Application of hierarchical matrices in spatial statistics

Large datasets with irregularly spatial (or spatio-temporal) locations are difficult to handle in many applications of Gaussian random fields, such as maxi- mum likelihood estimation (MLE) and prediction. We aim to approximate covariance functions in a format that facilitates the computation of MLE and prediction with very large datasets using a hierarchical matrix approach. We present a numerical study where we compare this approach with the covariance tapering method.