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MiS Preprint

Discrete Statistical Models with Rational Maximum Likelihood Estimator

Eliana Maria Duarte Gelvez, Orlando Marigliano and Bernd Sturmfels


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 due to Huh and Kapranov on Horn uniformization. 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.


Related publications

2021 Repository Open Access
Eliana Duarte, Orlando Marigliano and Bernd Sturmfels

Discrete statistical models with rational maximum likelihood estimator

In: Bernoulli, 27 (2021) 1, pp. 135-154