Model Building with Belief Networks and Influence Diagrams
Ross D. Shachter · Cambridge University Press eBooks · 2007
. Belief networks and influence diagrams use directed graphs to represent models for probabilistic reasoning and decision making under uncertainty. They have proven to be effective at facilitating communication with decision makers and with computers. Many of the important relationships among uncertainties, decisions, and values can be captured in the structure of these diagrams, explicitly revealing irrelevance and the flow of information. We explore a variety of examples illustrating some of these basic structures, along with an algorithm that efficiently analyzes their model structure. We also show how algorithms based on these structures can be used to resolve inference queries and determine the optimal policies for decisions. We have all learned how to translate models, as we prefer to think of them, into arcane representations that our computers can understand, or to simplify away key subtleties for the benefit of clients or students. Thus it has been an immense pleasure to work with graphical models where the representation is natural for the novice, convenient for computation, and yet powerful enough to convey difficult concepts among analysts and researchers. The graphical representations of belief networks and influence diagrams enable us to capture important relationships at the structural level of the graph where it easiest for people to see them and for algorithms to exploit them. Although the diagrams lend themselves to communication, there remains the challenge of synthesis, and building graphical models is still a challenging art.