Bayesian Integrals on Toric Varieties

Toric varieties have a strong combinatorial flavor: those algebraic varieties are described in terms of a fan. Based on joint work with M. Borinsky, B. Sturmfels, and S. Telen, I explain how to understand toric varieties as probability spaces. Bayesian integrals for discrete statistical models that are parameterized by a toric variety can be computed by a tropical sampling method. Our methods are motivated by the study of Feynman integrals and positive geometries in particle physics.