Spatial Gaussian Markov Random Fields: Modelling, Applications and Efficient Computations

[摘要] A powerful modelling tool for spatial data is the framework of Gaussian Markov random fields (GMRFs), which are discrete domain Gaussian random fields equipped with a Markov property. GMRFs allow us to combine the analytical results for the Gaussian distribution as well as Markov properties, thus allow for the development of computationally efficient algorithms. Here we briefly review popular spatial GMRFs, show how to construct them, and outline their recent developments and possible future work.

[关键词] Gaussian Markov random fields;Markov chain Monte Carlo;spatial statistics;Cholesky factorization;Integrated nested laplace approximation