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Markov-Modulated Nonhomogeneous Poisson Processes for Modeling Detections in Surveys of Marine Mammal Abundance

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  • Roland Langrock
  • David L. Borchers
  • Hans J. Skaug

Abstract

We consider Markov-modulated nonhomogeneous Poisson processes for modeling sightings of marine mammals in shipboard or aerial surveys. In such surveys, detection of an animal is possible only when it surfaces, and with some species a substantial proportion of animals is missed because they are diving and thus not available for detection. This needs to be adequately accounted for to avoid biased abundance estimates. The tendency of surfacing events of marine mammals to occur in clusters motivates consideration of the flexible class of Markov-modulated Poisson processes in this context. We embed these models in distance sampling models, introducing nonhomogeneity in the process to account for the fact that the observer's probability of detecting an animal decreases with increasing distance to the animal. We derive approximate expressions for the likelihood of Markov-modulated nonhomogeneous Poisson processes that enable us to estimate the model parameters through numerical maximum likelihood. The performance of the approach is investigated in an extensive simulation study, and applications to pilot and beaked whale tag data as well as to minke whale tag and survey data demonstrate its relevance in abundance estimation.

Suggested Citation

  • Roland Langrock & David L. Borchers & Hans J. Skaug, 2013. "Markov-Modulated Nonhomogeneous Poisson Processes for Modeling Detections in Surveys of Marine Mammal Abundance," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 108(503), pages 840-851, September.
  • Handle: RePEc:taf:jnlasa:v:108:y:2013:i:503:p:840-851
    DOI: 10.1080/01621459.2013.797356
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    Cited by:

    1. Avanzi, Benjamin & Taylor, Greg & Wong, Bernard & Xian, Alan, 2021. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," European Journal of Operational Research, Elsevier, vol. 290(1), pages 177-195.
    2. Benjamin Avanzi & Greg Taylor & Bernard Wong & Alan Xian, 2020. "Modelling and understanding count processes through a Markov-modulated non-homogeneous Poisson process framework," Papers 2003.13888, arXiv.org, revised May 2020.
    3. Kenneth F. Kellner & Arielle W. Parsons & Roland Kays & Joshua J. Millspaugh & Christopher T. Rota, 2022. "A Two-Species Occupancy Model with a Continuous-Time Detection Process Reveals Spatial and Temporal Interactions," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 27(2), pages 321-338, June.
    4. David Louis Borchers & Martin James Cox, 2017. "Distance sampling detection functions: 2D or not 2D?," Biometrics, The International Biometric Society, vol. 73(2), pages 593-602, June.

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