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Modelling group movement with behaviour switching in continuous time
Author(s) -
Niu Mu,
Frost Fay,
Milner Jordan E.,
Skarin Anna,
Blackwell Paul G.
Publication year - 2022
Publication title -
biometrics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.298
H-Index - 130
eISSN - 1541-0420
pISSN - 0006-341X
DOI - 10.1111/biom.13412
Subject(s) - ornstein–uhlenbeck process , brownian motion , stochastic differential equation , kalman filter , statistical physics , first hitting time model , markov chain , mathematics , movement (music) , tracking (education) , filter (signal processing) , stochastic process , computer science , control theory (sociology) , physics , statistics , artificial intelligence , psychology , computer vision , control (management) , pedagogy , acoustics
This article presents a new method for modelling collective movement in continuous time with behavioural switching, motivated by simultaneous tracking of wild or semi‐domesticated animals. Each individual in the group is at times attracted to a unobserved leading point. However, the behavioural state of each individual can switch between ‘following’ and ‘independent’. The ‘following’ movement is modelled through a linear stochastic differential equation, while the ‘independent’ movement is modelled as Brownian motion. The movement of the leading point is modelled either as an Ornstein‐Uhlenbeck (OU) process or as Brownian motion (BM), which makes the whole system a higher‐dimensional Ornstein‐Uhlenbeck process, possibly an intrinsic non‐stationary version. An inhomogeneous Kalman filter Markov chain Monte Carlo algorithm is developed to estimate the diffusion and switching parameters and the behaviour states of each individual at a given time point. The method successfully recovers the true behavioural states in simulated data sets , and is also applied to model a group of simultaneously tracked reindeer ( Rangifer tarandus ).