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Spatial prediction is commonly achieved under the assumption of a Gaussian random field (GRF) by obtaining maximum likelihood estimates of parameters, and then using the kriging equations to arrive at predicted values. For massive datasets,…
Spatial data are often derived from multiple sources (e.g. satellites, in-situ sensors, survey samples) with different supports, but associated with the same properties of a spatial phenomenon of interest. It is common for predictors to…
In this work, we propose a framework that combines the approximation-theory-based multifidelity method and Gaussian-process-regression-based multifidelity method to achieve data-model convergence when stochastic simulation models and sparse…
Spatial processes with nonstationary and anisotropic covariance structure are often used when modelling, analysing and predicting complex environmental phenomena. Such processes may often be expressed as ones that have stationary and…
Multivariate spatial fields are of interest in many applications, including climate model emulation. Not only can the marginal spatial fields be subject to nonstationarity, but the dependence structure among the marginal fields and between…
Iterative geostatistical history matching uses stochastic sequential simulation to generate and perturb subsurface Earth models to match historical production data. The areas of influence around each well are one of the key factors in…
We study the problem of estimating the covariance parameters of a one-dimensional Gaussian process with exponential covariance function under fixed-domain asymptotics. We show that the weighted pairwise maximum likelihood estimator of the…
Kriging based on Gaussian random fields is widely used in reconstructing unknown functions. The kriging method has pointwise predictive distributions which are computationally simple. However, in many applications one would like to predict…
Extreme values geostatistics make it possible to model the asymptotic behaviors of random phenomena which depends on space or time parameters. In this paper, we propose new models of the extremal coefficient within a spatial stationary…
Spatial process models popular in geostatistics often represent the observed data as the sum of a smooth underlying process and white noise. The variation in the white noise is attributed to measurement error, or micro-scale variability,…
In analyses of spatially-referenced data, researchers often have one of two goals: to quantify relationships between a response variable and covariates while accounting for residual spatial dependence or to predict the value of a response…
The rapid growth of earth observation systems calls for a scalable approach to interpolate remote-sensing observations. These methods in principle, should acquire more information about the observed field as data grows. Gaussian processes…
The problem of estimating the slope parameter in regression between two spatial processes under confounding by an unmeasured spatial process has received widespread attention in the recent statistical literature. Yet, a fundamental question…
In this work we define a spatial concordance coefficient for second-order stationary processes. This problem has been widely addressed in a non-spatial context, but here we consider a coefficient that for a fixed spatial lag allows one to…
Gaussian processes (GP) and Kriging are widely used in traditional spatio-temporal mod-elling and prediction. These techniques typically presuppose that the data are observed from a stationary GP with parametric covariance structure.…
Spatial prediction tasks are key to weather forecasting, studying air pollution impacts, and other scientific endeavors. Determining how much to trust predictions made by statistical or physical methods is essential for the credibility of…
Many scientific applications involve mixed spatially indexed outcomes of heterogeneous types that are driven by shared latent mechanisms. Modeling such data is challenging due to complex, nonlinear, and potentially nonstationary spatial…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…
Interpolating a skewed conditional spatial random field with missing data is cumbersome in the absence of Gaussianity assumptions. Maintaining spatial homogeneity and continuity around the observed random spatial point is also challenging,…
Gaussian processes are arguably the most important class of spatiotemporal models within machine learning. They encode prior information about the modeled function and can be used for exact or approximate Bayesian learning. In many…