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Biometrika 1972 59(3):581-589; doi:10.1093/biomet/59.3.581
© 1972 by Biometrika Trust
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Bayesian methods for binomial data

T. LEONARD*

University College London

*Now at University of Warwick.

A Bayesian procedure is obtained for the simultaneous estimation of the parameters of m binomial distributions. The method uses logistic transformations for the parameters and an exchangeable prior distribution. Information is combined between the binomial distributions to obtain estimates which, under certain circumstances, will be superior to the usual proportions. This paper is intended as a forerunner to a more general theory for the analysis of nonlinear models.

Key Words: Bayesian estimation of binomial parameters • Exchangeable prior distributions • Logistic models • Shrinkage of estimates • Discrete date • Contingency tables


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