A Probabilistic Characterization of Shark Movement Using Location Tracking Data

Our data consist of measurements of 22 sharks' movements within a 366-acre tidal basin. The measurements are made at irregular time points over a 16-month interval. Constant-length observation intervals would have been desirable, but are often infeasible in practice. We model the sharks' paths at short constant-length intervals by inferring their behavior (feeding vs transiting), interpolating their locations, and estimating parameters of motion (speed and turning angle) in environmental and ecological contexts. We are interested in inferring regional differences in the sharks' behavior, and behavioral interaction between them. Our method uses particle filters, a computational Bayesian technique designed to sequentially model a dynamic system. We discuss how resampling is used to approximate arbitrary densities, and illustrate its use in a simple example of a particle filter implementation of a state-space model. We then introduce a particular model formulation that uses conditioning to introduce unobserved parameters for the shark's behaviors. We show how the irregularly-observed shark locations can be modeled by interpolation as a set of movements at constant-length time intervals. We use a spline method for generating approximations of the ground truth at these intervals for comparison with our model. Finally, we demonstrate our model's estimates of the sharks' behavioral and ecological parameters of interest on a subset of the observed data.