Nonstationary covariance modeling for incomplete data: Monte Carlo EM approach

AMS Citation:
Matsuo, T., D. Nychka, and D. Paul, 2011: Nonstationary covariance modeling for incomplete data: Monte Carlo EM approach. Computational Statistics & Data Analysis, 55, 2059-2073, doi:10.1016/j.csda.2010.12.002.
Date:2011-06-01
Resource Type:article
Title:Nonstationary covariance modeling for incomplete data: Monte Carlo EM approach
Abstract: 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.
Subject(s):computational efficiency, Gaussian process, multi-resolution basis, regularized method of moment, sparse covariance matrix, surface ozone observation
Peer Review:Refereed
Copyright Information: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.
OpenSky citable URL: ark:/85065/d7h133k4
Publisher's Version: 10.1016/j.csda.2010.12.002
Author(s):
  • Tomoko Matsuo - NCAR/UCAR
  • Doug Nychka - NCAR/UCAR
  • Debashis Paul
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