Hierarchical Models, Marginal Polytopes, and Linear Codes
Thomas Kahle, Walter Wenzel, and Nihat Ay
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Submission date: 01. Apr. 2008 (revised version: November 2008)
published in: Kybernetika, 45 (2009) 2, p. 189-207
MSC-Numbers: 52B11, 94B05, 60C05
Keywords and phrases: 0/1 polytopes, linear codes, hierarchical models, exponential families
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In this paper, we explore a connection between binary hierarchical models, their marginal polytopes and codeword polytopes, the convex hulls of linear codes. The class of linear codes that are realizable by hierarchical models is determined. We classify all full dimensional polytopes with the property that their vertices form a linear code and give an algorithm that determines them.