Environmental Engineering Reference
In-Depth Information
Uncertain
consequences,
p
CA
(
c
A
)
Plan A
Use available
information
Plan B
p
CB
(
c
B
)
Plan A
p
CA
|
(c
A
| )
Plan B
Obtain
additional
information
p
CB
|
(c
B
| )
.
Uncertain
investigation
results,
p
E
( )
Plan A
p
CA
|
(c
A
| )
Plan B
p
CB
|
(c
B
| )
Figure 13.1
Decision tree framework for assessing value of information.
The value of obtaining additional information depends on what that information might
be, which is represented by a probability distribution,
p
E
()ε and how that information affects
the probability distribution for the possible consequences,
pc
C
ε
( |
For each possible out-
come of information, ε, the decision between the two alternatives is evaluated on the basis of
the expected consequence,
E
=∑ × , where the expected consequence for
the decision given a possible outcome of information is
(
C|
ε
)
c
p
()
c|
ε
C
ε
allc
EC forDecision with NewInformation
(
e
)
=
maxEC
AlternativeA
[(
e
),
(
C
AlternativeB
e
)]
(13.2)
The expected consequence associated with obtaining the new information is then obtained
from the Theorem of Total Probability
(
)
ECforDecision with NewInformation
(
)
×
=
∑
ECforDecisi
allc
on withNew Information
ε
p
E
()
ε
(13.3)
The value of information is defined as the maximum cost (negative consequence),
∆
c
NewInformation
, the decision maker would be willing to spend in obtaining that information:
EC forDecision withNew InformationIncluding
(
∆
c
NewInformation
)
=
EC forDecision
(
)
(13.4)
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