Unimodular binary hierarchical models

详细信息    查看全文

• 作者：Daniel Irving Bernstein ^{dibernst@ncsu.edu} ; Seth Sullivant ^{smsulli2@ncsu.edu}
• 关键词：Graver basis ; Algebraic statistics ; Log-linear models ; Hierarchical models ; Toric ideal
• 刊名：Journal of Combinatorial Theory, Series B
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：123
• 期：Complete
• 页码：97-125
• 全文大小：542 K
• 卷排序：123

文摘

Associated to each simplicial complex is a binary hierarchical model. We classify the simplicial complexes that yield unimodular binary hierarchical models. Our main theorem provides both a construction of all unimodular binary hierarchical models, together with a characterization in terms of excluded minors, where our definition of a minor allows the taking of links and induced complexes. A key tool in the proof is the lemma that the class of unimodular binary hierarchical models is closed under the Alexander duality operation on simplicial complexes.