Fitting theory to data in the presence of background uncertainties

TL;DR

This paper investigates how background shape uncertainties correlated with theoretical models affect data fitting, revealing that accounting for these correlations improves confidence region accuracy and challenges current fake data methods.

Contribution

It introduces a method to incorporate background shape correlations into fits, enhancing the reliability of confidence regions in data analysis.

Findings

Correlations in background and model shapes significantly impact fit results.

Including these correlations yields more accurate confidence regions.

Fake data methods may be suboptimal without considering shape correlations.

Abstract

When fitting theory to data in the presence of background uncertainties, the question of whether the spectral shape of the background happens to be similar to that of the theoretical model of physical interest has not generally been considered previously. These correlations in shape are considered in the present note and found to make important corrections to the calculations. The discussion is phrased in terms of $\chi^2$ fits, but the general considerations apply to any fits. Including these new correlations provides a more powerful test for confidence regions. Fake data studies, as used at present, may not be optimum.