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February 2021 Discrete statistical models with rational maximum likelihood estimator
Eliana Duarte, Orlando Marigliano, Bernd Sturmfels
Bernoulli 27(1): 135-154 (February 2021). DOI: 10.3150/20-BEJ1231

Abstract

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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Eliana Duarte. Orlando Marigliano. Bernd Sturmfels. "Discrete statistical models with rational maximum likelihood estimator." Bernoulli 27 (1) 135 - 154, February 2021. https://doi.org/10.3150/20-BEJ1231

Information

Received: 1 March 2019; Revised: 1 April 2020; Published: February 2021
First available in Project Euclid: 20 November 2020

zbMATH: 07282845
MathSciNet: MR4177364
Digital Object Identifier: 10.3150/20-BEJ1231

Rights: Copyright © 2021 Bernoulli Society for Mathematical Statistics and Probability

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Vol.27 • No. 1 • February 2021
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