A canonical moment approach to the analysis of binomial mixtures

Mixture of binomial distributions are often considered as a flexible model for count data which can account for sources of heterogeneity in the population and also as a device to deal with exchangeable binary sequences. For instance they are routinely used in a wide range of applied context such as psychological testing as well as in industrial sampling or in toxicological experiments, just to mention some of them. Different param- eterizations are presented in order to build up a convenient methodological framework for developing a default Bayesian analysis when no parametric form of the mixing distribu- tion is assumed. This approach can be exploited for estimation and prediction purposes. Also in this paper a first attempt to investigate its usefulness in model selection problems is carried out.