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 296 articles , 1 standard article )

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  1. Bardsley, Johnathan M.; Cui, Tiangang: Optimization-based Markov chain Monte Carlo methods for nonlinear hierarchical statistical inverse problems (2021)
  2. Brown, Paul T.; Joshi, Chaitanya; Joe, Stephen; Rue, Håvard: A novel method of marginalisation using low discrepancy sequences for integrated nested Laplace approximations (2021)
  3. 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)
  4. Chen, Wanfang; Castruccio, Stefano; Genton, Marc G.: Assessing the risk of disruption of wind turbine operations in Saudi Arabia using Bayesian spatial extremes (2021)
  5. Gangloff, Hugo; Courbot, Jean-Baptiste; Monfrini, Emmanuel; Collet, Christophe: Unsupervised image segmentation with Gaussian pairwise Markov fields (2021)
  6. Katzfuss, Matthias; Guinness, Joseph: A general framework for Vecchia approximations of Gaussian processes (2021)
  7. Maksimov, A. G.; Tulupyev, A. L.: Algebraic Bayesian networks: checking backbone connectivity (2021)
  8. Zilber, Daniel; Katzfuss, Matthias: Vecchia-Laplace approximations of generalized Gaussian processes for big non-Gaussian spatial data (2021)
  9. Azaïs, Jean-Marc; Bachoc, François; Lagnoux, Agnès; Nguyen, Thi Mong Ngoc: Semi-parametric estimation of the variogram scale parameter of a Gaussian process with stationary increments (2020)
  10. Bachoc, F.; Lagnoux, A.: Fixed-domain asymptotic properties of maximum composite likelihood estimators for Gaussian processes (2020)
  11. Bardsley, Johnathan M.; Hansen, Per Christian: MCMC algorithms for computational UQ of nonnegativity constrained linear inverse problems (2020)
  12. Barzegar, Zahra; Rivaz, Firoozeh: A scalable Bayesian nonparametric model for large spatio-temporal data (2020)
  13. Brown, Richard D.; Bardsley, Johnathan M.; Cui, Tiangang: Semivariogram methods for modeling Whittle-Matérn priors in Bayesian inverse problems (2020)
  14. Dolgov, Sergey; Anaya-Izquierdo, Karim; Fox, Colin; Scheichl, Robert: Approximation and sampling of multivariate probability distributions in the tensor train decomposition (2020)
  15. Fox, Colin; Cui, Tiangang; Neumayer, Markus: Randomized reduced forward models for efficient Metropolis-Hastings MCMC, with application to subsurface fluid flow and capacitance tomography (2020)
  16. Fuglstad, Geir-Arne; Castruccio, Stefano: Compression of climate simulations with a nonstationary global spatiotemporal SPDE model (2020)
  17. Garcia-Garcia, Belmar; Bouwmans, Thierry; Rosales Silva, Alberto Jorge: Background subtraction in real applications: challenges, current models and future directions (2020)
  18. Geirsson, Óli Páll; Hrafnkelsson, Birgir; Simpson, Daniel; Sigurdarson, Helgi: LGM split sampler: an efficient MCMC sampling scheme for latent Gaussian models (2020)
  19. Ip, Ryan H. L.; Wu, K. Y. K.: A note on discrete multivariate Markov random field models (2020)
  20. Kirsner, Daniel; Sansó, Bruno: Multi-scale shotgun stochastic search for large spatial datasets (2020)

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