Upper bounds for statistical uncertainties from normalization terms in neutron-scattering data-reduction

We have previously reported on a systematic underestimation of uncertainties by the error-propagation mechanism in neutron-scattering data-reduction software. The problem arises in one-to-many operations that apply a single term across multiple data points, such as normalization of detector counts to a neutron monitor spectrum. While we were able to compute the correct uncertainties for a number of concrete data-reduction workflows, the solution was not necessarily generalizable and could not be applied in interactive data analysis with an a priori unknown data-reduction workflow. In this contribution, we derive upper bounds for the correct uncertainties in workflows involving such one-to-many operations. The bounds are simple and fast to compute and can be applied on the fly during data-reduction.