• Bernoulli
  • Volume 27, Number 1 (2021), 135-154.

Discrete statistical models with rational maximum likelihood estimator

Eliana Duarte, Orlando Marigliano, and Bernd Sturmfels

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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.

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Bernoulli, Volume 27, Number 1 (2021), 135-154.

Received: March 2019
Revised: April 2020
First available in Project Euclid: 20 November 2020

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algebraic statistics discrete statistical models graphical models likelihood geometry maximum likelihood estimator real algebraic geometry


Duarte, Eliana; Marigliano, Orlando; Sturmfels, Bernd. Discrete statistical models with rational maximum likelihood estimator. Bernoulli 27 (2021), no. 1, 135--154. doi:10.3150/20-BEJ1231.

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