Spatial models with explanatory variables in the dependence structure

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Spatial modelling with R-INLA: A review (2018, background): “Lindgren et al. (2011) and Ingebrigtsen et al. (2014) include the covariates in the covariance structure by using the operator where the parameters vary in space as sums of known basis functions b k ( s ), and similarly for κ ( s ).”
Second-order non-stationary modeling approaches for univariate geostatistical data (2017, methodology): “Ingebrigtsen et al. (2014) point out that, in general, nonstatioary modeling approaches based on space deformation and SPDE are not equivalent.”
Constructing Priors that Penalize the Complexity of Gaussian Random Fields (2015, methodology): “The dataset was previously used by Ingebrigtsen, Lindgren, and Steinsland and Ingebrigtsen et al. (2015) to study the use of elevation as a covariate in the covariance structure and associated priors.”
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).”