环型上的贝叶斯积分

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

SIAM Journal on Applied Algebra and Geometry Pub Date : 2022-04-13 DOI:10.1137/22M1490569

M. Borinsky, Anna-Laura Sattelberger, B. Sturmfels, Simon Telen

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引用次数: 3

摘要

我们探讨统计模型的正几何在环面品种的设置。我们的重点在于离散数据的模型，这些模型以Cox坐标为参数化。我们发展了贝叶斯统计计算的几何理论，例如评估边际似然积分和从后验分布中抽样。这些都是基于计算物理学中费曼积分的热带抽样方法。本文将该方法从射影空间推广到任意环变空间。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Bayesian Integrals on Toric Varieties

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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来源期刊

SIAM Journal on Applied Algebra and Geometry MATHEMATICS, APPLIED-

CiteScore

2.20

自引率

0.00%

发文量