The efficient modelling of individual animal movement in continuous time

Animal movement data offer key insights into behavioural responses to ecological interactions and environmental change. However, recent advances in telemetry have outpaced the development of statistical methodology, leaving large datasets challenging to analyse due largely to computational limitations. Movement ecologists commonly analyse animal trajectories using discrete-time hidden Markov models (HMMs), which become restrictive when observations are irregular or behaviour changes rapidly relative to the sampling frequency of the data. Continuous-time formulations avoid these limitations but are typically computationally demanding, with existing approaches often relying on high-dimensional Bayesian MCMC inference, limiting their practical accessibility.

In this thesis, we develop a series of efficient modelling frameworks to facilitate the uptake of continuous-time methodology. We introduce the fast integrated continuous-time HMM (FInCH), which limits the number of behavioural changes between successive observations and integrates over their timing using a combination of analytical and numerical methods. This yields a close approximation of exact methods while enabling efficient computation in both Bayesian and frequentist settings. We further improve efficiency with the fast, refined integrated continuous-time HMM (FRInCH), which assumes at most one behavioural change in each half interval between observations, reducing computational cost and removing the need for tuning parameters. We then present the velocity-based continuous-time HMM (VB-CTHMM), which accounts for both the speed and directional persistence of an animal's movement while retaining the capacity for inference via direct likelihood maximisation in a multistate framework. Finally, we propose the density-level superset filtration (DSF) approach, a non-parametric method for order selection that avoids repeated model fitting by identifying behavioural states as stable clusters.

We demonstrate the proposed methods on simulated and real datasets, including case studies on kinkajou (Potos flavus), red fox (Vulpes vulpes), fisher (Pekania pennanti), reindeer (Rangifer tarandus), and domestic goat (Capra aegagrus hircus) data.