Inference for ETAS models with non-Poissonian mainshock arrival times

Kolev, Aleksandar A.; Ross, Gordon J.

doi:10.1007/s11222-018-9845-z

Cited by 11 publications

(6 citation statements)

References 42 publications

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“…This behaviour is called supercritical (Helmstetter and Sornette, 2002) or explosive (Browning et al, 2021). However, for real-life applications it can be desirable to limit the parameter space to non-explosive instances (Kolev and Ross, 2019). This is referred to as stability (Bremaud and Massoulie, 1996;Bacry et al, 2020), i.e.…”

Section: Stabilitymentioning

confidence: 99%

Bayesian Estimation of Multivariate Hawkes Processes with Inhibition and Sparsity

Deutsch¹,

Ross²

2022

Preprint

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Hawkes processes are point processes that model data where events occur in clusters through the self-exciting property of the intensity function. We consider a multivariate setting where multiple dimensions can influence each other with intensity function to allow for excitation and inhibition, both within and across dimensions. We discuss how such a model can be implemented and highlight challenges in the estimation procedure induced by a potentially negative intensity function.Furthermore, we introduce a new, stronger condition for stability that encompasses current approaches established in the literature. Finally, we examine the total number of offsprings to reparametrise the model and subsequently use Normal and sparsity-inducing priors in a Bayesian estimation procedure on simulated data.

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Section: Stabilitymentioning

confidence: 99%

Bayesian Estimation of Multivariate Hawkes Processes with Inhibition and Sparsity

Deutsch¹,

Ross²

2022

Preprint

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“…However, the assumption of an infinite time domain can be problematic. In Kolev and Ross (2019), it was shown that the infinite time assumption provides a poor performance regarding the North California seismic sequence, thus we prefer not to use it whenever possible. As such, we will avoid using it and instead work on the finite temporal region [0, T ].…”

Section: (Log-)likelihoodmentioning

confidence: 99%

“…. , i − 1}, with weights given by the above (Kolev and Ross, 2019). Note that unlike the MCMC sampler used in Rasmussen (2013) for Hawkes processes, this samples B (k+1) exactly from its conditional posterior, which drastically improves computational efficiency.…”

Section: Sampling Bmentioning

confidence: 99%

Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences

Kolev,

Ross

2020

Preprint

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Self-exciting Hawkes processes are used to model events which cluster in time and space, and have been widely studied in seismology under the name of the Epidemic Type Aftershock Sequence (ETAS) model. In the ETAS framework, the occurrence of the mainshock earthquakes in a geographical region is assumed to follow an inhomogeneous spatial point process, and aftershock events are then modelled via a separate triggering kernel. Most previous studies of the ETAS model have relied on point estimates of the model parameters due to the complexity of the likelihood function, and the difficulty in estimating an appropriate mainshock distribution. In order to take estimation uncertainty into account, we instead propose a fully Bayesian formulation of the ETAS model which uses a nonparametric Dirichlet process mixture prior to capture the spatial mainshock process. Direct inference for the resulting model is problematic due to the strong correlation of the parameters for the mainshock and triggering processes, so we instead use an auxiliary latent variable routine to perform efficient inference.

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“…They reported that the improvement in fit based on the renewal main-shock arrival process was adequate to describe the temporal characteristics of the catalog. Kolev and Ross (2018) applied an analogous modification to the temporal ETAS model by assuming the waiting time distribution between main-shocks follows a gamma or Brownian passage time (BPT) distribution. Their model was illustrated on two earthquake catalogs from New Madrid and Northern California.…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal ETAS model with a renewal main-shock arrival process

Stindl¹,

Chen²

2021

Preprint

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This article proposes a spatiotemporal point process model that enhances the classical Epidemic-Type Aftershock Sequence (ETAS) model by incorporating a renewal main-shock arrival process, which we term the renewal ETAS (RETAS) model. This modification is similar in spirit to the renewal Hawkes (RHawkes) process but the conditional intensity process supports a spatial domain. It empowers the main-shock intensity with the capability to reset upon the arrival of main-shocks and therefore allows for heavier clustering of earthquakes than the spatiotemporal ETAS model introduced by Ogata (1998). We introduce a likelihood evaluation algorithm for parameter estimation and provide a novel procedure to evaluate the fitted model's goodness-of-fit based on a sequential application of the Rosenblatt transformation. A simulation algorithm for the RETAS model is developed and applied to validate the numerical performance of the likelihood evaluation algorithm and goodness-of-fit test procedure. We illustrate the proposed model and procedures on various earthquake catalogs around the world each with distinctly different seismic activity. These catalogs will demonstrate that the RETAS model affords additional flexibility in comparison to the classical spatiotemporal ETAS model and has the potential for superior modeling and forecasting of seismicity.

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Inference for ETAS models with non-Poissonian mainshock arrival times

Cited by 11 publications

References 42 publications

Bayesian Estimation of Multivariate Hawkes Processes with Inhibition and Sparsity

Bayesian Estimation of Multivariate Hawkes Processes with Inhibition and Sparsity

Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences

Spatiotemporal ETAS model with a renewal main-shock arrival process

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