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Harold Jeffreys' Theory of Probability revisited

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Date
2009
Notes
http://projecteuclid.org/euclid.ss/1263478373
Link to item file
http://hal.archives-ouvertes.fr/hal-00274631/en/
Dewey
Probabilités et mathématiques appliquées
Sujet
non-informative prior; Bayesian foundations; sigma-finite measure; Jeffreys' prior; Kullback divergence; tests; Bayes factor; goodness of fit.; p-values
JEL code
C11
Journal issue
Statistical Science
Volume
24
Number
2
Publication date
05-2009
Article pages
141-172
Publisher
Institute of Mathematical Statistics
DOI
http://dx.doi.org/10.1214/09-STS284
URI
https://basepub.dauphine.fr/handle/123456789/3222
Collections
  • CEREMADE : Publications
Metadata
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Author
Chopin, Nicolas
Robert, Christian P.
Rousseau, Judith
Type
Article accepté pour publication ou publié
Abstract (EN)
Published nearly seventy years ago, Jeffreys' 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 rigorousness. 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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