Citation Link: https://doi.org/10.1007/s13171-023-00321-x
The Case of the Jeffreys-Lindley-paradox as a Bayes-frequentist Compromise: A Perspective Based on the Rao-Lovric-Theorem
Publication Type
Article
Author(s)
Subjects
Frequentist inference
Bayesian probability
Bayes' theorem
Bayes factor
Inference
Mathematics
Mathematical economics
Frequentist probability
Bayesian inference
Statistical inference
Prior probability
Null hypothesis
Econometrics
Null (SQL)
Statistics
Computer science
Artificial intelligence
Date Issued
2023
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.
Owning collection