Evaluating Influence Diagrams

Abstract

An influence diagram is a graphical structure for modeling uncertain variables and decisions and explicitly revealing probabilistic dependence and the flow of information. It is an intuitive framework in which to formulate problems as perceived by decision makers and to incorporate the knowledge of experts. At the same time, it is a precise description of information that can be stored and manipulated by a computer. We develop an algorithm that can evaluate any well-formed influence diagram and determine the optimal policy for its decisions. Since the diagram can be analyzed directly, there is no need to construct other representations such as a decision tree. As a result, the analysis can be performed using the decision maker's perspective on the problem. Questions of sensitivity and the value of information are natural and easily posed. Modifications to the model suggested by such analyses can be made directly to the problem formulation, and then evaluated directly.

On computations with causal compositional models

“…Here we employ Pearl's idea of extension used in his front-door adjustment [7]. The reader can realize that it is the way how to take into account the mutual dependence of variables C, D, O (notice that it plays the same role that is realized by inheritance of parents in Shachters edge reversal rule [9]). …”

Probability Elicitation in Influence Diagram Modeling by Using Interval Probability

“…Obviously it is inefficient. Shachter presents a way to evaluate influence diagrams with two operations: node-removal and arcreversal [20]. By recursively using the two operations, an influence diagram is transformed into a diagram with only a utility node.…”

The Usage of Influence Diagram for Decision Making in Textiles

“…However this approach brings the problem that the number of variables in the problem increases almost exponentially and thus, calculation effectiveness evantually decreases. In the technique developed by Shachter (1986), nodes in the influence diagram are deleted one by one till the one node that shows the expected utility remains, afterwhich the expected utility value is calculated. The solution process includes a series of transformations that Shachter (1986) calls value-preserving reduction.…”

“…The arc reversal processes are realized in accordance with the Bayes' Theorem (Shachter, 1986) as follows:  Barren Node Removal: A chance or decision node will be called a barren node if it is a sink, that is, it has no successors. No matter what value is assigned to the barren node variable no other node is affected, so it may be removed from the diagram.…”

“…In the solution process of influence diagrams, how the nodes relate to their predecessors and consequents are really important. Steps included in the approach developed by Shachter (1986) to solve influence diagram are as follows (Clemen, 1996): www.ccsenet.org/ass Asian Social Science Vol. 8, No.…”