Maximum Likelihood Estimation from a Tropical and a Bernstein--Sato Perspective

TL;DR

This paper explores the use of Tropical Geometry and Bernstein--Sato theory to analyze maximum likelihood estimation, focusing on critical points, asymptotics, and their geometric and algebraic connections.

Contribution

It introduces a novel approach combining tropical geometry and Bernstein--Sato theory to study the asymptotic behavior of maximum likelihood estimation.

Findings

Characterization of critical points of very affine varieties

Connection between asymptotics and tropical variety rays

Relation of Bernstein--Sato ideals to MLE analysis

Abstract

In this article, we investigate Maximum Likelihood Estimation with tools from Tropical Geometry and Bernstein--Sato theory. We investigate the critical points of very affine varieties and study their asymptotic behavior. We relate these asymptotics to particular rays in the tropical variety as well as to Bernstein--Sato ideals and give a connection to Maximum Likelihood Estimation in Statistics.