By Havard Rue, Leonhard Held
-------------------Description-------------------- Researchers in spatial facts and snapshot research are acquainted with Gaussian Markov Random Fields (GMRFs), and they're ordinarily one of the few who use them. There are, although, a variety of purposes for this system, from structural time-series research to the research of longitudinal and survival information, spatio-temporal types, graphical types, and semi-parametric records. With such a lot of purposes and with such frequent use within the box of spatial records, it's fabulous that there is still no entire reference at the topic.
Gaussian Markov Random Fields: idea and purposes offers this type of reference, utilizing a unified framework for representing and knowing GMRFs. quite a few case experiences illustrate using GMRFs in advanced hierarchical versions, during which statistical inference is barely attainable utilizing Markov Chain Monte Carlo (MCMC) ideas. The preeminent specialists within the box, the authors emphasize the computational points, build speedy and trustworthy algorithms for MCMC inference, and supply a web C-library for quick and specific simulation.
This is a perfect instrument for researchers and scholars in facts, fairly biostatistics and spatial facts, in addition to quantitative researchers in engineering, epidemiology, photo research, geography, and ecology, introducing them to this strong statistical inference process. ---------------------Features--------------------- · offers a accomplished remedy of GMRFs utilizing a unified framework · comprises sections which are self-contained and extra complex sections that require historical past wisdom, supplying fabric for either newbies and skilled researchers · Discusses the relationship among GMRFs and numerical equipment for sparse matrices, intrinsic GMRFs (IGMRFs), how GMRFs are used to approximate Gaussian fields, the right way to parameterize the precision matrix, and built-in Wiener technique priors as IGMRFs · Covers spatial types in addition to space-state types · Describes a variety of varieties of IGMRFs: at the line, the lattice, the torus, and abnormal graphs · contains particular case reports and an internet C-library for speedy and distinct simulation ---------------------Contents--------------------- PREFACE creation heritage The Scope of This Monograph purposes of GMRFs conception OF GAUSSIAN MARKOV RANDOM FIELDS Preliminaries Definition and uncomplicated houses of GMRFs Simulation From a GMRF Numerical tools for Sparse Matrices A Numerical Case learn of general GMRFs desk bound GMRFs Parameterization of GMRFs Bibliographic Notes INTRINSIC GAUSSIAN MARKOV RANDOM FIELDS Preliminaries GMRFs lower than Linear Constraints IGMRFs of First Order IGMRFs of upper Order non-stop Time Random Walks Bibliographic Notes CASE reports IN HIERARCHICAL MODELING MCMC for Hierarchical GMRF versions basic reaction versions Auxiliary Variable versions Non-Normal reaction types Bibliographic Notes APPROXIMATION concepts GMRFs as Approximations to Gaussian Fields Approximating Hidden GMRFs Bibliographic Notes APPENDIX A: universal DISTRIBUTIONS APPENDIX B: THE LIBRARY GMRFLIB The Graph item and the functionality Qfunc Sampling from a GMRF enforcing Block Updating Algorithms REFERENCES writer INDEX topic INDEX
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