Nonparametric predictive comparison of proportions

We use the lower and upper predictive probabilities from Coolen [1998. Low structure imprecise predictive inference for Bayes’ problem. Statist. Probab. Lett. 36, 349–357] to compare future numbers of successes in Bernoulli trials for different groups. We consider both pairwise and multiple comparisons. These inferences are in terms of lower and upper probabilities that the number of successes in m future trials from one group exceeds the number of successes in m future trials from another group, or such numbers from all other groups. We analyse these lower and upper probabilities via application to two data sets from the literature, and discuss the imprecision in relation to m.