Modelling time-inhomogeneous incomplete records of point processes using variants of hidden Markov models

Simple item page
dc.citation.volumeLatest Articles
dc.contributor.authorShahzadi A
dc.contributor.authorWang T
dc.contributor.authorParry M
dc.contributor.authorBebbington M
dc.date.accessioned2025-06-16T01:04:25Z
dc.date.available2025-06-16T01:04:25Z
dc.date.issued2025-04-23
dc.description.abstractMany point processes such as earthquakes or volcanic eruptions have incomplete records with the degree of incompleteness varying over time. For these point processes, the number of missing events between each pair of consecutively observed events can be a random variable that may depend on time, effecting the estimation of parameters or hazard. Such incomplete point processes can be modelled by compound renewal processes where the sum of renewal processes is a random variable because of random variable number of missing events. We propose shifted compound Poisson-Gamma and time-dependent shifted compound Poisson-Gamma renewal processes. Since the number of missing events can be regarded as an unobserved process, the proposed renewal processes are introduced to use in the framework of different types of homogeneous and inhomogeneous hidden Markov models to model the time-dependent variable number of missing events between each pair of consecutively observed events of incomplete point processes. Simulation experiments are employed to check the performance of proposed renewal processes with hidden Markov models. We apply the proposed models to the large magnitude explosive volcanic eruptions database to analyze the time-dependent incompleteness and demonstrate how we estimate the completeness of the record and the future hazard rate.
dc.description.confidentialfalse
dc.identifier.author-urlhttps://orcid.org/0000-0003-3504-7418
dc.identifier.citationShahzadi A, Wang T, Parry M, Bebbington M. (2025). Modelling time-inhomogeneous incomplete records of point processes using variants of hidden Markov models. Advances in Data Analysis and Classification. Latest Articles.
dc.identifier.doi10.1007/s11634-025-00632-x
dc.identifier.eissn1862-5355
dc.identifier.elements-typejournal-article
dc.identifier.issn1862-5347
dc.identifier.urihttps://mro.massey.ac.nz/handle/10179/73052
dc.languageEnglish
dc.publisherSpringer Nature
dc.publisher.urihttps://link.springer.com/article/10.1007/s11634-025-00632-x
dc.relation.isPartOfAdvances in Data Analysis and Classification
dc.rights(c) 2025 The Author/s
dc.rightsCC BY 4.0
dc.rights.licensehttps://creativecommons.org/licenses/by/4.0/
dc.subjectHazard
dc.subjectInhomogeneous hidden Markov models
dc.subjectPoint process
dc.subjectShifted compound Poisson-gamma renewal process
dc.subjectThe LaMEVE database
dc.subjectTime-inhomogeneous incompleteness
dc.titleModelling time-inhomogeneous incomplete records of point processes using variants of hidden Markov models
dc.typeJournal article
pubs.elements-id500588
pubs.organisational-groupOther
Files
Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
500588 PDF.pdf
Size:
2.11 MB
Format:
Adobe Portable Document Format
Description:
Published version.pdf
Download
License bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
license.txt
Size:
9.22 KB
Format:
Plain Text
Description:
Download
Collections
Journal Articles