Gaussian Markov random fields: theory and applications

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. ---------------------Features--------------------- · 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 spatia