Chapter Bayesian Approach for X-Ray and Neutron Scattering Spectroscopy

The rapidly improving performance of inelastic scattering instruments has prompted tremendous advances in our knowledge of the high-frequency dynamics of disordered systems, yet also imposing new demands to the data analysis and interpretation. This ongoing effort is likely to reach soon an impasse, unless new protocols are developed in the data modeling. This need stems from the increasingly detailed information sought for in typical line shape measurements, which often touches or crosses the boundaries imposed by the limited experimental accuracy. Given this scenario, the risk of a bias and an over-parametrized data modeling represents a concrete threat for further advances in the field. Being aware of the severity of the problem, we illustrate here the new hopes brought in this area by Bayesian inference methods. Making reference to recent literature results, we demonstrate the superior ability of these methods in providing a probabilistic and evidence-based modeling of experimental data. Most importantly, this approach can enable hypothesis test involving competitive line shape models and is intrinsically equipped with natural antidotes against the risk of over-parametrization as it naturally enforces the Occam maximum parsimony principle, which favors intrinsically simple models over overly complex ones