Corollary: Simultaneous battery radius

Condition on $K$ checkpoints independent of the assessment blocks. For $J$ predeclared probe means, each estimated from $n$ independent example blocks,

is a simultaneous accuracy radius with confidence at least $1-\delta$.

Noise repetitions within one example may first be averaged. They do not multiply the independent population sample count. Within-example dependence across checkpoints or probes is allowed.

Proof. Apply the bounded-example-block evaluation interface in Psy03-A thm:evaluation and allocate its union bound over all $KJ$ means CheungPsy03A,Hoeffding.