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

By Alexander Etz, Eric-Jan Wagenmakers. 2015

118 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Management Science and Operations Research, Statistics and Probability

View Paper: https://www.semanticscholar.org/paper/e421d97f044959a2ac9b8b6247bc3b2c6a76c9c6

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Citations in the corpus

The JASP guidelines for conducting and reporting a Bayesian analysis (2019, methodology): “Hypothesis testing The principled approach to Bayesian hypothesis testing is by means of the Bayes factor (e.g., Etz & Wagenmakers, 2017; Jeffreys, 1939; Ly, Verhagen, & Wagenmakers, 2016; Wrinch & Jeffreys, 1921).”
bridgesampling: An R Package for Estimating Normalizing Constants (2017, unknown): “(3) The change in odds brought about by the data is given by the ratio of the marginal likelihoods of the models and is known as the Bayes factor (Jeﬀreys 1961; Kass and Raftery 1995; Etz and Wagenmakers 2017).”
A Tutorial on Conducting and Interpreting a Bayesian ANOVA in JASP (2019, unknown): “…the relative predictive performance of the rival models, that is, the change in relative model plausibility that is brought about by the data (Etz & Wagenmakers, 2017; Jeffreys, 1939; Kass & Raftery, 1995; Wrinch & Jeffreys, 1921): When the Bayes factor BF10 equals 20, the observed data are…”
E-values: Calibration, combination and applications (2019, unknown): “In Figure 3 we report the results for the closures of five methods, three of them producing p-values (Simes’s, Bonferroni’s, and Fisher’s) and two producing e-values (average and product); see Section 5 for self-contained descriptions of the last two methods (Algorithms 1 and 2). For the methods pro”