An Ad-Hoc Method for Obtaining chi**2 Values from Unbinned Maximum Likelihood Fits

TL;DR

This paper introduces an ad-hoc approach to derive chi-squared values from unbinned maximum likelihood fits, enabling goodness-of-fit assessment without data binning in complex multi-dimensional analyses.

Contribution

The paper presents a novel, binning-free method to obtain chi-squared values from unbinned maximum likelihood fits, enhancing goodness-of-fit evaluation in multi-dimensional data analysis.

Findings

Provides a practical procedure for goodness-of-fit assessment

Applicable to multi-dimensional unbinned data

Avoids data binning complexities

Abstract

A common goal in an experimental physics analysis is to extract information from a reaction with multi-dimensional kinematics. The preferred method for such a task is typically the unbinned maximum likelihood method. In fits using this method, the likelihood is a goodness-of-fit quantity in that it effectively discriminates between available hypotheses; however, it does not provide any information as to how well the best hypothesis describes the data. In this paper, we present an {\em ad-hoc} procedure for obtaining chi**2/n.d.f. values from unbinned maximum likelihood fits. This method does not require binning the data, making it very applicable to multi-dimensional problems.