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.

Dirichlet distribution, including the one-category case

Definition

Assume Countable Choice. For $k \geq 2$ and $α_{j} > 0$ , the Dirichlet distribution $Dirichlet (α_{1}, \dots, α_{k})$ is the probability law on the open probability simplex with density $\frac{Γ (α_{+})}{\prod_{j} Γ (α_{j})} \prod_{j} p_{j}^{α_{j} - 1}$ relative to $d p_{1} \dots d p_{k - 1}$ , with $p_{k} = 1 - \sum_{j < k} p_{j}$ . Its normalization is Dirichlet density normalization by iterated Beta integrals. For $k = 1$ , define the law to be the point mass at $p_{1} = 1$ . All coordinates of the parameter vector must be strictly positive.

Depends on

Used by

Dependency tree · two levels

23 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., §3.4 (standard reference, not scraped)
Gero Walter, A Technical Note on the Dirichlet-Multinomial Model, 2013 (standard reference, not scraped)