zmVault/uncertainty.md

id, aliases, tags, title

id	aliases	tags	title
uncertainty		authorship/original destiny/permanent status/incomplete topic/risk type/encyclopedia	Uncertainty

Uncertainty

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

Information

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*}

[!info] Expectation Notation 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.

In Construction Estimating

This concept provides the basis for the solution of one or more open-problems-in-estimating. To reduce risk in construction-estimating, an organization pays in estimator hours. These hours have a direct cost in salary and benefits, however the greater cost is the opportunity cost of tying up an estimator who could otherwise be starting a new project.

In many cases, the utility of doubled throughput far outweighs the increased risk of individual bids.

Types of Uncertainty

Aleatory Uncertainty

[!info] Also Known As

• statistical uncertainty
• stochastic uncertainty
• random error

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

Epistemic Uncertainty

[!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.