Before revision:  The intervals are centered at the usual  empirical Bayes estimator, but use a larger critical value to account for the effect of shrinkage. We show that in this setting, parametric EBCIs based on the assumption that the means are normally distributed (Morris, 1983) can have coverage substantially below the nominal level when the normality assumption is violated, and we derive a simple rule of thumb for gauging the potential coverage distortion.
After revision:  The intervals are centered at the usual empirical Bayes estimator, but use a critical value accounting for shrinkage. Parametric EBCIs that assume a normal distribution for the means (Morris, 1983) can have coverage substantially below the nominal level when the normality assumption is violated, and we derive a simple rule of thumb for gauging the potential coverage distortion.