Related papers: A Multidimensional Fractional Hawkes Process for M…
Using the ETAS branching model of triggered seismicity, we apply the formalism of generating probability functions to calculate exactly the average difference between the magnitude of a mainshock and the magnitude of its largest aftershock…
Multivariate point processes are widely applied to model event-type data such as natural disasters, online message exchanges, financial transactions or neuronal spike trains. One very popular point process model in which the probability of…
Hawkes processes are a class of self-exciting point processes that are used to model complex phenomena. While most applications of Hawkes processes assume that event data occurs in continuous-time, the less-studied discrete-time version of…
Hawkes processes are a special class of temporal point processes which exhibit a natural notion of causality, as occurrence of events in the past may increase the probability of events in the future. Discovery of the underlying influence…
Multivariate Hawkes processes are past-dependant point processes originally introduced to model excitation effects, later extended to a nonlinear framework to account for the opposite effect, known as inhibition. Motivated by applications…
The Epidemic Type Aftershock Sequence (ETAS) model is one of the most widely-used approaches to seismic forecasting. However most studies of ETAS use point estimates for the model parameters, which ignores the inherent uncertainty that…
A prominent feature of earthquakes is their empirical laws including memory (clustering) in time and space. Several earthquake forecasting models, like the EpidemicType Aftershock Sequence (ETAS) model, were developed based on earthquake…
The Hawks process is a point process with a self-exciting property. It has been used to model earthquakes, social media events, infections, etc., and is getting a lot of attention. However, as a real problem, there are often situations…
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…
Using the simple ETAS branching model of seismicity, which assumes that each earthquake can trigger other earthquakes, we quantify the role played by the cascade of triggered seismicity in controlling the rate of aftershock decay as well as…
The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the…
Earthquakes are one of the most devastating natural disasters that plague society. A skilled, reliable earthquake forecasting remains the ultimate goal for seismologists. Using the detrended fluctuation analysis (DFA) and conditional…
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 driving concept behind one of the most successful statistical forecasting models, the ETAS model, has been that the seismicity is driven by spontaneously occurring background earthquakes that cascade into multitudes of triggered…
Multivariate Hawkes process provides a powerful framework for modeling temporal dependencies and event-driven interactions in complex systems. While existing methods primarily focus on uncovering causal structures among observed…
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…
We consider a branching model of triggered seismicity, the ETAS (epidemic-type aftershock sequence) model which assumes that each earthquake can trigger other earthquakes (``aftershocks''). An aftershock sequence results in this model from…
This chapter first presents a rather personal view of some different aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties…
Following Hergarten and Neugebauer [2002] who discovered aftershock and foreshock sequences in the Olami-Feder-Christensen (OFC) discrete block-spring earthquake model, we investigate to what degree the simple toppling mechanism of this…
We proposed a data-driven approach to dissect multivariate time series in order to discover multiple phases underlying dynamics of complex systems. This computing approach is developed as a multiple-dimension version of Hierarchical Factor…