Does non-stationary spatial data always require non-stationary random fields?

Geir Arne Fuglstad*, Daniel Simpson, Finn Lindgren, Håvard Rue

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

44 Scopus citations

Abstract

A stationary spatial model is an idealization and we expect that the true dependence structures of physical phenomena are spatially varying, but how should we handle this non-stationarity in practice? We study the challenges involved in applying a flexible non-stationary model to a dataset of annual precipitation in the conterminous US, where exploratory data analysis shows strong evidence of a non-stationary covariance structure. The aim of this paper is to investigate the modelling pipeline once non-stationarity has been detected in spatial data. We show that there is a real danger of over-fitting the model and that careful modelling is necessary in order to properly account for varying second-order structure. In fact, the example shows that sometimes non-stationary Gaussian random fields are not necessary to model non-stationary spatial data.

Original languageEnglish (US)
Pages (from-to)505-531
Number of pages27
JournalSpatial Statistics
Volume14
DOIs
StatePublished - Nov 1 2015

Keywords

  • Annual precipitation
  • Gaussian Markov random fields
  • Gaussian random fields
  • Non-stationary spatial modelling
  • Penalized maximum likelihood
  • Stochastic partial differential equations

ASJC Scopus subject areas

  • Statistics and Probability
  • Computers in Earth Sciences
  • Management, Monitoring, Policy and Law

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