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Title: Continuous-time discrete-space (CTDS) movement models over two- and three-dimensional space Authors:  Joshua Hewitt - Duke University (United States) [presenting]
Robert Schick - Duke University (United States)
Alan Gelfand - Duke University (United States)
Abstract: Continuous-time discrete-space (CTDS) processes for animal movement model trajectories across discretely observed spatial domains, which arise via gridded remote sensing products in 2D, or via underwater sound propagation models in 3D. CTDS models are approximately estimated from finite observations of animal location because the exact likelihood has $O(N^3)$ computational complexity, where $N$ is the size of the spatial domain. The usual approximation averages estimates from multiple imputations of the complete, unobserved trajectory. However, imputations typically discretize output from continuous-space surrogate models that do not account for complex boundaries like coastlines and bathymetry. As a result, parameter and location estimates may be biased by imputations that are inconsistent with respect to physical barriers. We remedy this issue by proposing a discrete-time likelihood approximation. We also develop additional theory and interpretation for CTDS model formulation, which supports the approximation. We demonstrate the improvement of the discrete-time approximation in simulation. We also demonstrate improvement in an application, by combining GPS locations and depth measurements with bathymetry data to refine estimates of a beaked whales position during exposure to anthropogenic sound.