Download Chapter 12, Value of Information

Chapter 12
• Value of Information
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Chapter 12, Value of information
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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
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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.
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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.
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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.
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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.
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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
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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?
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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.
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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
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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
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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
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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.
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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.
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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.
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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.
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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.
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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
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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;
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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
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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
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