Decision rule
= Decision rule
{title2=$\delta:\mathcal X\to\mathcal A$}
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A measurable choice of an action from observed data, with a randomized rule allowing a conditional distribution of actions. Its performance under a loss function is the <risk function> $R(\theta,\delta)=\mathbb E_\theta L(\theta,\delta(X))$. Admissibility compares risks pointwise, Bayes optimality integrates risk under a prior, and minimax optimality minimizes the worst-case risk.