When analyzing data from computationally expensive simulation codes, surrogate modeling methods are firmly established as facilitators for design space exploration, sensitivity analysis, visualization and optimization. Kriging is a popular surrogate modeling technique used for the Design and Analysis of Computer Experiments (DACE). Hence, the past decade Kriging has been the subject of extensiv...

1. Abstract Over three decades, metamodeling has been widely applied to design optimization problems to build a surrogate model of computation-intensive engineering models. The Kriging method has gained significant interests for developing the surrogate model. However, traditional Kriging methods, including the ordinary Kriging and the universal Kriging, use fixed polynomials basis functions to...

In the practice of interpolating near-surface soil moisture measured by a wireless sensor network (WSN) grid, traditional Kriging methods with auxiliary variables, such as Co-kriging and Kriging with external drift (KED), cannot achieve satisfactory results because of the heterogeneity of soil moisture and its low correlation with the auxiliary variables. This study developed an Extended Krigin...

This paper discusses the use of robust geostatistical methods on a data set of rainfall measurements for Switzerland. The variables are detrended via nonparametric estimation penalized with a smoothing parameter. The optimal trend is computed with a smoothing parameter based on cross-validation. The variogram is then estimated by a highly robust estimator of scale. The parametric variogram mode...

When analysing data from computationally expensive simulation codes or process measurements, surrogate modelling methods are firmly established as facilitators for design space exploration, sensitivity analysis, visualisation and optimisation. Kriging is a popular surrogate modelling technique for data based on deterministic computer experiments. There exist several types of Kriging, mostly dif...

This article reviews Kriging (also called spatial correlation modeling). It presents the basic Kriging assumptions and formulas—contrasting Kriging and classic linear regression metamodels. Furthermore, it extends Kriging to random simulation, and discusses bootstrapping to estimate the variance of the Kriging predictor. Besides classic one-shot statistical designs such as Latin Hypercube Sampl...

In many global optimization problems motivated by engineering applications, the number of function evaluations is severely limited by time or cost. To ensure that each of these evaluations contributes to the localization of good candidates for the role of global minimizer, a sequential choice of evaluation points is usually carried out. In particular, when Kriging is used to interpolate past ev...

There is growing evidence in the epidemiologic literature of the relationship between air pollution and adverse health outcomes. Prediction of individual air pollution exposure in the Environmental Protection Agency (EPA) funded Multi-Ethnic Study of Atheroscelerosis and Air Pollution (MESA Air) study relies on a flexible spatio-temporal prediction model that integrates land-use regression with...

Spatial estimations are increasingly used to estimate geocoded ambient particulate matter (PM) concentrations in epidemiologic studies because measures of daily PM concentrations are unavailable in most U.S. locations. This study was conducted to a) assess the feasibility of large-scale kriging estimations of daily residential-level ambient PM concentrations, b) perform and compare cross-valida...