Abstract
We discuss a rule for selection of prior distributions in a hierarachical Bayes model for inference of binomial parameters. Attention is particularly paid to prior distributions defined in [0, 1] such as the beta and logistic-normal distributions. We show that when employing the beta distributions, inference of the binomial parameters and hyperparameters is sensitive to selection of hyperprior distributions and that on the other hand, when employing the logistic-normal distribution, a Bayesian update strongly emerge on the inference and consequently, the inference becomes robust against the selection of the hyperprior distributions. We conclude that in order to obtain a significant Bayesian update for the binomial parameter inference in the hierarchical Bayes model, the logistic-normal prior distribution, rather than the beta prior distribution, should be chosen.
