Gaussian Markov Random Fields: Theory And Applications (Monographs on Statistics and Applied Probability)

By Håvard Rue, Leonhard Held. 2005

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Effective Bayesian Modeling of Groups of Related Count Time Series (2014, background): “The second line of this equation expresses a prior over jointly normally-distributed variables with a highly structured (and very sparse) precision matrix, a Gaussian Markov random field (GMRF, see Rue & Held, 2005), to which we now turn.”
Approximate Bayesian computational methods (2011, methodology): “In others situations, the normalizing constant of the likelihood Z θ is unknown This is typically the case of Gibbs random ﬁelds used to model the dependency within spatially correlated data, with applications in epidemiology and image analysis, among others (e.g. Rue and Held 2005).”
A comparison study of extreme precipitation from six different regional climate models via spatial hierarchical modeling (2010, background): “Usually one assumes a Gaussian formulation, and additionally one assumes the conditional relationships have a Markov property, in which case the resulting CAR is a Gaussian Markov random field (GMRF, Rue and Held 2005).”
Bayesian structured additive distributional regression with an application to regional income inequality in Germany (2015, methodology): “For the structured spatial effect, we assume spatial correlations defined implicitly by assuming a Gaussian Markov random field prior [Rue and Held (2005)] for a suitable neighbourhood structure derived from the spatial orientation of the data.”
Maximum likelihood estimation of spatially varying coefficient models for large data with an application to real estate price prediction (2020, methodology): “One can define a Bayesian SVC model using the link between Gaussian Markov random fields (GMRF, see Rue and Held, 2005) and GP via a stochastic partial differential equation (SPDE, see Lindgren et al., 2011).”