose comments helped to improve the exposition of the paper. We would also like to acknowledge Stephen E. Fienberg and Bernd Sturmfels for their advice and support. Aleksandra B. Slavkovic was supported in part by National Science Foundation Grant No. EIA-0131884 to the National Institute of Statistical Sciences, while the author was in the Department of Statistics, Carnegie Mellon University.",

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AU - Sullivant, Seth

N1 - Funding Information: The authors wish to thank the referees whose comments helped to improve the exposition of the paper. We would also like to acknowledge Stephen E. Fienberg and Bernd Sturmfels for their advice and support. Aleksandra B. Slavkovic was supported in part by National Science Foundation Grant No. EIA-0131884 to the National Institute of Statistical Sciences, while the author was in the Department of Statistics, Carnegie Mellon University.

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N2 - 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.

AB - 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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The space of compatible full conditionals is a unimodular toric variety

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