Reduced Dimension Hierarchical Statistical Models For Spatial And Spatio Temporal Data

Moreover, we extend the SRE model to the Spatio-Temporal Random Effects (STRE) model for massive spatio-temporal datasets. We explicitly model the measurement error, the non-dynamic fine-scale variation, the dynamic spatial variation, and the trend. The optimal spatio-temporal predictions are derived efficiently through the fixed-rank model and a rapid recursive updating procedure through the Kalman filter. Formulas for optimal smoothing, filtering, and forecasting are derived. The improvement of combining past and current data using the methodology called Fixed Rank Filtering (FRF) to predict the current hidden process of interest, is illustrated with a simulation experiment. The methodology is also applied to a large spatio-temporal remote-sensing dataset.