Harold Jeffreys' Theory of Probability revisited
Chopin, Nicolas; Robert, Christian P.; Rousseau, Judith (2009), Harold Jeffreys' Theory of Probability revisited, Statistical Science, 24, 2, p. 141-172. http://dx.doi.org/10.1214/09-STS284
TypeArticle accepté pour publication ou publié
External document linkhttp://hal.archives-ouvertes.fr/hal-00274631/en/
Journal nameStatistical Science
Institute of Mathematical Statistics
MetadataShow full item record
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.
Subjects / Keywordsnon-informative prior; Bayesian foundations; sigma-finite measure; Jeffreys' prior; Kullback divergence; tests; Bayes factor; goodness of fit.; p-values
Showing items related by title and author.
Bayesian nonparametric estimation of the spectral density of a long or intermediate memory Gaussian process Rousseau, Judith; Chopin, Nicolas; Liseo, Brunero (2012) Article accepté pour publication ou publié
Inherent difficulties of non-Bayesian likelihood-based inference, as revealed by an examination of a recent book by Aitkin Gelman, Andrew; Robert, Christian P.; Rousseau, Judith (2013) Article accepté pour publication ou publié