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

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Presentation transcript:

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

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

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  $  $0 = $50, which is the same as not having bet at all. N

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

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 Problem Statement N

10 Risk Aversion N R  A B C D

11 Observations N

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

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

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