Spatial models generated by nested stochastic partial differential equations, with an application to global ozone mapping

By David Bolin, Finn Lindgren. 2011

142 citations recorded by the source corpus.

A new class of stochastic field models is constructed using nested stochastic partial differential equations (SPDEs). The model class is computationally efficient, applicable to data on general smooth manifolds, and includes both the Gaussian Matern fields and a wide family of fields with oscillating covariance functions. Nonstationary covariance models are obtained by spatially varying the parameters in the SPDEs, and the model parameters are estimated using direct numerical optimization, which is more efficient than standard Markov Chain Monte Carlo procedures. The model class is used to estimate daily ozone maps using a large data set of spatially irregular global total column ozone data.

Subfields: Atmospheric Science, Economics and Econometrics, Environmental Engineering

View Paper: https://www.semanticscholar.org/paper/0838a7f6c7a3e53ac11163f9c784467e5a9acf37

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Citations in the corpus

Estimation of a non-stationary model for annual precipitation in southern Norway using replicates of the spatial field (2014, methodology): “The SPDE formulation of Lindgren et al. (2011) also provides ways to easily introduce non-stationarity by letting the parameters or operators vary in space (Lindgren et al., 2011; Bolin and Lindgren, 2011; Fuglstad et al., 2014b,a; Ingebrigtsen et al., 2014).”
Spatial models with explanatory variables in the dependence structure (2014, background): “It was introduced by Lindgren et al. in 2011 and has since been extended and applied in various contexts (Bolin and Lindgren, 2011, 2013; Simpson et al., 2012a,b; Cameletti et al., 2013).”
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach (2011, methodology): “Kernel convolution methods, as mentioned by Furrer, Furrer, and Nychka, are useful theoretical tools, but can in practice be cumbersome and computationally intensive (Bolin and Lindgren, 2009).”
Strictly and non-strictly positive definite functions on spheres (2011, background): “mationtechnique (Das, 2000), methodsusingexpansionsin spherical harmonicsStein (2007), approaches basedon differentialoperators and nested stochasticpartialdifferential equations(Jun and Stein, 2008; Bolin and Lindgren, 2011), and the approach of Katzfuss (2011, Section 4.3) that builds on the work ”
Geostatistical Modelling Using Non‐Gaussian Matérn Fields (2015, background): “…is commonly referred to as trans-Gaussian Kriging (Cressie, 1993) and common transformations include the square-root transform (Cressie, 1993; Huerta et al., 2004; Berrocal et al., 2010; Sahu & Mardia, 2005) and the log transform (Cressie, 1993; Cameletti et al., 2013; Bolin & Lindgren, 2011).”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, methodology): “2011), ozone data (Bolin and Lindgren 2011), annual precipitation data in southern Norway (Ingebrigtsen et al.”
Spatial modelling with R-INLA: A review (2018, methodology): “, 2013b,a; Bolin and Wallin, 2018) and to generate more flexible anisotropic and oscillating covariance structures both on Rd and on the sphere (Bolin and Lindgren, 2011; Barman and Bolin, 2018).”
Bayesian Spatial Modelling with R-INLA (2015, methodology): “Beyond the main paper Lindgren et al. (2011), this is further discussed by Simpson, Lindgren, and Rue (2012a,b).”