Corpus ID: 237563014

Families of polytopes with rational linear precision in higher dimensions

@inproceedings{Davies2021FamiliesOP,
  title={Families of polytopes with rational linear precision in higher dimensions},
  author={Isobel Davies and Eliana Duarte and Irem Portakal and Miruna-Stefana Sorea},
  year={2021}
}
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… Expand

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References

SHOWING 1-10 OF 14 REFERENCES
The maximum likelihood degree of toric varieties
TLDR
The maximum likelihood (ML) degree of toric varieties, known as discrete exponential models in statistics, is studied, showing that the ML degree is equal to the degree of the toric variety for generic scalings, while it drops if and only if the scaling vector is in the locus of the principal A-determinant. Expand
Discrete statistical models with rational maximum likelihood estimator
A discrete statistical model is a subset of a probability simplex. Its maximum likelihood estimator (MLE) is a retraction from that simplex onto the model. We characterize all models for which thisExpand
Linear precision for parametric patches
TLDR
The connection between linear precision for toric surface patches and maximum likelihood degree for discrete exponential families in algebraic statistics, and how iterative proportional fitting may be used to compute toric patches is established. Expand
Moment maps, strict linear precision, and maximum likelihood degree one
We study the moment maps of a smooth projective toric variety. In particular, we characterize when the moment map coming from the quotient construction is equal to a weighted Fubini-Study moment map.Expand
Primitive collections and toric varieties
This paper studies Batyrev’s notion of primitive collection. We use primitive collections to characterize the nef cone of a quasi-projective toric variety whose fan has convex support, a resultExpand
TORIC VARIETIES
We study toric varieties over a field k that split in a Galois extension K/k using Galois cohomology with coefficients in the toric automorphism group. This Galois cohomology fits into an exactExpand
Varieties with maximum likelihood degree one
We show that algebraic varieties with maximum likelihood degree one are exactly the images of reduced A-discriminantal varieties under monomial maps with finite fibers. The maximum likelihoodExpand
Linear Precision for Toric Surface Patches
TLDR
This work identifies a family of toric patches with trapezoidal shape, each of which has linear precision, and classifies the homogeneous polynomials in three variables whose toric polar linear system defines a Cremona transformation. Expand
Conditional independence and chain event graphs
TLDR
This work introduces a new mixed graphical structure called the chain event graph that is a function of this event tree and a set of elicited equivalence relationships that is more expressive and flexible than either the Bayesian network-equivalent in the symmetric case-or the probability decision graph. Expand
Toric Surface Patches
TLDR
A toric surface patch associated with a convex polygon, which has vertices with integer coordinates, is defined, which naturally generalizes classical Bézier surfaces. Expand
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