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First two moments and cross-moments of some coalescent times of the pure birth tree

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Krzysztof Bartoszek, Bayu Brahmantio, Woodrow Hao Chi Kiang

Probability · Submitted 25 Feb 2025

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

The authors' main claim We present here a thorough study of the first two moments and cross-moments for the pure birth tree's height and for the coalescent time of a randomly sampled pair of tips.

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arXiv ID2502.18159 (version 2)
Pith IDR2GHTUMP, Pith's permanent record of this paper and its review
CitationBayu Brahmantio, Krzysztof Bartoszek, Woodrow Hao Chi Kiang. "First two moments and cross-moments of some coalescent times of the pure birth tree." arXiv:2502.18159 (2025). https://pith.science/paper/R2GHTUMP
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Compiled by classifier-1.13.0 via TypeSafe API, question bank abstract-p1-20260923, 2026-09-23: 1 request, 2,272 input tokens.

What the abstract itself states, as probabilities: claims first 0.10 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.02 · states quantitative result 0.11 · compares with prior results 0.05 · mentions code or data availability 0.02.

The abstract, sentence by sentence

arXiv listing abstract v2. Results and the main claim are underlined; .

We present here a thorough study of the first two moments and cross-moments for the pure birth tree's height and for the coalescent time of a randomly sampled pair of tips. We consider also the first two moments of the conditional, on the tree, expectation of this coalescent time.

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 present here a thorough study of the first two moments and cross-moments for the pure birth tree's height and for the coalescent time of a randomly sampled pair of tips. contribution 1.00 0.94 0.28 asserted 0.99
s1 We consider also the first two moments of the conditional, on the tree, expectation of this coalescent time. contribution 1.00 0.91 0.08 asserted 0.83

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

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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 present here a thorough study of the first two moments and cross-moments for the pure birth tree's height and for the coalescent time of a randomly sampled pair of tips. We consider also the first two moments of the conditional, on the tree, expectation of this coalescent time.

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