A Multi-resolution Gaussian process model for the analysis of large spatial data sets

Douglas Nychka, Soutir Bandyopadhyay, Dorit Hammerling, Finn Lindgren, Stephan Sain

Research output: Contribution to journalArticle

100 Citations (Scopus)
179 Downloads (Pure)

Abstract

A multi-resolution model is developed to predict two-dimensional spatial fields based on irregularly spaced observations. The radial basis functions at each level of resolution are constructed 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 Matérn 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.
Original languageEnglish
Pages (from-to)579-599
JournalJournal of Computational and Graphical Statistics
Volume24
Issue number2
Early online date16 May 2014
DOIs
Publication statusPublished - 16 Jun 2015

Keywords

  • Spatial estimator
  • Kriging
  • Fixed Rank Kriging
  • Sparse Cholesky Dekomposition
  • Multi-resolution

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