Harold Jeffreys (1891–1989) was one of the most remarkable scientists of the twentieth century. A geophysicist by training and profession, he made lasting contributions to seismology, planetary science, and fluid dynamics, while simultaneously developing one of the most complete and rigorous treatments of Bayesian statistical inference ever produced. His 1939 book Theory of Probability was the first systematic attempt to build all of scientific inference on Bayesian foundations, and it introduced ideas—Jeffreys priors, Bayes factors, and automatic reference priors—that remain central to statistics today.
Early Life and Scientific Career
Jeffreys was born in Fatfield, County Durham, and educated at Armstrong College (now part of Newcastle University) and St John's College, Cambridge, where he spent the rest of his career. His primary scientific work was in geophysics: he demonstrated that the Earth's core is liquid, produced (with K. E. Bullen) the standard model of seismic travel times known as the Jeffreys-Bullen tables, and made important contributions to the theory of the Earth's thermal history and the dynamics of the atmosphere.
Theory of Probability
Jeffreys' Theory of Probability, first published in 1939 and revised in subsequent editions (the third edition of 1961 is considered definitive), was a landmark in statistical thought. Writing at a time when frequentist methods dominated, Jeffreys argued that probability should be interpreted as a degree of reasonable belief and that Bayes' theorem was the proper tool for scientific inference. He addressed model comparison, parameter estimation, significance testing, and the role of prior information with a rigor and thoroughness that was unprecedented.
Jeffreys developed his Bayesian framework largely in opposition to the dominant frequentist school of Fisher, Neyman, and Pearson. He and Fisher, both at Cambridge, engaged in decades of vigorous disagreement. Despite his relative isolation in the statistical community, Jeffreys persisted, and his ideas found new life in the Bayesian revival of the latter twentieth century.
The Jeffreys Prior
One of Jeffreys' most influential contributions is the prior distribution that bears his name. The Jeffreys prior is defined as the square root of the determinant of the Fisher information matrix, making it invariant under reparameterization. This property was crucial: it meant that the same inference would result regardless of how the parameter was expressed, resolving a longstanding objection to Bayesian methods.
Bayes Factors and Hypothesis Testing
Jeffreys also pioneered the use of Bayes factors for comparing scientific hypotheses. Unlike frequentist p-values, Bayes factors provide a direct measure of the evidence in favor of one hypothesis relative to another. Jeffreys proposed a scale of interpretation for Bayes factors that is still widely used, and he developed methods for handling point null hypotheses within the Bayesian framework.
“An hypothesis that has survived some real attempt to refute it has had a genuine success, and is to some extent confirmed.”— Harold Jeffreys, Theory of Probability (1939)
Born on 22 April in Fatfield, County Durham.
Elected Fellow of St John's College, Cambridge.
Published Scientific Inference, an early formulation of his Bayesian philosophy.
Published the first edition of Theory of Probability.
Knighted for contributions to science.
Third edition of Theory of Probability, considered the definitive version.
Died on 18 March in Cambridge, aged ninety-seven.