  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.
