This note develops modifications of the chi-square and maximum likelihood tests for the homogeneity of the success probabilities pi of k binomial variables when the number of trials, ni, vary widely and all pi are small. With N = [Sigma]ni, and letting the ni/N approach fixed fractions, [gamma]i...

There are several approaches to setting priors in Bayesian data analysis. Some attempt to minimize the impact of the prior on the posterior, allowing the data to "speak for themselves," or to provide Bayesian inferences that have good frequentist properties. In contrast, this note focuses on...