Methodological considerations for semialgebraic hypothesis testing with incomplete U-statistics

TL;DR

This paper evaluates a stochastic hypothesis testing method for polynomial models, demonstrating its robustness near irregular points and discussing practical considerations for its application in biological models.

Contribution

It provides an empirical assessment of a general-purpose semialgebraic hypothesis testing method on phylogenetic models, highlighting its strengths and practical challenges.

Findings

Method performs well across various models

Identifies issues for effective application

Robust near singularities and boundaries

Abstract

Recently, Sturma, Drton, and Leung proposed a general-purpose stochastic method for hypothesis testing in models defined by polynomial equality and inequality constraints. Notably, the method remains theoretically valid even near irregular points, such as singularities and boundaries, where traditional testing approaches often break down. In this paper, we evaluate its practical performance on a collection of biologically motivated models from phylogenetics. While the method performs remarkably well across different settings, we catalogue a number of issues that should be considered for effective application.