Assessing the value of information to design site investigation and construction quality assurance programs - Risk and Reliability in Geotechnical Engineering - page 488

0.95

(a) 1.0

0.9
0.8
0.7
0.6
0.5
0.4

0.3
0.2
0.1
0

0.05

10 20

Consequence ($ MM)

Prior probability

(b) 1.0

0.9
0.8
0.7
0.6
0.5
0.4

0.6

0.3
0.2
0.1
0

0.1

10 20

Consequence ($ MM)

Likelihood function

(c) 1.0

0.9
0.8
0.7
0.6
0.5
0.4

0.76

0.24

0.3
0.2
0.1
0

10 20

Consequence ($ MM)

Updated probability

Figure 13.10 Illustrative example showing that uncertainty can increase with additional information.

likelihood function ( Figure 13.10b ) amplifies the probability of a $20 MM consequence,
reduces the probability of a $10 MM consequence, and produces an updated probability
distribution with more uncertainty in the consequence ( Figure 13.10c ).
The magnitude of uncertainty in a probability distribution is rationally and conveniently
measured with the theory of information entropy (e.g., Shannon 1948; Jaynes 1957; Tribus
1969):

∑

[ ] ×

Entropy of Information =− lnp c () pc ()

(13.8)

Ci Ci

allc

i