Combining exponential expansion theory with Bayesian inference for the analysis of inelastic scattering spectra

Over the past decade, advances in inelastic x-ray and neutron scattering instrumentation have created a demand for probabilistically grounded data analysis. To address this, we proposed a Bayesian method that uses Monte Carlo techniques and a reversible jump routine to support the determination of the number of modes that contribute to the spectrum of density fluctuations S(Q, ω). So far, a similar approach has been applied to models that fail to satisfy the proper sum rules governing the moments of the distribution S(Q, ω), typically consisting of multiple damped harmonic oscillator modes, along with additional central peaks. We show that applying Bayesian inference to an exponential expansion theory-based model, which explicitly enforces the relevant sum rules, provides a rigorous and physically constrained framework for the analysis and interpretation of experimental spectra. In particular, this result enables analysis of the complex and relatively unstructured shape of terahertz inelastic spectra of disordered systems.