Page 170 - Artificial Intelligence for the Internet of Everything

156 Artificial Intelligence for the Internet of Everything

Fig. 9.3 Surface plot of nontrivial values, for L 2 [0, 2], μ 2 [0, 2], of dhVie , with point
b
(L ¼ 2, μ ¼ 0.5, dhVie ¼ 9=32) highlighted.
b
Let us pause and think about VoI. Is there any additional value in learning
more about C other than its mean? No! This realization is an important
understanding.
Also, if we are at a point in the nontrivial region, what is more important
to learn with respect to hhVii, a change in L or a change in EðCÞ? That is, if we
have to prioritize the information that is sent to a decision maker and we can
only send one “fact” at a time, which one would we send first, information
about a change in L or EðCÞ? Consider the total differential:

∂hhVii ∂hhVii
dL + dμ (9.14)
dhhVii ¼
∂L ∂μ
μ

1 2 1 μ
dμ (9.15)
¼ 1 dL 1
4 L 2 L
2
Then, using 1 x ¼ (1 x)(1 + x), we see that:

∂hhVii ∂hhVii ∂hhVii
<
< 2 (9.16)
∂L ∂L
∂μ
In the infinitesimal sense, the value of EðCÞ is more important than the
value of L, but not by much. Therefore, if we have to prioritize information
sent to a decision maker, it should be EðCÞ, then L.