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Decision theory

In decision theory, a **decision rule** is a function which maps an observation to an appropriate action. Decision rules play an important role in the theory of statistics and economics, and are closely related to the concept of a strategy in game theory.

In order to evaluate the usefulness of a decision rule, it is necessary to have a loss function detailing the outcome of each action under different states.

## Formal definition Edit

Given an observable random variable *X* over the probability space , determined by a parameter *θ* ∈ *Θ*, and a set *A* of possible actions, a (deterministic) **decision rule** is a function *δ* : → *A*.

## Examples of decision rules Edit

- An estimator is a decision rule used for estimating a parameter. In this case the set of actions is the parameter space, and a loss function details the cost of the discrepancy between the true value of the parameter and the estimated value.
- Out of sample prediction in regression and classification models.

## See also Edit

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