Chapter 4R Part II


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Chapter 4R Part II

  1. 1. Chapter 4R Part II ISDS 2001 - Matt Levy
  2. 2. Risk Analysis and Sensitivity Analysis Risk Analysis exists to help the decision maker recognize the difference between the EV of a decision alternative and the payoff that may occur. Sensitivity Analysis exists to describe how changes in the states of nature probabilities and/or changes in the payoff affect the decision alternative. We can use risk and sensitivity analysis to detect what variables cause small changes and which ones cause large changes in the decision alternatives. This helps us determine how much care should be put into ensuring the accuracy of certain variables. In other words, if we are doing a lot of calculating and re-calculating work, we want it to be for the right reasons.
  3. 3. Risk Analysis and Sensitivity Analysis In the case we have two states of nature (e.g. strong demand and weak demand) we can look at things graphically, such as what is depicted in Figure 4.6. To find the probability of the 2nd state of nature (s2): P(s2) = 1 - P(s1) = 1 - p For example: S = the payoff of decision alternative d3 when demand is strong. W = the payoff of decision alternative d3 when demand is weak. Using P(s1) = 0.8 and P(s2) = 0.2, the general expression for the EV of d3: EV(d3) = 0.8S + 0.2W
  4. 4. Decision Analysis with Sample Information Most of the time decision makers have some notion of prior probability. But to make the best decision, we normally want to go out and collect sample information about the states of nature. From our sample information we get new sample probabilities that we may use to revise or update prior probabilities. These new probabilities are called posterior probabilities. With new information we can build Influence Diagrams and Decision Trees (see Figures 4.7 and 4.8).
  5. 5. Decision Strategy A sequence of decision and chance outcomes based on yet to be determined outcomes of chance events. We can build this using a backward pass through a decision tree. - At chance nodes compute the EV by multiplying the payoff at the end of each branch by the corresponding branch probabilities. - At decision nodes, select the decision branch that leads to the best EV. This EV becomes the EV at the decision node.
  6. 6. Expected Value of Sample Information EVSI = |EVwSI - EVwoSI| EVSI = Expected Value of Sample Information EVwSI = Expected Value with Sample Information EVwoSI = Expected Value without Sample Information This effectively tells us the power of our sample information used to determine the optimal decision strategy.
  7. 7. Efficiency of Sample Information Our research or experiments we conduct to gather sample data will never yield perfect information. What we can do is use an efficiency measure to express the value of our research information. Perfect information will have an efficiency rating of 100%. Hence we can calculate efficiency as such: E = EVSI / EVPI where: EVSI = Expected Value of Sample Information EVPI = Expected Value of Perfect Information
  8. 8. Computing Branch Probabilities Uses Bayes Theorem to compute: To compute using the following steps (easiest with Excel): 1. a. Enter the states of nature in Column 1. b. Enter the prior probabilities in Column 2. c. Enter conditional probabilities in Column 3. 2. Compute the Joint Probabilities in Column 4 by multiplying Column 2 by Column 3. 3. Sum the joint probabilities in Column 4 4. Divide each joint probability in Column 4 by Step 3 to obtain the revised posterior probabilities.
  9. 9. The End Read the Chapter. This section will be on Exam 3. I apologize for the work over Spring Break :-)