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# Influence Diagrams Essay

2136 words - 9 pages

INFLUENCE DIAGRAMS
Taken from Encyclopedia of Medical Decision Making, 2010.
Written by E. Borgonovo, Bocconi University, Milan.
The utilization of decision-support models is necessary to improve the decision-making
process and to identify the optimal policy. The models allow to unveil the decisions to be
taken, their consequences and the uncertain events involved in the problem. Influence
diagrams are graphical tools for the representation and solution of decision-making
problems. By representation, one means the identification of the decision-making
problem elements. In particular, an influence diagram reveals the probabilistic
dependences among the uncertain quantities and the state of information at each decision
stage. By solution, one means the determination of the preferred alternative (best strategy
selection) given the state of information. Influence diagrams grant decision-makers the
possibility of representing complex decision-making problems in a thorough albeit
compact fashion. It is this strength over other representation techniques that have made
the use of influence diagrams widespread in medical applications. This Section is
organized as follows. It provides a description of influence diagrams by means of a
sample medical example. The discussion of the properties and levels of influence
diagrams follows. This discussion preludes to a synthetic description of influence
diagram solution algorithms. The relationship between influence diagrams, decision trees
and a brief mention to other graphical representation techniques conclude the entry.
Influence Diagram Description
An influence diagram is a directed graph composed of nodes and arcs (Figure 1).

Figure 1: An influence diagram with two chance nodes, two decision nodes and the value node. The order
of nodes is: Decision 1, Chance Node 1, Decision 2, Chance Node 2 and Value Node
The graph is acyclic. There are three types of nodes: decision, chance and value. A
decision node is represented by a rectangular box. A chance node is represented by a
circular box. There is one unique value node displayed by a diamond or rhombus,
occasionally an octagon is used. The value node ends the diagram and an influence
diagram containing a value node is said to be oriented. In the case there are no value
nodes and no decision nodes, the influence diagram coincides with a Bayesian Network.
As an example, the influence diagram in Figure 1 displays the following decision-making
problem.
A physician must select the treatment for a patient. The first stage of the treatment
foresees to choose between cures A or B. The two cures have a different efficacy, with
their overall effect strongly dependent on the patient's response. After one week the
physician re-evaluates the patient's conditions. Depending on the evaluation results, the
Decision 1: A or B?
Patient Conditions
1 Value Node
Patient Conditions
2
Decision 2: A, B or C
Conditional Arc
Probabilistic Dependence
Informational Arc
Sequential...

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