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).

中文翻译：

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用连续时间的行为切换对群体运动进行建模

本文提出了一种通过同时跟踪野生或半驯养动物的行为来模拟连续时间集体运动的新方法。小组中的每个人有时都会被一个未被观察到的领先点所吸引。然而，每个人的行为状态可以在“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”运动建模为布朗运动。前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更高维的 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器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。该方法成功地恢复了模拟数据集中的真实行为状态，并应用于模拟一组同时跟踪的驯鹿 (牵牛花）。