Post-data Power Estimation

Abstract

Under a robust Bayesian framework, we study the properties of observed power and p-values as post-data evidences in hypotheses testing problems. For the one-sided hypotheses testing problem for the normal mean, both measures correspond to MLE for functions of unknown parameters. We show that for a reasonable families of priors, MLE tends to be extreme in some sense. Implications on the controversies of ir/reconcilability of p-values in Berger and Delampady (1987) and Casella and Berger (1987) will also be addressed.