An inhomogeneous Weibull–Hawkes process to model underdispersed acoustic cues

Funding: TAM time covered by ACCURATE, funded by the US Navy Living Marine Resources program (contract no. N3943019C2176). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020). This work was supported by Marsden F...

Full description

Bibliographic Details
Published in:Journal of Agricultural, Biological and Environmental Statistics
Main Authors: Van Helsdingen, Alec B.M., Marques, Tiago A., Jones-Todd, Charlotte M.
Other Authors: University of St Andrews.School of Mathematics and Statistics, University of St Andrews.Centre for Research into Ecological & Environmental Modelling, University of St Andrews.Statistics
Format: Article in Journal/Newspaper
Language:English
Published: 2024
Subjects:
Overdispersion
Point patterns
Self-excitement
Sperm whale
Underdispersion
Statistics and Probability
General Environmental Science
Agricultural and Biological Sciences (miscellaneous)
General Agricultural and Biological Sciences
Statistics
Probability and Uncertainty
Applied Mathematics
DAS
Hawkes
Hawkes Point
Marsden
Online Access:https://hdl.handle.net/10023/29870
https://doi.org/10.1007/s13253-024-00626-w
Description
Summary:Funding: TAM time covered by ACCURATE, funded by the US Navy Living Marine Resources program (contract no. N3943019C2176). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UIDB/00006/2020). This work was supported by Marsden Fund proposal UOA 3723517 and Asian Office of Aerospace Research & Development grant FA2386-21-1-4028. 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. Peer reviewed

Similar Items