Related papers: Kriging prediction with isotropic Mat\'ern correla…
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…
For estimation and predictions of random fields it is increasingly acknowledged that the kriging variance may be a poor representative of true uncertainty. Experimental designs based on more elaborate criteria that are appropriate for…
Gaussian process (GP) models are effective non-linear models for numerous scientific applications. However, computation of their hyperparameters can be difficult when there is a large number of training observations (n) due to the O(n^3)…
In this paper, we further investigate the problem of selecting a set of design points for universal kriging, which is a widely used technique for spatial data analysis. Our goal is to select the design points in order to make simultaneous…
Spatial prediction in an arbitrary location, based on a spatial set of observations, is usually performed by Kriging, being the best linear unbiased predictor (BLUP) in a least-square sense. In order to predict a continuous surface over a…
Exact Kriging and conditional simulation (CS) for uncertainty quantification are computationally infeasible for modern spatial analyses with large numbers of observations and dense prediction grids. We present a rapid approximation to the…
Kriging is a widely recognized method for making spatial predictions. On the sphere, popular methods such as ordinary kriging assume that the spatial process is intrinsically homogeneous. However, intrinsic homogeneity is too strict in many…
Spatial prediction requires expensive computation to invert the spatial covariance matrix it depends on and also has considerable storage needs. This work concentrates on computationally efficient algorithms for prediction using very large…
We consider the problem of predicting values of a random process or field satisfying a linear model $y(x)=\theta^\top f(x) + \varepsilon(x)$, where errors $\varepsilon(x)$ are correlated. This is a common problem in kriging, where the case…
Conformal prediction (CP) provides distribution-free, finite-sample coverage guarantees but critically relies on exchangeability, a condition often violated under distribution shift. We study the robustness of split conformal prediction…
This paper is motivated by a computer experiment conducted for optimizing residual stresses in the machining of metals. Although kriging is widely used in the analysis of computer experiments, it cannot be easily applied to model the…
Machine learning and geostatistics are two fundamentally different frameworks for predicting and spatially mapping soil properties. Geostatistics leverages the spatial structure of soil properties, while machine learning captures the…
Georeferenced compositional data are prominent in many scientific fields and in spatial statistics. This work addresses the problem of proposing models and methods to analyze and predict, through kriging, this type of data. To this purpose,…
Scientists and engineers commonly use simulation models to study real systems for which actual experimentation is costly, difficult, or impossible. Many simulations are stochastic in the sense that repeated runs with the same input…
Kriging is a fundamental tool for spatial prediction, but its computational complexity of $O(N^3)$ becomes prohibitive for large datasets. While local kriging using $K$-nearest neighbors addresses this issue, the selection of $K$ typically…
We introduce a sparse estimation in the ordinary kriging for functional data. The functional kriging predicts a feature given as a function at a location where the data are not observed by a linear combination of data observed at other…
Stochastic kriging is a popular metamodeling technique for representing the unknown response surface of a simulation model. However, the simulation model may be inadequate in the sense that there may be a non-negligible discrepancy between…
Conformal prediction is a powerful tool to generate uncertainty sets with guaranteed coverage using any predictive model, under the assumption that the training and test data are i.i.d.. Recently, it has been shown that adversarial examples…
Kriging and Gaussian Process Regression are statistical methods that allow predicting the outcome of a random process or a random field by using a sample of correlated observations. In other words, the random process or random field is…
Kriging is a widely employed technique, in particular for computer experiments, in machine learning or in geostatistics. An important challenge for Kriging is the computational burden when the data set is large. This article focuses on a…