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 onlineFDR reference semantics for overlapping scope.
Extension: Implemented in this package but not a direct onlineFDR counterpart.
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, `wealth <= reward`, and `wealth + reward <= alpha`	Proven + Parity	The default dependent-LORD sequence is scaled by `alpha / reward`; its wealth constraint is enforced.
`LordDiscard`	FDR	Conservative/null-adaptive regime with valid `tau` and `wealth <= tau * alpha`	Parity	Requires `0 < tau < 1` and the scaled initial-wealth budget.
`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`	Penalty-weighted FDR; penalty-weighted memory FDR when `decay < 1`	Independent valid p-values, predictable monotone weights, feasible nonnegative rewards	Proven + Extension	Ordinary FDR requires unit penalty weights and `decay=1`. The corrected prior cap is tested against the paper's reward constraints.
`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, summable allocations chosen before observing the corresponding p-value, and conditional positive dependence	Proven + Extension	Uses the identity shape; independent p-values with fixed weights are a supported special case. Arbitrary dependence requires reshaping, which is not implemented.
`BatchBHOfficial`	FDR	Independent null p-values, monotone batch procedure, one gamma profile per stream	Extension	Uses the authors' experimental update. Its fixed gamma budget does not certify monotonicity for adversarial inputs.
`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 plus onlineFDR (2.18.0).
E-value toolbox helpers are construction utilities. They do not make an invalid input stream valid by themselves.

Weighted GAI++ uses the penalty-weighted ratio sum(penalty_weight * false_rejection) / max(sum(penalty_weight * rejection), 1). With memory decay, each term also receives the factor decay ** age. Controlling the expectation of these ratios does not generally control ordinary FDR. Its error_rate is therefore "weighted FDR" or "weighted mem-FDR", including when an individual call happens to use unit weights.

The TOAD identity-shape guarantee uses Fisher's conditional positive-dependence assumption (Theorem 1, part 1). A sufficiently simple supported setup uses independent p-values and prespecified weights. Adaptive weights also need the paper's predictability and monotonicity conditions; choosing weights after seeing their own p-values invalidates the guarantee. Summable weights alone do not establish FDR control for arbitrarily dependent p-values.

Guarantee Matrix¶

Status Labels¶

Method Matrix¶

Important Scope Notes¶

References¶