the Efficient modelling of individual animal movement in continuous time

When making statistical inference on individual animal movement data, it is normally sensible to assume that the animal’s observed movement pattern is determined by some underlying (hidden) behaviour.  Ecologists tend to represent the underlying behavioural process of the animal as a Markov chain. The simplest variation of this sort of model is the Hidden Markov model (HMM), which represents animal behaviour as a discrete-time Markov chain, allowing for changes in behaviour at observation times. The HMM allows for very fast inference via maximum likelihood estimation, making it a very popular approach amongst ecologists. However, discrete-time models are problematic when faced with irregular data, missing observations, or when trying to compare separate analyses on contrasting timescales. Furthermore, they lack accuracy when faced with an animal which changes behaviour frequently between observations. 

Alternatively, models may be formulated in continuous time, representing animal behaviour as a continuous-time Markov chain, such that behavioural changes occur independently of observation times. Such approaches serve as an example of a ‘switching diffusion’ model; conditional on behaviour, the animal movement follows a given diffusion process (e.g. Blackwell, 1997, 2003). Variations of Markovian switching diffusion models are often used in trading (Smith, 2002; Zhang & Zhang, 2022; Zhu & Yang, 2016; Hainaut & Moraux, 2019). Continuous-time models are time scale invariant but lack the simplicity and efficiency of their discrete-time counterparts. For example, we are not able to carry out such statistical inference in continuous time outside of a somewhat complicated Markov chain Monte Carlo (MCMC) framework, which is far less accessible for an ecologist than direct optimisation using an HMM. The popularity of discrete time models with ecologists is further increased by R packages such as ‘moveHMM’ or ‘momentuHMM’ (Michelot et al., 2016; McClintock & Michelot, 2018). 

With this in mind, we hope to improve the accessibility of continuous-time switching-diffusion models for ecologists by rigorously approximating existing methods such that we allow for inference via maximum likelihood estimation or via Bayesian methods that are faster and more straightforward. We have the overall aim of producing an R package for user-friendly implementation for ecologists, taking inspiration from the popularity of R packages for inference in discrete time. 

 Please feel free to contact me at dpdgrainger1[at]sheffield.ac.uk