Environmental Engineering Reference
In-Depth Information
Expected
consequence
Decision
No additional
information
Select A
-$24 mm
Te st result
Successful
(0.45)
Select B
-$17 mm
+
Δ
c
test
Questionable
(0.17)
Select A
-$24 mm
+
Δ
c
test
Conduct pilot test
E
(
C
with test)
=
-17*0.45
+
-24*(0.17
+
0.38)
+
Δ
c
test
=
-$21 mm
+
Δ
c
test
Unsuccessful
(0.38)
Select A
-$24 mm
+
Δ
c
test
Figure 13.6
Decision tree to assess value of information for pilot test in contaminated lagoon.
whether or not to conduct a pilot test; if a pilot test costs <$3 MM, then pursuing it is pre-
ferred compared to not conducting the test (
Figure 13.6
).
Bounds on the value of information can be established. A lower bound is
No Information
in which the updated probabilities for the decision outcomes are not changed by the
additional information. In this example, the case of
No Information
corresponds to
PW
U U= At this limit, no possible
outcome for the additional information will change the preferred decision alternative, giving
a value of information equal to zero (i.e., ∆=
(
S
)
=
PF PW
(
S
),(
Q
)
=
PQF
(
),
and
PW
(
)
PF
(
).
B
B
B
B
B
B
c
test
0). An upper bound is
Perfect Information
in which the information is perfectly reliable at indicating which consequence will be real-
ized. A decision tree to assess the value of perfect information about the performance of the
in situ
bioremediation approach is shown in
Figure 13.7
.
The value of perfect information
about the performance of the
in situ
bioremediation is ∆=−
45MM Therefore, no
matter how reliable the pilot test is, it would not be preferred to pursue it if the cost is >$4.5
MM. This value of perfect information provides practical guidance because it is straightfor-
ward to obtain from the original decision tree without needing to account for the reliability
of a test.
c
test
$.
.
Expected
consequence
Decision
No additional
information
Select A
-$24 mm
Te st result
B will work
(0.5)
Select B
-$15 mm
+
Δ
c
test
Run perfect test
E
(
C
with test)
=
-15*0.5
+
-24*0.5
+
Δ
c
test
=
-$19.5 mm
+
Δ
c
test
B will fail
(0.5)
Select A
-$24 mm
+
Δ
c
test
Figure 13.7
Decision tree to assess value of information for pilot test in contaminated lagoon.
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