On the Authentic Notion, Relevance, and Solution of the Jeffreys-Lindley Paradox in the Zettabyte Era

Abstract

The Jeffreys-Lindley paradox is the most quoted divergence between the frequentist and Bayesian approaches to statistical inference. It is embedded in the very foundations of statistics and divides frequentist and Bayesian inference in an irreconcilable way. This paradox is the Gordian Knot of statistical inference and Data Science in the Zettabyte Era. If statistical science is ready for revolution confronted by the challenges of massive data sets analysis, the first step is to finally solve this anomaly. For more than sixty years, the Jeffreys-Lindley paradox has been under active discussion and debate. Many solutions have been proposed, none entirely satisfactory. The Jeffreys-Lindley paradox and its extent have been frequently misunderstood by many statisticians and non-statisticians. This paper aims to reassess this paradox, shed new light on it, and indicates how often it occurs in practice when dealing with Big data.