Gaussian Markov Random Field Models

Havard Rue, Leonhard Held - Collection Monographs on Statistics and Applied Probability

272 pages, parution le 18/02/2005

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Résumé

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 is, 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.

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.

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.

Provides a comprehensive treatment of GMRFs using a unified framework
Contains sections that are self-contained and more advanced sections that require background knowledge, offering material for both novices and experienced researchers
Discusses the connection between GMRFs and numerical methods for sparse matrices, intrinsic GMRFs (IGMRFs), how GMRFs are used to approximate Gaussian fields, how to parameterize the precision matrix, and integrated Wiener process priors as IGMRFs
Covers spatial models as well as space-state models
Describes various types of IGMRFs: on the line, the lattice, the torus, and irregular graphs
Includes detailed case studies and an online C-library for fast and exact simulation

L'auteur - Havard Rue

Havard Rue NTNU, Trondheim, Norway

L'auteur - Leonhard Held

Leonhard Held:University of Munich, Munich, Germany

Sommaire

Introduction
Theory Of Gaussian Markov Random Fields
Intrinsic Gaussian Markov Random Fields
Case Studies In Hierarchical Modeling
Approximation Techniques
Appendix A: Common Distributions
Appendix B: The Library GMRFLib

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Caractéristiques techniques

	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Havard Rue, Leonhard Held
Collection	Monographs on Statistics and Applied Probability
Parution	18/02/2005
Nb. de pages	272
Format	16 x 23,5
Couverture	Relié
Poids	500g
Intérieur	Noir et Blanc
EAN13	9781584884323
ISBN13	978-1-58488-432-3