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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…
Gaussian processes (GPs) are a popular model for spatially referenced data and allow descriptive statements, predictions at new locations, and simulation of new fields. Often a few parameters are sufficient to parameterize the covariance…
The Gaussian process (GP) is a widely used probabilistic machine learning method with implicit uncertainty characterization for stochastic function approximation, stochastic modeling, and analyzing real-world measurements of nonlinear…
Gaussian processes (GPs) are commonplace in spatial statistics. Although many non-stationary models have been developed, there is arguably a lack of flexibility compared to equipping each location with its own parameters. However, the…
The Gaussian process (GP) is a popular statistical technique for stochastic function approximation and uncertainty quantification from data. GPs have been adopted into the realm of machine learning in the last two decades because of their…
Gaussian processes (GPs) defined through intrinsic random fields provide a flexible framework for modeling spatial phenomena, and have been advocated in a variety of applications over the past several decades. Nevertheless, their adoption…
Gaussian Processes (GPs) are powerful non-parametric Bayesian models for regression of scalar fields, formulated under the assumption that measurement locations are perfectly known and the corresponding field measurements have Gaussian…
Gaussian process (GP) models that combine both categorical and continuous input variables have found use in analysis of longitudinal data and computer experiments. However, standard inference for these models has the typical cubic scaling,…
Geophysical and other natural processes often exhibit non-stationary covariances and this feature is important to take into account for statistical models that attempt to emulate the physical process. A convolution-based model is used to…
Gaussian processes are a flexible Bayesian nonparametric modelling approach that has been widely applied but poses computational challenges. To address the poor scaling of exact inference methods, approximation methods based on sparse…
A Gaussian Process (GP) is a prominent mathematical framework for stochastic function approximation in science and engineering applications. This success is largely attributed to the GP's analytical tractability, robustness, non-parametric…
Gaussian processes (GPs) have gained popularity as flexible machine learning models for regression and function approximation with an in-built method for uncertainty quantification. However, GPs suffer when the amount of training data is…
When an agent, person, vehicle or robot is moving through an unknown environment without GNSS signals, online mapping of nonlinear terrains can be used to improve position estimates when the agent returns to a previously mapped area.…
Variational Gaussian process (GP) approximations have become a standard tool in fast GP inference. This technique requires a user to select variational features to increase efficiency. So far the common choices in the literature are…
Geostatistics is a branch of statistics concerned with stochastic processes over continuous domains, with Gaussian processes (GPs) providing a flexible and principled modelling framework. However, the high computational cost of simulating…
Gaussian processes (GP) are a popular and powerful tool for spatial modelling of data, especially data that quantify environmental processes. However, in stationary form, whether covariance is isotropic or anisotropic, GPs may lack the…
In many real-world applications we are interested in approximating costly functions that are analytically unknown, e.g. complex computer codes. An emulator provides a fast approximation of such functions relying on a limited number of…
Gaussian processes are popular and flexible models for spatial, temporal, and functional data, but they are computationally infeasible for large datasets. We discuss Gaussian-process approximations that use basis functions at multiple…
With the development of new remote sensing technology, large or even massive spatial datasets covering the globe become available. Statistical analysis of such data is challenging. This article proposes a semiparametric approach to model…
Gaussian Processes (GPs) has experienced tremendous success in geoscience in general and for bio-geophysical parameter retrieval in the last years. GPs constitute a solid Bayesian framework to formulate many function approximation problems…