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Discrete statistical models with rational maximum likelihood estimator

2020; Chapman and Hall London; Volume: 27; Issue: 1 Linguagem: Inglês

10.3150/20-bej1231

1573-9759

Eliana Duarte, Orlando Marigliano, Bernd Sturmfels,

Topological and Geometric Data Analysis

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