1 Chapter 12 Value of Information

2 Chapter 12, Value of information Learning Objectives: Probability and Perfect Information The Expected Value of Information Expected value of Imperfect Information Value of information in Complex Problems Value of information and Experts

3 Chapter 12,Value of Information Decision Maker often gather information to reduce uncertainty Information gathering includes: – Consulting experts, conducting surveys – Performing mathematical or statistical analysis –Doing research, or simply reading books, journals, and newspapers.

4 Value of Information Value of Information: Some Basic Ideas Probability and perfect information Use conditional probabilities and Bayes’ theorem to evaluate information in any decision setting.

5 Value of Information The Expected Value of Information By considering the expected value, we can decide whether: – An expert is worth consulting – Whether a test is worth performing –Or which of several information sources would be the best to consult.

6 The Expected Value of Information The worst possible case: Regardless of the information we hear, we still would make the same choice that we would have made in the first place. In this case, the information has zero expected value.

7 The Expected Value of Information Make a difference choice, then the expected value of the information must be positive The expected value of information can be zero or positive, but never negative. Different people in different situation may place different values on the same information

8 Expected Value of Perfect Information The optimal choice in any decision making situation is the one with the highest Expected Monetary Value (EMV) How much would he be willing to pay for information that would help you to make the right decision?

9 Expected Value of Perfect Information To find the value of these information, find the EMV for each situation and then subtract them. We can interpret this quantity as the maximum amount that the investor should be willing to pay for perfect information.

10 Expected Value of Imperfect Information We rarely have access to perfect information. In fact, our information sources usually are subject to considerable error. Thus, we must extend our analysis to deal with imperfect information. We still consider the expected value of the information before obtaining it, and we will call it the (EVII).

11 Value of Information in Complex Problems In most of previous example there was only one uncertain event Most real-world problems involves considerably more complex uncertainty models. In complex situation we must consider two specific situation

12 Value of Information in Complex Problems First how to handle continuous probability distribution Second, what happen when there are many uncertain events and information is available about some or all of them Evaluate decision option with and without the information, and find the difference in the EMV

13 Value of Information Sensitivity Analysis, and Structuring The first step is using a tornado diagram, those variables to which the decision was sensitive. The second step, after constructing a probabilistic model, may be to perform sensitivity analysis on the probabilities.

14 Value of Information A third step in the structuring of a probabilistic model would be to calculate the EVPI for each uncertain event. If EVPI is very low for an event, then there is little sense in spending a lot of effort in reducing the uncertainty by collecting information.

15 Value of Information But if EVPI for an event is relatively high, it may need to collecting of information Such information can have a relatively large payoffs by reducing uncertainty This information can also improving the decision maker’s EMV.

16 Value of Information Value of Information and Nonmonetary Objectives In most cases the only objective that matters is making money However in many decision situations there are multiple objectives. For example, consider the FAA bomb- detection case again.

17 Value of Information FAA was interested in maximizing the detection effectiveness and passenger acceptance of the system while at the same time minimizing the cost and time to implementation. Minimizing cost happens to be one of the objectives.

18 Value of Information The answer would be to find the additional cost Additional cost make the net expected value of getting the information equal to the expected value without the information Trade-off always establish to value the information

19 Value of Information Suppose one objective is to minimize the decision maker’s time Different choices and different outcomes require different amounts of time from the decision maker. Information can be valued in terms of time;

20 Value of Information Value of Information and Expert Expert information typically is somewhat interrelated and redundant. The real challenge in expert use is to recruiting experts who look at the same problem from very different perspectives. Use of expert from different field

21 Value of Information Summary Make better decisions by considering the expected value of information Both influence diagrams and decision trees can be used for calculating expected values How to solve value-of-information problems in more complex situations