This article uses a sequentialized experimental design to select simulation input combinations for global optimization, based on Kriging (also called Gaussian process or spatial correlation modeling); this Kriging is used to analyze the input/output data of the simulation model (computer code). This design and analysis adapt the classic "expected improvement" (EI) in "e¢ cient global optimizati...

for optimum planning, utilization, and management of lands, recognition of spatial variability of soil properties is necessary. this research was conducted to evaluate spatial variability of soil properties in 5000 ha of arsenjan plain in fars province. for this purpose, soil salinity, ph, particle size percentage, sodium, potassium, and organic carbon (oc) were measured on a systematic squared...

We develop a novel multi-fidelity framework that goes far beyond the classical AR(1) Co-kriging scheme of Kennedy and O’Hagan (2000). Our method can handle general discontinuous cross-correlations among systems with different levels of fidelity. A combination of multi-fidelity Gaussian Processes (AR(1) Co-kriging) and deep neural networks enables us to construct a method that is immune to disco...

The packages geoR and geoRglm are contributed packages to the statistical software system R, implementing methods for model-based geostatistical data-analysis. In this paper we focus on the capabilities of the packages, the computational implementation and related issues, and indicate directions for future developments. geoR implements methods for Gaussian and transformed Gaussian models. The p...

The best unbiased linear predictor for a stochastic process is the best unbiased predictor (i.e., the linearity constraint is removed) if the process is Gaussian. This provides a stronger justi cation for the universal kriging predictor than is generally o ered. For log-Gaussian processes, we show that the standard predictor (obtained by correcting the bias of the exponential of the best unbias...

The estimation of pollution fields, especially in densely populated areas, is an important application in the field of environmental science due to the significant effects of air pollution on public health. In this paper, we investigate the spatial distribution of three air pollutants in Tehran’s atmosphere: carbon monoxide (CO), nitrogen dioxide (NO2), and atmospheric particulate matters less ...

In this paper we address two issues common to the analysis of large spatial datasets. One is the modeling of non-stationarity, and the other is the computational challenges in doing likelihood based estimation and kriging prediction. We model the spatial process as a convolution of independent Gaussian processes, with the spatially varying kernel function given by the modified Bessel functions....

The main issue in the analysis of computer experiments is an uncertainty of prediction and related inferences. To address the uncertainty analysis, the Bayesian analysis of deterministic computer models has been actively developed in the last decade. In the Bayesian approach, the uncertainty is expressed through a Gaussian process model. As a consequence, the resulting analysis is rather sensit...

Recently, Spöck and Pilz (2010), demonstrated that the spatial sampling design problem for the Bayesian linear kriging predictor can be transformed to an equivalent experimental design problem for a linear regression model with stochastic regression coefficients and uncorrelated errors. The stochastic regression coefficients derive from the polar spectral approximation of the residual process. ...

The estimation of pollution fields, especially in densely populated areas, is an important application in the field of environmental science due to the significant effects of air pollution on public health. In this paper, we investigate the spatial distribution of three air pollutants in Tehran’s atmosphere: carbon monoxide (CO), nitrogen dioxide (NO2), and atmospheric particulate matters less ...