Alphabeta MathHow 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.
Shape-rate Gamma distribution
Definition
Assume Countable Choice. For shape and rate , the shape-rate Gamma distribution is the probability measure on with density relative to Lebesgue measure. Its normalization is proved in The shape-rate Gamma density is normalized. The second argument is a rate, not a scale.
Depends on
Used by
- Affine second-moment bounds for normalized complex Gaussian block products Lemma
- Dirichlet parameters add under coarsening Lemma
- Finite Dirichlet gamma representation and weighted Bernstein bound Lemma
- Existence of a Dirichlet process by normalized gamma Poisson random measure Theorem
- Exposure-adjusted Gamma-Poisson conjugate update Theorem
Dependency tree · two levels
18 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
- Johnson, Ott & Dogucu, Bayes Rules!, Chapter 5, §§5.2.1–5.2.2 (standard reference, not scraped)
- Gelman et al., Bayesian Data Analysis, 3rd ed., §2.4 (standard reference, not scraped)