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Spatial modeling with R‐INLA: A review

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Coming up with Bayesian models for spatial data is easy, but performing inference with them can be challenging. Writing fast inference code for a complex spatial model with realistically‐sized datasets from scratch is time‐consuming, and if changes are made to the model, there is little guarantee that the code performs well. The key advantages of R‐INLA are the ease with which complex models can be created and modified, without the need to write complex code, and the speed at which inference can be done even for spatial problems with hundreds of thousands of observations. R‐INLA handles latent Gaussian models, where fixed effects, structured and unstructured Gaussian random effects are combined linearly in a linear predictor, and the elements of the linear predictor are observed through one or more likelihoods. The structured random effects can be both standard areal model such as the Besag and the BYM models, and geostatistical models from a subset of the Matérn Gaussian random fields. In this review, we discuss the large success of spatial modeling with R‐INLA and the types of spatial models that can be fitted, we give an overview of recent developments for areal models, and we give an overview of the stochastic partial differential equation (SPDE) approach and some of the ways it can be extended beyond the assumptions of isotropy and separability. In particular, we describe how slight changes to the SPDE approach leads to straight‐forward approaches for nonstationary spatial models and nonseparable space–time models. This article is categorized under: Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory Statistical Models > Bayesian Models Data: Types and Structure > Massive Data
Example correlation surface for the barrier model by Bakka et al. (). The gray region acts as a physical barrier to spatial correlation, forcing the model to smooth around this barrier
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Simulation from the model by Ingebrigtsen et al. (), as you decrease or increase τ, increasing or decreasing the variance, from west to east
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An example mesh, constructed for the Norwegian fjord “Sognefjorden”
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Besag model. The left plot shows an example dataset over regions in Germany, and the right plot shows the sparse precision matrix Q
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Example function f (left plot) and g = 1Df (right plot). The black pluses are the vector f representing the continuous function f (black line), similarly with g and g. The blue circles are the discrete operator applied to the vector, that is, L1Df, which is close to the discretization g of g
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A simulation of a Matérn stochastic partial differential equation model driven by normal inverse Gaussian noise
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Simulation for the nonseparable model by Krainski () on the sphere, for six time points (left to right, top to bottom)
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Simulation of anisotropic field from the model by Fuglstad, Simpson, et al. (). In the west part of the plot there is a strong horisontal dependence, while in the east part, there is a strong vertical dependence
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Statistical and Graphical Methods of Data Analysis > Bayesian Methods and Theory
Statistical Models > Bayesian Models
Data: Types and Structure > Massive Data

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