Maximilian Wiesmann: Arrangements and Likelihood

Abstract: We establish connections between hypersurface arrangements and likelihood geometry. Thereby arises a new description of the prime ideal of the likelihood correspondence of a parametrised statistical model. The likelihood correspondence captures the relation between data and critical points of the log-likelihood function. The description rests on the Rees algebra of the likelihood module of the arrangement, a module that is closely related to the module of logarithmic derivations introduced by Saito for a general hypersurface. Our new description is often computationally advantageous, simplifying an expensive saturation step.