Methods for Analyzing Decision Problems

							Methods for Analyzing Decision Problems

        Value of information



            Aleksandr Tkatsenko

                20.05.2009
Outline
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     Value of information

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     Example

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     Information scenarios, utility value function

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     Non-utility value functions

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     Handling many tests
Value of information
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     Decision types:
          –   action decisions – change state of other variables
          –   test decision – look for more evidence ($$)
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     Model:
          –   only one utility function U
          –   one action decision D
          –   1..n tests
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     Related questions:
          –   which test to perform, if any?
          –   in what order?
          –   is the test worth its price?
Example: Test for Infected Milk?
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     Hypothesis variable: Inf = {yes, no}
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     Action: D = {pour, discard}
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     Test:
             –   cost: 0.06$
             –   P(Test = pos | Inf = no) = P(Test = neg | Inf = yes) = 0.001
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     P(Inf = yes) = 0,0007
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     Utility:
             –   U(D = pour, Inf = no) = 100$
             –   U(D = pour, Inf = yes) = 0$
             –   U(D = discard, Inf = no) = U(D = discard, Inf = yes) = 98$
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    Value function:




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    Performing test T which yields t:




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    Expected value of performing test T with cost C:




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    Expected benefit:




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    Expected profit:
Non-utility value functions
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     Entropy:




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     Variance:




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     Convex functions:
          –   expected benefit of performing a test is never negative
Handling many tests
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     Need to examine all possible sequences of tests → intractable
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     Myopic approach: choose repeatedly a test with the highest
     positive expected profit
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     Effective computation:
          –   propagate the states of H to each test node Ti.
          –   Apply Bayes' rule:
Many tests with junction trees




     if MEU1 – MEU2 > Cost(C) → don't observe C