The estimation, change-detection, and multiplicity results the measurement and sampling conventions rest on.
Wilson, E. B. · J. Amer. Statist. Assoc. 22(158), 209–212 · 1927
Derives the score confidence interval for a proportion that carries its name — the interval this publication's conventions use for a visibility probability estimated from repeated sampling, because it behaves well at the small counts and extreme rates that naive intervals mishandle.
Clopper, C. J. & Pearson, E. S. · Biometrika 26(4), 404–413 · 1934
Gives the exact binomial confidence interval, the conservative alternative to Wilson's: it guarantees coverage at the stated level at the cost of width. Together the two bound the defensible interval choices for a disclosed visibility estimate.
Efron, B. & Morris, C. · J. Amer. Statist. Assoc. 70(350), 311–319 · 1975
Demonstrates empirical-Bayes shrinkage — that estimating many related quantities jointly beats estimating each one alone — which is the statistical basis for pooling across query cells rather than reading each in isolation. The gains depend on the units being genuinely related.
Gelman, A. & Hill, J. · Cambridge University Press (book) · 2007
Data Analysis Using Regression and Multilevel/Hierarchical Models
The standard applied treatment of hierarchical models, and the reference for the multilevel estimator the sampling convention specifies when pooling visibility across cells. As a textbook it standardizes practice rather than establishing a new result; being a print book, it carries no URL to cite.
Benjamini, Y. & Hochberg, Y. · J. R. Stat. Soc. Ser. B 57(1), 289–300 · 1995
Introduces false-discovery-rate control, the multiplicity correction the Barkhausen Criterion invokes when many query cells are monitored at once — less conservative than family-wise control and appropriate when a bounded rate of false positives is tolerable. It is the standard tool for the multiplicity disclosure the Criterion requires.
Page, E. S. · Biometrika 41(1-2), 100–115 · 1954
The CUSUM change-detection method, and the classical basis for flagging the engine-change points the Criterion excludes — a broad, synchronous shift across unrelated queries. It establishes sequential change detection as a frequentist counterpart to the Bayesian method below.
Adams, R. P. & MacKay, D. J. C. · arXiv:0710.3742 · 2007
Gives an online Bayesian method for detecting when a data stream's generating process changes, applicable to distinguishing a genuine visibility shift from an engine-change artifact in a running monitor. It is a preprint, and its behavior depends on the priors chosen.
Wald, A. · Ann. Math. Statist. 16(2), 117–186 · 1945
Founds sequential analysis — testing as evidence accrues rather than at a fixed sample size — which is the theoretical root of the sustainment logic behind checking a visibility change across successive windows. It establishes that a stopping rule changes the inference that follows.
Lan, K. K. G. & DeMets, D. L. · Biometrika 70(3), 659–663 · 1983
Provides the alpha-spending approach to interim analyses, controlling error when a result is inspected repeatedly over time — the discipline a sustained-monitoring visibility claim needs so that looking often does not inflate significance. It was developed for clinical trials; the transfer here is by analogy.
Webber, W.; Moffat, A. & Zobel, J. · ACM Trans. Inf. Syst. 28(4), Article 20 · 2010
Defines rank-biased overlap, a top-weighted similarity for comparing two rankings that may differ in length and membership — the appropriate measure for the ranked source lists AI answers return, where the top positions carry most of the weight. It is a principled alternative to naive list overlap.