Downloadable - About University

Eliciting decision tree representations 161
diagram must contain no circles of influence arrows (loops). A loop
would show that a node (variable) both influences and is influenced
by another node. Such a relationship could not be represented by the
left-to-right ordering of influences represented by a decision tree. Second,
since decision trees are conventionally used to aid a single decision
maker who is knowledgeable about all temporally prior acts and events,
then those nodes that have direct influence (shown by direct arrows) on
a particular decision must be a subset of the influences on subsequent
decisions. If such an ordering is not represented in an influence diagram
(for example, the combination of Figures 6.12(a) and 6.12(b)) then at least
two decision trees need to be developed to represent the diagram.
Obviously, a decision tree representation must preserve the ordering
represented by the arrows in an influence diagram and the tree must not
have an event node as a predecessor of a decision node for which it is
not directly linked by an arrow in the influence diagram. If the tree did,
it would imply that the decision depends on the event node which, from
the influence diagram, is not the case.
One step-by-step procedure for turning an influence diagram into a
decision tree is as follows:
(1) Identify a node with no arrows pointing into it (since there can be
no loops at least one node will be such).
(2) If there is a choice between a decision node and an event node,
choose the decision node.
(3) Place the node at the beginning of the tree and ‘remove’ the node
from the influence diagram.
(4) For the now-reduced diagram, choose another node with no arrows
pointing into it. If there is a choice a decision node should be chosen.
(5) Place this node next in the tree and ‘remove’ it from the influence
diagram.
(6) Repeat the above procedure until all the nodes have been removed
from the influence diagram.
For practice, try this procedure on the content of Figure 6.12(a). You
should achieve the decision tree represented in Figure 6.13. To complete
the tree, the possible choices at each decision node and the possible
events at each event node must now be specified. Finally, subjective
probabilities must be assessed for the events and utilities must be
assigned to the end points in the decision tree.
Very complex decision trees can be represented as one-page influence
diagrams. However, the use of influence diagrams to construct decision
trees where subsequent events and acts depend on the initial decision (i.e.