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.

Beta distribution

Definition

Assume Countable Choice. For $α, β > 0$ , the Beta distribution $Beta (α, β)$ is the probability measure on $(0, 1)$ with density $f_{α, β} (p) = \frac{p^{α - 1} (1 - p)^{β - 1}}{B (α, β)}$ relative to Lebesgue measure. The finite positive normalization follows from The Beta density has finite positive Lebesgue integral. The open interval is the parameter domain; no endpoint atoms are included.

Depends on

Used by

Quantile Monte Carlo standard error Algorithm
Beta-Binomial conjugate update Theorem

Dependency tree · two levels

25 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

Gelman et al., Bayesian Data Analysis, 3rd ed., §2.1 (standard reference, not scraped)
Johnson, Ott & Dogucu, Bayes Rules!, Chapter 3, §3.1 (standard reference, not scraped)