Biological & Soft Matter Seminar: Characterizing diffusion using Bayesian analysis and large-deviation theory

The link to the meeting is: https://zoom.us/j/96354349546 - Meeting ID: 963 5434 9546

Abstract: 

Particle diffusion in heterogeneous systems poses the following question: Can a single model describe the entire dynamics of a particle in complex biological, soft matter systems? Indeed, often several different physical mechanisms are at work and it is more insightful to rank them based on the likelihood of them explaining the dynamics. The first part of this talk will discuss — within the Bayesian framework—,(a) how maximum-likelihood model selection can be done by assigning probabilities to each feasible model and (b) how to estimate the parameters of each model. In particular, the implementation of this powerful statistical tool using the Nested Sampling algorithm to compare—at the single trajectory level—models of Brownian motion, viscoelastic anomalous diffusion and normal yet non-Gaussian diffusion will be discussed. Finally, the application of this method to experimental data of tracer diffusion in polymer-based hydrogels (mucin) will be presented. Viscoelastic anomalous diffusion is often found to be most probable, followed by Brownian motion, while the model with a diffusing diffusion coefficient is only realised rarely. Also, diffusion of tracers in the mucin gels is found to be mostly non-Gaussian and non-ergodic at low pH that corresponds to the most heterogeneous networks. As we will see in the first part of the talk, Bayesian analysis although very useful, can be computationally expensive and technically involved. Moreover, the model comparison using Bayesian analysis ranks models from a list and as such, its efficiency depends on having the relevant models in the list of models compared. The second part of the talk will discuss how large-deviation theory applied to the routinely measured time-averaged mean-squared displacement can be used as a computationally inexpensive yet efficient tool to garner important information about the underlying stochastic process of measured trajectories and thereby complement the Bayesian analysis.