Graphical ModelsClarendon Press, 02.05.1996 - 308 Seiten The idea of modelling systems using graph theory has its origin in several scientific areas: in statistical physics (the study of large particle systems), in genetics (studying inheritable properties of natural species), and in interactions in contingency tables. The use of graphical models in statistics has increased considerably over recent years and the theory has been greatly developed and extended. This book provides the first comprehensive and authoritative account of the theory of graphical models and is written by a leading expert in the field. It contains the fundamental graph theory required and a thorough study of Markov properties associated with various type of graphs. The statistical theory of log-linear and graphical models for contingency tables, covariance selection models, and graphical models with mixed discrete-continous variables in developed detail. Special topics, such as the application of graphical models to probabilistic expert systems, are described briefly, and appendices give details of the multivarate normal distribution and of the theory of regular exponential families. The author has recently been awarded the RSS Guy Medal in Silver 1996 for his innovative contributions to statistical theory and practice, and especially for his work on graphical models. |
Inhalt
| 1 | |
Conditional independence and Markov properties | 28 |
Contingency tables | 62 |
Multivariate normal models | 123 |
Models for mixed data | 158 |
Further topics | 221 |
Appendices | 237 |
B Linear algebra and random vectors | 243 |
The multivariate normal distribution | 254 |
Exponential models | 266 |
| 278 | |
| 295 | |
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algorithm assume asymptotic block-recursive calculated canonical parameter canonical statistic CG density CG distribution chain components chain graph model cliques of G complete conditional distribution conditional independence consider corresponding covariance matrix covariance selection model decomposable graph decomposable models denote deviance test direct join directed acyclic graph discrete variables edge equivalent example factorization follows given graph G graphical models H₁ Hence hierarchical model homogeneous hypergraph implies iterative Lauritzen Lemma likelihood function linear log-affine model log-linear models marginal table marked graph Markov property maximizing maximum likelihood estimate model with graph moral graph multinomial sampling n(id normal distribution obtained pairwise partitioned perfect sequence positive definite probability Proof Proposition quadratic random variables restrictions result satisfies saturated model Section space subgraph subsets sufficient statistic Theorem triangulated undirected graph vertex vertices weakly zero ΕΙ θα