Error analysis for small angle neutron scattering datasets using Bayesian inference

Abstract

We present a Bayesian methodology for extracting correlation lengths from small-angle neutron scattering (SANS) experiments. For demonstration, we apply the technique to data from a previous paper, which investigated the presence of dipolar ferromagnetism in assemblies of ferromagnetic Co nanoparticles. Bayesian analysis confirms the presence of multiparticle dipolar domains even at zero magnetic field, but higher-field correlation lengths were found to be much smaller than previously believed, yielding new information on the maximum lengthscale which the instrument can reliably probe. We use two complementary types of graph to visualize the results. Plots of standardized residual distributions show quality of fit, and guide model refinement. These principles can be applied to other types of sample, and even to other small-angle scattering techniques.