Confidence intervals for the means of multiple normal populations are often based on a hierarchical normal model. While commonly used interval procedures based on such a model have the nominal coverage rate on average across a population of groups, their actual coverage rate for a given group will be above or below the nominal rate, depending on the value of the group mean.

In this talk I present confidence interval procedures that have constant frequentist coverage rates and that make use of information about across-group heterogeneity, resulting in constant-coverage intervals that are narrower than standard t-intervals on average across groups.
These intervals are obtained by inverting Bayes-optimal frequentist tests, and so are “frequentist, assisted by Bayes” (FAB). I present some asymptotic optimality results and some extensions to other scenarios, such as linear regression and tensor analysis.