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Decision Analysis A method for determining optimal strategies when faced with several decision alternatives and an uncertain pattern of future events.

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The Decision Analysis Approach Identify the decision alternatives - d i Identify possible future events - s j mmutually exclusive - only one state can occur eexhaustive - one of the states must occur Determine the payoff associated with each decision and each state of nature - V ij Apply a decision criterion

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Types of Decision Making Situations Decision making under certainty sstate of nature is known ddecision is to choose the alternative with the best payoff

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Decision making under uncertainty TThe decision maker is unable or unwilling to estimate probabilities AApply a common sense criterion

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Decision Making Under Uncertainty Maximin Criterion (for profits) - pessimistic llist minimum payoff for each alternative cchoose alternative with the largest minimum payoff

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Maximax Criterion (for profits) - optimistic llist maximum payoff for each alternative cchoose alternative with the largest maximum payoff

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Minimax Regret Criterion ccalculate the regret for each alternative and each state llist the maximum regret for each alternative cchoose the alternative with the smallest maximum regret

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Minimax Regret Criterion RRegret - amount of loss due to making an incorrect decision - opportunity cost

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Types of Decision Making Situations Decision making under risk Expected Value Criterion ccompute expected value for each decision alternative sselect alternative with “best” expected value

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Computing Expected Value Let: PP(s j )=probability of occurrence for state s j and NN=the total number of states

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Since the states are mutually exclusive and exhaustive

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Types of Decision Making Situations Then the expected value of any decision d i is

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Decision Trees A graphical representation of a decision situation Most useful for sequential decisions

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Decision Making Under Risk: Another Criterion Expected Regret Criterion CCompute the regret table CCompute the expected regret for each alternative CChoose the alternative with the smallest expected regret The expected regret criterion will always yield the same decision as the expected value criterion.

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Expected Regret Criterion The expected regret for the preferred decision is equal to the Expected Value of Perfect Information - EVPI EVPI is the expected value of knowing which state will occur.

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EVPI – Alternative to Expected Regret EVPI – Expected Value of Perfect Information EVwPI – Expected Value with Perfect Information about the States of Nature EVwoPI – Expected Value without Perfect Information about the States of Nature EVPI=|EVwPI-EVwoPI|

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Bayes Law In this equation, P(B) is called the prior probability of B and P(B|A) is called the posterior, or sometimes the revised probability of B. The idea here is that we have some initial estimate of the probability of B, we get some additional information about whether A happens or not, and then we use Bayes Law to compute this revised probability of B.

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Expected Value of Sample Information – EVSI EVSI – Expected Value of Sample Information EVwSI – Expected Value with Sample Information about the States of Nature EVwoSI – Expected Value without Sample Information about the States of Nature EVSI=|EVwSI-EVwoSI|

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Efficiency of Sample Information – E Perfect Information has an efficiency rating of 100%, the efficiency rating E for sample information is computed as follows: Note: Low efficiency ratings for sample information might lead the decision maker to look for other types of information

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Accounting for Risk in Decision Analysis Mean-Variance

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Accounting for Risk in Decision Analysis Utility Theory replacing the payoffs with a unitless scale that accounts for both the value of the payoff and the decision makers risk attitude Risk Aversion A decision maker is risk averse if he/she would prefer a certain x dollars to a risky alternative with ER=x dollars.

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Accounting for Risk in Decision Analysis Direct assessment of utility Utility functions

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Chapter 18 Statistical Decision Theory Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Statistics for Business and Economics 7 th.

Chapter 18 Statistical Decision Theory Copyright © 2010 Pearson Education, Inc. Publishing as Prentice Hall Statistics for Business and Economics 7 th.

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