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2024 Defining a Credible Interval Is Not Always Possible with “Point-Null” Priors: A Lesser-Known Correlate of the Jeffreys-Lindley Paradox
Harlan Campbell, Paul Gustafson
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Bayesian Anal. Advance Publication 1-54 (2024). DOI: 10.1214/23-BA1397

Abstract

In many common situations, a Bayesian credible interval will be, given the same data, very similar to a frequentist confidence interval, and researchers will interpret these intervals in a similar fashion. However, no predictable similarity exists when credible intervals are based on model-averaged posteriors whenever one of the two nested models under consideration is a so called “point-null”. Not only can this model-averaged credible interval be quite different than the frequentist confidence interval, in some cases it may be undefined. This is a lesser-known correlate of the Jeffreys-Lindley paradox and is of particular interest given the popularity of the Bayes factor for testing point-null hypotheses.

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Harlan Campbell. Paul Gustafson. "Defining a Credible Interval Is Not Always Possible with “Point-Null” Priors: A Lesser-Known Correlate of the Jeffreys-Lindley Paradox." Bayesian Anal. Advance Publication 1 - 54, 2024. https://doi.org/10.1214/23-BA1397

Information

Published: 2024
First available in Project Euclid: 17 July 2023

Digital Object Identifier: 10.1214/23-BA1397

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