J. B. S. Haldane's Contribution to the Bayes Factor Hypothesis Test

TL;DR

This paper explores the historical development of the Bayes factor hypothesis test, highlighting J. B. S. Haldane's significant yet underappreciated contribution involving mixture priors.

Contribution

It uncovers Haldane's 1932 proposal of mixture priors, suggesting he played a larger role in Bayes factor development than previously recognized.

Findings

Haldane proposed the use of mixture priors with a point mass.

Jeffreys was influenced by Haldane's work.

The development of the Bayes factor involved multiple key contributors.

Abstract

This article brings attention to some historical developments that gave rise to the Bayes factor for testing a point null hypothesis against a composite alternative. In line with current thinking, we find that the conceptual innovation - to assign prior mass to a general law - is due to a series of three articles by Dorothy Wrinch and Sir Harold Jeffreys (1919, 1921, 1923). However, our historical investigation also suggests that in 1932 J. B. S. Haldane made an important contribution to the development of the Bayes factor by proposing the use of a mixture prior comprising a point mass and a continuous probability density. Jeffreys was aware of Haldane's work and it may have inspired him to pursue a more concrete statistical implementation for his conceptual ideas. It thus appears that Haldane may have played a much bigger role in the statistical development of the Bayes factor than has hitherto been assumed.