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Decision Analysis Study Guide for ES205 Yu-Chi Ho Jonathan T. Lee Jan. 24, 2001
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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
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3 Outline Simple Example Rewards Utility Function Problem Statement Observations Applications
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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
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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
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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
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7 Utility Function U(r): R N R
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8 Notations Outcomes: Decisions: d D Rewards: r R Reward function: (d, ) R Utility function: U(r): R Probability of outcomes: P(, d) N
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9 Problem Statement N
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10 Risk Aversion N R A B C D
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11 Observations N
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12 Applications Inventory Theory Engineering Economics Management Psychology Gambling Systems Information Theory N
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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.
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14 Ingredients of a Decision Problem Uncertainties Subjective assessment of uncertainties Consequences (rewards or costs) Subjective preference of consequences Alternatives Systematic procedure of solution
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