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May 2009 Harold Jeffreys’s Theory of Probability Revisited
Christian P. Robert, Nicolas Chopin, Judith Rousseau
Statist. Sci. 24(2): 141-172 (May 2009). DOI: 10.1214/09-STS284


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.


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Christian P. Robert. Nicolas Chopin. Judith Rousseau. "Harold Jeffreys’s Theory of Probability Revisited." Statist. Sci. 24 (2) 141 - 172, May 2009.


Published: May 2009
First available in Project Euclid: 14 January 2010

zbMATH: 1328.62012
MathSciNet: MR2655841
Digital Object Identifier: 10.1214/09-STS284

Keywords: Bayes factor , Bayesian foundations , goodness of fit , Jeffreys’s prior , Kullback divergence , noninformative prior , P-values , tests , σ-finite measure

Rights: Copyright © 2009 Institute of Mathematical Statistics


Vol.24 • No. 2 • May 2009
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