University:
California State University, Northridge
Course:
MATH 340 | Introduction to Probability and Statistics
Academic year:

2024
Views:

89

Pages:

21
Author:

Herbosambx

Chapter 12 • Value of Information 1 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 2 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. 3 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. 4 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. 5 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. 6 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 7 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? 8 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. 9 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 10 call it the (EVII). 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 11 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 12 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. 13 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. 14 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. 15 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 bombdetection case again. 16 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. 17 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 18 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; 19 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 20 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 21

Value of Information

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