Bio: Jay Bartroff joined the University of Texas at Austin's Statistics & Data Sciences Department in January 2022 as Professor and Associate Chair. Prior to that he was Professor of Mathematics and Vice-Chair for Statistics at the University of Southern California for 15 years. Before that he was an NSF postdoc in the Stanford Statistics Department, following his PhD at Caltech and his undergraduate degree at U.C. Berkeley. His research interests include sequential analysis, multiple testing, Stein's method, and a variety of biomedical applications including clinical trial design and methods for wearable alcohol biosensors. Jay's research has been supported by the NSF, NIH, FDA, and NSA. His publications include a textbook on sequential methods coauthored with Lai and Shih, published by Springer.
Abstract: We present an efficient method of calculating exact confidence intervals for the hypergeometric number of successes. The method inverts minimum-width acceptance intervals after shifting them to make their endpoints nondecreasing while preserving their level. The resulting set of confidence intervals achieves minimum possible average width, and even in comparison with confidence sets not required to be intervals it attains the minimum possible cardinality most of the time, and always within 1. The method compares favorably with existing methods not only in the size of the intervals but also in the time required to compute them. A similar approach can be taken for optimal confidence intervals for an unknown population size, such as in capture-recapture problems.