105 lines
2.4 KiB
Markdown
105 lines
2.4 KiB
Markdown
---
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id: uncertainty
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aliases: []
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tags:
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- authorship/original
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- destiny/permanent
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- status/incomplete
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- topic/risk
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- type/encyclopedia
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title: Uncertainty
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dg-publish: true
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---
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# Uncertainty
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%%
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## TALK
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## TODO
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%%
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The term "uncertainty" refers to the possibility of multiple outcomes.
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## Information
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In statistical inference and [[strategy]],
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**information** is the resolution of uncertainty.
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### Value of Information
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> [!quote]
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> **Value of information** (VOI or VoI)
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> is the amount a decision maker would be willing to pay
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> for information prior to making a decision.
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Suppose information $I$ is available to a decision maker.
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Consider these two scenarios:
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1. the decision maker does not purchase the information
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and makes \$9,000. $P(D)=9000$
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2. the decision maker purchases the information
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and makes \$10,000 $P(D)|I=10000$
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The monetary value of $I$ is the difference between the payout
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without ($P(D)$) and with ($P(D)|I$) the information $I$.
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$$
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\begin{align*}
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V(I) &= P(D)|I - P(D) \\
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&= (10000) - (9000) \\
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&= 1000
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\end{align*}
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$$
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When forecasting, the payout of decisions is unknown,
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thus
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$$
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\mathbb{E}\left[V(I)\right] = \mathbb{E}\left[P(D)\right] - \mathbb{E}\left[P(D)|I\right]
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$$
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### Expected Value of Perfect Information
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Expected value of perfect information (EVPI)
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is the price that one would be willing to pay
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in order to gain access to perfect information.
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> [!info] Perfect Information
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> Perfect information is hypothetical information
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> that would eliminate all uncertainty.
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The perceived _value_ of decreased uncertainty
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must be weighed against its _cost_.
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## Types of Uncertainty
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### Aleatory Uncertainty
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> [!info] Also Known As
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> * statistical uncertainty
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> * stochastic uncertainty
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> * random error
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Aleatory uncertainty is inherent randomness in data that can't be explained away.
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### Epistemic Uncertainty
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> [!info] Also Known As
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> * systematic uncertainty
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> * model uncertainty
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Epistemic uncertainty is that which arises from a lack of knowledge,
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and can be eliminated with access to [[#information]].
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Under Bayesian statistics,
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all uncertainty is epistemic.
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## See Also
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* [Uncertainty analysis](https://en.wikipedia.org/wiki/Uncertainty_analysis)
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* [Uncertainty quantification](https://en.wikipedia.org/wiki/Uncertainty_quantification)
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* [Propagation of uncertainty](https://en.wikipedia.org/wiki/Propagation_of_uncertainty)
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* [Sensitivity analysis](https://en.wikipedia.org/wiki/Sensitivity_analysis) |