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.

Posterior median

Definition

For a probability measure $Π_{y}$ on $R$ , a posterior median is any $m \in R$ satisfying $Π_{y} ((- \infty, m]) \geq \frac{1}{2} and Π_{y} ([m, \infty)) \geq \frac{1}{2} .$ The two inequalities, rather than a density-based definition, apply to discrete, continuous, and mixed posteriors and permit more than one median.

Remarks

The lower posterior median is a measurable rule constructs a measurable median rule from a posterior probability kernel.

Depends on

Used by

Dependency tree · two levels

7 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

Ryan Martin, Lecture Notes on Advanced Statistical Theory, §5.3.1, PDF pp. 104–105 (standard reference, not scraped)
Andrew Gelman et al., Bayesian Data Analysis, 3rd ed., §2.5 (standard reference, not scraped)