On the Jeffreys-Lindley's paradox

TL;DR

This paper examines the Jeffreys-Lindley's paradox, highlighting its implications for the foundations of classical and Bayesian statistics, and critically evaluates existing resolutions from a philosophical perspective.

Contribution

It provides a comprehensive analysis of the paradox's dual interpretation and assesses prior proposed solutions, emphasizing its foundational significance.

Findings

The paradox illustrates fundamental differences between Bayesian and frequentist approaches.

Existing resolutions often overlook the paradox's philosophical implications.

The paradox underscores challenges in using improper priors for hypothesis testing.

Abstract

This paper discusses the dual interpretation of the Jeffreys--Lindley's paradox associated with Bayesian posterior probabilities and Bayes factors, both as a differentiation between frequentist and Bayesian statistics and as a pointer to the difficulty of using improper priors while testing. We stress the considerable impact of this paradox on the foundations of both classical and Bayesian statistics. While assessing existing resolutions of the paradox, we focus on a critical viewpoint of the paradox discussed by Spanos (2013) in Philosophy of Science.