Graphical Models

Erscheinungsjahr 1996
ISBN: 978-0-19-852219-5
Verlag: OUP Oxford

Buch, Englisch, 308 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 634 g

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.

Autoren/Hrsg.

Lauritzen, Steffen L.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Stochastik Mathematische Statistik
• Mathematik | Informatik Mathematik Stochastik Wahrscheinlichkeitsrechnung

Inhaltsverzeichnis

- Introduction

- 1: Graphs and Hypergraphs

- 2: Conditional Independence and Markov Properties

- 3: Contingency Tables

- 4: Multivariate Normal Models

- 5: Models for Mixed Data

- 6: Further topics

- A Various Prerequisites

- B Linear Algebra and Random Vectors

- C The Multivariate Distribution

- D Exponential Models

Über Autor(innen)

Steffen L. Lauritzen is a Professor in the Department of Mathematics and Computer Science at the University of Aalborg, Denmark and was previously Professor of Statistics at Oxford University.