School of Mathematics and Statistics, University of Glasgow, Glasgow, UK.
School of Mathematics and Statistics, University of Sheffield, Sheffield, UK.
Biometrics. 2022 Mar;78(1):286-299. doi: 10.1111/biom.13412. Epub 2020 Dec 17.
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).
本文提出了一种新的方法来对连续时间中的集体运动进行建模，该方法具有行为切换，其动机是同时对野生动物或半驯化动物进行跟踪。群体中的每个个体有时都会被一个未被观察到的引导点吸引。然而，每个个体的行为状态可以在“跟随”和“独立”之间切换。“跟随”运动通过线性随机微分方程建模，而“独立”运动则通过布朗运动建模。引导点的运动被建模为 Ornstein-Uhlenbeck（OU）过程或布朗运动（BM），这使得整个系统成为一个高维的 Ornstein-Uhlenbeck 过程，可能是一个内在的非平稳版本。开发了一种非齐次卡尔曼滤波马尔可夫链蒙特卡罗算法来估计扩散和切换参数以及每个个体在给定时间点的行为状态。该方法成功地从模拟数据集恢复了真实的行为状态，并且还应用于对一群同时跟踪的驯鹿（Rangifer tarandus）进行建模。
