DefinitionDefinition: Literature-sourcedProof: Not applicablePipeline-generatedjudge pass (gpt-6-luna)

How statement and proof provenance work

The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.

Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.

These labels describe origin, not correctness: citations and verification chips remain separate evidence.

Confidence sequences

Definition

Let $Θ$ be a parameter set and $(P_{θ})_{θ \in Θ}$ a family of probability laws on a common discrete filtered measurable space $(Ω, F, (F_{t})_{t \geq 0})$ Filtration and filtered probability space. For $α \in (0, 1)$ , a $(1 - α)$ confidence sequence is a sequence of set-valued rules $C_{t} (ω) \subseteq Θ$ such that, for each fixed $θ \in Θ$ , the membership event ${θ \in C_{t}}$ belongs to $F_{t}$ for every $t$ and $P_{θ} (θ \in C_{t} for every t \geq 0) \geq 1 - α .$

The coverage is simultaneous over all discrete times. The definition makes no claim of conditional-on-covariates coverage or validity under a changed sampling law.

Depends on

Filtration and filtered probability space

Used by

Dependency tree · two levels

3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.

Sources

Steven R. Howard, Aaditya Ramdas, Jon McAuliffe and Jasjeet Sekhon, Time-Uniform, Nonparametric, Nonasymptotic Confidence Sequences, Introduction (standard reference, not scraped)
Aaditya Ramdas, Peter Grunwald, Vladimir Vovk and Glenn Shafer, Game-Theoretic Statistics and Safe Anytime-Valid Inference, §2.8 (standard reference, not scraped)