Inference for ETAS Models With Non-Poissonian Mainshock Arrival Times

Gordon Ross, Aleksandar A. Kolev

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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 main-shocks instead follows alternative renewal distributions such as the Gamma or Brownian Passage Time (BPT). 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.
Original languageEnglish
Pages (from-to)915-931
Number of pages17
JournalStatistics and Computing
Volume29
Issue number5
Early online date13 Dec 2018
DOIs
Publication statusPublished - 30 Sept 2019

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