Inference for Proportions in a 2 × 2 Contingency Table: HPD or not HPD?




Summary 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.