[Statistics & Probability Seminar]
Bayesian inference for continuous-time models of animal movement
Realistic models of wildlife movement present substantial challenges for statistical inference. The models need to take account of variation in behaviour over time, usually through an unobserved behavioural state, and need to be formulated in continuous time, to allow coherent interpretation, comparison and handling of irregular observations. A suitable class of models, which are ecologically and intuitively appealing, can be defined by representing an animal's behaviour as a continuous-time Markov chain, with transition rates that depend on time and on habitat, and representing its movement as a two-dimensional diffusion process, with parameters determined by its behaviour. The complex relationship between location, behaviour and movement in these models makes inference difficult, and often a simplistic discrete-time approximation is used.
In this talk I will describe some recent progress in Bayesian inference for such models, using a Markov chain Monte Carlo algorithm. This method uses a uniformization approach to represent the unobserved changes in behaviour as a thinned Poisson process, avoiding any time-discretization error.
These ideas will be illustrated using data on individual fishers, Martes pennanti (courtesy of Scott LaPoint, Max Planck Institute for Ornithology, Konstanz) and wild boar, Sus scrofa (courtesy of Mark Lambert, Animal and Plant Health Agency, York). I will also look at extensions to multiple animals, using data on a group of simultaneously tracked reindeer, Rangifer tarandus (courtesy of Anna Skarin, Swedish University of Agricultural Sciences, Uppsala).
This is joint work with Mu Niu.