How good are your fits? Unbinned multivariate goodness-of-fit tests in high energy physics

TL;DR

This paper evaluates various unbinned multivariate goodness-of-fit tests in high energy physics, demonstrating their application in real analyses and their ability to compare data with simulations without parametric models.

Contribution

It introduces and assesses multiple unbinned goodness-of-fit methods tailored for high energy physics, including non-parametric sample comparison techniques.

Findings

Several methods effectively assess fit quality in complex analyses.

Some techniques enable non-parametric comparison of data and simulations.

Methods are demonstrated in a Dalitz-plot analysis context.

Abstract

Multivariate analyses play an important role in high energy physics. Such analyses often involve performing an unbinned maximum likelihood fit of a probability density function (p.d.f.) to the data. This paper explores a variety of unbinned methods for determining the goodness of fit of the p.d.f. to the data. The application and performance of each method is discussed in the context of a real-life high energy physics analysis (a Dalitz-plot analysis). Several of the methods presented in this paper can also be used for the non-parametric determination of whether two samples originate from the same parent p.d.f. This can be used, e.g., to determine the quality of a detector Monte Carlo simulation without the need for a parametric expression of the efficiency.