Decision Analysis II

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Decision Analysis II

• Risk Profile
• Expected Value of Perfect Information
• Sensitivity Analysis

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Last Time

• Decision Analysis Framework
• Alternatives, states of nature, payoffs
• EMV (Expected monetary value) criterion
• Decision Trees
• decision nodes (choice)
• event nodes (chance)
• fold back the tree to find the best strategy
• Bayes theorem

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Earth Slides

• Immediate Actions Possible
• Do nothing
• Build retaining wall
• Conduct geological test
• Decision Tree
• Systematically map out all possible scenarios
• Fold back tree to identify best strategy
• EMV Criterion

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Is Expected Monetary Value Criterion Appropriate?

• one time decision ?
• reasonable when stakes are small compared to the
  resources of the decision-maker
• money is not everything?
• Risk?

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Risk Profiles

• Strategy 1 Do nothing
• Outcome Probability
• Slide 1,000 0.01
• No slide 0 0.99

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Risk Profiles

• Strategy 2 Build wall
• Outcome Probability
• Wall,Slide,Fail 1,040 0.0005
• Wall,NoSlide/ 40 0.9995
• Slide,Wall Hold

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Risk Profiles

• Strategy 3 Test - If , build wall
• If -, do nothing
• Outcome Probability
• Test,,Wall,Slide,Fail 1,043 0.0005
• Test,-,NoWall,Slide 1,003 0.0010
• Test,,Wall,NoSlide/Slide,Hold 43 0.1570
• Test,-,NoWall,NoSlide 3 0.8415

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Risk Profiles

• Strategy 4 Test - If , build wall
• If -, build wall
• Outcome Probability
• Test,Wall,Slide,Fail 1,043 0.0005
• Test,Wall,NoSlide/Slide,Hold 43 0.9995
• Dominated Strategy

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Risk Profiles

• Strategy 5 Test - If , do nothing
• If -, build wall
• Outcome Probability
• Test,-,Wall,Slide,Fail 1,043 0.00005
• Test,,NoWall,Slide 1,003 0.0090
• Test,-,Wall,NoSlide/Slide,Hold 43 0.84245
• Test,,NoWall,NoSlide 3 0.1485
• Perverse Strategy

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Expected Value vs. Risk
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Next ...

• What if we could get some related information
  before we make a decision?
• Expected Value of Perfect Information
• Expected Value of Sample Information
• What if the data we have about the probabilities
  or the payoff is not correct? Would we still be
  making the optimal decision?
• Sensitivity Analysis

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Back to Earthslides ...

• Strategy
• 1. Do nothing 2. Build wall 3. Test , build
  wall -, do nothing
• Expected Monetary Value
• 10 40.5 10.76
• What if the test were cheaper?
• What if the test were more accurate?

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EVSI --- Expected Value of Sample Information

• If the geological test were free, then Expected
  Cost of Strategy 3 (Test) is 7.76.
• Without the test available, lowest expected cost
  is 10 . (Strategy 1 do nothing).
• Expected value of Sample Information EVSI
• (Expected value of best decision with sample
  info)
• - (Expected value of best decision with
  original info)
• (- 7.76 ) - (-10) 2.24 thousand
  dollars.

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More Accurate Test

• Suppose P(- no slide) 0.9
• (instead of 0.85 and test is free), then
• Expected Monetary Cost of Strategy 3 is
• 5.77 (thousands)
• EVSI Expected Value of Sample Information
• (Best EMV with Test) - (Best EMV without
  Test)
• - 5.77 - (-10) 4.23
• This test is worth the cost of 3,000 !

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Expected Value of Perfect Information

• What is the perfect test?
• P( slide) 1 P(- no slide) 1
• Expected Monetary Cost of Strategy 3 is only
  0.9 (thousands)

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Expected Value of Perfect Info

• For Earthslides
• (Best EMV with Perfect Test)
• - (Best EMV without Test)
• - 0.9 - (-10) 9.1 (thousand dollars)
• This is called the Expected Value of Perfect
  Information (EVPI).
• Can a test be worth more than 9,100?

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Expected Value of Perfect Information (EVPI)

• EVPI is the Expected Value when Decision Maker
  has knowledge of which state will occur before
  making the decision
• EVPI gives an upper bound of how much any test is
  worth!
• Note it does not change the probability
  distribution of the states of nature

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Sensitivity Analysis

• Decisions depend on estimates of values of
  costs/benefits and probabilities.
• Accurate estimates may be difficult to obtain
• Would the optimal strategy be different if the
  true costs/benefits slightly different than
  estimated?
• When in doubt, DO the RIGHT THING!

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Earth Slides - Sensitivity Analysis

• Back to Earthslides
• We are unsure about the cost of building the
  retaining wall.
• If the wall cost less than 40,000, would it
  still be optimal to not build the wall?
• Let the cost of building the retaining wall be x
  thousand dollars.

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Aside Medical Testing

• Rare disease P(infected) 0.0001
• Test P( infected) 0.98
• P(- not infected) 0.99
• P() (0.0001)(0.98)(0.9999)(0.01) 0.010097
• False negative P(infected -)
• (0.0001)(0.02)/(0.989903)0.00000203
• False positive P(not infected )
• (0.9999)(0.01)/(0.010097) 0.9903 !!

Drug testing?
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Drug Testing
.009
(0.9)
Pr (NotAddict ) 0.099/(0.0990.009) 0.92
!!
- (0.1)
- .001
Addict
0.01
.099
0.99
(0.1)
Not addict
- (0.9)
- .891
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Drug Testing
Pr (NotAddict ) 0.0099 /(0.00990.0081)
.55
.0081
- .0009
- .0009
Addict
-- .0001
0.01
.0099
- .0891
0.99
- .0891
Not addict
-- .8019
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Summary

• Framework for Decision Making
• Decision Trees
• Risk vs. Expected Value
• EVPI
• Sensitivity Analysis
• Bayes Theorem

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Decision Analysis

• no decision is dictatorial. Its purpose is
  to help decision makers understand where the
  balance of their beliefs and preferences lies and
  so guide them towards a better informed
  decision.
• Simon French (1989)

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Decision Analysis

• Force hard thinking about the problem area
  generation of alternatives, anticipation of
  future contingencies, examination of dynamic
  secondary effects, and so forth
• Should illuminate controversy to find out where
  basic differences exist in values and
  uncertainties, to facilitate compromise, to
  increase the level of debate and undercut
  rhetoric,
• In short, to promote decision making.
• Keeney and Raiffa (1972)

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• Testimonial for Decision Analysis
• Chevrons vice-chairman,
• George Kirkland
• http//www.youtube.com/chevronp/u/12/JRCxZA6ay3M