Related papers: Bayesian Modelling of Nonstationary Extreme Values…
The Hawkes process is a widely used model in many areas, such as finance, seismology, neuroscience, epidemiology, and social sciences. Estimation of the Hawkes process from continuous observations of a sample path is relatively…
Modelling of precipitation and its extremes is important for urban and agriculture planning purposes. We present a method for producing spatial predictions and measures of uncertainty for spatio-temporal data that is heavy-tailed and…
Classic estimation methods for Hawkes processes rely on the assumption that observed event times are indeed a realisation of a Hawkes process, without considering any potential perturbation of the model. However, in practice, observations…
We consider hyperbolic partial differential equations (PDEs) for a dynamic description of the traffic behavior in road networks. These equations are coupled to a Hawkes process that models traffic accidents taking into account their…
Extreme events in society and nature, such as pandemic spikes, rogue waves, or structural failures, can have catastrophic consequences. Characterizing extremes is difficult as they occur rarely, arise from seemingly benign conditions, and…
Datasets containing large samples of time-to-event data arising from several small heterogeneous groups are commonly encountered in statistics. This presents problems as they cannot be pooled directly due to their heterogeneity or analyzed…
Hawkes process is a class of simple point processes that is self-exciting and has clustering effect. The intensity of this point process depends on its entire past history. It has wide applications in finance, insurance, neuroscience,…
Learning the causal-interaction network of multivariate Hawkes processes is a useful task in many applications. Maximum-likelihood estimation is the most common approach to solve the problem in the presence of long observation sequences.…
We construct a two-tailed peak-over-threshold Hawkes model that captures asymmetric self- and cross-excitation in and between left- and right-tail extreme values within a time series. We demonstrate its applicability by investigating…
We consider online monitoring of the network event data to detect local changes in a cluster when the affected data stream distribution shifts from one point process to another with different parameters. Specifically, we are interested in…
Extreme events occur across the natural, engineering, and socioeconomic sciences, where rare but high-impact episodes can lead to disproportionate consequences that pose major challenges for prediction and risk management. Existing studies…
Hawkes process is a class of simple point processes with self-exciting and clustering properties. Hawkes process has been widely applied in finance, neuroscience, social networks, criminology, seismology, and many other fields. In this…
The Bayesian two-step change point detection method is popular for the Hawkes process due to its simplicity and intuitiveness. However, the non-conjugacy between the point process likelihood and the prior requires most existing Bayesian…
Data-driven anomaly detection methods typically build a model for the normal behavior of the target system, and score each data instance with respect to this model. A threshold is invariably needed to identify data instances with high (or…
nsEVDx is an open-source Python package for fitting stationary and nonstationary Extreme Value Distributions (EVDs) to extreme value data. It can be used to model extreme events in fields like hydrology, climate science, finance, and…
A Bayesian non-parametric framework for studying time-to-event data is proposed, where the prior distribution is allowed to depend on an additional random source, and may update with the sample size. Such scenarios are natural, for…
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…
Hawkes processes have recently gained increasing attention from the machine learning community for their versatility in modeling event sequence data. While they have a rich history going back decades, some of their properties, such as…
In this chapter, we show how to efficiently model high-dimensional extreme peaks-over-threshold events over space in complex non-stationary settings, using extended latent Gaussian Models (LGMs), and how to exploit the fitted model in…
Fueled in part by recent applications in neuroscience, the multivariate Hawkes process has become a popular tool for modeling the network of interactions among high-dimensional point process data. While evaluating the uncertainty of the…