A Bayesian approach for the study of time correlation functions in a soft complex system

In the last decades, the steady improvement of instrumental performance in research and in particular in the field of spectroscopy made available an enormous amount of new data on a variety of physical systems. While in the early years, a merely phenomenological observation of new spectral features was considered a result per se, warranting scientific attention, the increased accuracy in data acquisition shifted the objective towards a more quantitative and physically insightful scrutiny of the line shape. Somehow paradoxically, the improved quality of measurements, rather than minimizing uncertainties, has often encouraged bold speculations which ultimately challenge scientific rigor and accuracy. To overthrow this course of events, the scientific community is in need of new data analysis protocols capable of quantifying the reliability of a given model, avoiding over-parameterization, minimizing subjectivity in the model choice and, ultimately, warning investigators against hazardous speculations. To advance in this impervious route, we have applied a Bayesian approach, previously used on (energy-resolved) Brillouin neutron and x-ray spectra, to model the time decay of the intermediate scattering functions (ISF) measured by Spin Echo Spectroscopy on aqueous solutions of polymer functionalized gold nanoparticles.