Bayesian Analysis

Objective Bayesian Inference for Bilateral Data

Cyr Emile M’lan and Ming-Hui Chen

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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.

Article information

Source
Bayesian Anal., Volume 10, Number 1 (2015), 139-170.

Dates
First available in Project Euclid: 28 January 2015

Permanent link to this document
https://projecteuclid.org/euclid.ba/1422468426

Digital Object Identifier
doi:10.1214/14-BA890

Mathematical Reviews number (MathSciNet)
MR3420900

Zentralblatt MATH identifier
1334.62193

Keywords
Bayes factor Dallal’s model Jeffreys’ prior Odds ratio Product tri- nomial distribution Reference prior Risk difference Risk ratio

Citation

M’lan, Cyr Emile; Chen, Ming-Hui. Objective Bayesian Inference for Bilateral Data. Bayesian Anal. 10 (2015), no. 1, 139--170. doi:10.1214/14-BA890. https://projecteuclid.org/euclid.ba/1422468426


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