Multi-level restricted maximum likelihood covariance estimation and kriging for large non-gridded spatial datasets
KAUST DepartmentCenter for Uncertainty Quantification in Computational Science and Engineering (SRI-UQ)
Computer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
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AbstractWe develop a multi-level restricted Gaussian maximum likelihood method for estimating the covariance function parameters and computing the best unbiased predictor. Our approach produces a new set of multi-level contrasts where the deterministic parameters of the model are filtered out thus enabling the estimation of the covariance parameters to be decoupled from the deterministic component. Moreover, the multi-level covariance matrix of the contrasts exhibit fast decay that is dependent on the smoothness of the covariance function. Due to the fast decay of the multi-level covariance matrix coefficients only a small set is computed with a level dependent criterion. We demonstrate our approach on problems of up to 512,000 observations with a Matérn covariance function and highly irregular placements of the observations. In addition, these problems are numerically unstable and hard to solve with traditional methods.
CitationMulti-level restricted maximum likelihood covariance estimation and kriging for large non-gridded spatial datasets 2015 Spatial Statistics