In this paper a Bayesian approach is applied to the correlated binomial model, CB (n, p, ρ), proposed by Luceño (Comput. Statist. Data Anal. 20 (1995) 511-520). The data augmentation scheme is used in order to overcome the complexity of the mixture likelihood. MCMC methods, including Gibbs sampling and Metropolis within Gibbs, are applied to estimate the posterior marginal for the probability of success p and for the correlation coefficient ρ. The sensitivity of the posterior is studied taking into account several reference priors and it is shown that the posterior characteristics appear not to be influenced by these prior distributions. The article is motivated by a study of plant selection.

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This paper develops an empirical Bayesian analysis for the von Mises distribution, which is the most useful distribution for statistical inference of angular data. A two‐stage informative prior is proposed, in which the hyperparameter is obtained from the data in one of the stages. This empirical or approximate Bayes inference is justified on the basis of maximum entropy, and it eliminates the modified Bessel functions. An example with real data and a realistic prior distribution for the regression coefficients is considered via a Metropolis‐within‐Gibbs algorithm.

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