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| Value of Information |
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Value of Information
In decision-theory, the value of information (VOI or VoI) is a framework for quantifying the impact of some reduction in uncertainty. It is the amount a rational party would be willing to pay to gain access to information prior to making a decision.
Example
Suppose a decision maker has the opportunity to purchase information I.
Consider these two scenarios:
-
the decision maker does not purchase the information and makes $9,000.
P(D)=9000 -
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.