Optimal weights and priors in simultaneous fitting of multiple small-angle scattering datasets

Abstract

Small-angle X-ray and neutron scattering (SAXS and SANS) are powerful techniques in material science and soft matter. In this study, it was addressed how multiple SAXS or SANS datasets are best weighted when doing simultaneous fitting. Three weighting schemes were tested: (1) equal weighting of all datapoints, (2) equal weighting of each dataset through normalization with the number of datapoints, (3) weighting proportional to the information content. The weighing schemes were assessed by model refinement against synthetic data under numerous conditions. The first weighting scheme led to the most accurate parameter estimation, especially when one dataset substantially outnumbered the other(s). Furthermore, it was demonstrated that inclusion of Gaussian priors significantly improved the accuracy of the refined parameters, as compared to common practice, where each parameter is constrained uniformly within an allowed interval.