Uncertainty

TALK

The term "uncertainty" refers to the possibility of multiple outcomes.

In statistical inference and strategy, information is the resolution of uncertainty.

[!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:

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 (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.

[!info] Also Known As

statistical uncertainty

stochastic uncertainty

random error

Aleatory uncertainty is inherent randomness in data that can't be explained away.

[!info] Also Known As

systematic uncertainty

model uncertainty

Epistemic uncertainty is that which arises from a lack of knowledge, and can be eliminated with access to #information.

Under Bayesian statistics, all uncertainty is epistemic.