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week7 -prob

# week7 -prob - Spring 2010 DecisionAnalysis MS405 Subjective...

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring, 20 Spring, 20 10 Decision Analysis   MS 405    Subjective Probability Kemal Kılıç Faculty of Engineering and Natural Sciences 1 Week 7

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring, 20 Spring, 20 10 Subjective Probability An important element of decision analysis. How to make a subjective assessment? What a subjective probability means? There are three interpretations of probability: Canonical Long run frequency Subjective 2 Week 7
Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring, 20 Spring, 20 10 Probability: A Subjective Interpretation Does the long-run frequency always make sense? What is the probability that man will go to Venus before 2020? Probability represents an individual’s degree of belief that a particular outcome will occur. Different people have different probabilities. How about if your assessed prob. is different from other person’s assessed prob.? 3 Week 7

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring, 20 Spring, 20 10 Assessing Discrete probabilities – Method 1 Simply ask the decision maker, his/her degree of belief regarding probability. “What is your belief regarding the probability that event such and such will occur?” DM may or may not give an answer to a direct question like this and may place little confidence in the answer given. 4 Week 7
Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring, 20 Spring, 20 10 Idea is, to find a specific amount to win or lose such that the decision maker is indifferent about two bets which are symmetric in the sense that they are opposites of the same bet. Then an equation will be established to be solved for the subjective probability. Assessing Discrete probabilities – Method 2 5 Week 7

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Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring, 20 Spring, 20 10 Example: Suppose that F.B. and G.S. are playing the cup finals next year. We are interested in finding DM’s probability that F.B. will win the cup. The DM is willing to take either of the following two bets: Bet 1 : Win \$X if F.B. win Lose \$Y if F.B. lose Bet 2 : Lose \$X if F.B. win Win \$Y if F.B. lose Assessing Discrete probabilities – Method 2 6 Week 7
Kemal Kılıç, Sabancı Üniversitesi Kemal Kılıç, Sabancı Üniversitesi Spring, 20 Spring, 20 10 If DM is indifferent between the bets, then their expected values must be equal (assume risk neutrality or X and Y are so small that the DM is risk neutral for those amounts.) Assessing Discrete probabilities – Method 2 F.B. Win F.B. Lose F.B. Win F.B. Lose X - X - Y Y X.P(Win) – Y.[1- P(Win)] = -X.P(Win) +Y.[1- P(Win)] 2[X.P(Win) – Y.[1- P(Win)]] =0 X.P(Win) –Y+Y P(Win)]=0 Y=P(Win)[X+Y] P (F.B. Win) = Y/[X+Y] 7 Week 7

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week7 -prob - Spring 2010 DecisionAnalysis MS405 Subjective...

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