Bayesian Spatial Modelling with R-INLA

Bayesian Spatial Modelling with R-INLA

January 2015, Volume 63, Issue 19 | Finn Lindgren, Håvard Rue
The paper presents Bayesian spatial modelling using R-INLA, a software package that implements the integrated nested Laplace approximation (INLA) method for efficient Bayesian inference. INLA is designed for latent Gaussian models, including spatial and spatio-temporal models, and combines with stochastic partial differential equations (SPDEs) to handle geographically referenced data. The software supports stationary and non-stationary spatial models, as well as spatio-temporal models, and is applicable in fields such as epidemiology, ecology, and environmental risk assessment. The interface allows for flexible model specification, including non-stationary fields and spatial point processes. The paper discusses the theoretical foundations of SPDEs and Gaussian Markov random fields (GMRFs), and describes the implementation of these models in R-INLA. It also covers the use of basis functions, precision matrices, and parameterisation strategies for efficient computation. The software provides tools for mesh construction, spatial mapping, and model building, and supports advanced predictor manipulation and Bayesian inference through the INLA method. The paper highlights the practical advantages of using INLA for continuous domain spatial models, including computational efficiency and the ability to handle complex spatial dependencies. The implementation includes support for various spatial domains, including 2D, 3D, and spherical domains, and allows for the construction of non-separable and non-stationary models. The paper also discusses the use of the R-INLA package for Bayesian inference, including the specification of linear predictors, the use of prior distributions, and the generation of posterior predictions. The software provides a flexible and efficient framework for spatial modelling, with a focus on continuous domains and the use of SPDEs and GMRFs for accurate and computationally efficient inference.The paper presents Bayesian spatial modelling using R-INLA, a software package that implements the integrated nested Laplace approximation (INLA) method for efficient Bayesian inference. INLA is designed for latent Gaussian models, including spatial and spatio-temporal models, and combines with stochastic partial differential equations (SPDEs) to handle geographically referenced data. The software supports stationary and non-stationary spatial models, as well as spatio-temporal models, and is applicable in fields such as epidemiology, ecology, and environmental risk assessment. The interface allows for flexible model specification, including non-stationary fields and spatial point processes. The paper discusses the theoretical foundations of SPDEs and Gaussian Markov random fields (GMRFs), and describes the implementation of these models in R-INLA. It also covers the use of basis functions, precision matrices, and parameterisation strategies for efficient computation. The software provides tools for mesh construction, spatial mapping, and model building, and supports advanced predictor manipulation and Bayesian inference through the INLA method. The paper highlights the practical advantages of using INLA for continuous domain spatial models, including computational efficiency and the ability to handle complex spatial dependencies. The implementation includes support for various spatial domains, including 2D, 3D, and spherical domains, and allows for the construction of non-separable and non-stationary models. The paper also discusses the use of the R-INLA package for Bayesian inference, including the specification of linear predictors, the use of prior distributions, and the generation of posterior predictions. The software provides a flexible and efficient framework for spatial modelling, with a focus on continuous domains and the use of SPDEs and GMRFs for accurate and computationally efficient inference.
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[slides and audio] Bayesian Spatial Modelling with R-INLA