Objective Bayesian Inference for Bilateral Data

TL;DR

This paper develops three objective Bayesian methods for analyzing bilateral data under specific models, deriving priors and posterior distributions for key parameters, and validating the approach with real data and simulations.

Contribution

It introduces new objective Bayesian approaches for bilateral data analysis, including derivation of priors and posterior distributions for risk measures under Dallal's and saturated models.

Findings

Derived Jeffreys' and Bernardo's reference priors for the models

Provided methods for sampling from posterior distributions of risk difference and ratio

Validated the methods with real data and simulation studies

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.