Neighborliness of Marginal Polytopes
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Submission date: 04. Sep. 2008
published in: Beiträge zur Algebra und Geometrie, 51 (2010) 1, p. 45-56
MSC-Numbers: 52B05, 60C05
Keywords and phrases: Marginal Polytopes, Markov Bases, hierarchical models
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A neighborliness property of marginal polytopes of hierarchical models, depending on the cardinality of the smallest non-face of the underlying simplicial complex, is shown. The case of binary variables is studied explicitly, then the general case is reduced to the binary case. A Markov basis for binary hierarchical models whose simplicial complexes is the complement of an interval is given.