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.

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