Confidence in confidence distributions!

TL;DR

This paper compares Bayesian and frequentist methods for satellite conjunction analysis, demonstrating that confidence distributions avoid the false confidence issues associated with Bayesian approaches.

Contribution

It introduces confidence distributions as a robust frequentist alternative to Bayesian methods in satellite conjunction analysis, addressing false confidence problems.

Findings

Confidence distributions are free from false confidence syndrome.

Bayesian methods exhibit issues with false confidence in this context.

Frequentist confidence distributions provide reliable inference for satellite conjunctions.

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.