Decision Analysis.

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Presentation transcript:

Decision Analysis

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

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)

Example problem

Expected Values

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

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.

Consultant’s Track Record

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

Joint Probabilities

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

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