To analyze the input/output behavior of simulation models with multiple responses, we may apply either univariate or multivariate Kriging (Gaussian process) metamodels. In multivariate Kriging we face a major problem: the covariance matrix of all responses should remain positive-definite; we therefore use the recently proposed “nonseparable dependence” model. To evaluate the performance of univ...

Truncated Gaussian simulation (TGS) and plurigaussian simulation (PGS) are widely accepted methods for generating realisations of geological domains (lithofacies) that reproduce contact relationships. The realisations can be used to evaluate transfer functions related to the lithofacies occurrence, the simplest ones of which are the probability of occurrence of each lithofacies and the most pro...

gamma-rays emitted from the ground surface relate to the primary mineralogy and geochemistryof the bedrock, and the secondary weathered materials. this information can contribute significantly to anunderstanding of the geochemical and pedogenetic history of a region. the main aim of this paper was to study the relationship between ground gamma-ray data and basement geochemistry in the lese catc...

Probability maps are used to define areas with high and low certainty of exceeding a threshold value. The most popular methods for creating these maps are variants of indicator kriging. However, such methods are questionable when the data exhibit a trend or contain measurement errors, the latter of which is common in most data sets. This paper presents an alternative approach that maps the risk...

The covariance structure of spatial Gaussian predictors aka Kriging predictors is generally modeled by parameterized covariance functions; the associated hyperparameters in turn are estimated via the method of maximum likelihood. In this work, the asymptotic behavior of the maximum likelihood of spatial Gaussian predictor models as a function of its hyperparameters is investigated theoretically...

In this paper, we perform an experimental study to investigate directional variograms in punctual kriging and consequently its effect on image restoration. We employ punctual kriging in conjunction with fuzzy logic typeII and fuzzy smoothing based approaches to remove white Gaussian noise from corrupted images. Images degraded with Gaussian white noise are restored by first utilizing fuzzy logi...

gamma-rays emitted from the ground surface relate to the primary mineralogy and geochemistryof the bedrock, and the secondary weathered materials. this information can contribute significantly to anunderstanding of the geochemical and pedogenetic history of a region. the main aim of this paper was to study the relationship between ground gamma-ray data and basement geochemistry in the lese catc...

Sodium is an integral part of water, and its excessive amount in drinking water causes high blood pressure and hypertension. In the present paper, spatial distribution of sodium concentration in drinking water is modeled and optimized sampling designs for selecting sampling locations is calculated for three divisions in Punjab, Pakistan. Universal kriging and Bayesian universal kriging are used...

Spatial data sets are analysed in many scientific disciplines. Kriging, i.e. minimum mean squared error linear prediction, is probably the most widely used method of spatial prediction. Computation time and memory requirement can be an obstacle for kriging for data sets with many observations. Calculations are accelerated and memory requirements decreased by using a Gaussian Markov random field...

The computation required for Gaussian process regression with n training examples is about O(n) during training and O(n) for each prediction. This makes Gaussian process regression too slow for large datasets. In this paper, we present a fast approximation method, based on kd-trees, that significantly reduces both the prediction and the training times of Gaussian process regression.