On optimal point and block prediction in log-gaussian random fields

This work discusses the problems of point and block prediction in log-Gaussian random fields with unknown mean. New point and block predictors are derived that are optimal in mean squared error sense within certain families of predictors that contain the corresponding lognormal kriging point and block predictors, as well as a block predictor originally motivated under the assumption of 'preservation of lognormality', and hence improve upon them. A comparison between the optimal, lognormal kriging and best linear unbiased predictors is provided, as well as between the two new block predictors. Somewhat surprisingly, it is shown that the corresponding optimal and lognormal kriging predictors are almost identical under most scenarios. It is also shown that one of the new block predictors is uniformly better than the other.