1. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 1

2. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 2 Define the terms state of nature, event, decision alternatives, payoff, and utility Organize information in a payoff table or a decision tree Compute opportunity loss and utility function Find an optimal decision alternative based on a given decision criterion When you have completed this chapter, you will be able to: Assess the expected value of additional information

3. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 3 T erminology Classical Statistics … focuses on estimating a parameter, such as the population mean, constructing confidence intervals, or hypothesis testing. Statistical Decision Theory … (Bayesian statistics) is concerned with determining which decision, from a set of possible decisions, is optimal.

4. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 4 E lements of a Decision  Payoffs … possible alternatives or acts …numerical gain to the decision maker for each combination of decision alternative and state of nature …these are future events that are not under the control of the decision maker  Available choices  States of Nature There are three components to any decision- making situation:

5. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 5 Payoff Table …is a listing of all possible combinations of decision alternatives and states of nature T erminology Expected Payoff or Expected Monetary Value (EMV) …is the Expected Value for each decision

6. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 6 A business example Nortel is considering introducing a new wireless telecommunication device into the market. They are considering three alternatives: I. Build a new full scale plant for manufacturing the new product II. Build a medium size plant III. Do not market the product If they decide to market the product, the annual profit will depend on the market response to the product. Nortel is considering introducing a new wireless telecommunication device into the market. They are considering three alternatives: I. Build a new full scale plant for manufacturing the new product II. Build a medium size plant III. Do not market the product If they decide to market the product, the annual profit will depend on the market response to the product. Suppose preliminary market analysis indicates that the market response to the product may be highly favourable, moderately favourable, or unfavourable. What decision should they make?

7. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 7 Available Choices I.Build a new full scale plant D1 II.Build a medium size plant D2 III.Do not market the product D3 I.Build a new full scale plant D1 II.Build a medium size plant D2 III.Do not market the product D3 Market response to the product may be highly favourable S1 moderately favourable S2 unfavourable S3 (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Payoff Table (Values … Millions of dollars)

8. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 8 …determine the payoff value for each decision alternative …choose the alternative for which the associated payoff value is maximum

9. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 9 (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Non-Probabilistic Criteria Note the minimum payoff for each decision alternative We don’t have any information about the probabilities of the 3 states of nature, except that they are each non-zero Maximin Criterion This Pessimistic view results in Decision 3 … do not market the product Select the decision for which this is maximum Payoff Table (Values … Millions of dollars)

10. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 10 Non-Probabilistic Criteria Note the maximum payoff for each decision alternative We don’t have any information about the probabilities of the 3 states of nature, except that they are each non-zero Maximax Criterion This Optimistic view results in Decision 1 … build a new full scale plant Select the decision for which this maximum payoff is maximum (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Payoff Table (Values … Millions of dollars)

11. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 11 Non-Probabilistic Criteria Choose a number alpha between 0 and 1 (called the pessimistic-optimistic index) The Pessimistic-Optimistic Index Criterion of Hurwicz The value for each decision alternative is then: Alpha (minimum payoff) + (1-alpha)(maximum payoff) The value for each decision alternative is then: Alpha (minimum payoff) + (1-alpha)(maximum payoff) (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Payoff Table C ontinued…

12. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 12 This view results in D ecision 2 – …build a medium sized plant For D1: (0.4)(-800)+(0.6)(400) Let alpha = 0.4 = $ -80 million For D2: (0.4)(-50)+(0.6)(80) = $ 28 million For D3: (0.4)(0)+(0.6)(0) = $ 0 million Non-Probabilistic Criteria The Pessimistic-Optimistic Index Criterion of Hurwicz (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Payoff Table Alpha (minimum payoff) + (1-alpha)(maximum payoff)

13. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 13 Probabilistic Criteria Calculate the EMV for each decision alternative We assume that we have prior information about the p robabilities of the 3 states of nature (usually based on historical data or subjective estimates) Expected Monetary Value Criterion Select the decision for which this is maximum 0.40.50.1 (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 C ontinued… Payoff Table

14. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 14 This view results in Decision 1 – build a full sized plant EMV (D1): (0.4)(400)+(0.5)(20) +(0.1)(-800) = $90 m. EMV (D2): (0.4)(80)+(0.5)(60)+(0.1)(-50) = $57 m. EMV (D3): (0.4)(0)+(0.5)(0)+(0.1)(0) = $ 0 m. Expected Monetary Value Criterion Select the decision for which this is maximum 0.40.50.1 (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Probabilistic Criteria Payoff Table

15. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 15 … is the loss because the exact state of nature is not known at the time a decision is made …the opportunity loss is computed by taking the difference between the optimal decision for each state of nature and the other decision alternatives Criteria Based on Opportunity Loss (Regret) Suppose that Nortel decided to build a medium sized plant…. If market conditions are very favourable (S1), then what is the expected profit?

16. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 16 Expected Profit Criteria Based on Opportunity Loss (Regret) Suppose that Nortel decided to build a medium sized plant…. If market conditions are highly favourable (S1), then what is the expected profit? (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Payoff Table But, had they known in advance that the market conditions would be favourable, they would have gone with D1 and achieved an expected profit of $400 million! Therefore, there is an Opportunity Loss of $320 million

17. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 17 Criteria Based on Opportunity Loss (Regret) Expected Profit Suppose that Nortel decided to build a medium sized plant…. If market conditions are moderately favourable (S2), then what is the expected profit? (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Payoff Table Therefore, there is an Opportunity Loss of $0 million...they actually gained $40 million ($60 - $20)!

18. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 18 Opportunity Loss Table Opportunity Loss Table Pessimistic Criterion These are the worst case scenarios for each decision alternative The “best” of these “worst cases” is D2 Market Response Decision (S1)(S2)(S3) (D1)040 800 (D2)320 0 50 (D3)400600

19. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 19 T erminology Value of Perfect Information i.e. … what is the worth of information known in advance before a strategy is employed? Expected Value of Perfect Information (EVPI) … is the difference between the expected payoff if the state of nature were known and the optimal decision under the conditions of uncertainty

20. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 20 T erminology Sensitivity Analysis … examines the effects of various probabilities for the states of nature on the expected values for the decision alternatives. Decision Trees … are useful for structuring the various alternatives. They present a picture of the various courses of action and the possible states of nature. See the following Decision Tree Examples…

21. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 21 (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Decision Tree Decision Tree Examples…

22. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 22 Decision Tree (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Decision Tree Examples…

23. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 23 (S1)(S2)(S3) (D1)40020-800 (D2)8060-50 (D3)000 Decision Tree Examples… Decision Tree

24. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 24 Test your learning … www.mcgrawhill.ca/college/lind Click on… Online Learning Centre for quizzes extra content data sets searchable glossary access to Statistics Canada’s E-Stat data …and much more!

25. Copyright © 2004 by The McGraw-Hill Companies, Inc. All rights reserved. 19 - 25 This completes Chapter 19