Likelihood degenerations
Agostini, Daniele
Agostini
Daniele
Brysiewicz, Taylor
Brysiewicz
Taylor
Fevola, Claudia
Fevola
Claudia
Kühne, Lukas
Kühne
Lukas
Sturmfels, Bernd
Sturmfels
Bernd
Telen, Simon
Telen
Simon
Lam, Thomas
Lam
Thomas
Computing all critical points of a monomial on a very affine variety is a fundamental task in algebraic statistics, particle physics and other fields. The number of critical points is known as the maximum likelihood (ML) degree. When the variety is smooth, it coincides with the Euler characteristic. We introduce degeneration techniques that are inspired by the soft limits in CEGM theory, and we answer several questions raised in the physics literature. These pertain to bounded regions in discriminantal arrangements and to moduli spaces of point configurations. We present theory and practise, connecting complex geometry, tropical combinatorics, and numerical nonlinear algebra.(c) 2023 Elsevier Inc. All rights reserved.
414
Elsevier
2023