Superstatistical analysis and modelling of heterogeneous random walks. Metzner, C., Mark, C., Steinwachs, J., Lautscham, L., Stadler, F., & Fabry, B. Nat Commun, Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved., 2015. Paper abstract bibtex 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.
@ARTICLE{Metzner2015,
author = {Metzner, Claus and Mark, Christoph and Steinwachs, Julian and Lautscham,
Lena and Stadler, Franz and Fabry, Ben},
title = {Superstatistical analysis and modelling of heterogeneous random walks},
journal = {Nat Commun},
year = {2015},
volume = {6},
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.},
comment = {Supplementary information available for this article at http://www.nature.com/ncomms/2015/150625/ncomms8516/suppinfo/ncomms8516_S1.html},
file = {:ncomms8516.pdf:PDF},
owner = {Tiago Marques},
publisher = {Nature Publishing Group, a division of Macmillan Publishers Limited.
All Rights Reserved.},
timestamp = {2015.07.16},
url = {http://dx.doi.org/10.1038/ncomms8516}
}
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