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In Peter Hoff's "A first course in Bayesian statistical methods," he states:

"Most authors refer to intervals of high probability as 'credible intervals' as opposed to confidence intervals. Doing so fails to recognize that Bayesian intervals do have frequentist coverage, often being very close to the specified Bayesian coverage level (Welch and Peers, 1963; Hartigan 1966, Severini 1991)."

Is the use of "Bayesian confidence interval" in place of "Bayesian credible interval" accepted terminology? This nomenclature is useful for me, as most non-statistician collaborators and reviewers for the papers I coauthor get confused and are uncomfortable with the "credible interval" terminology, even when they don't have an issue with Bayesian inference itself.

Hoff PD. A first course in Bayesian statistical methods. New York: Springer; 2009 Jun 2.

Richard Hardy
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damarsh
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    It's a good point, if using a mostly non-informative prior, the Bayesian intervals can approximate frequentist results and/or have good frequentist operating characteristics. Of course, if using Bayesian methods this way, one could ask you why you don't just use the frequentist method. And if you're using the Bayesian interpretation of probability, it's the classic confidence interval that specifically doesn't make sense. – AdamO Jan 10 '22 at 22:22
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    To some, 'confidence' is an accommodation to frequentists who complain about using 'probability'. // Personally, I would not complain if a Bayesian used 'confidence', but I would wonder why. And for a Bayesian interval estimate of a parameter, I would use something like "95% posterior interval" or "95% Bayesian credible interval." // Some authors wish terminology were standard and act as if theirs is the standard, but attempting an honest survey across the board seems to reveal little consistency. – BruceET Jan 10 '22 at 22:27
  • Credible intervals "often" having frequentist coverage oversells it somewhat: it requires probability-matching priors, which are difficult to construct in practice because they are (generally) only implicitly defined as solutions to a nonlinear PDE involving the Fisher information. – Durden Jun 21 '23 at 04:53

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