March 2023 Time-discretization approximation enriches continuous-time discrete-space models for animal movement
Joshua Hewitt, Alan E. Gelfand, Robert S. Schick
Author Affiliations +
Ann. Appl. Stat. 17(1): 740-760 (March 2023). DOI: 10.1214/22-AOAS1649


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.

Funding Statement

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.


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Joshua Hewitt. Alan E. Gelfand. Robert S. Schick. "Time-discretization approximation enriches continuous-time discrete-space models for animal movement." Ann. Appl. Stat. 17 (1) 740 - 760, March 2023.


Received: 1 December 2021; Revised: 1 June 2022; Published: March 2023
First available in Project Euclid: 24 January 2023

MathSciNet: MR4539051
zbMATH: 07656996
Digital Object Identifier: 10.1214/22-AOAS1649

Keywords: Directional persistence , hidden Markov modeling , infinitesimal generator , measurement error , posterior approximation

Rights: Copyright © 2023 Institute of Mathematical Statistics


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Vol.17 • No. 1 • March 2023
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