Process Convolution Approaches for Modeling Interacting Trajectories

• Activity Number: 288 - Advances in Nonlinear and Non-Gaussian Spatio-Temporal Dynamical Models for Environmental and Ecological Processes
• Type: Topic Contributed
• Date/Time: Tuesday, August 1, 2017 : 8:30 AM to 10:20 AM
• Sponsor: Section on Bayesian Statistical Science
• Author(s): Henry Scharf* and Mevin Hooten and Devin Johnson and John Durban
• Companies: Colorado State University and Colorado State University and NOAA Alaska Fisheries Science Center and NOAA Southwest Fisheries Science Center
• Keywords: Gaussian process ; process convolution ; animal movement ; dynamic social network

Abstract

Gaussian processes are a fundamental statistical tool used in a wide range of statistical applications. In the spatiotemporal setting, the covariance of a Gaussian process is typically a function of relative locations in space and time. However, many commonly used covariance functions can be insufficient in some situations. In contrast, process convolutions represent a flexible, interpretable approach to defining the covariance of a Gaussian process, and have modest requirements to ensure validity. We introduce a generalization to the process convolution approach that employs multiple convolutions in sequence to form what we term a "process convolution chain." We demonstrate an application of process convolution chains to study the movement of killer whales, in which the paths of multiple individuals are not independent, but reflect dynamic social interactions within the population. Our proposed model for dependent movement provides inference for the latent dynamic social structure in the study population. Additionally, we achieve a reduction in uncertainty for the estimated locations of the whales, compared to a model that treats paths as independent.