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Uncovering the distribution of magnitudes and arrival times of aftershocks is a key to comprehend the characteristics of the sequence of earthquakes, which enables us to predict seismic activities and hazard assessments. However,…
The ETAS models are currently the most popular in the field of earthquake forecasting. The MCMC method is time-consuming and limited by parameter correlation while bringing parameter uncertainty. The INLA-based method "inlabru" solves these…
The Hawkes process, a self-exciting point process, has a wide range of applications in modeling earthquakes, social networks and stock markets. The established estimation process requires that researchers have access to the exact time…
Predicting discrete events in time and space has many scientific applications, such as predicting hazardous earthquakes and outbreaks of infectious diseases. History-dependent spatio-temporal Hawkes processes are often used to…
The acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event-event triggering are independent of the details of the experiment and the materials used…
We present the first exact analysis of some of the temporal properties of multivariate self-excited Hawkes conditional Poisson processes, which constitute powerful representations of a large variety of systems with bursty events, for which…
Here we focus on a basic statistical measure of earthquake catalogs that has not been studied before, the asymmetry of interevent time series (e.g., reflecting the tendency to have more aftershocks than spontaneous earthquakes). We define…
Among the statistical tools for online information diffusion modeling, both epidemic models and Hawkes point processes are popular choices. The former originate from epidemiology, and consider information as a viral contagion which spreads…
The statistics of recurrence times in broad areas have been reported to obey universal scaling laws, both for single homogeneous regions (Corral, 2003) and when averaged over multiple regions (Bak et al.,2002). These unified scaling laws…
We propose a new method to test the effectiveness of a spatial point process forecast based on a log-likelihood score for predicted point density and the information gain for events that actually occurred in the test period. The method…
Many point process models have been proposed for describing and forecasting earthquake occurrences in seismically active zones such as California, but the problem of how best to compare and evaluate the goodness of fit of such models…
Earthquake aftershock identification is closely related to the question "Are aftershocks different from the rest of earthquakes?" We give a positive answer to this question and introduce a general statistical procedure for clustering…
Aftershocks of aftershocks - and their aftershock cascades - substantially contribute to the increased seismicity rate and the associated elevated seismic hazard after the occurrence of a large earthquake. Current state-of-the-art…
Across a wide variety of applications, the self-exciting Hawkes process has been used to model phenomena in which the history of events influences future occurrences. However, there may be many situations in which the past events only…
Over the past decades much effort has been devoted towards understanding and forecasting natural hazards. However, earthquake forecasting skill is still very limited and remains a great scientific challenge. The limited earthquake…
The empirical Bath's law states that the average difference in magnitude between a mainshock and its largest aftershock is 1.2, regardless of the mainshock magnitude. Following Vere-Jones [1969] and Console et al. [2003], we show that the…
The Peaks Over Threshold (POT) method is the most popular statistical method for the analysis of univariate extremes. Even though there is a rich applied literature on Bayesian inference for the POT, the asymptotic theory for such proposals…
We quantify the correlation between earthquakes and use the same to distinguish between relevant causally connected earthquakes. Our correlation metric is a variation on the one introduced by Baiesi and Paczuski (2004). A network of…
We prove ergodicity of a point process earthquake model combining the classical stress release model for primary shocks with the Hawkes model for aftershocks.
The Hawkes process is a popular point process model for event sequences that exhibit temporal clustering. The intensity process of a Hawkes process consists of two components, the baseline intensity and the accumulated excitation effect due…