Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field

Rikke Ingebrigtsen, Finn Lindgren, Ingelin Steinsland, Sara Martino

Research output: Contribution to journalArticlepeer-review

17 Citations (Scopus)

Abstract

Estimation of stationary dependence structure parameters using only a single realisation of the spatial process, typically leads to inaccurate estimates and poorly identified parameters. A common way to handle this is to fix some of the parameters, or within the Bayesian framework, impose prior knowledge. In many applied settings, stationary models are not flexible enough to model the process of interest, thus non-stationary spatial models are used. However, more flexible models usually means more parameters, and the identifiability problem becomes even more challenging. We investigate aspects of estimation of a Bayesian non-stationary spatial model for annual precipitation using observations from multiple years. The model contains replicates of the spatial field, which increases precision of the estimates and makes them less prior sensitive. Using R-INLA, we analyse precipitation data from southern Norway, and investigate statistical properties of the replicate model in a simulation study. The non-stationary spatial model we explore belongs to a recently introduced class of stochastic partial differential equation (SPDE) based spatial models. This model class allows for non-stationary models with explanatory variables in the dependence structure. We derive conditions to facilitate prior specification for these types of non-stationary spatial models.

Original languageEnglish
Pages (from-to)338-364
JournalSpatial Statistics
Volume14
Issue numberPart C
Early online date11 Jul 2015
DOIs
Publication statusPublished - Nov 2015

Keywords

  • Annual precipitation
  • Bayesian inference
  • Gaussian Markov random fields
  • Gaussian random fields
  • Non-stationary spatial modelling
  • Stochastic partial differential equations

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