Data from: Exact Bayesian inference for animal movement in continuous time

It is natural to regard most animal movement as a continuous-time process, generally observed at discrete times. Most existing statistical methods for movement data ignore this; the remainder mostly use discrete-time approximations, the statistical properties of which have not been widely studied, or are limited to special cases. We aim to facilitate wider use of continuous-time modelling for realistic problems. We develop novel methodology which allows exact Bayesian statistical analysis for a rich class of movement models with behavioural switching in continuous time, without any need for time discretization error. We represent the times of changes in behaviour as forming a thinned Poisson process, allowing exact simulation and Markov chain Monte Carlo inference. The methodology applies to data that are regular or irregular in time, with or without missing values. We apply these methods to GPS data from two animals, a fisher (Pekania [Martes] pennanti) and a wild boar (Sus scrofa), using models with both spatial and temporal heterogeneity. We are able to identify and describe differences in movement behaviour across habitats and over time. Our methods allow exact fitting of realistically complex movement models, incorporating environmental information. They also provide an essential point of reference for evaluating other existing and future approximate methods for continuous-time inference.

将多数动物运动视为连续时间过程，而这类运动通常仅在离散时刻被观测记录，这是十分自然的理解。现有多数针对运动数据的统计方法都忽略了这一特性；其余方法大多采用离散时间近似方案，但此类近似的统计特性尚未得到广泛研究，或仅适用于特定场景。本研究旨在推动连续时间建模在实际研究问题中的更广泛应用。我们提出了全新的方法论，可针对一类包含行为切换机制的丰富连续时间运动模型开展精确的贝叶斯统计分析，完全规避了时间离散化带来的误差。我们将行为发生改变的时刻建模为稀疏泊松过程（thinned Poisson process），以此实现精确模拟与马尔可夫链蒙特卡洛（Markov chain Monte Carlo）推断。该方法论可适配时间规则或不规则、存在或不存在缺失值的各类运动数据。我们将所提方法应用于两种动物的GPS（Global Positioning System）跟踪数据：渔貂（*Pekania [Martes] pennanti*）与野猪（*Sus scrofa*），并采用兼具空间与时间异质性的运动模型。借此我们得以识别并刻画不同生境间以及随时间推移的运动行为差异。我们的方法可实现融入环境信息的复杂现实运动模型的精确拟合，同时也为评估现有及未来各类连续时间推断近似方法提供了关键的参考基准。