Spatial modeling with R‐INLA: A review. (5th July 2018)

• Record Type: Journal Article
• Authors: Bakka, Haakon; Rue, Håvard; Fuglstad, Geir‐Arne; Riebler, Andrea; Bolin, David; Illian, Janine; Krainski, Elias; Simpson, Daniel; Lindgren, Finn
• Is Part Of: Wiley interdisciplinary reviews. Volume 10:Number 6(2018)
• Page Start: n/a
• Page End: n/a
• Publication Date: 2018-07-05
• Subjects: approximate Bayesian inference -- Gaussian Markov random fields -- Laplace approximations -- sparse matrices -- spatial statistics -- stochastic partial differential equations; Mathematical statistics -- Data processing -- Periodicals; Science -- Data processing -- Periodicals; Social sciences -- Data processing -- Periodicals; Mathematical statistics -- Periodicals; 519.50285
• DOI: 10.1002/wics.1443
• Languages: English
• ISSNs: 1939-5108

Abstract

Abstract : 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 Abstract : In spatial statistics, an important problem is how to represent spatial models in a way that is computationally efficient, accurate, and convenient to use. Models in R‐INLA focus on sparse precision (inverse covariance) matrices to compute inference quickly. Hence, our implementations of spatial models focus on how to represent the spatial field in such a way that the precision matrix for the "representation" is very sparse. This graphic shows a representation of a Norwegian fjord with a mesh, from which basis functions are built in the finite element method. We use sums of these basis functions to represent the spatial field. This representation has many advantages, but requires some mathematical effort to understand and to set up.