Kolev, Aleksandar Atanasov;
(2020)
Extensions of self-exciting point processes with applications in seismology and ecology.
Doctoral thesis (Ph.D), UCL (University College London).
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Abstract
This thesis focuses on extending the ETAS model. ETAS is a special case of the Hawkes process - a self-exciting point process that provides the opportunity for a multilayered intensity structure that addresses the rate of events as a function of previous events' history. Triggering and clustering behaviours are naturally captured. The most simplistic version of the Hawkes process takes into account a single temporal sequence. Additional features such as marks, spatial information, other labels and multivariate scenarios can be considered. In this thesis we contribute primarily to three main aspects of a Hawkes process - temporal, spatial and multivariate analyses. Each of these challenges were addressed by incorporating new functionalities into the base process. Then we also solved the emerging estimation needs. We began by exploring a renewal immigration concept where the main (immigrant) events follow a non-Poissonian distribution that provides an inhomogeneous temporal ground modelling. Then we explored a non-parametric spatial kernel estimation for the inference of the main events spatial aggregation. This Bayesian density estimation relies on a Dirichlet process application in a multivariate Normal distribution mixture modelling. Finally, we explored the application of self-exciting process in the context of spatially explicit capturing data. We introduced discrete space, continuous time, multivariate Hawkes process that is tailored towards limited number of observations from multiple objects that share common behaviour. The introduced models and methods suggest superior performance compared to conventional techniques. They are directly applicable to fields where spatio-temporal clustering is observed. Some of the examples include crime, financial indicators change, earthquake modelling, people and animal movement.
| Type: | Thesis (Doctoral) |
|---|---|
| Qualification: | Ph.D |
| Title: | Extensions of self-exciting point processes with applications in seismology and ecology |
| Event: | UCL |
| Open access status: | An open access version is available from UCL Discovery |
| Language: | English |
| Additional information: | Copyright © The Author 2020. Original content in this thesis is licensed under the terms of the Creative Commons Attribution 4.0 International (CC BY 4.0) Licence (https://creativecommons.org/licenses/by/4.0/). Any third-party copyright material present remains the property of its respective owner(s) and is licensed under its existing terms. Access may initially be restricted at the author’s request. |
| Keywords: | ETAS, Bayesian, Earthquake, SCR, Dirichlet process, Latent variable MCMC, Hawkes process |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Chemical Engineering |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10110902 |
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