= Solution
A <loss function> $L(\theta,a)$ quantifies the cost of taking action $a$ when the parameter is $\theta$. A <decision rule> $d$ is a measurable map from the observation space to the action space (or, for randomized rules, a conditional action distribution). Its <risk function> is $R(\theta,d)=\mathbb E_\theta L(\theta,d(X))$. For a prior <probability> distribution $\pi$, its <Bayes risk> is
$$
r(\pi,d)=\int_\Theta R(\theta,d)\,\pi(d\theta).
$$
A <minimax> rule minimizes $\sup_\theta R(\theta,d)$.
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