title: Objective Bayesian Inference for Bilateral Data.
abstract: This paper presents three objective Bayesian methods for analyzing bilateral data under Dallal's model and the saturated model. Three parameters are of interest, namely, the risk difference, the risk ratio, and the odds ratio. We derive Jeffreys' prior and Bernardo's reference prior associated with the three parameters that characterize Dallal's model. We derive the functional forms of the posterior distributions of the risk difference and the risk ratio and discuss how to sample from their posterior distributions. We demonstrate the use of the proposed methodology with two real data examples. We also investigate small, moderate, and large sample properties of the proposed methodology and the frequentist counterpart via simulations.
authors.affiliation: William E. Wecker Associates, Inc., 270 E Simpson Avenue, Jackson, WY 83001, USA.
authors.forename: Cyr Emile
authors.initials: CE
authors.lastname: M'lan
authors.affiliation: Department of Statistics, University of Connecticut, Storrs, CT 06269, USA.
authors.forename: Ming-Hui
authors.initials: MH
authors.lastname: Chen
keywords: Bayes factor; Dallal’s model; Jeffreys’ prior; Odds ratio; Product trinomial distribution; Reference prior; Risk difference; Risk ratio