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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…
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…
Spatio-temporal Hawkes point processes are a particularly interesting class of stochastic point processes for modeling self-exciting behavior, in which the occurrence of one event increases the probability of other events occurring. These…
Existing spatio-temporal Hawkes process models typically rely on either parametric or semiparametric assumptions, limiting the model's ability to capture complex endogenous and exogenous event dynamics. We propose a fully Bayesian…
The event sequence of many diverse systems is represented as a sequence of discrete events in a continuous space. Examples of such an event sequence are earthquake aftershock events, financial transactions, e-commerce transactions, social…
Point processes are widely used statistical models for continuous-time discrete event data, such as medical records, crime reports, and social network interactions, to capture the influence of historical events on future occurrences. In…
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…
Analysis of gun violence in the United States has utilized various models based on spatiotemporal point processes. Previous studies have identified a contagion effect in gun violence, characterized by bursts of diffusion across urban…
The Hawkes process and its extensions effectively model self-excitatory phenomena including earthquakes, viral pandemics, financial transactions, neural spike trains and the spread of memes through social networks. The usefulness of these…
We consider a general stochastic branching process, which is relevant to earthquakes as well as to many other systems, and we study the distributions of the total number of offsprings (direct and indirect aftershocks in seismicity) and of…
We investigate spatio-temporal event analysis using point processes. Inferring the dynamics of event sequences spatiotemporally has many practical applications including crime prediction, social media analysis, and traffic forecasting. In…
Self-exciting spatio-temporal point process models predict the rate of events as a function of space, time, and the previous history of events. These models naturally capture triggering and clustering behavior, and have been widely used in…
As a tool for capturing irregular temporal dependencies (rather than resorting to binning temporal observations to construct time series), Hawkes processes with exponential decay have seen widespread adoption across many application…
We present a new kind of critical stochastic finite-time-singularity, relying on the interplay between long-memory and extreme fluctuations. We illustrate it on the well-established epidemic-type aftershock (ETAS) model for aftershocks,…
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…
We propose an effective method to solve the event sequence clustering problems based on a novel Dirichlet mixture model of a special but significant type of point processes --- Hawkes process. In this model, each event sequence belonging to…
Forecast models in statistical seismology are commonly evaluated with log-likelihood scores of the full distribution P(n) of earthquake numbers, yet heavy tails and out-of-range observations can bias model ranking. We develop a tail-aware…
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…
We present two models for estimating the probabilities of future earthquakes in California, to be tested in the Collaboratory for the Study of Earthquake Predictability (CSEP). The first, time-independent model, modified from Helmstetter et…
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…