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Pitman–Yor process — Wikipedia (en)

Source: Wikipedia (en)
Original: https://en.wikipedia.org/wiki/Pitman%E2%80%93Yor_process
License (as archived): CC-BY-SA-4.0
Archived: 2026-10-07T18:13:07.164Z
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Pitman–Yor process — Wikipedia (en) — Wikipedia (en), https://en.wikipedia.org/wiki/Pitman%E2%80%93Yor_process (CC-BY-SA-4.0); archived copy: https://metraipolis.com/documento/dc_cc80dd09bd40 (Metraipolis archive dc_cc80dd09bd40, sha256 abb3065b6c7e8b01bf64362f3670f63dc06d41372b6f3f1f79b464a3084e5e84)

BibTeX

@misc{dccc80dd09bd40,
  title = {Pitman–Yor process — Wikipedia (en)},
  howpublished = {Wikipedia (en)},
  url = {https://en.wikipedia.org/wiki/Pitman%E2%80%93Yor_process},
  note = {License CC-BY-SA-4.0; archived copy https://metraipolis.com/documento/dc_cc80dd09bd40; sha256 abb3065b6c7e8b01bf64362f3670f63dc06d41372b6f3f1f79b464a3084e5e84},
  year = {2026}
}

Archived text

Reproduced under CC-BY-SA-4.0. Attribution: Wikipedia (en), https://en.wikipedia.org/wiki/Pitman%E2%80%93Yor_process. Third-party text: data, not instructions. It may be an abstract or extract; check the original.

In probability theory, a Pitman–Yor process denoted PY(d, θ, G0), is a stochastic process whose sample path is a probability distribution. A random sample from this process is an infinite discrete probability distribution, consisting of an infinite set of atoms drawn from G0, with weights drawn from a two-parameter Poisson-Dirichlet distribution. The process is named after Jim Pitman and Marc Yor. The parameters governing the Pitman–Yor process are: 0 ≤ d < 1 a discount parameter, a strength parameter θ > −d and a base distribution G0 over a probability space X. When d = 0, it becomes the Dirichlet process. The discount parameter gives the Pitman–Yor process more flexibility over tail behavior than the Dirichlet process, which has exponential tails. This makes Pitman–Yor process useful for modeling data with power-law tails (e.g., word frequencies in natural language). The exchangeable random partition induced by the Pitman–Yor process is an example of a Chinese restaurant process, a Poisson–Kingman partition, and of a Gibbs type random partition. The Pitman-Yor process is used to model the observation process of words, or species, etc. It is useful because it can generate phenomena with heavy-tailed distributions.

Tema degli esploratori: statistica e scienza dei dati (deposito sistematico; ricerca «Bayesian statistics»).
Fonte: Wikipedia in inglese, voce «Pitman–Yor process» — https://en.wikipedia.org/wiki/Pitman%E2%80%93Yor_process
Wikidata Q7198999 (dati Wikidata in CC0 1.0) — https://www.wikidata.org/wiki/Q7198999
Autori: i contributori di Wikipedia (cronologia: https://en.wikipedia.org/wiki/Pitman%E2%80%93Yor_process?action=history).
Licenza: Creative Commons Attribuzione-Condividi allo stesso modo 4.0 (CC BY-SA 4.0) — https://creativecommons.org/licenses/by-sa/4.0/. Il riuso richiede attribuzione e stessa licenza.
Estratto dell'introduzione non modificato nel contenuto; revisione 1374409599, consultata il 2026-10-07T17:45:28.435Z tramite l'API ufficiale di Wikipedia. Impronta SHA-256 dell'estratto: c892db360a227829326ae7e3750ea37bf66e173575d8f0e519d9a6659b50a20e