Normal Binary Hierarchical Models

ABSTRACT

Each simplicial complex and integer vector yields a vector configuration whose combinatorial properties are important for the analysis of contingency tables. We study the normality of these vector configurations including a description of operations on simplicial complexes that preserve normality, constructions of families of minimally nonnormal complexes, and computations classifying all of the normal complexes on up to six vertices. We repeat this analysis for compressed vector configurations, classifying all of the compressed complexes on up to six vertices.

KEYWORDS:

• algebraic statistics
• contingency tables
• Hilbert basis
• Groebner basis
• combinatorics

2000 AMS SUBJECT CLASSIFICATION:

• 14Q99
• 52C07
• 62Q05
• 90C10

Acknowledgments

Thanks to Winfried Bruns and Christof Söger for computations with the development version of Normaliz that allowed us to complete the classification of normal complexes on six vertices.

Funding

Daniel Irving Bernstein was partially supported by the US National Science Foundation (DMS 0954865). Seth Sullivant was partially supported by the David and Lucille Packard Foundation and the US National Science Foundation (DMS 0954865).