Related papers: A criterion and incremental design construction fo…
Engineering design involves demanding models encompassing many decision variables and uncontrollable parameters. In addition, unavoidable aleatoric and epistemic uncertainties can be very impactful and add further complexity. 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…
This article focuses on the estimation and design aspects of a bivariate collocated cokriging experiment. For a large class of covariance matrices, a linear dependency criterion is identified, which allows the best linear unbiased estimator…
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…
This work investigates the prediction performance of the kriging predictors. We derive some error bounds for the prediction error in terms of non-asymptotic probability under the uniform metric and $L_p$ metrics when the spectral densities…
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…
We study large-scale spatial systems that contain exogenous variables, e.g. environmental factors that are significant predictors in spatial processes. Building predictive models for such processes is challenging because the large numbers…
Inductive spatio-temporal kriging infers signals at unobserved locations from observed sensors, but real-world observations are often incomplete and exhibit block-wise missingness caused by failures, interruptions, or maintenance. A common…
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…
In spatial statistics, a common objective is to predict values of a spatial process at unobserved locations by exploiting spatial dependence. Kriging provides the best linear unbiased predictor using covariance functions and is often…
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,…
This paper develops a novel change point identification method for high-dimensional data using random projections. By projecting high-dimensional time series into a one-dimensional space, we are able to leverage the rich literature for…
With computational models becoming more expensive and complex, surrogate models have gained increasing attention in many scientific disciplines and are often necessary to conduct sensitivity studies, parameter optimization etc. In the…
Computer simulators are nowadays widely used to understand complex physical systems in many areas such as aerospace, renewable energy, climate modeling, and manufacturing. One fundamental issue in the study of computer simulators is known…
An explicit optimal linear spatial predictor is derived. The spatial correlations are imposed by means of Gibbs energy functionals with explicit coupling coefficients instead of covariance matrices. The model inference process is based on…
We present Blitzkriging, a new approach to fast inference for Gaussian processes, applicable to regression, optimisation and classification. State-of-the-art (stochastic) inference for Gaussian processes on very large datasets scales…
We investigate two new strategies for the numerical solution of optimal stopping problems within the Regression Monte Carlo (RMC) framework of Longstaff and Schwartz. First, we propose the use of stochastic kriging (Gaussian process)…
Optimal design facilitates intelligent data collection. In this paper, we introduce a fully Bayesian design approach for spatial processes with complex covariance structures, like those typically exhibited in natural ecosystems. Coordinate…
Analyzing massive spatial datasets using Gaussian process model poses computational challenges. This is a problem prevailing heavily in applications such as environmental modeling, ecology, forestry and environmental heath. We present a…
Spatial prediction is a fundamental task in geography. In recent years, with advances in geospatial artificial intelligence (GeoAI), numerous models have been developed to improve the accuracy of geographic variable predictions. Beyond…