edu.ucar.opensky::articles:18147 UCAR/NCAR - Library OpenSky Support PO Box 3000 Boulder CO 80307-3000 opensky@ucar.edu http://opensky.ucar.edu/ homepage pointOfContact 2025-12-26T13:34:38.051149 ISO 19115-2 Geographic Information - Metadata - Part 2: Extensions for Imagery and Gridded Data ISO 19115-2:2009(E) https://n2t.org/ark:/85065/d7h133k4 Nonstationary covariance modeling for incomplete data: Monte Carlo EM approach 2011-06-01T00:00:00Z publication https://n2t.org/ark:/85065/d7h133k4 https://doi.org/10.1016/j.csda.2010.12.002 Matsuo, Tomoko author Nychka, Douglas author Paul, D. author UCAR/NCAR - Library publisher A multi-resolution basis can provide a useful representation of nonstationary two-dimensional spatial processes that are typically encountered in the geosciences. The main advantages are its flexibility for representing departures from stationarity and importantly the scalability of algorithms to large numbers of spatial locations. The key ingredients of our approach are the availability of fast transforms for wavelet bases on regular grids and enforced sparsity in the covariance matrix among wavelet basis coefficients. In support of this approach we outline a theoretical proposition for decay properties of the multi-resolution covariance for mixtures of Matérn covariances. A covariance estimator, built upon a regularized method of moment, is straightforward to compute for complete data on regular grids. For irregular spatial data the estimator is implemented by using a conditional simulation algorithm drawn from a Monte Carlo Expectation Maximization approach, to translate the problem to a regular grid in order to take advantage of efficient wavelet transforms. This method is illustrated with a Monte Carlo experiment and applied to surface ozone data from an environmental monitoring network. The computational efficiency makes it possible to provide bootstrap measures of uncertainty and these provide objective evidence of the nonstationarity of the surface ozone field. 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 NOTICE: This is the author's version of a work submitted for publication by Elsevier. Changes resulting from the publishing process, including peer review, editing, corrections, structural formatting and other quality control mechanisms, may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. None eng geoscientificInformation