Bernoulli

  • 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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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.

Article information

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

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

Permanent link to this document
https://projecteuclid.org/euclid.bj/1605841239

Digital Object Identifier
doi:10.3150/20-BEJ1231

Mathematical Reviews number (MathSciNet)
MR4177364

Zentralblatt MATH identifier
07282845

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

Citation

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. https://projecteuclid.org/euclid.bj/1605841239


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