Kolev, A;
Ross, G;
(2018)
Inference for ETAS models with non-Poissonian mainshock arrival times.
Statistics and Computing
10.1007/s11222-018-9845-z.
(In press).
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Abstract
The Hawkes process is a widely used statistical model for point processes which produce clustered event times. A specific version known as the ETAS model is used in seismology to forecast earthquake arrival times under the assumption that mainshocks follow a Poisson process, with aftershocks triggered via a parametric kernel function. However, this Poissonian assumption contradicts several aspects of seismological theory which suggest that the arrival time of mainshocks instead follows alternative renewal distributions such as the Gamma or Brownian Passage Time. We hence show how the standard ETAS/Hawkes process can be extended to allow for non-Poissonian distributions by introducing a dependence based on the underlying process’ behaviour. Direct maximum likelihood estimation of the resulting models is not computationally feasible in the general case, so we also present a novel Bayesian MCMC algorithm for efficient estimation using a latent variable representation.
| Type: | Article |
|---|---|
| Title: | Inference for ETAS models with non-Poissonian mainshock arrival times |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1007/s11222-018-9845-z |
| Publisher version: | http://doi.org/10.1007/s11222-018-9845-z |
| Language: | English |
| Additional information: | Copyright © The Author(s) 2018 Open Access. This article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made. |
| Keywords: | ETAS, Stress release, Renewal process, Hawkes process, Brownian passage times, RHawkes |
| 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/10069525 |
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