2015
DOI: 10.1016/j.spasta.2015.10.001
|View full text |Cite
|
Sign up to set email alerts
|

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

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-stationar… Show more

Help me understand this report

Search citation statements

Order By: Relevance

Paper Sections

Select...
2
1
1
1

Citation Types

4
79
0

Year Published

2015
2015
2024
2024

Publication Types

Select...
9
1

Relationship

1
9

Authors

Journals

citations
Cited by 98 publications
(83 citation statements)
references
References 56 publications
4
79
0
Order By: Relevance
“…In particular, the use of prior knowledge would avoid un-identifiability issues, which would otherwise be inevitably involved in such a flexible modeling of anisotropic and non-stationary spatial variation. See also Fuglstad et al (2015), that extend the approach based on Gaussian random fields and stochastic PDEs introduced in Lindgren et al (2011). In the application to Switzerland rainfall data, if information about wind stream or air circulation were available, it could be used to define a PDE with anisotropic and non-stationary diffusion and transport terms; in particular, the transport terms can be used to induce unidirectional smoothing effects in the direction of the wind streams.…”
Section: Possible Model Extensions and Directions Of Future Researchmentioning
confidence: 99%
“…In particular, the use of prior knowledge would avoid un-identifiability issues, which would otherwise be inevitably involved in such a flexible modeling of anisotropic and non-stationary spatial variation. See also Fuglstad et al (2015), that extend the approach based on Gaussian random fields and stochastic PDEs introduced in Lindgren et al (2011). In the application to Switzerland rainfall data, if information about wind stream or air circulation were available, it could be used to define a PDE with anisotropic and non-stationary diffusion and transport terms; in particular, the transport terms can be used to induce unidirectional smoothing effects in the direction of the wind streams.…”
Section: Possible Model Extensions and Directions Of Future Researchmentioning
confidence: 99%
“…Work on parameterising and performing inference on non-stationary SPDE models with varying local anisotropy has been undertaken by Fuglstad et al (2015a). The SPDE based non-stationary models have been applied to different data sets: weather on the continents , ozone data (Bolin and Lindgren 2011), annual precipitation data in southern Norway (Ingebrigtsen et al 2014(Ingebrigtsen et al , 2015 and the United States (Fuglstad et al 2015b). Figure 5a, c show realizations of Gaussian random functions defined on the unit square and based on a non-stationary SPDE model with respectively, a spatially varying range and a spatially varying anisotropy direction.…”
Section: Stoch Environ Res Risk Assessmentioning
confidence: 99%
“…In practice, the evaluation of the likelihood at a particular data location turns out to be a weighted sum of the values of the GMRF on the nearest three vertices. The above strategy can be used with a wide range of likelihoods and the SPDE can also be extended to a variety of non-stationary models (Lindgren et al, 2011; Fuglstad et al, 2015a). …”
Section: Building Appropriate Spatial Modelsmentioning
confidence: 99%