Gaussian Influence Diagrams

Ross D. Shachter and C. Robert Kenley
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Ross D. Shachter: Department of Engineering-Economic Systems, Stanford University, Stanford, California 94305
C. Robert Kenley: Tiburon Systems, Inc., 2085 Hamilton Avenue, San Jose, California 95125

Management Science, 1989, vol. 35, issue 5, 527-550

Abstract: An influence diagram is a network representation of probabilistic inference and decision analysis models. The nodes correspond to variables that can be either constants, uncertain quantities, decisions, or objectives. The arcs reveal probabilistic dependence of the uncertain quantities and information available at the time of the decisions. The influence diagram focuses attention on relationships among the variables. As a result, it is increasingly popular for eliciting and communicating the structure of a decision or probabilistic model. This paper develops the framework for assessment and analysis of linear-quadratic-Gaussian models within the influence diagram representation. The "Gaussian influence diagram" exploits conditional independence in a model to simplify elicitation of parameters for the multivariate normal distribution. It is straightforward to assess and maintain a positive (semi-)definite covariance matrix. Problems of inference and decision making can be analyzed using simple transformations to the assessed model, and these procedures have attractive numerical properties. Algorithms are also provided to translate between the Gaussian influence diagram and covariance matrix representations for the normal distribution.

Keywords: influence diagram; Gaussian decision model; multivariate normal assessment (search for similar items in EconPapers)
Date: 1989
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Citations: View citations in EconPapers (23)

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