Bayesian data fusion approaches to predicting spatial tracks: Application to marine mammals

Abstract

Bayesian Melding (BM) and downscaling are two Bayesian approaches commonly used to combine data from different sources for statistical inference. We extend these two approaches to combine accurate but sparse direct observations with another set of high-resolution but biased calculated observations. We use our methods to estimate the path of a moving or evolving object and apply them in a case study of tracking northern fur seals. To make the BM approach computationally feasible for high-dimensional (big) data, we exploit the properties of the processes along with approximations to the likelihood to break the high-dimensional problem into a series of lower dimensional problems. To implement the alternative, downscaling approach, we use R-INLA to connect the two sources of observations via a linear mixed effect model. We compare the predictions of the two approaches by cross-validation as well as simulations. Our results show that both approaches yield similar results—both provide accurate, high resolution estimates of the at-sea locations of the northern fur seals, as well as Bayesian credible intervals to characterize the uncertainty about the estimated movement paths.