Harold Jeffreys's Theory of Probability Revisited

被引：108

作者：

Robert, Christian P. ^{[1
,2
]}

Chopin, Nicolas ^{[10
]}

Rousseau, Judith ^{[1
]}

Bernardo, Jose M. ^{[3
]}

Gelman, Andrew ^{[4
,5
]}

Kass, Robert ^{[6
,7
]}

Lindley, Dennis

Senn, Stephen ^{[8
]}

Zellner, Arnold ^{[9
]}

机构：

[1] Univ Paris 09, Dept Appl Math, CEREMADE, F-75775 Paris 16, France

[2] Natl Inst Stat & Econ Studies INSEE, CREST, Stat Lab, Paris, France

[3] Univ Valencia, Fac Matemat, E-46100 Valencia, Spain

[4] Columbia Univ, Dept Stat, New York, NY 10027 USA

[5] Columbia Univ, Dept Polit Sci, New York, NY 10027 USA

[6] Carnegie Mellon Univ, Dept Stat, Machine Learning Dept, Pittsburgh, PA 15213 USA

[7] Carnegie Mellon Univ, Ctr Neural Basis Cognit, Pittsburgh, PA 15213 USA

[8] Univ Glasgow, Dept Stat, Glasgow G12 8QW, Lanark, Scotland

[9] U Chicago, Booth Business Sch, Chicago, IL 60637 USA

[10] INSEE, CREST ENSAE, F-92245 Malakoff, France

来源：

STATISTICAL SCIENCE | 2009年 / 24卷 / 02期

关键词：

Bayesian foundations; noninformative prior; sigma-finite measure; Jeffreys's prior; Kullback divergence; tests; Bayes factor; p-values; goodness of fit; POSTERIOR DISTRIBUTIONS; NONINFORMATIVE PRIORS; BAYES; INFERENCE; FREQUENTIST; STATISTICS; HYPOTHESIS; SELECTION;

D O I：

10.1214/09-STS284

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

Published exactly seventy years ago, Jeffreys's Theory of Probability (1939) has had a unique impact on the Bayesian community and is now considered to be one of the main classics in Bayesian Statistics as well as the initiator of the objective Bayes school. In particular, its advances on the derivation of noninformative priors as well as on the scaling of Bayes factors have had a lasting impact on the field. However, the book reflects the characteristics of the time, especially in terms of mathematical rigor. In this paper we point out the fundamental aspects of this reference work, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences. Our major aim here is to help modern readers in navigating in this difficult text and in concentrating on passages that are still relevant today.

引用

页码：141 / 194

页数：54

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