Continuous time discrete state models are a valuable tool for explaining animal movement. However, data collection to fit such models over a specified window of time can be misaligned with the actual realization of the movement process. This necessitates approximate model fitting, at present, through approximate imputation distributions (AIDs). Here, we propose a direct time-discretization approximation to the likelihood. The approach employs familiar ideas from hidden Markov modeling. Computation is implemented through the induced infinitesimal generator matrix. Linearization of this matrix expedites computation time. Through simulation and a real data application involving whale movement, we demonstrate that this model fitting strategy can outperform AID approaches.
The authors were funded by the United States Office of Naval Research grant N000141812807 under the project entitled Phase II Multi-study Ocean acoustics Human effects Analysis (Double MOCHA). This contribution is Double MOCHA White Paper #07.
Support for the Atlantic BRS is provided by Naval Facilities Engineering Command Atlantic under Contract No. N62470-15-D-8006, Task Order 18F4036, Issued to HDR, Inc.
The data analyzed here were collected as part of the Atlantic Behavioral Response Study under NMFS permit #22156, issued to Doug Nowacek. We thank Andy Read of Duke University and Brandon Southall of Southall Environmental Associates for allowing us use of the data.
We acknowledge and thank several people for stimulating conversation that spurred our thinking and development of the model, including Richard Glennie, Catriona Harris, Theo Michelot, and Len Thomas—all from the University of St Andrews. We also thank Will Cioffi and Nicola Quick from Duke University. Computing was performed on the Duke Compute Cluster at Duke University. We thank the Editor and two anonymous reviewers for their feedback, which has helped to improve the manuscript.
"Time-discretization approximation enriches continuous-time discrete-space models for animal movement." Ann. Appl. Stat. 17 (1) 740 - 760, March 2023. https://doi.org/10.1214/22-AOAS1649