# A method and tool for combining differential or inclusive measurements obtained with simultaneously constrained uncertainties

## TL;DR

This paper introduces a novel method and software tool for combining measurements with correlated uncertainties, especially when full likelihood information is unavailable, improving accuracy over traditional methods.

## Contribution

It presents a new approach that uses publicly available covariance or Hessian matrices to accurately combine measurements with correlated uncertainties, validated against the full likelihood method.

## Key findings

- Method effectively accounts for correlations in uncertainties.
- Software implementation supports both text and C++ interfaces.
- Validated against full likelihood approach, showing improved accuracy.

## 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 maximisation 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.