A Bayesian homogeneity test for comparing Poisson populations

Abstract

For a wide class of daily applications in industrial quality control, there may be interest in comparing several Poisson means. A large catalogue of frequentist procedures for this hypothesis testing problem is available. However, some common drawbacks of them are their low power, interpretation of the (Formula presented.) -values for multiple comparison, among many others. In this paper, we present a unified Bayesian approach to the problem based on a model selection approach developed using a product partition clustering model. The posterior probabilities for models obtained are derived directly from the associated Bayes factors which are calculated by considering a simple hierarchical prior structure which has a quasi–closed form, easily computed by numerical procedures. This approach constitutes a readily implementable alternative to frequentist multiple testing procedures where uncertainty concerning all possible “types of homogeneity” is ignored. The proposed methodology allows for an intuitive interpretation based directly on posterior probabilities of the partitions involved in the testing problem. We illustrate its performance with three real data sets.