Related papers: Approximation of bayesian Hawkes process models wi…

We present a unified view of likelihood based Gaussian progress regression for simulation experiments exhibiting input-dependent noise. Replication plays an important role in that context, however previous methods leveraging replicates have…

Most point process models for earthquakes currently in the literature assume the magnitude distribution is i.i.d. potentially hindering the ability of the model to describe the main features of data sets containing multiple earthquake…

The Hawkes model is suitable for describing self and mutually exciting random events. In addition, the exponential decay in the Hawkes process allows us to calculate the moment properties in the model. However, due to the complexity of the…

In this work, we study the event occurrences of individuals interacting in a network. To characterize the dynamic interactions among the individuals, we propose a group network Hawkes process (GNHP) model whose network structure is observed…

The rapid growth of social media has been witnessed during recent years as a result of the prevalence of the internet. This trend brings an increasing interest in simulating social media which can provide valuable insights to both academic…

Due to its clustering and self-exciting properties, the Hawkes process has been used extensively in numerous fields ranging from sismology to finance. Since data is often aquired on regular time intervals, we propose a piece-wise constant…

Solving inverse problems using Bayesian methods can become prohibitively expensive when likelihood evaluations involve complex and large scale numerical models. A common approach to circumvent this issue is to approximate the forward model…

The Hawkes process is used to model point process data where events occur in clusters and bursts. In a standard multivariate Hawkes process, every event that occurs in a dimension has an equal impact on the process intensity. However, this…

The Hawkes process is a simple point process that has long memory, clustering effect, self-exciting property and is in general non-Markovian. The future evolution of a self-exciting point process is influenced by the timing of the past…

We define a new model using a Hawkes process as a subordinator in a standard Brownian motion. We demonstrate that this Hawkes subordinated Brownian motion or more succinctly, variance-Hawkes process can be fit to 2018 and 2019 natural gas…

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,…

The Hawkes process is a class of point processes whose future depends on their own history. Previous theoretical work on the Hawkes process is limited to a special case in which a past event can only increase the occurrence of future…

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…

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…

The aim of this paper is to provide a new method for the detection of either favored or avoided distances between genomic events along DNA sequences. These events are modeled by a Hawkes process. The biological problem is actually complex…

In this paper, we discuss integer-valued autoregressive time series (INAR), Hawkes point processes, and their interrelationship. Besides presenting structural analogies, we derive a convergence theorem. More specifically, we generalize the…

This chapter provides an accessible introduction for point processes, and especially Hawkes processes, for modeling discrete, inter-dependent events over continuous time. We start by reviewing the definitions and the key concepts in point…

This article introduces epidemia, an R package for Bayesian, regression-oriented modeling of infectious diseases. The implemented models define a likelihood for all observed data while also explicitly modeling transmission dynamics: an…

With the growing digital transformation of the worldwide economy, cyber risk has become a major issue. As 1 % of the world's GDP (around $1,000 billion) is allegedly lost to cybercrime every year, IT systems continue to get increasingly…

The kernel function and its hyperparameters are the central model selection choice in a Gaussian proces (Rasmussen and Williams, 2006). Typically, the hyperparameters of the kernel are chosen by maximising the marginal likelihood, an…