Systematic underestimation of uncertainties by widespread neutron-scattering data-reduction software

Data-reduction software used at neutron-scattering facilities around the world, Mantid and Scipp, ignore correlations when propagating uncertainties in arithmetic operations. Normalization terms applied during data-reduction frequently have a lower dimensionality than the quantities being normalized. We show how the lower dimensionality introduces correlations, which the software does not take into account in subsequent data-reduction steps such as histogramming, summation, or fitting. As a consequence, any uncertainties in the normalization terms are strongly suppressed and thus effectively ignored. This can lead to erroneous attribution of significance to deviations that are actually pure noise, or to overestimation of significance in final data-reduction results that are used for further data analysis. We analyze this flaw for a number of different cases as they occur in practice. For the two concrete experiments that are comprised in these case studies the underestimation turns out to be of negligible size. There is however no reason to assume that this generalizes to other measurements at the same or at different neutron-scattering beamlines. We describe and implement a potential solution that yields not only corrected error estimates but also the full variance-covariance matrix of the reduced result with minor additional computational cost.