Comment: Fuzzy and Bayesian p-Values and u-Values
It is a pleasure to discuss this fascinating paper, which presents a new way to express uncertainty in p-values for composite null hypotheses. I particularly like the graphical display above equation (1.2). I have some brief comments about the confidence interval for binomial proportions and then some more to say about the relationship to Bayesian p-values. Geyer and Meeden’s fuzzy p-values are related to Bayesian p-values in that they recognize the uncertainty inherent in testing a composite null hypothesis. Fuzzy and Bayesian p-values also both allow for test statistics to depend on missing data, latent data and parameters, as well as on observed data. There is the potential to generalize these ideas to graphical test statistics and connect to exploratory data analysis.