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Gaussian processes models are widely adopted for nonparameteric/semi-parametric modeling. Identifiability issues occur when the mean model contains polynomials with unknown coefficients. Though resulting prediction is unaffected, this leads…

Gaussian process (GP) models have received increasing attention in recent years due to their superb prediction accuracy and modeling flexibility. To address the computational burdens of GP models for large-scale datasets, distributed…

Simulating turbulent fluid flows is a computationally prohibitive task, as it requires the resolution of fine-scale structures and the capture of complex nonlinear interactions across multiple scales. This is particularly the case in direct…

Expensive ultrasonic anemometers are usually required to measure wind speed accurately. The aim of this work is to overcome the loss of accuracy of a low cost hot-wire anemometer caused by the changes of air temperature, by means of a…

In this paper we concentrate on an alternative modeling strategy for positive data that exhibit spatial or spatio-temporal dependence. Specifically we propose to consider stochastic processes obtained trough a monotone transformation of…

Bayesian posterior distributions arising in modern applications, including inverse problems in partial differential equation models in tomography and subsurface flow, are often computationally intractable due to the large computational cost…

Modeling nonstationary processes is of paramount importance to many scientific disciplines including environmental science, ecology, and finance, among others. Consequently, flexible methodology that provides accurate estimation across a…

Wind speed forecasting has received a lot of attention in the recent past from researchers due to its enormous benefits in the generation of wind power and distribution. The biggest challenge still remains to be accurate prediction of wind…

The Gaussian process (GP) regression model is a widely employed surrogate modeling technique for computer experiments, offering precise predictions and statistical inference for the computer simulators that generate experimental data.…

Recognizing the successes of treed Gaussian process (TGP) models as an interpretable and thrifty model for nonparametric regression, we seek to extend the model to classification. Both treed models and Gaussian processes (GPs) have,…

Continuous-time trajectory estimation is an attractive alternative to discrete-time batch estimation due to the ability to incorporate high-frequency measurements from asynchronous sensors while keeping the number of optimization parameters…

This paper is centered around the approximation of dynamical systems by means of Gaussian processes. To this end, trajectories of such systems must be collected to be used as training data. The measurements of these trajectories are…

We consider the accuracy of an approximate posterior distribution in nonparametric regression problems by combining posterior distributions computed on subsets of the data defined by the locations of the independent variables. We show that…

Graph Gaussian Processes (GGPs) provide a data-efficient solution on graph structured domains. Existing approaches have focused on static structures, whereas many real graph data represent a dynamic structure, limiting the applications of…

We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and…

Data assimilation in models representing spatio-temporal phenomena poses a challenge, particularly if the spatial histogram of the variable appears with multiple modes. The traditional Kalman model is based on a Gaussian initial…

We develop a Bayesian non-parametric framework based on multi-task Gaussian processes, appropriate for temporal shrinkage. We focus on a particular class of dynamic hierarchical models to obtain evidence-based knowledge of infectious…

Recently nonparametric functional model with functional responses has been proposed within the functional reproducing kernel Hilbert spaces (fRKHS) framework. Motivated by its superior performance and also its limitations, we propose a…

In this paper we investigate a link between state- space models and Gaussian Processes (GP) for time series modeling and forecasting. In particular, several widely used state- space models are transformed into continuous time form and…

In this work, a Gaussian process regression(GPR) model incorporated with given physical information in partial differential equations(PDEs) is developed: physics-assisted Gaussian processes(PAGP). The targets of this model can be divided…