Combining Second-Order Belief Distributions with Qualitative Statements in Decision Analysis

  • Ola CasterEmail author
  • Love Ekenberg
Conference paper
Part of the Lecture Notes in Economics and Mathematical Systems book series (LNE, volume 658)


There is often a need to allow for imprecise statements in real-world decision analysis. Joint modeling of intervals and qualitative statements as constraint sets is one important approach to solving this problem, with the advantage that both probabilities and utilities can be handled. However, a major limitation with interval-based approaches is that aggregated quantities such as expected utilities also become intervals, which often hinders efficient discrimination. The discriminative power can be increased by utilizing second-order information in the form of belief distributions, and this paper demonstrates how qualitative relations between variables can be incorporated into such a framework. The general case with arbitrary distributions is described first, and then a computationally efficient simulation algorithm is presented for a relevant sub-class of analyses. By allowing qualitative relations, our approach preserves the ability of interval-based methods to be deliberately imprecise. At the same time, the use of belief distributions allows more efficient discrimination, and it provides a semantically clear interpretation of the resulting beliefs within a probabilistic framework.


Decision Tree Decision Situation Dirichlet Distribution Probability Group Qualitative Statement 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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The authors wish to thank Alina Kuznetsova for valuable suggestions that helped improve the contents of this paper.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  1. 1.WHO Collaborating Centre for International Drug MonitoringUppsala Monitoring CentreUppsalaSweden
  2. 2.Department of Computer and Systems SciencesStockholm UniversityKistaSweden

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