Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences

Kolev, Aleksandar A.; Ross, Gordon J.

doi:10.48550/arxiv.2002.01706

Cited by 2 publications

(3 citation statements)

References 47 publications

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“…As mentioned earlier Kolev and Ross (2020) propose an alternative semiparametric framework of the ETAS model, which assumes a Dirichlet process prior over the background intensity. Such a model is more related to the classical KDE approach than the model proposed in our work.…”

Section: Case Study: L'aquila Italymentioning

confidence: 99%

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GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

et al. 2022

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The spatio-temporal epidemic type aftershock sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a fully Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l’Aquila region, Italy, with the devastating event on 6 April 2009, is presented.

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Section: Case Study: L'aquila Italymentioning

confidence: 99%

“…But these studies rarely consider the spatio-temporal ETAS model and only with strong simplifications, e.g., a constant background intensity μ (Rasmussen 2013). Recently, however, Kolev and Ross (2020) considered an inhomogeneous background intensity modelled via a Dirichlet process.…”

Section: Introductionmentioning

confidence: 99%

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

et al. 2022

View full text Add to dashboard Cite

show abstract

“…But these studies rarely consider the spatio-temporal ETAS model and only with strong simplifications, e.g., a constant background intensity µ (Rasmussen, 2013). Recently, however, (Kolev and Ross, 2020) considered an inhomogeneous background intensity modelled via a Dirichlet process.…”

Section: Introductionmentioning

confidence: 99%

GP-ETAS: Semiparametric Bayesian inference for the spatio-temporal Epidemic Type Aftershock Sequence model

Molkenthin¹,

Donner²,

Reich³

et al. 2020

Preprint

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The spatio-temporal Epidemic Type Aftershock Sequence (ETAS) model is widely used to describe the self-exciting nature of earthquake occurrences. While traditional inference methods provide only point estimates of the model parameters, we aim at a full Bayesian treatment of model inference, allowing naturally to incorporate prior knowledge and uncertainty quantification of the resulting estimates. Therefore, we introduce a highly flexible, non-parametric representation for the spatially varying ETAS background intensity through a Gaussian process (GP) prior. Combined with classical triggering functions this results in a new model formulation, namely the GP-ETAS model. We enable tractable and efficient Gibbs sampling by deriving an augmented form of the GP-ETAS inference problem. This novel sampling approach allows us to assess the posterior model variables conditioned on observed earthquake catalogues, i.e., the spatial background intensity and the parameters of the triggering function. Empirical results on two synthetic data sets indicate that GP-ETAS outperforms standard models and thus demonstrate the predictive power for observed earthquake catalogues including uncertainty quantification for the estimated parameters. Finally, a case study for the l'Aquila region, Italy, with the devastating event on 6 April 2009, is presented.

show abstract

Semiparametric Bayesian Forecasting of Spatial Earthquake Occurrences

Cited by 2 publications

References 47 publications

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

GP-ETAS: semiparametric Bayesian inference for the spatio-temporal epidemic type aftershock sequence model

GP-ETAS: Semiparametric Bayesian inference for the spatio-temporal Epidemic Type Aftershock Sequence model

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