Discrete Statistical Models with Rational Maximum Likelihood Estimator
Eliana Maria Duarte Gelvez, Orlando Marigliano, and Bernd Sturmfels
Contact the author: Please use for correspondence this email.
Submission date: 15. Mar. 2019
Download full preprint: PDF (293 kB)
Link to arXiv: See the arXiv entry of this preprint.
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 due to Huh and Kapranov on Horn uniformization. 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.