FLORENTINA ANDRE29114312

YP52A

Decision trees and influence diagrams

The process of constructing a decision tree is usually iterative, with many changes being made to the original structure as the decision maker’s understanding of the problem develops. Because the intention is to help the decision maker to think about the problem, very large and complex trees, which are designed to represent every possible scenario which can occur, can be counterproductive in many circumstances. Decision trees are models, and as such are simplifications of the real problem. The simplification is the very strength of the modeling process because it fosters the understanding and insight which would be obscured by detail and complexity. Influence diagrams offer an alternative way of structuring a complex decision problem and some analysts find that people relate to them much more easily. Constructing a decision treeA square is used to represent a decision node and, because each branch emanating from this node presents an option, the decision maker can choose which branch to follow. A circle, on the other hand, is used to represent a chance node. The branches which stem from this sort of node represent the possible outcomes of a given course of action and the branch which is followed will be determined, not by the decision maker, but by circumstances which lie beyond his or her control. The branches emanating from a circle are therefore labeled with probabilities which represent the decision maker’s estimate of the probability that a particular branch will be followed. Obviously, it is not sensible to attach probabilities to the branches which stem from a square.Determining the optimal policyIt can be seen that our decision tree consists of a set of policies. A policy is a plan of action stating which option is to be chosen at each decision node that might be reached under that policy. The technique for determining the optimal policy in a decision tree is known as the rollback method. To apply this method, we analyze the tree from right to left by considering the later decisions first.Decision trees and utilityThe procedure for analyzing the tree when utilities are involved is exactly the same as that which we used for the EMV criterionDecision trees involving continuous probability distributionsIn the decision problem we considered above there were only two possible outcomes for each course of action, namely success and failure. However, in some problems the number of possible outcomes may be very large or even infinitePractical applications of decision treesA large number of applications of decision trees have been published over the years, and we give below a summary of a few of these applications to show the variety of contexts where the method has been successfully used.Assessment of decision structureAlthough Expected Utility may be an optimal decision principle there is no normative technique for eliciting the structure of the decision problem from the decision maker. It is really a matter of the decision analyst’s judgment as to whether the elicited tree is a fair representation of the decision maker’s decision problem. Once a structure is agreed then the computation of expected utility is fairly straightforward. Structuring is therefore a major problem in decision analysis, for if the structuring is wrong then it is a necessary consequence that assessments of utilities and probabilities may be inappropriate and the expected utility computations may be invalid.Eliciting decision tree representations

Influence diagrams which are designed to summarize the dependencies that are seen to exist among events and acts within a decision. Such dependencies may be mediated by the flow of time, as we saw in our examples of decision trees. As we shall see, a close relationship exists between influence diagrams and the more familiar decision trees. Indeed, given certain conditions, influence diagrams can be converted to trees. The advantage of starting with influence diagrams is that their graphic representation is more appealing to the intuition of decision makers who may be unfamiliar with decision technologies. In addition, influence diagrams are more easily revised and altered as the decision maker iterates with the decision analyst. Decision trees, because of their strict temporal ordering of acts and events, need completely respecifying when additional acts and events are inserted into preliminary representations. We shall illustrate the applicability of influence diagrams through a worked example