BOHAI ZHANG 
PhD Candidate, Department of Statistics
Texas A&M University
“Statistical Methods for Large Spatial Datasets”
ABSTRACT
Gaussian process models are widely used for analyzing spatial datasets, its computational complexity however grows cubically with sample size, imposing obstacles for its applications to large spatial datasets. We propose a Smooth Full-Scale Approximation approach (SFSA) for analyzing large geostatistical datasets. It extends the FSA-Block approach (Sang et al. 2011) by correcting the approximation errors of residual covariance among neighboring data blocks. By applying the block conditional likelihood approximation to the residual likelihood, the residual covariance of neighboring blocks can be partially preserved. The proposed method inherits the merits of both the FSA-Block and the block version of the nearest neighbor Gaussian process methods. Compared with the FSA-Block approach, the SFSA approach can alleviate the prediction errors for block boundary locations. In addition, due to the additional corrections of residual covariance across data blocks, the SFSA approach is less sensitive to the knot set than the FSA-Block approach. We show that the proposed approach can result in a valid Gaussian process so that both parameter estimation and prediction can be performed in a unified framework. We illustrate the effectiveness of the proposed method through simulation studies and a precipitation dataset.
