vault backup: 2026-03-23 17:15:27

uncertainty.md

@@ -27,52 +27,7 @@ The term "uncertainty" refers to the possibility of multiple outcomes.
 In statistical inference and [[strategy]],
 **information** is the resolution of uncertainty.
 
-### Value of Information
-
-> [!quote]
-> **Value of information** (VOI or VoI)
-> is the amount a decision maker would be willing to pay
-> for information prior to making a decision.
-
-Suppose information $I$ is available to a decision maker.
-Consider these two scenarios:
-
-1. the decision maker does not purchase the information
-  and makes \$9,000. $P(D)=9000$
-
-2. the decision maker purchases the information
-  and makes \$10,000 $P(D)|I=10000$
-
-The monetary value of $I$ is the difference between the payout
-without ($P(D)$) and with ($P(D)|I$) the information $I$.
-
-$$
-\begin{align*}
-V(I) &= P(D)|I - P(D) \\
-&= (10000) - (9000) \\
-&= 1000
-\end{align*}
-$$
-
-When forecasting, the payout of decisions is unknown,
-thus
-
-$$
-\mathbb{E}\left[V(I)\right] = \mathbb{E}\left[P(D)\right] - \mathbb{E}\left[P(D)|I\right]
-$$
-
-### Expected Value of Perfect Information
-
-Expected value of perfect information (EVPI)
-is the price that one would be willing to pay
-in order to gain access to perfect information.
-
-> [!info] Perfect Information
-> Perfect information is hypothetical information
-> that would eliminate all uncertainty.
-
-The perceived _value_ of decreased uncertainty
-must be weighed against its _cost_.
+[[value-of-information]]
 
 ## Types of Uncertainty