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An Inhomogeneous Weibull–Hawkes Process to Model Underdispersed Acoustic Cues

Author

Listed:
  • Alec B. M. Van Helsdingen

    (University of Auckland)

  • Tiago A. Marques

    (University of St Andrews
    Faculdade de Ciências, Universidade de Lisboa)

  • Charlotte M. Jones-Todd

    (University of Auckland)

Abstract

A Hawkes point process describes self-exciting behaviour where event arrivals are triggered by historic events. These models are increasingly becoming a popular choice in analysing event-type data. Like all other inhomogeneous Poisson point processes, the waiting time between events in a Hawkes process is derived from an exponential distribution with mean one. However, as with many ecological and environmental data, this is an unrealistic assumption. We, therefore, extend and generalise the Hawkes process to account for potential under- or overdispersion in the waiting times between events by assuming the Weibull distribution as the foundation of the waiting times. We apply this model to the acoustic cue production times of sperm whales and show that our Weibull–Hawkes model better captures the inherent underdispersion in the interarrival times of echolocation clicks emitted by these whales.

Suggested Citation

  • Alec B. M. Van Helsdingen & Tiago A. Marques & Charlotte M. Jones-Todd, 2025. "An Inhomogeneous Weibull–Hawkes Process to Model Underdispersed Acoustic Cues," Journal of Agricultural, Biological and Environmental Statistics, Springer;The International Biometric Society;American Statistical Association, vol. 30(1), pages 39-62, March.
    • Handle: RePEc:spr:jagbes:v:30:y:2025:i:1:d:10.1007_s13253-024-00626-w
    DOI: 10.1007/s13253-024-00626-w
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