Sankhya: The Indian Journal of Statistics

2001, Volume 63, Series B, Pt. 3, pp. 270--285

BAYESIAN ANALYSIS OF CORRELATED PROPORTIONS

By

MARIA KATERI, *University of Ioannina*

TAKIS PAPAIOANNOU, *University of Pireaus*

and

PETROS DELLAPORTAS, *Athens University of Economics and Business*

*SUMMARY.* In this paper we present a
Bayesian analysis of 2 X 2 contingency tables,
corresponding to matched pairs designs. We provide Bayes and
empirical Bayes estimates for the cell probabilities of these
tables as well as the Bayes factor for testing the equality of
correlated proportions. The approximate highest posterior
density (HPD) region for the difference of the correlated
proportions is also obtained. Finally, a Bayesian variable
selection approach is applied to a hierarchical logistic
regression model and posterior model probabilities for the
equality of the correlated proportions are estimated. This
latter approach has the feature that the posterior model
probabilities depend on the main-diagonal cells.

*AMS (1991) subject classification.* Primary 62F15; secondary 62H17.

*Key words and phrases.* Bayes factor, empirical bayes,
Gibbs variable selection, hierarchical logistic regression,
highest posterior density region, matched pairs, Markov chain
Monte Carlo.