Confidence in confidence distributions!

Abstract

The recent article `Satellite conjunction analysis and the false confidence theorem' (Balch, Martin, and Ferson, 2019, Proceedings of the Royal Society, Series A) points to certain difficulties with Bayesian analysis when used for models for satellite conjuntion and ensuing operative decisions. Here we supplement these previous analyses and findings with further insights, uncovering what we perceive of as being the crucial points, explained in a prototype setup where exact analysis is attainable. We also show that a different and frequentist method, involving confidence distributions, is free of the false confidence syndrome.

5 pages, 2 figures. Statistical Research Report, Department of Mathematics, University of Oslo, February 2020, here arXiv'd February 2026. Published in Proceedings of the Royal Society, Series A, 2020, vo. 476, at this url: royalsocietypublishing.org/rspa/article/476/2237/20190781/56889