A Bayesian Approach in the analysis of Inelastic Neutron Brillouin Spectra

In this work we describe a Bayesian approach to the analysis of Neutron Brillouin Scattering (NBS) data. Specifically, when dealing with spectra related to liquids and disordered systems, which are typically characterized by a poor definition of the excitation lines and, generally speaking, of spectroscopic features, the central issue is to establish how many excitation modes are justified by the experimental data and to support the related choices about model parameters on a probability basis. Furthermore when overdamped excitations are present, commonly used and widespread fitting algorithms are particularly affected by the initial values of the parameters that may lead to an inefficient exploration of the parameters space and, consequently, to output results corresponding to a local minimum the algorithm is not able to escape from. The statistical method we discuss here could turn out of great importance in determining the reliability and significance of physical information extracted from experimental data, especially in those cases where the measurement of spectral features is rendered difficult not only by the kind of sample, but also by the limited instrumental resolution and count statistics. An algorithm based on Markov chain Monte Carlo and Reversible Jump techniques has been applied to model simulated data generated by different combination of several Damped Harmonic Oscillator functions. The output will be the most probable number of components in the simulated neutron Brillouin scattering spectra (and of course the posterior distribution function for the variable "number of lines") together with a posterior distribution function of all the relevant dynamical parameters. Finally we show how the algorithm manage to fit on real experimental data on liquid gold, collected on the Brillouin Spectrometer Brisp at the Institut Laue Langevin and how the results are consistent with the rigorous analysis already assessed in literature. We also envisage the very interesting possibility, offered by this approach, to apply physical constraints to fitting models, such as theoretically known sum rules or the finiteness of higher-order frequency moments of the dynamic structure factor.