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This innovative volume explores graphical models using belief functions as a representation of uncertainty, offering an alternative approach to problems where probability proves inadequate. Graphical Belief Modeling makes it easy to compare the two approaches while evaluating their relative strengths and limitations.
The author examines both theory and computation, incorporating practical notes from the author's own experience with the BELIEF software package. As one of the first volumes to apply the Dempster-Shafer belief functions to a practical model, a substantial portion of the book is devoted to a single example—calculating the reliability of a complex system. This special feature enables readers to gain a thorough understanding of the application of this methodology.
The first section provides a description of graphical belief models and probablistic graphical models that form an important subset: the second section discusses the algorithm used in the manipulation of graphical models: the final segment of the book offers a complete description of the risk assessment example, as well as the methodology used to describe it.
Graphical Belief Modeling offers researchers and graduate students in artificial intelligence and statistics more than just a new approach to an old reliability task: it provides them with an invaluable illustration of the process of graphical belief modeling.
This book attempts to bridge the gap between artificial intelligence and statistics. Almond explores graphical models using both probability and belief functions as primary representations of uncertainty. The book covers both theory and computation, with many practical notes based on the author's experience implementing the BELIEF software package. 75 illustrations.
Introduction to Graphical Belief Models. Overview of Graphical Belief Models. Probability. Basic Belief Functions. Graphical Models. Manipulating Graphical Belief Models. Specifying and Storing Valuations. Belief Functions and Probabilities. The Fusion and Propagation Algorithm. Model Exploration. Belief Risk Assessment: An Example. Fault Trees. Belief Function Models for Components. Models for Simple Series and Parallel Systems. Information (Common Parameter) Dependence. Three Examples. Belief Risk Assessment and Public Policy. Appendices: Resources for Graphical Modelers. Annotated Examples. BELIEF Package and Other Software.