Decision rule

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.

Given an observable random variable X over the probability space ${\displaystyle \scriptstyle ({\mathcal {X}},\Sigma ,P_{\theta })}$, determined by a parameter θ ∈ Θ, and a set A of possible actions, a (deterministic) decision rule is a function δ : ${\displaystyle \scriptstyle {\mathcal {X}}}$→ A.

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