Interpreting the Terahertz Spectrum of Complex Materials: The Unique Contribution of the Bayesian Analysis

In the last few decades, experimental studies of the terahertz spectrum of density fluctuations have considerably improved our knowledge of the mesoscopic dynamics of disordered materials, which also have imposed new demands on the data modelling and interpretation. Indeed, lineshape analyses are no longer limited to the phenomenological observation of inelastic features, as in the pioneering stage of Neutron or X-ray spectroscopy, rather aiming at the extraction from their shape of physically relevant quantities, as sound velocity and damping, relaxation times, or other transport coefficients. In this effort, researchers need to face both inherent and practical obstacles, respectively stemming from the highly damped nature of terahertz modes and the limited energy resolution, accessible kinematic region and statistical accuracy of the typical experimental outcome. To properly address these challenges, a global reconsideration of the lineshape modelling and the enforcement of evidence-based probabilistic inference is becoming crucial. Particularly compelling is the possibility of implementing Bayesian inference methods, which we illustrated here through an in-depth discussion of some results recently obtained in the analysis of Neutron and X-ray scattering results.