The Jeffreys–Lindley paradox, a pivotal issue in statistical inference, arises from the divergence between frequentist and Bayesian methodologies, particularly in the context of large sample sizes. Pioneered by Harold Jeffreys and later explored by Dennis Lindley, this paradox highlights fundamental disagreements in hypothesis testing, specifically when evaluating point null hypotheses in a Gaussian model with a known variance. The paradox becomes apparent when the p-value, a crucial frequentist measure, and the Bayes factor, a fundamental Bayesian measure, lead to conflicting decisions as the sample size increases.

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Jeffreys-Lindley Paradox

  • Miodrag Lovric

摘要

The Jeffreys–Lindley paradox, a pivotal issue in statistical inference, arises from the divergence between frequentist and Bayesian methodologies, particularly in the context of large sample sizes. Pioneered by Harold Jeffreys and later explored by Dennis Lindley, this paradox highlights fundamental disagreements in hypothesis testing, specifically when evaluating point null hypotheses in a Gaussian model with a known variance. The paradox becomes apparent when the p-value, a crucial frequentist measure, and the Bayes factor, a fundamental Bayesian measure, lead to conflicting decisions as the sample size increases.