Harold Jeffreys's Theory of Probability Revisited

TL;DR

This paper revisits Jeffreys's 1939 influential work on Bayesian probability, highlighting its core contributions to noninformative priors and Bayes factors, and aims to guide modern readers through its historically rigorous content.

Contribution

It provides a detailed analysis of Jeffreys's original text, emphasizing its fundamental aspects and relevance to current Bayesian methods.

Findings

Jeffreys's work laid the foundation for objective Bayesian analysis.

The book's coverage of noninformative priors remains relevant today.

It offers insights into the historical development of Bayesian testing.

Abstract

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.