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The Case of the Jeffreys-Lindley-paradox as a Bayes-frequentist Compromise: A Perspective Based on the Rao-Lovric-Theorem

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  • Riko Kelter

    (University of Siegen)

Abstract

Testing a precise hypothesis can lead to substantially different results in the frequentist and Bayesian approach, a situation which is highlighted by the Jeffreys-Lindley paradox. While there exist various explanations why the paradox occurs, this article extends prior work by placing the less well-studied point-null-zero-probability paradox at the center of the analysis. The relationship between the two paradoxes is analyzed based on accepting or rejecting the existence of precise hypotheses. The perspective provided in this paper aims at demonstrating how the Bayesian and frequentist solutions can be reconciled when paying attention to the assumption of the point-null-zero-probability paradox. As a result, the Jeffreys-Lindley-paradox can be reinterpreted as a Bayes-frequentist compromise. The resolution shows that divergences between Bayesian and frequentist modes of inference stem from (a) accepting the existence of a precise hypothesis or not, (b) the assignment of positive measure to a null set and (c) the use of unstandardized p-values or p-values standardized to tail-area probabilities.

Suggested Citation

  • Riko Kelter, 2024. "The Case of the Jeffreys-Lindley-paradox as a Bayes-frequentist Compromise: A Perspective Based on the Rao-Lovric-Theorem," Sankhya A: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 86(1), pages 337-363, February.
    • Handle: RePEc:spr:sankha:v:86:y:2024:i:1:d:10.1007_s13171-023-00321-x
    DOI: 10.1007/s13171-023-00321-x
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    References listed on IDEAS

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    1. Sander Greenland, 2019. "Valid P-Values Behave Exactly as They Should: Some Misleading Criticisms of P-Values and Their Resolution With S-Values," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 106-114, March.
    2. Ronald L. Wasserstein & Allen L. Schirm & Nicole A. Lazar, 2019. "Moving to a World Beyond “p," The American Statistician, Taylor & Francis Journals, vol. 73(S1), pages 1-19, March.
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