Superstatistical analysis and modelling of heterogeneous random walks. Metzner, C.; Mark, C.; Steinwachs, J.; Lautscham, L.; Stadler, F.; and Fabry, B. Nat Commun, Nature Publishing Group, a division of Macmillan Publishers Limited. All Rights Reserved., 2015.
Superstatistical analysis and modelling of heterogeneous random walks [link]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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