Title: Satellite conjunction analysis and the false confidence theorem,
Abstract: Satellite conjunction analysis is the assessment of collision risk during a
close encounter between a satellite and another object in orbit. A
counterintuitive phenomenon has emerged in the conjunction analysis literature:
probability dilution, in which lower quality data paradoxically appear to
reduce the risk of collision. We show that probability dilution is a symptom of
a fundamental deficiency in epistemic probability distributions. In
probabilistic representations of statistical inference, there are always false
propositions that have a high probability of being assigned a high degree of
belief. We call this deficiency false confidence. In satellite conjunction
analysis, it results in a severe and persistent underestimation of collision
risk exposure.
We introduce the Martin--Liu validity criterion as a benchmark by which to
identify statistical methods that are free from false confidence. If expressed
using belief functions, such inferences will necessarily be non-additive. In
satellite conjunction analysis, we show that $K \sigma$ uncertainty ellipsoids
satisfy the validity criterion. Performing collision avoidance maneuvers based
on ellipsoid overlap will ensure that collision risk is capped at the
user-specified level. Further, this investigation into satellite conjunction
analysis provides a template for recognizing and resolving false confidence
issues as they occur in other problems of statistical inference.