Point and Block Prediction in Log-GaussianRandom Fields:
The Non-Constant Mean Case

Changxiang Rui
Department of Mathematical Sciences
University of Arkansas


        This work considers the problems of optimal point and block prediction in Log-Gaussian random fields with non-constant mean functions depending linearly on unknown parameters and arbi-trary known covariance functions. First, we generalize the optimal point predictor obtained in De Oliveira (2006), who considered the case of Log-Gaussian random fields with constant mean function, and compare this predictor to the commonly used lognormal kriging point predictor. Second, we show that previous results on optimal block prediction cannot be extended to the case of random fields with non-constant mean functions. Specifically, we show that both families of predictors considered by De Oliveira lack an optimal predictor (in mean square error sense).

            Finally, we numerically compare two block predictors and show that one of them is uniformly better than the other.

This is joint work with Victor De Oliveira, University of Texas, San Antonio