Monotonic influence diagrams: Extension to stochastic programming and application to probabilistic design

Monotonic influence diagrams: Extension to stochastic programming and application to probabilistic design

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Article ID: iaor1994704
Country: United Kingdom
Volume: 21
Issue: 2
Start Page Number: 99
End Page Number: 120
Publication Date: Jul 1993
Journal: Engineering Optimization
Authors: ,
Keywords: graphs, gradient methods, programming: probabilistic
Abstract:

In this paper the theory of monotonic influence diagrams is extended to deal with uncertainty. Monotonic influence diagrams (MID) are a synthesis of influence diagrams and monotonicity analysis. Formally, a monotonic influence diagram is a directed graph consisting of nodes and arcs. The nodes represent design variables and the arcs reveal their relationships. Nodes in a MID can represent either deterministic or uncertain quantities. An arc in a MID is associated with the qualitative relation between the corresponding variables. A deterministic qualitative relation between two variables is given by the sign of the partial derivative of the function defining one of the variables with respect to the other variable. A probabilistic qualitative relation is defined in terms of a constraint on the joint probability distribution of the variables. Both deterministic and probabilistic quantities and relationships will be addressed in this paper.

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