# Discrete statistical models with rational maximum likelihood estimator

@article{Duarte2019DiscreteSM, title={Discrete statistical models with rational maximum likelihood estimator}, author={Eliana Duarte and Orlando Marigliano and Bernd Sturmfels}, journal={arXiv: Statistics Theory}, year={2019} }

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…

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