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Gaussian Markov Random Fields: Theory and Applications
Gaussian Markov Random Field (GMRF) models are most widely used in spatial statistics, a very active area of research in which few up-to-date reference works are available. Gaussian Markov Random… Expand
An explicit link between Gaussian fields and Gaussian Markov random fields: the stochastic partial differential equation approach
Continuously indexed Gaussian fields (GFs) are the most important ingredient in spatial statistical modelling and geostatistics. The specification through the covariance function gives an intuitive… Expand
Fast sampling of Gaussian Markov random fields
- H. Rue
This paper demonstrates how Gaussian Markov random fields (conditional autoregressions) can be sampled quickly by using numerical techniques for sparse matrices. The algorithm is general and… Expand
Bayesian Spatial Modelling with R-INLA
The principles behind the interface to continuous domain spatial models in the RINLA software package for R are described. The integrated nested Laplace approximation (INLA) approach proposed by Rue,… Expand
Bayesian computing with INLA: New features
- Thiago G. Martins, D. Simpson, F. Lindgren, H. Rue
- Mathematics, Computer Science
- Comput. Stat. Data Anal.
- 1 October 2012
The INLA approach for approximate Bayesian inference for latent Gaussian models has been shown to give fast and accurate estimates of posterior marginals and also to be a valuable tool in practice… Expand
An explicit link between Gaussian fields and Gaussian Markov random fields; The SPDE approach
Continuously indexed Gaussian fields (GFs) is the most important ingredient in spatial statistical modelling and geo-statistics. The specification through the covariance function gives an intuitive… Expand
Bayesian inference for generalized linear mixed models.
Generalized linear mixed models (GLMMs) continue to grow in popularity due to their ability to directly acknowledge multiple levels of dependency and model different data types. For small sample… Expand
Spatio-temporal modeling of particulate matter concentration through the SPDE approach
In this work, we consider a hierarchical spatio-temporal model for particulate matter (PM) concentration in the North-Italian region Piemonte. The model involves a Gaussian Field (GF), affected by a… Expand
On Block Updating in Markov Random Field Models for Disease Mapping
Gaussian Markov random field (GMRF) models are commonly used to model spatial correlation in disease mapping applications. For Bayesian inference by MCMC, so far mainly single-site updating… Expand