# Regensburg 2019 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 43: Anomalous diffusion / Brownian motion

### DY 43.6: Vortrag

### Donnerstag, 4. April 2019, 11:15–11:30, H3

**Bayesian statistics for models of diffusion: theory and applications** — •Samudrajit Thapa^{1}, Michael A. Lomholt^{2}, Jens Krog^{2}, Andrey G. Cherstvy^{1}, and Ralf Metzler^{1} — ^{1}Institute for Physics & Astronomy, University of Potsdam, 14476 Potsdam-Golm, Germany — ^{2}MEMPHYS, Department of Physics, Chemistry & Pharmacy, University of Southern Denmark, 5230 Odense M, Denmark

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. 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.

[1] S. Thapa, M. A. Lomholt, J. Krog, A. G. Cherstvy, & R. Metzler, *Bayesian analysis of single-particle tracking data using the nested-sampling algorithm:
maximum-likelihood model selection applied to stochastic-diffusivity data*,Phys. Chem. Chem. Phys.,
**20** 29018 (2018).