Manuscript Psy04-B@1 · Psy04-B-v1.tex · theorem · 62c2b6f0

Theorem: Complete-record retrieval score

Complete records and robust score allowances › Independent loss and assignment model · lines 1514–1539 · proof included or linked

Psy04-B@1#thm:completescore, Psy04-B@1#eq:completescore

For the code and storage above, under Assumption ass:flags,

Q_{score} (T) = \frac{1}{2} + \frac{p v ( 1 - 2 ϵ ) r _{T}}{2 2} .

It exceeds $3/4$ exactly when

p v (1 - 2 ϵ) r_{T} > 1/ 2 .

Proof. Conditional on a valid observation, assignment noise gives

\frac{1}{2} + (1 - 2 ϵ) (Q_{Q} (T) - 1/2) .

Valid observations have probability $p v$ . All remaining attempts contribute $1/2$ . Substitute (eq:retentionscore).

Displayed formulas in this passage

Psy04-B@1#eq:completescore · line 1518
$Q_{score} (T) = \frac{1}{2} + \frac{p v ( 1 - 2 ϵ ) r _{T}}{2 2} .$
unlabeled · line 1526
$p v (1 - 2 ϵ) r_{T} > 1/ 2 .$
unlabeled · line 1533
$\frac{1}{2} + (1 - 2 ϵ) (Q_{Q} (T) - 1/2) .$