Abstract
The paper proposes a spatio-temporal process that improves the assessment of events in space and time, considering a contagion model (branching process) within a regression-like framework to take covariates into account. The proposed approach develops the forward likelihood for prediction method for estimating the ETAS model, including covariates in the model specification of the epidemic component. A simulation study is carried out for analysing the misspecification model effect under several scenarios. Also an application to the Italian seismic catalogue is reported, together with the reference to the developed R package.
Highlights
Contagious phenomena are well described in space and time by self-exciting point processes, such that the conditional intensity function is obtained as the sum of the long-term variation component and the short-term variation one
Extending the model formulation proposed by Meyer et al (2012) in the context of infectious disease transmission, we suggest the use of a specific branching-type model for earthquake description in a regression-oriented version modelling, accounting for external covariates, expected to explain some of the overall variability of the studied phenomenon and lead to a decrease in the unpredictable variability
From previous studies (e.g., Adelfio and Chiodi 2015b) on the basis of the diagnostic results, the need of a more flexible model for the triggered component of the Epidemic-Type Aftershock Sequences (ETAS) model revealed, noticing that even if the background seismicity is well described by the FLP estimated intensity, at least if compared with existing methods, something is still missing in the description of the space-time triggered part
Summary
Contagious phenomena are well described in space and time by self-exciting point processes, such that the conditional intensity function is obtained as the sum of the long-term variation component (the so-called endemic) and the short-term variation one (the epidemic part). An example of such two-component temporal point process regression modelling for independent individuals is the additive-multiplicative model (Lin and Ying 1995; Sasieni 1996), such that the conditional intensity consist of additive endemic (the risk of infection from external sources, independent of the past) and epidemic components (individual-to-individual transmission of the disease and depends on the internal history of the process). In this paper, using the terminology of the survival analysis, we propose a more general additive-multiplicative model for the conditional intensity function of a space-time self-exciting point process with covariates which may vary continuously in space, incorporating their effect in the triggering effect, using the FLP approach as in Chiodi and Adelfio (2017b) for the estimation of the background intensity.
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