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Title: Likelihood approximation and prediction for large datasets of spatial data using hierarchical matrices Authors:  Anastasiia Gorshechnikova - University of Padova (Italy) [presenting]
Carlo Gaetan - Ca Foscari University of Venice (Italy)
Abstract: Large datasets with $n$ irregularly sited locations are difficult to handle for several applications of Gaussian random fields such as maximum likelihood estimation (MLE) and kriging prediction since they require a computational complexity of order $O(n^3)$. For relatively large $n$, the exact computation becomes unfeasible and alternative methods are necessary. Several approaches have been proposed to tackle this problem. Most of them assume a specific form for the spatial covariance function and use different methods to approximate the resulting covariance matrix. A methodology was developed using hierarchical matrices that resulted in a log-linear computational cost due to the partitioning of the matrix into dense and low-rank blocks according to specific given conditions. The approximation of the covariance matrix in this format allowed for fast computation of the matrix-vector products and matrix factorisations followed by the efficient MLE and kriging prediction. This method was then applied to a real dataset on the atmospheric carbon dioxide mole fraction of the earth and the prediction accuracy and computational time were compared with other methods. The first experiments show that the developed approach is the most efficient in terms of the root mean-squared prediction error and computational time.