Discrete statistical models with rational maximum likelihood estimator

• Type: Article in International Scientific Journal
• Date: 2021

Authors

Duarte E. (Author) FCUP; Marigliano O. (Author) Other; Sturmfels B. (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: Bernoulli

Vol. 27

Pages: 135-154

ISSN: 13507265

Indexing

Scopus - 2 Citations

Other information

Authenticus ID: P-00X-9EN

DOI: 10.3150/20-bej1231

Abstract (EN): 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.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 19