Discrete statistical models with rational maximum likelihood estimator

A discrete statistical model is a subset of probability simplex. Its maximum likelihood estimator (MLE) retraction from that simplex onto the model. We characterize all models for which this rational function. This contribution via real algebraic geometry rests on results Horn uniformization due to Huh and Kapranov. present an algorithm constructing with MLE, we demonstrate it range instances. Our focus lies familiar statisticians, like Bayesian networks, decomposable graphical staged trees.