Multivariate Goodness of Fit Procedures for Unbinned Data: An Annotated Bibliography

TL;DR

This paper reviews multivariate goodness-of-fit methods for unbinned data, highlighting the lack of comprehensive studies on their performance in realistic multi-dimensional problems.

Contribution

It provides an annotated bibliography of multivariate goodness-of-fit procedures, emphasizing the need for further research on their effectiveness in practical scenarios.

Findings

Univariate goodness-of-fit methods are well-studied.

Multivariate test powers are rarely analyzed on realistic data.

No definitive best method for multivariate goodness-of-fit has been established.

Abstract

Unbinned maximum likelihood is a common procedure for parameter estimation. After parameters have been estimated, it is crucial to know whether the fit model adequately describes the experimental data. Univariate Goodness of Fit procedures have been thoroughly analyzed. In multi-dimensions, Goodness of Fit test powers have rarely been studied on realistic problems. There is no definitive answer to regarding which method is better. Test performance is strictly related to specific analysis characteristics. In this work, a review of multi-variate Goodness of Fit techniques is presented.