Goldstein-Kac telegraph processes with random speeds: Path probabilities, likelihoods, and reported Lévy flights

Aaron Sim, Juliane Liepe, and Michael P. H. Stumpf
Phys. Rev. E 91, 042115 – Published 15 April 2015

Abstract

The Goldstein-Kac telegraph process describes the one-dimensional motion of particles with constant speed undergoing random changes in direction. Despite its resemblance to numerous real-world phenomena, the singular nature of the resultant spatial distribution of each particle precludes the possibility of any a posteriori empirical validation of this random-walk model from data. Here we show that by simply allowing for random speeds, the ballistic terms are regularized and that the diffusion component can be well-approximated via the unscented transform. The result is a computationally efficient yet robust evaluation of the full particle path probabilities and, hence, the parameter likelihoods of this generalized telegraph process. We demonstrate how a population diffusing under such a model can lead to non-Gaussian asymptotic spatial distributions, thereby mimicking the behavior of an ensemble of Lévy walkers.

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  • Received 6 November 2014
  • Revised 20 February 2015

DOI:https://doi.org/10.1103/PhysRevE.91.042115

©2015 American Physical Society

Authors & Affiliations

Aaron Sim*, Juliane Liepe, and Michael P. H. Stumpf

  • Centre for Integrative Systems Biology and Bioinformatics, Department of Life Sciences, Imperial College London, SW7 2AZ, United Kingdom

  • *aaron.sim11@imperial.ac.uk
  • m.stumpf@imperial.ac.uk

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Vol. 91, Iss. 4 — April 2015

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