title: Superstatistical analysis and modelling of heterogeneous random walks.
abstract: Stochastic time series are ubiquitous in nature. In particular, random walks with time-varying statistical properties are found in many scientific disciplines. Here we present a superstatistical approach to analyse and model such heterogeneous random walks. The time-dependent statistical parameters can be extracted from measured random walk trajectories with a Bayesian method of sequential inference. The distributions and correlations of these parameters reveal subtle features of the random process that are not captured by conventional measures, such as the mean-squared displacement or the step width distribution. We apply our new approach to migration trajectories of tumour cells in two and three dimensions, and demonstrate the superior ability of the superstatistical method to discriminate cell migration strategies in different environments. Finally, we show how the resulting insights can be used to design simple and meaningful models of the underlying random processes.
authors.affiliation: Department of Physics, Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen 91052, Germany.
authors.forename: Claus
authors.initials: C
authors.lastname: Metzner
authors.affiliation: Department of Physics, Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen 91052, Germany.
authors.forename: Christoph
authors.initials: C
authors.lastname: Mark
authors.affiliation: Department of Physics, Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen 91052, Germany.
authors.forename: Julian
authors.initials: J
authors.lastname: Steinwachs
authors.affiliation: Department of Physics, Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen 91052, Germany.
authors.forename: Lena
authors.initials: L
authors.lastname: Lautscham
authors.affiliation: Department of Physics, Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen 91052, Germany.
authors.forename: Franz
authors.initials: F
authors.lastname: Stadler
authors.affiliation: Department of Physics, Biophysics Group, Friedrich-Alexander-Universität Erlangen-Nürnberg (FAU), Erlangen 91052, Germany.
authors.forename: Ben
authors.initials: B
authors.lastname: Fabry
mesh_terms: D001499:Bayes Theorem; D045744:Cell Line, Tumor; D002465:Cell Movement / Q000502:physiology*; D006801:Humans; D008954:Models, Biological; D015233:Models, Statistical; D013269:Stochastic Processes; D013499:Surface Properties; D013997:Time Factors