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

If we could repeat a measurement many times, the average of the results would provide a robust estimate of our observations. However, a measurement is usually a single-time event from which some general law needs to be deduced. In this situation, the help of Bayesian inference [1], here implemented within a Markov Chain Monte Carlo (MCMC) numerical recipe integrated with a Reversible Jump algorithm [2], becomes invaluable. Furthermore, the use of a multi-exponential expansion of the Neutron Spin Echo (NSE) signal, in principle extendable to any time correlation function [3], enabled us to capture the ‘fine-structure’ of relaxation processes in polymer-coated, gold nano particles (PEG-AuNP) (figure 1, left) and to compare them with the dynamics of the free polymer chain solution. Disentanglement of the internal dynamics of polymer chains from other contributions, whenever achievable, would not be possible with a commonly used description of the time correlation function decay in terms of stretched exponentials.