Introduction to Toric Geometry

Telen, Simon

doi:10.48550/arxiv.2203.01690

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Toric Varieties and Their Canonical Forms1

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2022

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References 17 publications

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“…We review the set-up of toric geometry, leading up to the integrals studied in this paper. For complete details we refer to the textbook [4] and the notes [17]. Let T be an n-dimensional complex algebraic torus with character lattice M and co-character lattice N = Hom Z (M, Z).…”

Section: Toric Varieties and Their Canonical Formsmentioning

confidence: 99%

Bayesian Integrals on Toric Varieties

Borinsky¹,

Sattelberger²,

Sturmfels³

et al. 2022

Preprint

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We explore the positive geometry of statistical models in the setting of toric varieties. Our focus lies on models for discrete data that are parameterized in terms of Cox coordinates. We develop a geometric theory for computations in Bayesian statistics, such as evaluating marginal likelihood integrals and sampling from posterior distributions. These are based on a tropical sampling method for evaluating Feynman integrals in physics. We here extend that method from projective spaces to arbitrary toric varieties.

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Section: Toric Varieties and Their Canonical Formsmentioning

confidence: 99%