Journal for History of Mathematics (한국수학사학회지)

The Korean Society for History of Mathematics (한국수학사학회)
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Bayes' Excuse for the Introduction of Prior Uniform Distribution

베이즈의 사전균등분포의 도입에 대한 변명

  • Received : 2022.11.05
  • Accepted : 2022.12.21
  • Published : 2022.12.31
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Abstract

This study discusses in terms of historical genesis whether it is reasonable for Bayes to introduce a prior uniform distribution. In this study, we try to analyze the way he dealt with postulates, lemmas, and propositions in Bayes' essay and to understand its characteristics. The results of the study show that Bayes used random variables for two parameters and that the two random variables were converted to each other through cumulative distribution. Furthermore, it is revealed that the introduction of prior uniform distribution can be justified by this way.

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Acknowledgement

이 연구는 2021학년도 영남대학교 학술연구조성비에 의한 것임.

References

  1. T. BAYES, An Essay toward Solving a Problem in the Doctrine of Chances, Philosophical Transactions of the Royal Society of London 53 (1763), 370-418.
  2. A. I. DALE, A History of Inverse Probability from Thomas Bayes to Karl Pearson, Springer, 1999.
  3. A. W. F. EDWARDS, Commentary on the arguments of Thomas Bayes, Scandinavian Journal of Statistics 5 (1978), 116-118.
  4. D. A. GILLIES, Was Bayes a Bayesian?, Historia Mathematica 14 (1987), 325-346. https://doi.org/10.1016/0315-0860(87)90065-6
  5. I. HACKING, The Emergence of Probability, Cambridge University Press, 1975.
  6. A. HALD, A History of Mathematical Statistics from 1750 to 1930, John Wiley & 5. Sons, 1998.
  7. V. J. KATZ, A History of Mathematics, Harper Collins College Publishers, 1993.
  8. S. B. MCGRAYNE, The Theory that Would not Die, Yale University Press, 2011. (translated by Lee, G. S., 2013).
  9. G. SHAFER, Bayes's Two Arguments for the Rule of Conditioning, The Annals of Statistics 10 (1982), 1078-1089. https://doi.org/10.1214/aos/1176345974
  10. S. M. STIGLER, Who discovered Bayes's Theorem?, The American Statistician 37 (1983), 290-296. https://doi.org/10.2307/2682766
  11. S. M. STIGLER, The History of Statistics, Harvard University Press, 1986. (translated by Cho, J. G, 2002).