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Problem Session 5 - Discretization

# Problem Session 5 - Discretization - MS&E 352 Decision...

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MS&E 352 Decision Analysis II Problem Session 5

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On our agenda for today… Discretization of Continuous Distributions Why do we discretize distributions? Equal Areas Method Moment Matching Method Shortcuts Tornado Diagrams What are they? How can we build them in Excel? Homework & Case Study Questions
Discretization of Continuous Probability Distributions

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Subject - Lucas Terman Auditorium, Stanford University Date - 11/11/2003, 11:30am Assessment by Prof. Howard 0% 20% 40% 60% 80% 100% 0 10 20 30 40 50 60 70 80 Do you remember how we assessed the weight of a chair in DA1? Probability encoding is a process that will help you elicit the numbers you need for your analysis. Therefore, your analysis will be as good as your probability encoding was. But many issues arise when you use continuous probability distributions…
Some issues with continuous probability distributions... They make probability calculations more complicated . Amount of Oil Seismic Test Result They are not practical – how do you represent them in software and spreadsheets? How do you deal with conditional probability assessments?

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Practical Decision Analysis often requires approximation of continuous distributions. Our goal is to get from here… … to there. Cost (\$ millions) 0% 20% 40% 60% 80% 100% 0 10 20 30 40 50 60 70 80 0.25 High 0.5 Base 0.25 Low Cost (\$ millions) Low High Base 25% 75% x y z Each branch represents an interval of the CDF. But we could have chosen other branch probabilities than .25, .5 and .25.
The Equal Areas Method

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The Equal Areas method provides us with a graphical approach to achieving this result. We choose the conditional mean on each interval as x, y and z. Cost (\$ millions) 0% 20% 40% 60% 80% 100% 0 10 20 30 40 50 60 70 80 0.25 High 0.5 Base 0.25 Low Cost (\$ millions) Low 25% 75% x 1. Choose x = mean of distribution given that cost is low , i.e. such that a 1 = a 2 . a 1 a 2 x 27
The Equal Areas method provides us with a graphical approach to achieving this result. We choose the conditional mean on each interval as x, y and z. Cost (\$ millions) 0% 20% 40% 60% 80% 100% 0 10 20 30 40 50 60 70 80 0.25 High 0.5 Base 0.25 Low Cost (\$ millions) y Base 25% 75% 27 y 2. Choose y = mean of distribution given that cost is medium , i.e. such that a 3 = a 4 .

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