Inference for ETAS models with non-Poissonian mainshock arrival times

摘要

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.