Related papers: Bayesian Modelling of Nonstationary Extreme Values…
Deep Gaussian process models typically employ discrete hierarchies, but recent advancements in differential Gaussian processes (DiffGPs) have extended these models to infinite depths. However, existing DiffGP approaches often overlook the…
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…
Predictions of the uncertainty associated with extreme events are a vital component of any prediction system for such events. Consequently, the prediction system ought to be probabilistic in nature, with the predictions taking the form of…
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…
The Hawkes process is a simple point process, whose intensity function depends on the entire past history and is self-exciting and has the clustering property. The Hawkes process is in general non-Markovian. The linear Hawkes process has…
Detection heterogeneity is inherent to ecological data, arising from factors such as varied terrain or weather conditions, inconsistent sampling effort, or heterogeneity of individuals themselves. Incorporating additional covariates into a…
Many self-exciting systems change because endogenous amplification, as opposed to exogenous forcing, varies. We study a Hawkes process with fixed background rate and kernel, but piecewise time-varying productivity. For exponential kernels…
We present a stability study of the class of multivariate self-excited Hawkes point processes, that can model natural and social systems, including earthquakes, epileptic seizures and the dynamics of neuron assemblies, bursts of exchanges…
Classic results show that the Hawkes self-exciting point process can be viewed as a collection of temporal clusters, where exogenously generated initial events give rise to endogenously driven descendant events. This perspective provides…
We propose a novel probabilistic framework to model continuous-time interaction events data. Our goal is to infer the \emph{implicit} community structure underlying the temporal interactions among entities, and also to exploit how the…
A temporal point process is a stochastic process that predicts which type of events is likely to happen and when the event will occur given a history of a sequence of events. There are various examples of occurrence dynamics in the daily…
We investigate the nonparametric estimation problem of the density $\pi$, representing the stationary distribution of a two-dimensional system $\left(Z_t\right)_{t \in[0, T]}=\left(X_t, \lambda_t\right)_{t \in[0, T]}$. In this system, $X$…
Initially this paper reviews the mathematical issues surrounding the hydrostatic (HPE) and non-hydrostatic (NPE) primitive equations that have been used extensively in numerical weather prediction and climate modelling. Cao and Titi (2005,…
The paper constructs a multi-variate Hawkes process model of Bitcoin block arrivals and price jumps. Hawkes processes are selfexciting point processes that can capture the self- and cross-excitation effects of block mining and Bitcoin price…
We propose a tractable semiparametric estimation method for structural dynamic discrete choice models. The distribution of additive utility shocks in the proposed framework is modeled by location-scale mixtures of extreme value…
Hawkes process provides an effective statistical framework for analyzing the time-dependent interaction of neuronal spiking activities. Although utilized in many real applications, the classic Hawkes process is incapable of modelling…
Bayesian models offer great flexibility for clustering applications---Bayesian nonparametrics can be used for modeling infinite mixtures, and hierarchical Bayesian models can be utilized for sharing clusters across multiple data sets. For…
This paper presents a Bayesian generative model for dependent Cox point processes, alongside an efficient inference scheme which scales as if the point processes were modelled independently. We can handle missing data naturally, infer…
Extreme geophysical events are of crucial relevance to our daily life: they threaten human lives and cause property damage. To assess the risk and reduce losses, we need to model and probabilistically predict these events. Parametrizations…
Describing the complex dependence structure of extreme phenomena is particularly challenging. To tackle this issue we develop a novel statistical algorithm that describes extremal dependence taking advantage of the inherent hierarchical…