Bayesian Inference for animal movement in Continuous Time

Movement is an essential process for almost all species in the animal kingdom. For example, survival is the result of successfully finding food and avoiding predators. Also, reproductive success depends on encounters with mates. Over the last century, scientists have developed statistical methods to understand the nature and behaviour of species and have thus shed light on animal movement. The more we study the details of animal movement, the more we understand animal behaviour. Naturally and realistically, animal movement happens in continuous time, but movement data on tagged animals are observed in discrete time. Many statistical methods ignore this fact or consider animal movement to be time-continuous but use a discrete time approximation, which involves errors that are difficult to calculate. Blackwell et al. (2016; Methods in Ecology and Evolution, 7, 184-195) introduced a new statistical method to analyse complex animal movement with environmental information in continuous time, specifically without the need for approximation. In this thesis, continuous time Ornstein-Uhlenbeck (OU) diffusion processes have been used to model animal movement data, and Markov Chain Monte Carlo (MCMC) Bayesian methods have been applied to make inferences about the model. The purpose of this thesis is to extend and refine recently developed methods for statistically analysing animal movement data in continuous time. In practical terms, it aims to improve the efficiency of current algorithms and to allow more general models to be applied. The goals of this thesis are to extend the current continuous time models to allow for the estimation of unknown boundaries for the animal's home range or between different habitats, to extend the possible range of prior distributions that can be used for the behavioural process, and to generalise the model to allow for semi-Markov modelling. The information gained using these methods will help ecologists to learn more about animal behaviour and the environment. Ecologists study animal movement to explain the relationship between animal movement and major habitat features, interactions between species and how the animals use the habitat. We apply our methods to real data and explore their performance using simulated data.