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 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 ( X , Σ , P θ ) {displaystyle scriptstyle ({mathcal {X}},Sigma ,P_{ heta })} , determined by a parameter θ ∈ Θ, and a set A of possible actions, a (deterministic) decision rule is a function δ :  X {displaystyle scriptstyle {mathcal {X}}} → A.