Formula Lab
Same evidence, nine ways to decide how much of it to trust. Wassily's jar uses the Hoeffding bound; the other eight are here to compare against it.
Wassily uses · Hoeffding
Evidence
Shared with the proof panel on Overview
n₊ 723 · n₋ 1,623
Proven floor vs tokens sampled
AUC 0.580 · d 28 · survivors 30.8% · hover for values
All bounds, ranked by floor
n = 2,346 · AUC 0.580 · δ = 0.05 · highlighted: Wassily's formula
| Formula | Credit | ε | Floor | Jar |
|---|---|---|---|---|
Wilcoxon Wilcoxon–Mann–Whitney normal interval | Frank Wilcoxon; Mann & Whitney; Hanley & McNeil 1945 / 1947 / 1982 | 0.0213 | 0.5587 | 59% |
Bayes Bayes–Laplace posterior credible floor | Thomas Bayes; Pierre-Simon Laplace 1763 / 1774 | 0.0215 | 0.5585 | 59% |
HoeffdingWassily Hoeffding bound for U-statistics | Wassily Hoeffding 1963 | 0.0455 | 0.5345 | 34% |
Bernstein Bernstein inequality | Sergei Bernstein 1924 | 0.0477 | 0.5323 | 32% |
Chebyshev Chebyshev–Cantelli inequality | Pafnuty Chebyshev; Francesco Cantelli 1867 / 1928 | 0.0565 | 0.5235 | 23% |
Kolmogorov (DKW) Kolmogorov–Smirnov / DKW band | Andrey Kolmogorov; Dvoretzky–Kiefer–Wolfowitz; Massart 1933 / 1956 / 1990 | 0.0918 | 0.4882 | 0% |
VC bound Vapnik–Chervonenkis capacity bound | Vladimir Vapnik & Alexey Chervonenkis 1971 | 0.2737 | 0.3063 | 0% |
VC ∧ bootstrap min(VC floor, bootstrap floor) | Vapnik–Chervonenkis + Bradley Efron 1971 / 1979 | … | … | … |
Bootstrap Percentile bootstrap | Bradley Efron 1979 | … | … | … |