---
id: uncertainty
aliases: []
tags:
  - authorship/original
  - destiny/permanent
  - status/incomplete
  - topic/risk
  - type/encyclopedia
title: Uncertainty
---
# Uncertainty

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## TALK

## TODO



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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 $I$.

$$
\begin{align*}
V(I) &= P(D)|I - P(D) \\
&= (10000) - (9000) \\
&= 1000
\end{align*}
$$

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_.

## 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]].
