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An integral characterization of the Dirichlet process

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Paper breakdownThe authors' claims, conditions and measurements, as JSON Signed receiptProof this review has not been altered
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Günter Last

Probability · Submitted 30 Mar 2018

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim We give a new integral characterization of the Dirichlet process on a general phase space.

how it is stated · asserted 1.00 read the record →

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arXiv ID1803.11465 (version 1)
Pith IDJ2RKYFUG, Pith's permanent record of this paper and its review
CitationG\"unter Last. "An integral characterization of the Dirichlet process." arXiv:1803.11465 (2018). https://pith.science/paper/J2RKYFUG
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The compiled record

The paper's own sentences, arranged. Each label is drawn from a closed vocabulary; the number beside it is the probability the classifier gave that label. Numbers in the tables are the authors', checked by code. No sentence in this record was written by a model.

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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,892 input tokens.

What the abstract itself states, as probabilities: claims first 0.16 · states limitation 0.05 · human participants 0.02 · controlled comparison 0.01 · randomized assignment 0.01 · states quantitative result 0.04 · compares with prior results 0.25 · mentions code or data availability 0.01.

The abstract, sentence by sentence

arXiv listing abstract v1. Results and the main claim are underlined; .

We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new characterization of the Dirichlet distribution and a marked version of a classical characterization of the Poisson-Dirichlet distribution via invariance under size-biased sampling.

background contribution method result interpretation main claim

What the classifier reports for each sentence. The number is the probability it gave the label.
#sentencerolethe authors' own workstates the main conclusionstrength
s0 We give a new integral characterization of the Dirichlet process on a general phase space. contribution 0.99 0.95 0.83 asserted 1.00
s1 To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. method 0.88 0.91 0.05 asserted 1.00
s2 Two applications are a new characterization of the Dirichlet distribution and a marked version of a classical characterization of the Poisson-Dirichlet distribution via invariance under size-biased sampling. contribution 0.50 0.88 0.15 asserted 1.00

What kind of paper the classifier reports this is: theoretical result 1.00 · evidence from proof or derivation 1.00.

What was examined, and what was not

sources read
  • arXiv listing abstract v1
not examined
  • full text
  • figures and tables
  • references and citing sentences
  • relations to other papers
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  • P abstract
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  • S sections
  • T body sentences
  • C citations
  • R cross-paper relations

Every quoted sentence on this record is the authors'. Every label is from Pith's closed vocabulary, with the probability shown beside it. Every number in the measurements table is the authors', checked by code. Record as JSON

The paper
Original abstract

We give a new integral characterization of the Dirichlet process on a general phase space. To do so we first prove a characterization of the nonsymmetric Beta distribution via size-biased sampling. Two applications are a new characterization of the Dirichlet distribution and a marked version of a classical characterization of the Poisson-Dirichlet distribution via invariance under size-biased sampling.

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1 arXiv paper cite this in 2 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

Papers citing it · 1 sentence without a confident label

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What it cites · 2 sentences without a confident label

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