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Gaussian predictive process models for large spatial data sets.

Publication ,  Journal Article
Banerjee, S; Gelfand, AE; Finley, AO; Sang, H
Published in: Journal of the Royal Statistical Society. Series B, Statistical methodology
September 2008

With scientific data available at geocoded locations, investigators are increasingly turning to spatial process models for carrying out statistical inference. Over the last decade, hierarchical models implemented through Markov chain Monte Carlo methods have become especially popular for spatial modelling, given their flexibility and power to fit models that would be infeasible with classical methods as well as their avoidance of possibly inappropriate asymptotics. However, fitting hierarchical spatial models often involves expensive matrix decompositions whose computational complexity increases in cubic order with the number of spatial locations, rendering such models infeasible for large spatial data sets. This computational burden is exacerbated in multivariate settings with several spatially dependent response variables. It is also aggravated when data are collected at frequent time points and spatiotemporal process models are used. With regard to this challenge, our contribution is to work with what we call predictive process models for spatial and spatiotemporal data. Every spatial (or spatiotemporal) process induces a predictive process model (in fact, arbitrarily many of them). The latter models project process realizations of the former to a lower dimensional subspace, thereby reducing the computational burden. Hence, we achieve the flexibility to accommodate non-stationary, non-Gaussian, possibly multivariate, possibly spatiotemporal processes in the context of large data sets. We discuss attractive theoretical properties of these predictive processes. We also provide a computational template encompassing these diverse settings. Finally, we illustrate the approach with simulated and real data sets.

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Published In

Journal of the Royal Statistical Society. Series B, Statistical methodology

DOI

EISSN

1467-9868

ISSN

1369-7412

Publication Date

September 2008

Volume

70

Issue

4

Start / End Page

825 / 848

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics
 

Citation

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Banerjee, S., Gelfand, A. E., Finley, A. O., & Sang, H. (2008). Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society. Series B, Statistical Methodology, 70(4), 825–848. https://doi.org/10.1111/j.1467-9868.2008.00663.x
Banerjee, Sudipto, Alan E. Gelfand, Andrew O. Finley, and Huiyan Sang. “Gaussian predictive process models for large spatial data sets.Journal of the Royal Statistical Society. Series B, Statistical Methodology 70, no. 4 (September 2008): 825–48. https://doi.org/10.1111/j.1467-9868.2008.00663.x.
Banerjee S, Gelfand AE, Finley AO, Sang H. Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society Series B, Statistical methodology. 2008 Sep;70(4):825–48.
Banerjee, Sudipto, et al. “Gaussian predictive process models for large spatial data sets.Journal of the Royal Statistical Society. Series B, Statistical Methodology, vol. 70, no. 4, Sept. 2008, pp. 825–48. Epmc, doi:10.1111/j.1467-9868.2008.00663.x.
Banerjee S, Gelfand AE, Finley AO, Sang H. Gaussian predictive process models for large spatial data sets. Journal of the Royal Statistical Society Series B, Statistical methodology. 2008 Sep;70(4):825–848.
Journal cover image

Published In

Journal of the Royal Statistical Society. Series B, Statistical methodology

DOI

EISSN

1467-9868

ISSN

1369-7412

Publication Date

September 2008

Volume

70

Issue

4

Start / End Page

825 / 848

Related Subject Headings

  • Statistics & Probability
  • 4905 Statistics
  • 3802 Econometrics
  • 1403 Econometrics
  • 0104 Statistics
  • 0102 Applied Mathematics