Spline-based diffusion models and application to accelerometer data

Theo Michelot (University of St Andrews)

Thursday 14th November 14:00-15:00 Maths 311B

Abstract

Accelerometers are attached to animals to collect information about their activity at a high temporal resolution. New statistical methodology is needed to analyse those data and obtain biological inferences about animal movement and behaviour. Here, we model the three-dimensional acceleration of the animal as a continuous-time random process, and the variability in this process depends on how active the animal is. We specify the diffusion function of the process, which measures this variability, as a smooth function of time, using splines. We use this method to analyse accelerometer data of a Cuvier's beaked whale. The animal was equipped with an accelerometer, and exposed to controlled sounds, to observe its response and infer the impact of sonars and other anthropogenic noises on whale behaviour. In our approach, the sound exposure can be included as a covariate in the diffusion function, to estimate its effect on the activity of the whale. We found that, following the start of the exposure, the animal's activity increased, and it dived to get away from the noise source. These findings, in line with previous studies, indicate that beaked whales avoid anthropogenic noises, and that ships are a disturbance with possible impact on their foraging efficiency. The method can be extended to the case of a general diffusion process where both the drift and diffusion terms can depend on time-varying covariates, and I will discuss other possible applications.

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