A Fast, Optimal Spatial-Prediction Method for Massive Datasets

This article considers a class of multiresolution tree-structured models that are spatially shifted versions of each other and proposes a new spatial-prediction method that averages over the optimal spatial predictors produced from members of this class of models. As a consequence, the resulting predicted surface is smooth, even when the predictors generated separately from individual multiresolution tree-structured models are not. We call the new predictor the multiresolution spatial (MURS) predictor and develop a computationally efficient algorithm for it. The algorithm can handle massive datasets even when some observations are missing. Moreover, the MURS predictor can be shown to be the minimum mean squared error predictor for a large class of covariance functions. A simulation example for massive datasets shows that the MURS method consistently outperforms two commonly used filtering methods. Total column ozone data remotely sensed from a satellite are analyzed using the new methodology.