## Gaussian Markov Random Fields: Theory and ApplicationsGaussian Markov Random Field (GMRF) models are most widely used in spatial statistics - a very active area of research in which few up-to-date reference works are available. This is the first book on the subject that provides a unified framework of GMRFs with particular emphasis on the computational aspects. This book includes extensive case-studie |

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This is an exciting book for someone, like me, with interests at the intersection of computational mathematics (specifically numerical linear algebra) and computational statistics. It's chock full of interesting ideas, is well written, and is relevant to a range of applied math and stat researchers.

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26 matrice de precision inverse covariance dans equation

### Contents

1 Introduction | 1 |

2 Theory of Gaussian Markov random fields | 15 |

3 Intrinsic Gaussian Markov random fields | 85 |

4 Case studies in hierarchical modeling | 133 |

5 Approximation techniques | 183 |

Appendices | 217 |

237 | |

Author index | 255 |

259 | |

### Other editions - View all

Gaussian Markov Random Fields: Theory and Applications Havard Rue,Leonhard Held Limited preview - 2005 |

Gaussian Markov Random Fields: Theory and Applications Havard Rue,Leonhard Held No preview available - 2005 |

### Common terms and phrases

acceptance additional algorithm analysis applications approach assume autoregressive base block Cholesky circulant coefficients compared component compute consider constant constraints construct corresponding covariance defined Definition denote density depends derived diagonal dimension discuss displays distribution effect eigenvalues elements equals estimate evaluate example factorization fields Figure fixed full conditional function Gaussian gives GMRF approximation graph hence hierarchical IGMRFs illustrate improved independent joint lattice linear locations marginal Markov MCMC mean methods neighbors nodes nonzero normal Note O O O O O O O O O observed obtain parameters positive posterior precision matrix prior problem properties proposal random range regions requires sample scale shown similar simple simulation Solve space sparse spatial Statistical structure Theorem torus typically update variables variance vector zero