2016/12/25 by Chaoyu Yu, Peter D. Hoff, Yu, Chaoyu +1 · 7 citations
Decision Sciences · Mathematics · #62C12 #FOS: Computer and information sciences #Methodology (stat.ME) #Optimal Experimental Design Methods #Statistical Methods and Bayesian Inference #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.1612.08287
openalex publication_date 2016/12/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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. Alternatively, a coverage rate that is constant as a function of a group's mean can be simply achieved by using a standard t-interval, based on data only from that group. The standard t-interval, however, fails to share information across the groups and is therefore not adaptive to easily obtained information about the distribution of group-specific means. In this article we construct confidence intervals that have a constant frequentist coverage rate 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. Such intervals are constructed by inverting biased tests for the mean of a normal population. Given a prior distribution on the mean, Bayes-optimal biased tests can be inverted to form Bayes-optimal confidence intervals with frequentist coverage that is constant as a function of the mean. In the context of multiple groups, the prior distribution is replaced by a model of across-group heterogeneity. The parameters for this model can be estimated using data from all of the groups, and used to obtain confidence intervals with constant group-specific coverage that adapt to information about the distribution of group means.