Downloadable - About University

160 Decision trees and influence diagrams
A
C
E
The probabilities associated with chance
variable B depend on the outcome of
chance variable A
The probability of chance variable D
depends on decision C
The decision maker knows the outcome of
chance variable E when decision F
is made
G H
The decision maker knows decision G
when decision H is made
Figure 6.11 – Definitions used in influence diagrams
influence diagrams through a worked example. First, however, we will
present the basic concepts and representations underlying the approach.
Figure 6.11 presents the key concepts. As with the decision tree, event
nodes are represented by circles and decision nodes by squares. Arrowed
lines between nodes indicate the influence of one node to another. For
example, an arrow pointing to an event node indicates that either the
likelihood of events (contained in the node) are influenced by a prior
decision or on the occurrence (or not) of prior events. Alternatively, an
arrow pointing to a decision node indicates that either the decision is
influenced by a prior decision or on the occurrence (or not) of prior
events. The whole set of interconnected decisions and events is called an
influence diagram.
Figure 6.12(a) gives one exemplar influence diagram for the calculator
production problem and Figure 6.13 gives the decision tree representation
of this influence diagram. Two conditions must be met in order
for an influence diagram to be represented as a decision tree. First, the
B
D
F