Bayesian Integrals on Toric Varieties
arXiv:2204.06414 · doi:10.1137/22M1490569
Abstract
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.
26 pages, 3 figures; v2: minor corrections and improvements, version equivalent to the one published in SIAGA