# J.B.S. Haldane Could Have Done Better

## TL;DR

This paper reevaluates J.B.S. Haldane's use of priors in a Bayesian hypothesis test, arguing that his choice was unreasonable and proposing a superior prior based on available information.

## Contribution

It introduces a more appropriate prior for Haldane's genetic example and clarifies his original motivations and assumptions.

## Key findings

- Haldane's flat prior was unreasonable given the context
- A superior prior can be derived from available information
- Haldane's main focus was on exploring parameter regions

## Abstract

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 genetic example (Haldane 1932, A note on inverse probability. Mathematical Proceedings of the Cambridge Philosophical Society, 28, 55-61.). As Haldane never followed up on these ideas, it is difficult to gauge his motivation and intentions. I argue that contrary to Haldane's stated intention of replacing flat priors with more reasonable assumptions, he actually chose in this example an unreasonable flat prior. Considering the information available to Haldane, I derive a superior prior and compare to Haldane's flat prior. Haldane's main intent with his article seems to have been to explore the different parameter regions of the binomial and the conjugate beta. Furthermore, I agree with Etz and Wagenmakers that Haldane serendipitously adopted a mixture prior comprising a point mass and smooth distribution in his genetic example.