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UIUC ECE 307 - Value of Information

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ECE 307 – Techniques for Engineering Decisions 15. Value of InformationVALUE OF INFORMATION A SIMPLE INVESTMENT EXAMPLENOTION OF PERFECT INFORMATIONNOTION OF PERFECT INFORMATIONNOTION OF PERFECT INFORMATIONNOTION OF PERFECT INFORMATIONEVI ASSESSMENTA SIMPLE INVESTMENT EXAMPLE: COMPUTATION OF EVPICOMPUTATION OF EVPICOMPUTATION OF EVPICOMPUTATION OF EVPIEXPECTED VALUE OF IMPERFECT INFORMATIONEXPECTED VALUE OF IMPERFECT INFORMATIONEVII ASSESSMENTEVII ASSESSMENTEVII COMPUTATION: INCOMPLETE DECISION TREECOMPUTATION OF REVERSE CONDITIONAL PROBABILITIESEVII COMPUTATION: FLIPPING THE CONDITIONAL PROBABILITIESPOSTERIOR PROBABILITIESEVII COMPUTATIONEXPECTED VALUE OF IMPERFECT INFORMATIONEVII COMPUTATIONEXAMPLE OF VALUE OF INFORMATION EVPI FOR F ONLYEVPI FOR E ONLYEVPI FOR BOTH E AND F© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 1ECE 307 – Techniques for Engineering Decisions15. Value of InformationGeorge GrossDepartment of Electrical and Computer EngineeringUniversity of Illinois at Urbana–Champaign© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 2 While we cannot do away with uncertainty, there is always a natural desire to attempt to reduce the uncertainty impacts associated with future outcomes This quest for reduction in uncertainty impacts on future outcomes may provide us alternatives that strongly increase the chances for a good outcome We focus this lecture on the principles behind information valuationVALUE OF INFORMATION© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 3A SIMPLE INVESTMENT EXAMPLEsavings accountlow-risk stockmarket up (0.5)flat (0.3)down (0.2)up (0.5)flat (0.3)down (0.2)1,700 – 200 = 1,500300 – 200 = 100– 800 – 200 = – 1,0001,200 – 200 = 1,000400 – 200 = 200100 – 200 = – 100stock investment entails a brokerage fee of $200500invest $ 500© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 4NOTION OF PERFECT INFORMATION We say that an expert’s information is perfect if it is always correct; we may view an expert as a clairvoyant, whose future forecasts are correct We may quantify the value of information in a decision problem with the metric called the expected value of information ( EVI )© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 5NOTION OF PERFECT INFORMATION We consider the role of perfect information in the simple investment example In this decision problem, the optimal policy is to invest in high–risk stock since it produces the highest returns on an expected basis Suppose an expert predicts that the market goes up: this implies the investor still chooses the high–risk stock investment and consequently the perfect information of the expert appears to be of no added value© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 6NOTION OF PERFECT INFORMATION On the other hand, suppose the expert predicts a market decrease or a flat market: under this information, the investor’s choice is the savings account and the perfect information brings value as it leads to a changed outcome with improved results over those in the case without the expert Under worst case conditions, regardless of the information, we make the identical decision as© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 7NOTION OF PERFECT INFORMATIONwithout the information and consequently EVI = 0; the interpretation, then, is that we are equally well off without the expert information Cases in which we have information, which we use to change to a different optimal decision, lead to EVI > 0 since we make a decision that improves the outcome using the available information© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 8EVI ASSESSMENT It follows that the value of information is always nonnegative, EVI ≥ 0 Indeed, perfect information removes all uncertainty, and the expected value of perfect information EVPIprovides an upper bound for EVIEVI < EVPI© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 9A SIMPLE INVESTMENT EXAMPLE: COMPUTATION OF EVPI Absent any expert information, a value–maximi–zing investor selects the high–risk stock option  The introduction of an expert or clairvoyant brings in perfect information since there is perfect a priori knowledge of how the market will fare before the investor makes his decision and the investor’s decision is based on this information© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 10COMPUTATION OF EVPI We use a decision tree approach to compute EVPI and reverse the decision and uncertainty order:we view the value of information in an a priorisense and defineEVPI = E {decision with perfect information} –E {decision absent additional information}© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 11COMPUTATION OF EVPIhigh-risk stocklow-risk stocksavings accounthigh-risk stocklow-risk stocksavings accountsavings accountlow-risk stockup (0.5)flat (0.3)down (0.2)up (0.5)flat (0.3)down (0.2)market flathigh-risk stocklow-risk stocksavings accountconsult clairvoyant1500100−10001000200−10050015001000500100200500− 1000− 100500EMV = 540EMV = 1000(0.3)© 2006 – 2021 George Gross, University of Illinois at Urbana-Champaign, All Rights Reserved. 12COMPUTATION OF EVPI For the investment problem,EVPI = 1,000 – 580 = 420 We may view EVPI to represent the bound on the amount that the investor is willing to pay an expertfor the perfect information resulting in the


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