edu.ucar.opensky::technotes:517 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-26T03:35:44.575496 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.org/ark:/85065/d7w095cm A multi-resolution Gaussian process model for the analysis of large spatial data sets 2013-12-02T00:00:00Z publication https://n2t.org/ark:/85065/d7w095cm https://doi.org/10.5065/D6VH5KTJ Nychka, Douglas author Bandyopadhyay, S. author Hammerling, Dorit author Lindgren, F. author Sain, S. author UCAR/NCAR - Library publisher A multi-resolution basis is developed to predict two-dimensional spatial fields based on irregularly spaced observations. The basis functions at each level of resolution are constructed as radial basis functions using a Wendland compactly supported correlation function with the nodes arranged on a rectangular grid. The grid at each finer level increases by a factor of two and the basis functions are scaled to have a constant overlap. The coefficients associated with the basis functions at each level of resolution are distributed according to a Gaussian Markov random field (GMRF) and take advantage of the fact that the basis is organized as a lattice. Several numerical examples and analytical results establish that this scheme gives a good approximation to standard covariance functions such as the Matern and also has flexibility to fit more complicated shapes. The other important feature of this model is that it can be applied to statistical inference for large spatial datasets because key matrices in the computations are sparse. The computational efficiency applies to both the evaluation of the likelihood and spatial predictions. Although our framework has similarities to fixed rank Kriging, the model gives a better approximation to situations where the nugget variance is small and the spatial process is close to interpolating the observations. UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact PDF Text theme Resource Type 2016-01-01T00:00:00Z publication Statistical applications Weather research/forecast models theme U.S. National Aeronautics and Space Administration Global Change Master Directory GCMD 2021-09-17 revision 11.2 NASA Global Change Master Directory originator Valids List: Science and Services Keywords Copyright Author(s). This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License. None eng geoscientificInformation