Who Should Be Afraid of the Jeffreys-Lindley Paradox?

Abstract

The article revisits the large n (sample size) problem as it relates to the Jeffreys-Lindley paradox to compare the frequentist, Bayesian, and likelihoodist approaches to inference and evidence. It is argued that what is fallacious is to interpret a rejection of as providing the same evidence for a particular alternative , irrespective of n; this is an example of the fallacy of rejection. Moreover, the Bayesian and likelihoodist approaches are shown to be susceptible to the fallacy of acceptance. The key difference is that in frequentist testing the severity evaluation circumvents both fallacies but no such principled remedy exists for the other approaches.