Seminar Algebra and Geometry: Carlos Amendola (University of Munich)

Maximum Likelihood Estimation of Toric Fano Varieties

We study the maximum likelihood estimation problem for several classes of toric Fano models. We start by exploring the maximum likelihood degree for all 2-dimensional Gorenstein toric Fano varieties. We show that the ML degree is equal to the degree of the surface in every case except for the quintic del Pezzo surface with two singular points of type A1 and provide explicit expressions that allow to compute the maximum likelihood estimate in closed form whenever the ML degree is less than 5. We then explore the reasons for the ML degree drop using A-discriminants and intersection theory. Based on joint work with Dimitra Kosta and Kaie Kubjas.

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