Best Unbiased Prediction for Gaussian and LogGaussian Processes

The best unbiased linear predictor for a stochastic process is the best unbiased predictor (i.e., the linearity constraint is removed) if the process is Gaussian. This provides a stronger justi cation for the universal kriging predictor than is generally o ered. For log-Gaussian processes, we show that the standard predictor (obtained by correcting the bias of the exponential of the best unbiased predictor of the underlying Gaussian process) is in fact optimal among all unbiased predictors with respect to a weighted mean squared error prediction criterion.