Families of Polytopes with Rational Linear Precision in Higher Dimensions

In this article, we introduce a new family of lattice polytopes with rational linear precision. For this purpose, we define a new class of discrete statistical models that we call multinomial staged tree models. We prove that these models have rational maximum likelihood estimators (MLE) and give a...

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Bibliographic Details
Published in:Foundations of computational mathematics 2023-12, Vol.23 (6), p.2151-2202
Main Authors: Davies, Isobel, Duarte, Eliana, Portakal, Irem, Sorea, Miruna-Ştefana
Format: Article
Language:English
Subjects:
Applications of Mathematics
Combinatorial analysis
Computer Science
Economics
Linear and Multilinear Algebras
Math Applications in Computer Science
Mathematical analysis
Mathematics
Mathematics and Statistics
Matrix Theory
Maximum likelihood estimators
Numerical Analysis
Polytopes
Statistical models
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Summary:In this article, we introduce a new family of lattice polytopes with rational linear precision. For this purpose, we define a new class of discrete statistical models that we call multinomial staged tree models. We prove that these models have rational maximum likelihood estimators (MLE) and give a criterion for these models to be log-linear. Our main result is then obtained by applying Garcia-Puente and Sottile’s theorem that establishes a correspondence between polytopes with rational linear precision and log-linear models with rational MLE. Throughout this article, we also study the interplay between the primitive collections of the normal fan of a polytope with rational linear precision and the shape of the Horn matrix of its corresponding statistical model. Finally, we investigate lattice polytopes arising from toric multinomial staged tree models, in terms of the combinatorics of their tree representations.
ISSN:1615-3375
1615-3383
DOI:10.1007/s10208-022-09583-7