Contents 

PREFACE
INTRODUCTION
Background
The Scope of This Monograph
Applications of GMRFs
THEORY OF GAUSSIAN MARKOV RANDOM FIELDS
Preliminaries
Definition and Basic Properties of GMRFs
Simulation From a GMRF
Numerical Methods for Sparse Matrices
A Numerical Case Study of Typical GMRFs
Stationary GMRFs
Parameterization of GMRFs
Bibliographic Notes
INTRINSIC GAUSSIAN MARKOV RANDOM FIELDS
Preliminaries
GMRFs Under Linear Constraints
IGMRFs of First Order
IGMRFs of Higher Order
Continuous Time Random Walks
Bibliographic Notes
CASE STUDIES IN HIERARCHICAL MODELING
MCMC for Hierarchical GMRF Models
Normal Response Models
Auxiliary Variable Models
Non-Normal Response Models 
Bibliographic Notes
APPROXIMATION TECHNIQUES
GMRFs as Approximations to Gaussian Fields
Approximating Hidden GMRFs
Bibliographic Notes
APPENDIX A: COMMON DISTRIBUTIONS
APPENDIX B: THE LIBRARY GMRFLIB
The Graph Object and the Function Qfunc
Sampling from a GMRF
Implementing Block Updating Algorithms
REFERENCES
AUTHOR INDEX
SUBJECT INDEX