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Influence diagrams
1. Influence diagrams
An influence diagram is a way of looking at decision problems using decision nodes, chance nodes, value nodes, and arrows between them such that there are no cycles in the graph.
An influence diagram is similar in many respects to what is called a graphical model in Bayesian statistical models or Bayesian network.
2. Decision nodes
A
decision node represents the available decisions and is drawn as a rectangle.
3. Chance nodes
A
chance node represents states of nature and is drawn as an oval.
4. Value nodes
A
value node represents payoffs or utility that is to be maximized or minimized and is drawn as a rounded rectangle.
5. Arcs
Arcs connect nodes.
Arcs pointing to chance or value nodes indicate probabilistic or functional dependence.
Arcs pointing to decision nodes imply time precedence and are informational.
6. Cancer test problem
The unconditional probability, or prior probability, that one has cancer is known.
7. Cancer test problem
The conditional probability, or posterior probability, that one tests positive given that one has cancer is known.
8. Cancer test problem
Bayes' Rule is used to flip the arc so that the probability that one has cancer given that one tests positive can be determined.
9. Tree diagram
The tree diagram appears as follows.
10. Trees versus influence diagrams
The influence diagram is more concise than the tree diagram and works better for larger problem sizes.
11. End of page
