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

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

• An estimator could be chosen, for instance, using some optimization algorithm.

• Out of sample prediction in regression and classification models.

See also

• Admissible decision rule

• Bayes estimator

• Classification rule

• Scoring rule

References