Abstract
Highest posterior density intervals are common in Bayesian inference, but as noted by Agresti and Min (2005, Biometrics 61, 515-523) they are not invariant under transformations. Agresti and Min suggested central or "tail" intervals as preferable in the context of the relative risk and odds ratio. A modification to this is proposed for extreme outcomes, as invariance is maintained when replacing central intervals by one-sided intervals. Bayes-Laplace priors for the binomial parameters appear preferable here, compared to Jeffreys priors, contrary to Agresti and Min's suggestion based on frequentist coverage.
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