Bayesian inference of Levy walks via hidden Markov models

被引:13
作者
Park, Seongyu [1 ]
Thapa, Samudrajit [2 ,3 ]
Kim, Yeongjin [1 ]
Lomholt, Michael A. [4 ]
Jeon, Jae-Hyung [1 ]
机构
[1] Pohang Univ Sci & Technol POSTECH, Dept Phys, Pohang 37673, South Korea
[2] Tel Aviv Univ, Sackler Ctr Computat Mol & Mat Sci, IL-69978 Tel Aviv, Israel
[3] Tel Aviv Univ, Sch Mech Engn, IL-69978 Tel Aviv, Israel
[4] Univ Southern Denmark, Dept Phys Chem & Pharm, PhyLife, Campusvej 55, DK-5230 Odense M, Denmark
基金
新加坡国家研究基金会;
关键词
Bayesian inference; Levy walks; parameter estimation; model classification; SINGLE-PARTICLE TRACKING; ANOMALOUS DIFFUSION; SEARCH; PATTERNS; FLUCTUATIONS; MOVEMENT; FLIGHTS;
D O I
10.1088/1751-8121/ac31a1
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The Levy 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.
引用
收藏
页数:23
相关论文
共 94 条
[1]  
[Anonymous], 2008, ELECT NOISE FLUCTUAT
[2]   Swarming bacteria migrate by Levy Walk [J].
Ariel, Gil ;
Rabani, Amit ;
Benisty, Sivan ;
Partridge, Jonathan D. ;
Harshey, Rasika M. ;
Be'er, Avraham .
NATURE COMMUNICATIONS, 2015, 6
[3]   Differentiating the Levy walk from a composite correlated random walk [J].
Auger-Methe, Marie ;
Derocher, Andrew E. ;
Plank, Michael J. ;
Codling, Edward A. ;
Lewis, Mark A. .
METHODS IN ECOLOGY AND EVOLUTION, 2015, 6 (10) :1179-1189
[4]   A Levy flight for light [J].
Barthelemy, Pierre ;
Bertolotti, Jacopo ;
Wiersma, Diederik S. .
NATURE, 2008, 453 (7194) :495-498
[5]  
Bayes T., 1763, Philosophical Transactions of the Royal Society of London, V53, P370
[6]   A statistical physics view of swarming bacteria [J].
Be'er, Avraham ;
Ariel, Gil .
MOVEMENT ECOLOGY, 2019, 7 (1)
[7]   Superstatistics [J].
Beck, C ;
Cohen, EGD .
PHYSICA A-STATISTICAL MECHANICS AND ITS APPLICATIONS, 2003, 322 (1-4) :267-275
[8]   Detecting an orientation component in animal paths when the preferred direction is individual-dependent [J].
Benhamou, S .
ECOLOGY, 2006, 87 (02) :518-528
[9]   How many animals really do the Levy walk? [J].
Benhamou, Simon .
ECOLOGY, 2007, 88 (08) :1962-1969
[10]  
Brown R., 1828, PHILOS MAG, V4, P161, DOI [10.1080/14786442808674769, DOI 10.1080/14786442808674769]