title: Inference for proportions in a 2 x 2 contingency table: HPD or not HPD?
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.
authors.affiliation: ARC Centre for Complex Dynamic Systems and Control, University of Newcastle, NSW 2308, Australia. frank.tuyl@newcastle.edu.au
authors.forename: Frank
authors.initials: F
authors.lastname: Tuyl
authors.forename: Richard
authors.initials: R
authors.lastname: Gerlach
authors.forename: Kerrie
authors.initials: K
authors.lastname: Mengersen
mesh_terms: D001499:Bayes Theorem; D001699:Biometry / Q000379:methods*; D016017:Odds Ratio; D012306:Risk; D013223:Statistics as Topic / Q000379:methods*