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 222 articles , 1 standard article )

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  1. Junker, Philipp; Nagel, Jan: A relaxation approach to modeling the stochastic behavior of elastic materials (2019)
  2. Roininen, Lassi; Girolami, Mark; Lasanen, Sari; Markkanen, Markku: Hyperpriors for Matérn fields with applications in Bayesian inversion (2019)
  3. Arias-Castro, Ery; Bubeck, Sébastien; Lugosi, Gábor; Verzelen, Nicolas: Detecting Markov random fields hidden in white noise (2018)
  4. Bernardi, Mauro; Bottone, Marco; Petrella, Lea: Bayesian quantile regression using the skew exponential power distribution (2018)
  5. Bhattacharya, Arnab; Wilson, Simon P.: Sequential Bayesian inference for static parameters in dynamic state space models (2018)
  6. Bolin, David; Kirchner, Kristin; Kovács, Mihály: Weak convergence of Galerkin approximations for fractional elliptic stochastic PDEs with spatial white noise (2018)
  7. Castruccio, Stefano; Genton, Marc G.: Principles for statistical inference on big spatio-temporal data from climate models (2018)
  8. Cowles, Mary Kathryn; Bonett, Stephen; Seedorff, Michael: Independent sampling for Bayesian normal conditional autoregressive models with OpenCL acceleration (2018)
  9. Creasey, Peter E.; Lang, Annika: Fast generation of isotropic Gaussian random fields on the sphere (2018)
  10. Faulkner, James R.; Minin, Vladimir N.: Locally adaptive smoothing with Markov random fields and shrinkage priors (2018)
  11. Hardouin, Cécile; Cressie, Noel: Two-scale spatial models for binary data (2018)
  12. Ippoliti, L.; Martin, R. J.; Romagnoli, L.: Efficient likelihood computations for some multivariate Gaussian Markov random fields (2018)
  13. Joyce, Kevin T.; Bardsley, Johnathan M.; Luttman, Aaron: Point spread function estimation in X-ray imaging with partially collapsed Gibbs sampling (2018)
  14. Lindqvist, Bo H.; Taraldsen, Gunnar: On the proper treatment of improper distributions (2018)
  15. Marchetti, Yuliya; Nguyen, Hai; Braverman, Amy; Cressie, Noel: Spatial data compression via adaptive dispersion clustering (2018)
  16. Mescheder, L. M.; Lorenz, D. A.: An extended Perona-Malik model based on probabilistic models (2018)
  17. Opitz, Thomas; Huser, Raphaël; Bakka, Haakon; Rue, Håvard: INLA goes extreme: Bayesian tail regression for the estimation of high spatio-temporal quantiles (2018)
  18. Parker, Albert E.; Pitts, Betsey; Lorenz, Lindsey; Stewart, Philip S.: Polynomial accelerated solutions to a large Gaussian model for imaging biofilms: in theory and finite precision (2018)
  19. Ponciano, José M.; Taper, Mark L.; Dennis, Brian: Ecological change points: the strength of density dependence and the loss of history (2018)
  20. Rullière, Didier; Durrande, Nicolas; Bachoc, François; Chevalier, Clément: Nested kriging predictions for datasets with a large number of observations (2018)

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