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

Threshold and sample planning

Finite-sample certificate from bounded complete records › Threshold and sample planning · lines 742–765

Oai265-B@2#eq:threshold, Oai265-B@2#eq:samples

For $b < ε < 1$ , acceptance is equivalent to

F_{L} \geq 1 - \frac{( ε - b ) ^{2}}{4} .

For $b = 0, ε = 0.1$ , this requires $F_{L} \geq 0.9975$ .

For equal sample counts $n$ , an all-ideal-score dataset is certified by the Hoeffding procedure whenever

n \geq \frac{9}{8 q ^{2}} lo g \frac{6}{α _{s}}, q = \frac{( ε - b ) ^{2}}{4} - b_{cal} > 0.

Indeed $R_{s} \leq q$ under this allowance. If $q \leq 0$ , the announced calibration budget prevents this particular certificate from succeeding even on ideal scores.

These are sufficient allowances, not optimal sample lower bounds. Failure to certify does not show that the actual device error is large.

Displayed formulas in this passage

Oai265-B@2#eq:threshold · line 745
$F_{L} \geq 1 - \frac{( ε - b ) ^{2}}{4} .$
Oai265-B@2#eq:samples · line 753
$n \geq \frac{9}{8 q ^{2}} lo g \frac{6}{α _{s}}, q = \frac{( ε - b ) ^{2}}{4} - b_{cal} > 0.$