Guarantee Matrix¶
This page summarizes the guarantee status of each method in this package.
Status Labels¶
- Proven: Theoretical guarantee exists under the listed assumptions.
- Parity: Behavior is aligned to
onlineFDRreference semantics for overlapping scope. - Extension: Implemented in this package but not a direct
onlineFDRcounterpart. - Experimental: Utility method without formal FDR/FWER guarantee claim in this package.
- Tooling: Construction helper; validity depends on caller-supplied inputs and assumptions.
Method Matrix¶
| Method | Error Target | Assumptions | Status | Notes |
|---|---|---|---|---|
EBH | FDR | Valid e-values | Proven | Controls FDR under arbitrary dependence; large e-values are stronger evidence. |
ELond | Online FDR | Valid e-values and summable gamma sequence | Proven | e-LOND controls online FDR under arbitrary dependence. |
Lond | FDR | Independence / PRDS / dep-corrected mode | Proven + Parity | Use dependent=True for arbitrary dependence correction. |
LordThree | FDR | Independence, valid reward budget | Proven + Parity | Requires reward > 0 and wealth + reward <= alpha. |
LordPlusPlus | FDR | Independence, guaranteed payout regime | Proven + Parity | This implementation enforces reward == alpha. |
LordDependent | FDR | Arbitrary dependence (dependent LORD assumptions) | Proven + Parity | Uses dependent-LORD sequence scaling compatible with onlineFDR semantics. |
LordDiscard | FDR | Conservative/null-adaptive regime with valid tau | Parity | Requires 0 < tau < 1. |
Saffron | FDR | Independence | Proven + Parity | Candidate-threshold method; parity-tested against onlineFDR. |
SaffronAsync | mFDR | Independent p-values, asynchronous conflict-set assumptions | Proven + Extension | Lifecycle API; parity-tested against onlineFDR async reference paths. |
Addis | FDR/mFDR regime | Conservative nulls, 0 < tau < 1, 0 <= lambda < tau | Proven + Parity | Parameter checks enforce supported region. |
AddisAsync | mFDR | Conservative nulls plus asynchronous conflict-set assumptions | Proven + Extension | Lifecycle API with active unfinished tests counted in conflict accounting. |
Gai | FDR/mFDR | Alpha-investing assumptions | Parity | Strict guarantees depend on payout specification. |
WeightedGaiPlusPlus | FDR | Prior and penalty weights fixed independently of null p-values; valid memory decay | Proven + Extension | Implements weighted/memory GAI++ with author-code oracle tests. |
AlphaSpending | FWER | Valid finite-horizon spending rule | Proven + Parity | Finite horizon is enforced for finite-k rules. |
OnlineFallback | FWER | Online fallback assumptions | Proven + Parity | Boundary uses p <= alpha_t. |
BatchBH | FDR | Batching assumptions from reference | Parity | Empty batch is a no-op. |
BatchStoreyBH | FDR | Batching + Storey pi0 assumptions | Parity | R+ uses same-size replacement semantics. |
BatchPRDS | FDR | PRDS within-batch assumptions | Parity | Empty batch is a no-op. |
BatchBY | FDR-style batch control | BY within-batch correction; no direct onlineFDR reference | Extension | Added conservative extension beyond the onlineFDR overlap set. |
Toad | FDR | Decision deadlines and valid summable weights | Proven + Extension | Finite helper reduces to BH for a single uniform-deadline group. |
BatchBHOfficial | FDR | AISTATS supplementary implementation assumptions | Extension | Alternate BatchBH profile using the authors' adaptive gamma policy. |
LORDMemoryDecay | N/A (utility/monitoring use) | Application-specific | Experimental / Extension | Not claimed as a general FDR/FWER-control method in this package docs. |
| E-value calibrators | E-value construction | Valid input p-values and calibrator assumptions | Tooling | Construction-level guarantee only; FDR control comes from feeding valid e-values to a valid procedure. |
| E-value merging helpers | E-value construction | Fixed weights for arithmetic means; independence/conditional validity for products | Tooling | The package documents assumptions but cannot infer whether user-supplied evidence satisfies them. |
| E-process helpers | E-value construction | Caller-supplied model, betting, filtration, and stopping assumptions | Tooling | Stopped values are valid e-values only under the relevant e-process assumptions. |
Important Scope Notes¶
- Guarantees apply only under each method's stated assumptions.
- Parity means semantic alignment for overlapping functionality, not identity of every API surface.
- Live R parity tests (
rpy2) are required for parity-covered behavior and require R plusonlineFDR(2.18.0). - E-value toolbox helpers are construction utilities. They do not make an invalid input stream valid by themselves.
References¶
- https://www.bioconductor.org/packages/release/bioc/html/onlineFDR.html
- https://bioc-release.r-universe.dev/onlineFDR/doc/manual.html
- https://dsrobertson.github.io/onlineFDR/articles/theory.html
- https://dsrobertson.github.io/onlineFDR/reference/LORD.html
- https://dsrobertson.github.io/onlineFDR/reference/SAFFRON.html
- https://dsrobertson.github.io/onlineFDR/reference/BatchBH.html
- https://proceedings.mlr.press/v108/zrnic20a.html
- https://arxiv.org/abs/1812.05068
- https://arxiv.org/abs/1905.11465
- https://proceedings.neurips.cc/paper/7148-more-powerful-and-flexible-rules-for-online-fdr-control-with-memory-and-weights
- https://proceedings.mlr.press/v151/fisher22a.html
- https://academic.oup.com/jrsssb/article/84/3/822/7056146
- https://github.com/ruoduwang/e-BH
- https://proceedings.mlr.press/v238/xu24a.html
- https://github.com/neilzxu/evalue-omt
- https://doi.org/10.1214/20-AOS2020
- https://arxiv.org/abs/2502.08539