Abstract
A method is discussed that allows combining sets of differential or inclusive measurements. It is assumed that at least one measurement was obtained with simultaneously fitting a set of nuisance parameters, representing sources of systematic uncertainties. As a result of beneficial constraints from the data all such fitted parameters are correlated among each other. The best approach for a combination of these measurements would be the maximization of a combined likelihood, for which the full fit model of each measurement and the original data are required. However, only in rare cases this information is publicly available. In absence of this information most commonly used combination methods are not able to account for these correlations between uncertainties, which can lead to severe biases as shown in this article. The method discussed here provides a solution for this problem. It relies on the public result and its covariance or Hessian, only, and is validated against the combined-likelihood approach. A dedicated software package implementing this method is also presented. It provides a text-based user interface alongside a C++ interface. The latter also interfaces to ROOT classes for simple combination of binned measurements such as differential cross sections.
Highlights
Combination methodThe combination is performed using a χ 2 minimisation. The χ 2 is defined as χ2 =
The dedicated software tool “Convino” is presented in this article
The combination method presented in this document allows combining measurements obtained with simultaneous nuisance parameter fits consistently, taking into account the constraints from the data as well as correlations between systematic uncertainties within each measurement
Summary
The combination is performed using a χ 2 minimisation. The χ 2 is defined as χ2 =. It is composed of three terms: the term χs2,α represents the results of each measurement α and its statistical uncertainties It follows a Neyman or Pearson χ 2 definition, with the statistical uncertainty being fixed for each measurement or being scaled with the combined value, respectively. A single quantity can be measured, e.g. the mass of a particle from a fit of an invariant mass peak position, where the Neyman definition is presumably better suited to describe the measurement In both cases, the measured quantities are referred to as estimates in the following. The additional term χu2,α describes the correlations between the systematic uncertainties and constraints on them from the data for each measurement α. - firstly for results obtained through a simultaneous nuisance parameter fit and secondly for the specific case of orthogonal uncertainties
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