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This paper presents decision analysis networks (DANs) as a new type of probabilistic graphical model. Like influence diagrams (IDs), DANs are much more compact and easier to build than decision trees and can represent conditional independencies. In fact, for every ID there is an equivalent symmetric DAN, but DANs can also represent asymmetric problems involving partial orderings of the decisions (order asymmetry), restrictions between the values of the variables (domain asymmetry), and conditional observability (information asymmetry). Symmetric DANs can be evaluated with the same algorithms as IDs. Every asymmetric DAN can be evaluated by converting it into an equivalent decision tree or, much more efficiently, by decomposing it into a tree of symmetric DANs. Given that DANs can solve symmetric problems as easily and as efficiently as IDs, and are more appropriate for asymmetric problems—which include virtually all real-world problems—DANs might replace IDs as the standard type of probabilistic graphical model for decision support and decision analysis. We also argue that DANs compare favorably with other formalisms proposed for asymmetric decision problems. In practice, DANs can be built and evaluated with OpenMarkov, a Java open-source package for probabilistic graphical models. [ABSTRACT FROM AUTHOR]

Abstract: In the original formulation of influence diagrams (IDs), each model contained exactly one utility node. In 1990, Tatman and Shachtar introduced the possibility of having super value nodes that represent a combination of their parents’ utility functions. They also proposed an arc-reversal algorithm for IDs with super value nodes. In this paper we propose a variable-elimination algorithm for influence diagrams with super value nodes which is faster in most cases, requires less memory in general, introduces much fewer redundant (i.e., unnecessary) variables in the resulting policies, may simplify sensitivity analysis, and can speed up inference in IDs containing canonical models, such as the noisy OR. [Copyright &y& Elsevier]