Decision Analysis II
Risk Profile
Expected Value of Perfect Information
Sensitivity Analysis
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
Slide
1,000
No slide
0
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Probability
0.01
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
Prob (Cost > 1000)
0.016
0.014
0.012
1
0.01
5
0.008
0.006
0.004
0.002
3
2
0
0
5
10
15
20
25
30
35
40
4
45
50
Expected Cost
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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
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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)
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= 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)
1040
Build Wall
Test
+
-
40
0.01
Do Nothing
0.99
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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 !!
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Drug Testing
+ .009
− (0.1)
Addict
- .001
Pr (NotAddict | +)
= 0.099/(0.099+0.009)
= 0.92 !!
0.01
+ .099
0.99
Not addict
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− (0.9)
- .891
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Drug
Testing
Pr (NotAddict | ++)
= 0.0099 /(0.0099+0.0081) =.55
++ .0081
+- .0009
− (0.1)
Addict
-- .0001
0.01
++ .0099
+- .0891
0.99
Not addict
-+ .0009
− (0.1)
-+ .0891
-- .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
Chevron’s vice-chairman,
George Kirkland
http://www.youtube.com/chevron#p/u/12/JRCxZA6ay3M
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