J. B. S. Haldane’s contribution to the Bayes factor hypothesis test.

*(English)*Zbl 1381.62009Summary: 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 D. Wrinch and H. Jeffreys [Phil. Mag. (6) 38, 715–732 (1919; JFM 47.0486.03); ibid. 42, 369–390 (1921; JFM 48.1129.04); ibid. 45, 369–390 (1923; doi:10.1080/14786442308634125)]. However, our historical investigation also suggests that in 1932, J. B. S. Haldane [Proc. Camb. Philos. Soc. 28, 55–61 (1932; Zbl 0003.35602)] 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.

##### MSC:

62-03 | History of statistics |

01A60 | History of mathematics in the 20th century |

62F15 | Bayesian inference |