# ML Wiki

## Decision Analysis

### Decision Under Certainty

Let

• $A$ be a finite set of alternatives (possible decisions)
• $X$ be a set of consequences (usually some financial metrics)
• $c: A \mapsto X$ a consequence function
• $c(a) \in X$ is a consequence of implementing action $a \in A$

Problem:

• to compare alternatives and find the optimal one
• on the basis of their consequences

For these models we make a strong assumption:

• we can quantify the consequences of taking different actions with certainty

However this assumption is not always true

• we often can face situations when consequences $c(a)$ of taking a decision $a$ are not known with certainty

There are two categories of decision analysis tools that help model this:

### Decision Under Uncertainty

• we are not able to asses the distribution, but we can list all possible scenarios

Methods

### Decision Under Risk

• $c(a)$ is not known with certainty, but we know the probability distribution on the set of $X$