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Bayesian inference and the parametric bootstrap

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Bradley Efron

Applications · Submitted 14 Jan 2013

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

The authors' main claim The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions.

how it is stated · asserted 0.51 read the record →

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arXiv ID1301.2936 (version 1)
Pith IDYV2V3YGD, Pith's permanent record of this paper and its review
CitationBradley Efron. "Bayesian inference and the parametric bootstrap." arXiv:1301.2936 (2013). https://pith.science/paper/YV2V3YGD
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Compiled by classifier-1.13-20260917 via OpenRouter, question bank abstract-p1-20260923, 2026-09-23: 1 request, 4,139 input tokens, $0.0002 reported.

What the abstract itself states, as probabilities: claims first 0.03 · states limitation 0.06 · human participants 0.02 · controlled comparison 0.02 · randomized assignment 0.01 · states quantitative result 0.06 · compares with prior results 0.12 · mentions code or data availability 0.02.

The abstract, sentence by sentence

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

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting from Jeffreys invariant prior. Because of the i.i.d. nature of bootstrap sampling, familiar formulas describe the computational accuracy of the Bayes estimates. Besides computational methods, the theory provides a connection between Bayesian and frequentist analysis. Efficient algorithms for the frequentist accuracy of Bayesian inferences are developed and demonstrated in a model selection example.

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 The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. contribution 0.58 0.27 0.45 asserted 0.51
s1 Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting from Jeffreys invariant prior. method 0.59 0.48 0.10 asserted 1.00
s2 Because of the i.i.d. nature of bootstrap sampling, familiar formulas describe the computational accuracy of the Bayes estimates. result 0.37 0.40 0.10 asserted 1.00
s3 Besides computational methods, the theory provides a connection between Bayesian and frequentist analysis. interpretation 0.62 0.54 0.20 asserted 1.00
s4 Efficient algorithms for the frequentist accuracy of Bayesian inferences are developed and demonstrated in a model selection example. contribution 0.96 0.89 0.30 asserted 1.00

What kind of paper the classifier reports this is: method or tool 0.90 · evidence from proof or derivation 0.59.

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  • references and citing sentences
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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

The parametric bootstrap can be used for the efficient computation of Bayes posterior distributions. Importance sampling formulas take on an easy form relating to the deviance in exponential families and are particularly simple starting from Jeffreys invariant prior. Because of the i.i.d. nature of bootstrap sampling, familiar formulas describe the computational accuracy of the Bayes estimates. Besides computational methods, the theory provides a connection between Bayesian and frequentist analysis. Efficient algorithms for the frequentist accuracy of Bayesian inferences are developed and demonstrated in a model selection example.

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