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Aimed at progress in mega-electron volt (MeV) gamma-ray astronomy, which has not yet been well-explored, Compton telescope missions with a variety of detector concepts have been proposed so far. One of the key techniques for these future…

This paper studies the properties of the Multiply Iterated Poisson Process (MIPP), a stochastic process constructed by repeatedly time-changing a Poisson process, and its applications in ruin theory. Like standard Poisson processes, MIPPs…

In this article, we prove the Eyring-Kramers formula for non-reversible metastable diffusion processes that have a Gibbs invariant measure. Our result indicates that non-reversible processes exhibit faster metastable transitions between…

Gaussian processes (GPs) furnish accurate nonlinear predictions with well-calibrated uncertainty. However, the typical GP setup has a built-in stationarity assumption, making it ill-suited for modeling data from processes with sudden…

Yield curve forecasting is an important problem in finance. In this work we explore the use of Gaussian Processes in conjunction with a dynamic modeling strategy, much like the Kalman Filter, to model the yield curve. Gaussian Processes…

While there have been a lot of recent developments in the context of Bayesian model selection and variable selection for high dimensional linear models, there is not much work in the presence of change point in literature, unlike the…

In this paper, we present the double smoothed nonparametric approach for infinitesimal conditional volatility of jump-diffusion model based on high frequency data. Under certain minimal conditions, we obtain the strong consistency and…

In this paper, we present a new bivariate model for the joint description of the Bitcoin prices and the media attention to Bitcoin. Our model is based on the class of the L\'evy processes and is able to realistically reproduce the jump-type…

We study nonparametric Bayesian inference for the intensity function of a covariate-driven point process. We extend recent results from the literature, showing that a wide class of Gaussian priors, combined with flexible link functions,…

Estimation of the intensity of a point process is considered within a nonparametric framework. The intensity measure is unknown and depends on covariates, possibly many more than the observed number of jumps. Only a single trajectory of the…

At a geologic CO2 sequestration (GCS) site, geologic uncertainty usually leads to large uncertainty in the predictions of properties that influence metrics for leakage risk assessment, such as CO2 saturations and pressures in potentially…

We propose a method for detecting significant interactions in very large multivariate spatial point patterns. This methodology develops high dimensional data understanding in the point process setting. The method is based on modelling the…

A new probabilistic post-processing method for wind vectors is presented in a distributional regression framework employing the bivariate Gaussian distribution. In contrast to previous studies all parameters of the distribution are…

Temporal inhomogeneities observed in various natural and social phenomena have often been characterized in terms of scaling behaviors in the autocorrelation function with a decaying exponent $\gamma$, the interevent time distribution with a…

Gaussian Process Regression (GPR) is a Bayesian method for inferring profiles based on input data. The technique is increasing in popularity in the fusion community due to its many advantages over traditional fitting techniques including…

This article provides an introduction to the asymptotic analysis of covariance parameter estimation for Gaussian processes. Maximum likelihood estimation is considered. The aim of this introduction is to be accessible to a wide audience and…

Severe Ionosphere magnetic storms are feared events for integrity and continuity of navigation systems such as EGNOS, the European SBAS (Satellite-Based Augmentation System) complementing GPS and an accurate modelling of this event…

We propose an adaptive importance sampling scheme for the simulation of rare events when the underlying dynamics is given by a diffusion. The scheme is based on a Gibbs variational principle that is used to determine the optimal (i.e.…

We propose a general framework for studying jump-diffusion systems driven by both Gaussian noise and a jump process with state-dependent intensity. Of particular natural interest are the jump locations: the system evaluated at the jump…

We take a new look at the problem of disentangling the volatility and jumps processes of daily stock returns. We first provide a computational framework for the univariate stochastic volatility model with Poisson-driven jumps that offers a…