Bayesian Statistics in Action

Abstract

Although animal locations gained via GPS, etc. are typically observed on a discrete time scale, movement models formulated in continuous time are preferable in order to avoid the struggles experienced in discrete time when faced with irregular observations or the prospect of comparing analyses on different time scales. A class of models able to emulate a range of movement ideas are defined by representing movement as a combination of stochastic processes describing both speed and bearing.A method for Bayesian inference for such models is described through the use of a Markov chain Monte Carlo approach. Such inference relies on an augmentation of the animal's locations in discrete time that have been observed with error, with a more detailed movement path gained via simulation techniques. Analysis of real data on an individual reindeer Rangifer tarandus illustrates the presented methods.

Bayesian Inference for Multistate ‘Step and Turn’ Animal Movement in Continuous Time

“…In Fig. 2 of Parton et al (2017), the examples of reconstructed movement paths highlight that the characteristics of movement inferred from the observations are markedly different from a simple linear interpolation of such observations. Without accounting for observation error, as in many discrete-time methods, linearly interpolating between observations would lead to a small number of large (±π ) turning angles.…”

“…Popular variants on this include state space models to incorporate observation error (Patterson et al 2010;Jonsen et al 2013), hidden Markov models for efficiency (Langrock et al 2012) and change point analysis rather than Markov chains to identify behavioural switches (Gurarie et al 2009;Nams 2014). Parton et al (2017) introduce a continuous-time movement model based on similar quantities to those of the popular discrete-time 'step and turn' models. This provides familiar descriptive parameters for estimation, whilst respecting the inherent continuous-time characteristic of movement, having the ability to handle missing and irregular observations with ease.…”

“…To account for these, inference would describe movement that is tortuous (correlated random walk with low correlation). However, if observation error is accounted for, Parton et al (2017) show that the information provided by all the observations suggests movement that is persistent (correlated random walk with high correlation).…”

“…Describing only single-state movement limits Parton et al (2017) to applications with short-term sampling periods. Our aim here is to introduce a statistical, multistate movement model in continuous time able to provide intuitive and easily interpretable estimated parameters for the non-statistical user.…”

“…Our aim here is to introduce a statistical, multistate movement model in continuous time able to provide intuitive and easily interpretable estimated parameters for the non-statistical user. Multistate switching movement is introduced by extending Parton et al (2017) to include a continuous-time Markov chain behavioural process. Section 2 introduces our proposed model, and an approach for fully Bayesian inference given observed telemetry data is outlined in Sect.…”