Graphical Models [Hardcover]

The application of graph theory to modelling systems began in several scientific areas, among them statistical physics (the study of large particle systems), genetics (studying inheritable properties of natural species), and interactions in contingency tables. The use of graphical models in statistics has increased considerably in these and other areas such as artificial intelligence, and the theory has been greatly developed and extended. This is the first comprehensive and authoritative account of the theory of graphical models. Written by a leading expert in the field, it contains the fundamentals graph required and a thorough study of Markov properties associated with various type of graphs, the statistical theory of log-linear and graphical models, and graphical tables with mixed discrete-continuous 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 multivariate normal distribution and of the theory of regular exponential families.

1. Introduction
2. Graphs and hypergraphs
3. Conditional independence and Markov properties
4. Contingency tables
5. Multivariate normal models
6. Models for mixed data
7. Further topics
A Various prerequisites
B Linear algebra and random vectors
C The multivariate distribution
D Exponential models
Bibliography
Index

An excellent research monograph in mathematical statistics. . . .Highly recommended. --Choice

This research monograph provides a comprehensive account of the theory of graphical models in multivariate statistics written by a leading expert in the field. --Mathematical Review