Kriging is a method to interpolate the value of a function of interest at unobserved locations and has wide range of applications called metamodeling, due to computer stimulated experiments. Kriging considers response surface realization as a spatial random field and then using statistical methods to generate the responses at unobserved locations using the observed responses. Though Gaussian random fields (GRFs) are commonly used with stationary covariance they have some drawbacks such as reversion to the mean. This can be overcome by collecting more information from the neighborhood. The FBF model can handle such situation by providing more dense set of input sites. A kriging predictor with nonstationary GRFs that do not revert to mean are available. There are two such types of covariates available. The first type which this study focuses is associated with Brownian motion for which the increments of the variable are stationary but the variance may be unbounded. The approach is like autoregressive integrated moving average (ARIMA) that does not depend upon the long-term mean for predicting the future values. The second type of covariance nonstationarity is to model processes for which smoothness varies spatially by modifying standard stationary covariance functions to have parameters that vary spatially. The second type again reverts to the mean. Hence the first type that does not revert to mean is more suitable. This paper considers fractional Brownian field (FBF) as the general case of the Brownian motion in terms of an index coefficient. In intrinsic kriging weighted differences of the response observations are used where the weights are used to cancel the deterministic trend in the data. (31 refs.)
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