Title | The space of compatible full conditionals is a unimodular toric variety |
Author(s) | Aleksandra B. Slavkovic, Seth Sullivant |
Type | Article in Journal |
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. |
Keywords | Odds ratios, Toric ideal, Unimodular |
ISSN | 0747-7171 |
URL |
http://www.sciencedirect.com/science/article/pii/S0747717105001148 |
Language | English |
Journal | Journal of Symbolic Computation |
Volume | 41 |
Number | 2 |
Pages | 196 - 209 |
Year | 2006 |
Note | Computational Algebraic Statistics Computational Algebraic Statistics |
Edition | 0 |
Translation |
No |
Refereed |
No |