Handling uncertainties in background shapes: the discrete profiling method

TL;DR

The paper introduces a method to account for uncertainties in background shape modeling by treating the functional form as a discrete nuisance parameter, improving error estimation in data analysis.

Contribution

It presents a novel discrete profiling method that assigns uncertainties to background shape models by profiling over possible functional forms, enhancing analysis robustness.

Findings

Bias and coverage are good in realistic examples

The method effectively accounts for shape uncertainties

Improves error estimation in background modeling

Abstract

A common problem in data analysis is that the functional form, as well as the parameter values, of the underlying model which should describe a dataset is not known a priori. In these cases some extra uncertainty must be assigned to the extracted parameters of interest due to lack of exact knowledge of the functional form of the model. A method for assigning an appropriate error is presented. The method is based on considering the choice of functional form as a discrete nuisance parameter which is profiled in an analogous way to continuous nuisance parameters. The bias and coverage of this method are shown to be good when applied to a realistic example.