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

  title={J. B. S. Haldane's Contribution to the Bayes Factor Hypothesis Test},
  author={Alexander Etz and Eric-Jan Wagenmakers},
  journal={arXiv: Other Statistics},
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… 

Figures from this paper

J.B.S. Haldane Could Have Done Better
In a review on the contribution of J.B.S. Haldane to the development of the Bayes factor hypothesis test (arXiv:1511.08180), Etz and Wagenmakers focus on Haldane's proposition of a mixture prior in a
The Bayesian Methodology of Sir Harold Jeffreys as a Practical Alternative to the P Value Hypothesis Test
Harold Jeffreys’s Bayes factor methodology as implemented in the open-source software JASP is explained and its practical relevance is showcased with two examples.
History and Nature of the Jeffreys-Lindley Paradox
The Jeffreys-Lindley paradox exposes a rift between Bayesian and frequentist hypothesis testing that strikes at the heart of statistical inference. Contrary to what most current literature suggests,
Bayes factors for research workers
  • A. Ly
  • Computer Science
  • 2018
This dissertation advocate the use of Bayes factors in empirical research to replace or complement standard null hypothesis tests based on p-values, and implemented them in Jeffreys’s Amazing Statistics Program, JASP, which is freely available and open-source.
A Parsimonious Tour of Bayesian Model Uncertainty
This survey focuses on non-asymptotic out-of-sample performance of Bayesian model selection and averaging techniques, and describes recent extensions to wider classes of probabilistic frameworks including high-dimensional, unidentifiable, or likelihood-free models.
A review of issues about null hypothesis Bayesian testing.
It is argued that posterior model probabilities should be given more emphasis than Bayes factors, because only the former provide direct answers to the most common research questions under consideration.
Bayesian inference for psychology. Part II: Example applications with JASP
This part of this series introduces JASP (http://www.jasp-stats.org), an open-source, cross-platform, user-friendly graphical software package that allows users to carry out Bayesian hypothesis tests for standard statistical problems.
Popper’s Falsification and Corroboration from the Statistical Perspectives
The likelihood is introduced and its recent extension is highlighted via a discussion of two well-known logical fallacies in order to highlight that its lack of recognition may have led to unnecessary confusion in the discourse about falsification and corroboration of hypotheses.
Analysis of Bayesian posterior significance and effect size indices for the two-sample t-test to support reproducible medical research
  • Riko Kelter
  • Medicine
    BMC Medical Research Methodology
  • 2020
An extensive simulation study is conducted to compare common Bayesian significance and effect measures which can be obtained from a posterior distribution for one of the most important statistical procedures in medical research and in particular clinical trials, the two-sample Student's (and Welch’s) t-test.
Informed Bayesian t-Tests
A flexible t-prior for standardized effect size is proposed that allows computation of the Bayes factor by evaluating a single numerical integral and two measures for informed prior distributions that quantify the departure from the objective Bayes factors desiderata of predictive matching and information consistency are proposed.


The Bayesian Controversy in Statistical Inference
It appears to me that the experience of actuaries in the formation of categories as, for instance, by occupational group, as abstainers or non-abstainers, and so on, can be highly relevant to the effective use of Bayes's theorem in many wider contexts; and an examination of the principles underlying the Formation of categories should improve the insight into problems of statistical inference in general.
A History of Likelihood
The present paper traces the history of both likelihood and the method of maximum likelihood; it is essential to keep the distinction between the two clearly in mind.
Harold Jeffreys’s Theory of Probability Revisited
The fundamental aspects of this reference work are pointed out, especially the thorough coverage of testing problems and the construction of both estimation and testing noninformative priors based on functional divergences.
Using Bayes to get the most out of non-significant results
It is argued Bayes factors allow theory to be linked to data in a way that overcomes the weaknesses of the other approaches, and provides a coherent approach to determining whether non-significant results support a null hypothesis over a theory, or whether the data are just insensitive.
Studies in the history of probability and statistics: XI. Daniel Bernoulli on maximum likelihood
1. Almost as soon as the calculus of probabilities began to take a definite shape mathematicians were concerned with the use of probabilistic ideas in reconciling discrepant observations. James
Power-Expected-Posterior Priors for Variable Selection in Gaussian Linear Models
The result is that in practice the power-expected-posterior (PEP) methodology is sufficiently insensitive to the size n* of the training sample, due to PEP's unit-information construction, that one may take n* equal to the full-data sample size n and dispense with training samples altogether.
Inverse probability and the use of Likelihood
It is shown that this type of argument can be carried out with exactitude in a usefully large class of cases by means of conceptions somewhat different from those of the classical theory of probability.
The expected demise of the Bayes factor
When did Bayesian inference become "Bayesian"?
While Bayes’ theorem has a 250-year history and the method of inverse probability that flowed from it dominated statistical thinking into the twentieth century, the adjective “Bayesian” was not part