Bayesian inference of Lévy walks via hidden Markov models

12Citations
Citations of this article
5Readers
Mendeley users who have this article in their library.

This article is free to access.

Abstract

The Lévy walk (LW) is a non-Brownian random walk model that has been found to describe anomalous dynamic phenomena in diverse fields ranging from biology over quantum physics to ecology. Recurrently occurring problems are to examine whether observed data are successfully quantified by a model classified as LWs or not and extract the best model parameters in accordance with the data. Motivated by such needs, we propose a hidden Markov model for LWs and computationally realize and test the corresponding Bayesian inference method. We introduce a Markovian decomposition scheme to approximate a renewal process governed by a power-law waiting time distribution. Using this, we construct the likelihood function of LWs based on a hidden Markov model and the forward algorithm. With the LW trajectories simulated at various conditions, we perform the Bayesian inference for parameter estimation and model classification. We show that the power-law exponent of the flight-time distribution can be successfully extracted even at the condition that the mean-squared displacement does not display the expected scaling exponent due to the noise or insufficient trajectory length. It is also demonstrated that the Bayesian method performs remarkably inferring the LW trajectories from given unclassified trajectory data set if the noise level is moderate.

Cite

CITATION STYLE

APA

Park, S., Thapa, S., Kim, Y., Lomholt, M. A., & Jeon, J. H. (2021). Bayesian inference of Lévy walks via hidden Markov models. Journal of Physics A: Mathematical and Theoretical, 54(48). https://doi.org/10.1088/1751-8121/ac31a1

Register to see more suggestions

Mendeley helps you to discover research relevant for your work.

Already have an account?

Save time finding and organizing research with Mendeley

Sign up for free