Bayesian inference of Lévy walks via hidden Markov models

Seongyu Park, Samudrajit Thapa, Yeongjin Kim, Michael A. Lomholt*, Jae Hyung Jeon

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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.

OriginalsprogEngelsk
Artikelnummer484001
TidsskriftJournal of Physics A: Mathematical and Theoretical
Vol/bind54
Udgave nummer48
Antal sider24
ISSN1751-8113
DOI
StatusUdgivet - dec. 2021

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Publisher Copyright:
© 2021 The Author(s). Published by IOP Publishing Ltd

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