FInCH: Fast statistical inference for continuous-time animal movement

1. It is common for movement ecologists to model individual-level animal movement in discrete time using methods such as hidden Markov models (HMMs). Although often the fitting of HMMs is computationally efficient, the key assumptions required to model in discrete time become limiting when dealing with temporally irregular data or an animal that changes behaviour frequently, or when comparing separate analyses on different timescales.

2. Continuous-time models of animal movement, which can be formulated in a scale-invariant way, avoid these complications but typically lack computational efficiency. Most continuous-time methods only allow for inference in a Bayesian Markov Chain Monte Carlo (MCMC) framework, sampling from a parameter space of high dimensionality, which has rendered them inaccessible to biologists, inhibiting their uptake.

3. In this work, we seek to address this inaccessibility by rigorously approximating existing inference methods for a class of spatially homogeneous continuous-time models. We have developed a methodology that involves limiting the numbers of switches in behavioural state and then inte18 grating out the times of those switches, using a combination of analytical and numerical methods, known as the Fast Integrated Continuous-time HMM (FInCH) approach. Our method allows for rapid evaluation of the likelihood, permitting direct maximisation of the likelihood or the posterior density, or the use of off-the-shelf fixed-dimension MCMC.

4. We demonstrate this approach using a range of simulated and real data, showing that the FInCH approach competes with its discrete-time counterparts in terms of efficiency, while improving accuracy. By using spline-based interpolation of terms in the likelihood, the method extends to large datasets while remaining competitive. We include examples with up to 100,000 observations.