Systematic Uncertainties in Unfolding Considering the Likelihood Formalism

Abstract

This paper describes the treatment of systematic uncertainties in a Likelihood formalism. RooUnfold, which includes most of the unfolding methods that are commonly used in particle physics, is used to compare a newly implemented method inside this toolkit to existing methods. The interface with the RooFit statistical software package is used for the treatment of systematic uncertainties. The RooUnfold package with RooFit interface, commonly called RooFitUnfold, provides a common interface to unfolding algorithms as well as common uniform methods to evaluate their performance in terms of bias, variance and coverage. This paper exploits this common interface to compare the performance of unfolding with a Tikhonov regularisation term directly in the likelihood with an unfolding method that optimises a Tikhonov regularisation applied separately of the likelihood formalism. Comparisons are made with and without the treatment of (systematic) uncertainties and are applied to an example problem.