Manuscript Oai265-B@2 · Oai265-B-v2.tex · section · 94b6f42f

Optional stopping

Loss, heralding, drift, and reference safeguards › Optional stopping · lines 1012–1029

Ordinary fixed-sample intervals cannot be reused after repeatedly looking for a favorable stopping point without additional control.

For each setting and every prefix $n \geq 1$ , allocate

a_{j, n} = \frac{2 α _{s}}{π ^{2} n ^{2}} .

Their sum over all prefixes and three settings is $α_{s}$ . The radii

r_{j} (n) = \frac{2}{n} lo g \frac{π ^{2} n ^{2}}{α _{s}}

therefore cover all prefixes simultaneously under the independent stream model. This permits stopping at a data-dependent prefix; it is not the fixed-sample formula (eq:statistics).

Displayed formulas in this passage

unlabeled · line 1018
$a_{j, n} = \frac{2 α _{s}}{π ^{2} n ^{2}} .$
unlabeled · line 1023
$r_{j} (n) = \frac{2}{n} lo g \frac{π ^{2} n ^{2}}{α _{s}}$