Discrete statistical models with rational maximum likelihood estimator. (English) Zbl 1465.62184

Duarte, Eliana; Marigliano, Orlando; Sturmfels, Bernd

Bernoulli 27, No. 1, 135-154 (2021).

This paper is a study on the discrete statistical models. The authors show a look at algebraic statistics to build the maximum likelihood estimator (MLE). They present a theorem that characterizes all discrete statistical models whose MLE is a rational function. They examine models with rational MLE such as decomposable graphical models and Bayesian networks. The authors present an algorithm for constructing models with rational MLE, and they discuss its implementation and some experiments. The input is an integer matrix, and the output is a list of models derived from that matrix. Their results suggest that only a very small fraction of Huh’s varieties are statistical models.

Reviewer: Glauber Márcio Silveira Pereira (Ceará)

MSC:

62R01	Algebraic statistics
62H22	Probabilistic graphical models
14P10	Semialgebraic sets and related spaces

Keywords:

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

Software:

DiscreteStatisticalModelsWithRationalMLE; Macaulay2

References:

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