# SKM 2023 – wissenschaftliches Programm

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# DY: Fachverband Dynamik und Statistische Physik

## DY 26: Focus Session: From Inter-individual Variability to Heterogeneous Group Dynamics and Disorder in Active Matter (joint session DY/BP/CPP)

### DY 26.6: Vortrag

### Mittwoch, 29. März 2023, 11:45–12:00, ZEU 160

**How to infer parameter distributions in heterogeneous populations of active particles** — •Jan Albrecht^{1}, Robert Großmann^{1}, and Manfred Opper^{2,3} — ^{1}Institute of Physics and Astronomy, University of Potsdam, 14476 Potsdam, Germany — ^{2}TU Berlin, Fakultät IV-MAR 4-2, Marchstraße 23, 10587 Berlin, Germany — ^{3}Centre for Systems Modelling and Quantitative Biomedicine, University of Birmingham, B15 2TT, United Kingdom

Experiments with active particles, e.g., motile microorganisms like bacteria or amebae, provide information about their position at discrete points in time. However, most active particle models, like active Ornstein-Uhlenbeck particles for example, are commonly described by first order stochastic differential equations for the velocity or force. This leads to a second order model in position posing challenges for parameter inference, because there is no general way to obtain a closed form expression for the likelihood of the parameters in terms of those time-sampled trajectories. This would be needed to apply efficient Bayesian parameter estimation techniques. In this talk, we propose a filtering-like sequential method to address this problem. The likelihood is first expressed in terms of integrals over transition probabilities. Approximating the transition probability for small times makes these integrals analytically feasible, leading to a likelihood approximation that allows consistent parameter inference. Using a Bayesian approach, we furthermore show how to extend this framework to estimate the entire distribution of motility parameters in heterogeneous populations of particles efficiently.