Satellite conjunction analysis and the false confidence theorem

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.