Approximate inference in a State-Space Model for animal movemet using ABC

SOFIA RUIZ SUAREZ; JUAN MANUEL MORALES

Conferencia; International Statistical Ecology Conference; 2018

The way in which animals move is of fundamental importance in ecology. The study and analysis of animal movement can be framed as state-space models, allowing to contemplate both the process of intrinsic movement of the animal and the observation process. Several models have been proposed which differ primarily in the temporal conceptualization of the movement process, namely continuous and discrete time formulations. The continuous-time approach has the advantage that the inference analysis is (in principle) not affected by the choice of scale of observation. In addition, these kinds of models tend to be computationally efficient. In contrast, discrete-time models describe movement as a series of steps and turns (or movement directions) that are performed at regular occasions. These models are often viewed as more intuitive and interpretable than the continuous ones. It is easier to conceptualize the movement process as a series of steps and turns sampled from particular distributions than to deal with partial differential equations. However, animal movement occurs in continuous time but we observe it at fixed time intervals. As a compromise between the interpretability of models based on steps and turns and the realism of continuous time models, we use a random walk where movement decisions (steps and turns) are made in continuous time. The movement process is then observed at regular time intervals. Defining the likelihood function of such model is problematic because several or no directional changes could occur between observations. However, we show that under certain conditions it is possible to fit this model using likelihood free methods such as Approximate Bayesian Computation and synthetic likelihood. The applicability of these methods depends critically on the ratio between the temporal scale of the observation process and the mean time between changes of movement direction. Roughly, values between 0.3 and 3 of this ratio generate scenarios where it is possible to make inference using likelihood free methods. Further studies are needed to explore the possibility of using these methods for more realistic movement models, for example including changes in behaviour.