Statistical Science

Beyond the Valley of the Covariance Function

Daniel Simpson, Finn Lindgren, and Håvard Rue

Full-text: Open access

Article information

Source
Statist. Sci., Volume 30, Number 2 (2015), 164-166.

Dates
First available in Project Euclid: 3 June 2015

Permanent link to this document
https://projecteuclid.org/euclid.ss/1433341472

Digital Object Identifier
doi:10.1214/15-STS515

Mathematical Reviews number (MathSciNet)
MR3353097

Zentralblatt MATH identifier
1332.86015

Citation

Simpson, Daniel; Lindgren, Finn; Rue, Håvard. Beyond the Valley of the Covariance Function. Statist. Sci. 30 (2015), no. 2, 164--166. doi:10.1214/15-STS515. https://projecteuclid.org/euclid.ss/1433341472


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References

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  • Adler, R. J. and Taylor, J. (2007). Random Fields and Geometry. Springer, Berlin.
  • Bolin, D. and Lindgren, F. (2013). A comparison between Markov approximations and other methods for large spatial data sets. Comput. Statist. Data Anal. 61 7–32.
  • Higdon, D. (1998). A process-convolution approach to modelling temperatures in the North Atlantic Ocean. Environ. Ecol. Stat. 5 173–190.
  • Hu, X., Lindgren, F., Simpson, D. and Rue, H. (2013a). Multivariate Gaussian random fields with oscillating covariance functions using systems of stochastic partial differential equations. Dept. Mathematical Sciences, NTNU, Norway. Available at arXiv:1307.1384.
  • Hu, X., Simpson, D., Lindgren, F. and Rue, H. (2013b). Multivariate Gaussian random fields using systems of stochastic partial differential equations. Dept. Mathematical Sciences, NTNU, Norway. Available at arXiv:1307.1379.
  • Hu, X., Steinsland, I., Simpson, D., Martino, S. and Rue, H. (2013c). Spatial modelling of temperature and humidity using systems of stochastic partial differential equations. Dept. Mathematical Sciences, NTNU, Norway. Available at arXiv:1307.1402.
  • Lindgren, G. (2012). Stationary Stochastic Processes: Theory and Applications. Chapman & Hall/CRC, London.
  • Lindgren, F., Rue, H. and Lindström, J. (2011). An explicit link between Gaussian fields and Gaussian Markov random fields: The stochastic partial differential equation approach (with discussion). J. R. Stat. Soc. Ser. B. Stat. Methodol. 73 423–498.
  • Simpson, D., Lindgren, F. and Rue, H. (2012). In order to make spatial statistics computationally feasible, we need to forget about the covariance function. Environmetrics 23 65–74.
  • Simpson, D. P., Martins, T. G., Riebler, A., Fuglstad, G.-A., Rue, H. and Sørbye, S. H. (2014). Penalising model component complexity: A principled, practical approach to constructing priors. Preprint. Available at arXiv:1403.4630.
  • Zhang, H. (2004). Inconsistent estimation and asymptotically equal interpolations in model-based geostatistics. J. Amer. Statist. Assoc. 99 250–261.

See also

  • Main article: Cross-Covariance Functions for Multivariate Geostatistics.