Graphical Models: 41 (Oxford Statistical Science Series)

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. This new and extended edition of Graphical Models provides the basic mathematical and statistical theory of graphical models, incorporating the many advances that have been made in the field since the publication of the first edition in 1996.Lauritzen discusses basic graph theory and the fundamentals of conditional independence both in abstract form for conditional independence based on graphs and for probabilistic conditional independence.The associated Markov theory, forming the basis of all models in the book, is treated in some detail.The statistical theory based on likelihood methods and conjugate Bayesian analysis is developed for log-linear and Gaussian graphical models, as well as for graphical models involving mixed d