Bayesian approach to the analysis of neutron Brillouin scattering data on liquid metals

When the dynamics of liquids and disordered systems at mesoscopic level is investigated by means of inelasticscattering (e.g., neutron or x ray), spectra are often characterized by a poor definition of the excitation lines andspectroscopic features in general and one important issue is to establish howmany of these lines need to be includedin the modeling function and to estimate their parameters. Furthermore, when strongly damped excitations arepresent, commonly used and widespread fitting algorithms are particularly affected by the choice of initial valuesof the parameters. An inadequate choice may lead to an inefficient exploration of the parameter space, resultingin the algorithm getting stuck in a local minimum. In this paper, we present a Bayesian approach to the analysisof neutron Brillouin scattering data in which the number of excitation lines is treated as unknown and estimatedalong with the other model parameters. We propose a joint estimation procedure based on a reversible-jumpMarkov chain Monte Carlo algorithm, which efficiently explores the parameter space, producing a probabilisticmeasure to quantify the uncertainty on the number of excitation lines as well as reliable parameter estimates.The method proposed could turn out of great importance in extracting physical information from experimentaldata, especially when the detection of spectral features is complicated not only because of the properties of thesample, but also because of the limited instrumental resolution and count statistics. The approach is tested ongenerated data set and then applied to real experimental spectra of neutron Brillouin scattering from a liquidmetal, previously analyzed in a more traditional way.