Defining a credible interval is not always possible with "point-null” priors: A lesser-known consequence of the Jeffreys-Lindley paradox
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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 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 undefinable. This is a lesser-known consequence 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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