1. Decision Analysis Study Guide for ES205 Yu-Chi Ho Jonathan T. Lee Jan. 24, 2001

2. 2 Overview  Decision analysis “provides a systematic method of modeling and solving a problem and a framework in which to debate the solution.” (Ho)  How to make the best decisions in the face of uncertainty? N

3. 3 Outline  Simple Example  Rewards  Utility Function  Problem Statement  Observations  Applications

4. 4 Simple Example  Whether to place $50 on a bet or not given the probability is 50-50? If you win, you got $100 back. If you loss, you get nothing (lost the $50).  If we compute the expected value of return: 0.5  $100 + 0.5  $0 = $50, which is the same as not having bet at all. N

5. 5 Simple Example (cont.)  Some people would prefer to not bet even though the expected value is the same. We call those risk averse.  Some wouldn’t have cared. We call them risk neutral.  Still others would prefer to bet. We call them risk prone. N

6. 6 Rewards  R: set of all rewards  Assumption 1: Given r 1, r 2  R, then either r 1  r 2, r 1  r 2 or r 1 ~ r 2.  Assumption 2 (transitivity): For any rewards r 1, r 2, r 2  R, if r 1  r 2 and r 2  r 3, then r 1  r 3.  Assumption 3:  r 1, r 2  R such that r 1  r 2 or r 1  r 2. N

7. 7 Utility Function  U(r): R   N R 

8. 8 Notations  Outcomes:     Decisions: d  D  Rewards: r  R  Reward function: (d, )  R  Utility function: U(r): R    Probability of outcomes: P(, d) N

9. 9 Problem Statement N

10. 10 Risk Aversion N R  A B C D

11. 11 Observations N

12. 12 Applications  Inventory Theory  Engineering  Economics  Management  Psychology  Gambling Systems  Information Theory N

13. 13 References: DeGroot, M. H., Optimal Statistical Decisions, McGraw-Hill, 1970. Ho, Y.-C., class notes, ES201, Harvard University, 1997. Pratt, J. W., H. Raiifa and R. Schlaifer, Introduction to Statistical Decision Theory,MIT Press, 1995. Schick, I., class notes, ES201, Harvard University, 1996.

14. 14 Ingredients of a Decision Problem  Uncertainties  Subjective assessment of uncertainties  Consequences (rewards or costs)  Subjective preference of consequences  Alternatives  Systematic procedure of solution