1. Decision Analysis

2. What kinds of problems? Alternatives known
States of Nature and their probabilities are known.
Payoffs computable under different possible scenarios

3. Basic Terms Decision Alternatives
States of Nature (eg. Condition of economy)
Payoffs ($ outcome of a choice assuming a state of nature)
Criteria (eg. Expected Value)

4. Example problem

5. Expected Values

6. Decision Tree
300
0.3
340
0.6
350
0.1
400 A1
-100
0.3 A2
0.6
600 A2
400
400
0.1
700 A3
0.3
-1000
0.6
-200
-300
0.1
1200

7. Sequential Decisions
Would you hire a consultant (or a psychic) to get more info about states of nature?
How would additional info cause you to revise your probabilities of states of nature occuring?
Draw a new tree depicting the complete problem.

8. Consultant’s Track Record

9. Probabilities P(F/S1) = 0.2 P(U/S1) = 0.8 P(F/S2) = 0.6 P(U/S2) = 0.4
F= Favorable U=Unfavorable

10. Joint Probabilities

11. Posterior Probabilities
P(S1/F) = 0.06/0.49 = 0.122
P(S2/F) = 0.36/0.49 = 0.735
P(S3/F) = 0.07/0.49 = 0.143
P(S1/U) = 0.24/0.51 = 0.47
P(S2/U) = 0.24/0.51 = 0.47
P(S3/U) = 0.03/0.51 = 0.06

12. Solution
Solve the decision tree using the posterior probabilities just computed.