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The investigation of spatio-temporal couplings (STCs) of broadband light beams is becoming a key topic for the optimization as well as applications of ultrashort laser systems. This calls for accurate measurements of STCs. Yet, it is only…

In this paper, the proximal Gauss-Newton method for solving penalized nonlinear least squares problems is studied. A local convergence analysis is obtained under the assumption that the derivative of the function associated with the…

In this paper, we propose a Gaussian Process (GP) emulator for the calculation of a) tomographic weak lensing band-power spectra, and b) coefficients of summary data massively compressed with the MOPED algorithm. In the former case…

Due to their conjugate posteriors, Gaussian process priors are attractive for estimating the drift of stochastic differential equations with continuous time observations. However, their performance strongly depends on the choice of the…

The application of geostatistical and machine learning methods based on Gaussian processes to big space-time data is beset by the requirement for storing and numerically inverting large and dense covariance matrices. Computationally…

The solutions of Hamiltonian equations are known to describe the underlying phase space of a mechanical system. In this article, we propose a novel spatio-temporal model using a strategic modification of the Hamiltonian equations,…

A generator of spatio-temporal pseudo-random Gaussian fields that satisfy the "proportionality of scales" property (Tsyroulnikov, 2001) is presented. The generator is based on a third-order in time stochastic differential equation with a…

Knowledge of spatio-temporal couplings such as pulse-front tilt or curvature is important to determine the focused intensity of high-power lasers. Common techniques to diagnose these couplings are either qualitative or require hundreds of…

This study introduces an innovative local statistical moment approach for estimating Kramers-Moyal coefficients, effectively bridging the gap between nonparametric and parametric methodologies. These coefficients play a crucial role in…

Data-driven soft sensors have been widely applied in complex industrial processes. However, the interpretable spatio-temporal features extraction by soft sensors remains a challenge. In this light, this work introduces a novel method termed…

This paper generalizes stochastic collocation methods to handle correlated non-Gaussian random parameters. The key challenge is to perform a multivariate numerical integration in a correlated parameter space when computing the coefficient…

Nonstationary Gaussian processes (GPs) are essential for modeling complex, locally heterogeneous spatial data. A common modeling approach is the spatial deformation method that warps the domain to recover isotropy. However, this static…

The paper provides a thorough investigation of Direct loss minimization (DLM), which optimizes the posterior to minimize predictive loss, in sparse Gaussian processes. For the conjugate case, we consider DLM for log-loss and DLM for square…

Investigating the relationship, particularly the lead-lag effect, between time series is a common question across various disciplines, especially when uncovering biological process. However, analyzing time series presents several…

We develop a new statistical model for photographic images, in which the local responses of a bank of linear filters are described as jointly Gaussian, with zero mean and a covariance that varies slowly over spatial position. We optimize…

We propose a new splitting method for strong numerical solution of the Cox-Ingersoll-Ross model. For this method, applied over both deterministic and adaptive random meshes, we prove a uniform moment bound and strong error results of order…

Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…

Gaussian process (GP) modulated Cox processes are widely used to model point patterns. Existing approaches require a mapping (link function) between the unconstrained GP and the positive intensity function. This commonly yields solutions…

Recent developments in engineering techniques for spatial data collection such as geographic information systems have resulted in an increasing need for methods to analyze large spatial data sets. These sorts of data sets can be found in…

Second-order variational type equations for spatial point processes are established. In case of log linear parametric models for pair correlation functions, it is demonstrated that the variational equations can be applied to construct…