Arrangements and Likelihood

TL;DR

This paper introduces new methods for calculating the likelihood correspondence of hypersurface arrangements in projective space, extending known linear case tools to nonlinear scenarios with applications in statistics and physics.

Contribution

It develops novel tools based on the module of logarithmic derivations for nonlinear hypersurface arrangements, expanding beyond the well-studied linear case.

Findings

New computational tools for likelihood correspondence in nonlinear cases

Extension of logarithmic derivations to nonlinear hypersurfaces

Applications demonstrated in statistics and physics

Abstract

We develop novel tools for computing the likelihood correspondence of an arrangement of hypersurfaces in a projective space. This uses the module of logarithmic derivations. This object is well-studied in the linear case, when the hypersurfaces are hyperplanes. We here focus on nonlinear scenarios and their applications in statistics and physics.