Gaussian Markov random fields. Theory and applications. Researchers in spatial statistics and image analysis are familiar with Gaussian Markov Random Fields (GMRFs), and they are traditionally among the few who use them. There are, however, a wide range of applications for this methodology, from structural time-series analysis to the analysis of longitudinal and survival data, spatio-temporal models, graphical models, and semi-parametric statistics. With so many applications and with such widespread use in the field of spatial statistics, it is surprising that there remains no comprehensive reference on the subject.par Gaussian Markov Random Fields: Theory and Applications provides such a reference, using a unified framework for representing and understanding GMRFs. Various case studies illustrate the use of GMRFs in complex hierarchical models, in which statistical inference is only possible using Markov Chain Monte Carlo (MCMC) techniques. The preeminent experts in the field, the authors emphasize the computational aspects, construct fast and reliable algorithms for MCMC inference, and provide an online C-library for fast and exact simulation.par This is an ideal tool for researchers and students in statistics, particularly biostatistics and spatial statistics, as well as quantitative researchers in engineering, epidemiology, image analysis, geography, and ecology, introducing them to this powerful statistical inference method.

References in zbMATH (referenced in 309 articles , 1 standard article )

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  1. Coube-Sisqueille, Sébastien; Liquet, Benoît: Improving performances of MCMC for nearest neighbor Gaussian process models with full data augmentation (2022)
  2. Vono, Maxime; Dobigeon, Nicolas; Chainais, Pierre: High-dimensional Gaussian sampling: a review and a unifying approach based on a stochastic proximal point algorithm (2022)
  3. Allard, Denis; Hristopulos, Dionisios T.; Opitz, Thomas: Linking physics and spatial statistics: a new family of Boltzmann-Gibbs random fields (2021)
  4. Bardsley, Johnathan M.; Cui, Tiangang: Optimization-based Markov chain Monte Carlo methods for nonlinear hierarchical statistical inverse problems (2021)
  5. Brown, Paul T.; Joshi, Chaitanya; Joe, Stephen; Rue, Håvard: A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations (2021)
  6. Cao, Jian; Genton, Marc G.; Keyes, David E.; Turkiyyah, George M.: Sum of Kronecker products representation and its Cholesky factorization for spatial covariance matrices from large grids (2021)
  7. Chen, Wanfang; Castruccio, Stefano; Genton, Marc G.: Assessing the risk of disruption of wind turbine operations in Saudi Arabia using Bayesian spatial extremes (2021)
  8. Ferreira, Marco A. R.; Porter, Erica M.; Franck, Christopher T.: Fast and scalable computations for Gaussian hierarchical models with intrinsic conditional autoregressive spatial random effects (2021)
  9. Frommer, Andreas; Schimmel, Claudia; Schweitzer, Marcel: Analysis of probing techniques for sparse approximation and trace estimation of decaying matrix functions (2021)
  10. Gangloff, Hugo; Courbot, Jean-Baptiste; Monfrini, Emmanuel; Collet, Christophe: Unsupervised image segmentation with Gaussian pairwise Markov fields (2021)
  11. Hazra, Arnab; Huser, Raphaël: Estimating high-resolution red sea surface temperature hotspots, using a low-rank semiparametric spatial model (2021)
  12. Hepler, Staci A.; Waller, Lance A.; Kline, David M.: A multivariate spatiotemporal change-point model of opioid overdose deaths in Ohio (2021)
  13. Hrafnkelsson, Birgir; Siegert, Stefan; Huser, Raphaël; Bakka, Haakon; Jóhannesson, Árni V.: Max-and-smooth: a two-step approach for approximate Bayesian inference in latent Gaussian models (2021)
  14. Hristopulos, Dionissios T.; Pavlides, Andrew; Agou, Vasiliki D.; Gkafa, Panagiota: Stochastic local interaction model: an alternative to kriging for massive datasets (2021)
  15. Katzfuss, Matthias; Guinness, Joseph: A general framework for Vecchia approximations of Gaussian processes (2021)
  16. Lambert, Philippe: Fast Bayesian inference using Laplace approximations in nonparametric double additive location-scale models with right- and interval-censored data (2021)
  17. Maksimov, A. G.; Tulupyev, A. L.: Algebraic Bayesian networks: checking backbone connectivity (2021)
  18. Turčičová, Marie; Mandel, Jan; Eben, Kryštof: Score matching filters for Gaussian Markov random fields with a linear model of the precision matrix (2021)
  19. Wang, Craig; Furrer, Reinhard: Combining heterogeneous spatial datasets with process-based spatial fusion models: a unifying framework (2021)
  20. Zilber, Daniel; Katzfuss, Matthias: Vecchia-Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data (2021)

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