Likelihood degenerations

Computing all critical points of a monomial on very affine variety is fundamental task in algebraic statistics, particle physics and other fields. The number known as the maximum likelihood (ML) degree. When smooth, it coincides with Euler characteristic. We introduce degeneration techniques that are inspired by soft limits CEGM theory, we answer several questions raised literature. These pertain to bounded regions discriminantal arrangements moduli spaces point configurations. present theory practise, connecting complex geometry, tropical combinatorics, numerical nonlinear algebra.