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 26.5: Hauptvortrag
Mittwoch, 29. März 2023, 11:15–11:45, ZEU 160
Superstatistical Analysis and Modelling of Complex Dynamical Systems — •Claus Metzner1,2, Christoph Mark2, Ben Fabry2, Patrick Krauss1, Achim Schilling1, Maximilian Traxdorf3, and Holger Schulze1 — 1Neuroscience Lab, University Hospital Erlangen, Germany — 2Biophysics Lab, Friedrich-Alexander Universität Erlangen-Nürnberg — 3Department of Otorhinolaryngology, Head and Neck Surgery, Paracelsus Medical University, Nuremberg, Germany
On longer time scales, complex systems often pass through different dynamical attractors and thus produce 'anomalous' distributions and correlations when analyzed with conventional statistical tools. We argue that the most appropriate way of describing such systems is by hierarchical multilevel models, in which the lowest level is a relatively simple random walk model that can generate the observed time series on short time scales, but which depends on latent hyper-parameters that are themselves time-dependent and controlled by the higher levels of the model. First, our Bayesian method is introduced for the sequential inference of those gradual or abrupt parameter changes. We then review possible applications of the superstatistical framework in such diverse fields as biophysics, neuroscience, finance, or policy assessment. Finally, we discuss more recent extensions of the method for model selection and the use of machine learning models for estimating complex likelihood functions.