Manuscript Psy04-A@1 · Psy04-A-v1.tex · corollary · d5800e2a

Corollary: History-dependent device exclusion

Finite-sample exclusion certificates › Across-run memory · lines 1293–1314 · proof included or linked

Psy04-A@1#cor:devicememory

Under Assumption ass:conditionalboundary,

E [S_{i} ∣ F_{i - 1}] \leq c_{i} := min {1, 3/4 + e_{C, i}} .

For fixed $N$ , rejection based on

\frac{1}{N} i = 1 \sum^{N} (S_{i} - c_{i}) > r_{N} (δ)

has Type-I error at most $δ$ .

Proof. Condition on the pre-run state and history. The stochastic classical bound applies to the fresh current-run experiment. Average any hidden pre-run state and apply the conditional complete-law allowance. Then use Lemma lem:conditionalmgf.

Displayed formulas in this passage

unlabeled · line 1296
$E [S_{i} ∣ F_{i - 1}] \leq c_{i} := min {1, 3/4 + e_{C, i}} .$
unlabeled · line 1301
$\frac{1}{N} i = 1 \sum^{N} (S_{i} - c_{i}) > r_{N} (δ)$

Nearby in this section

assumption: Assumption: Fresh current-run bottleneck
section: Across-run memory