Decision Making Under Uncertainty Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing.

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Decision Making Under Uncertainty Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Two Basic Questions What are the possible actions (alternatives) for this problem? What is it about the future that affects the desirability of each action? Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Terms Descriptions of the future: states of nature The state of nature items are outcomes. –The key distinction between an action and a state of nature is that the action is taken is under your control, whereas the state of nature that occurs is strictly a matter of chance. The payoff is the result of an action (A) an a state of nature (S) Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Payoff Table State of Nature ActionS 1 S 2 S 3 ……. S n A 1  11  12  13 ……  1n A 2  21  22  23 ……  2n A 3  31  32  33 ……  3n  A k  k1  k2  k3 ……  kn Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Conservative (Minimax) Strategy The action chosen is that action that under the worst conditions produces the lowest “loss.” The opportunity loss, L ij, is the difference between the payoff for action I and the payoff for the action that would have the largest payoff under the state of nature j. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Minimax Strategy Construct an opportunity loss table by using the maximum payoff for each state of nature. Determine the maximum opportunity loss for each action. Find the minimum value of the opportunity losses found in step 2; the corresponding action is the one selected. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

The Gambler (Maximax) Strategy The Maximax strategy is to choose that action having the largest possible payoff. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

The Strategist (Maximizing the Expected Payoff) This strategy assigns a probability to each state of nature. The expected payoff of each action is determined. The action chosen is that action that produces the largest expected payoff Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Utility Utility combines the decision maker’s attitude toward the payoff and the corresponding risk of each alternative. The utility value of a particular outcome is used to measure both the attractiveness and the risk associated with this dollar amount. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Utility Value Step1: Assign a utility value of 0 to the smallest payoff amount (  min ) and a value of 100 to the largest (  max ). Step 2: The utility value for any payoff under consideration is found by using: U(  ij ) = P * 100 Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Utility Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Decision Trees and Bayes’ Rule A decision tree graphically represents the entire decision problem, including: –The possible actions facing the decision maker. –The outcomes that can occur. –The relationships between the actions and outcomes. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Decision Trees Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Decision Trees and Bayes’ Rule Bayes’ rule allows you to revise a probability in light of certain information that is provided. Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Use of Bayes’ Rule Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Deriving the Posterior Probabilities Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Resulting Decision Tree Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing

Deriving the Posterior Probabilities Introduction to Business Statistics, 5e Kvanli/Guynes/Pavur (c)2000 South-Western College Publishing