In 2015, a colleague working as a satellite navigator came to Dr. Balch with a simple complaint, "My collision risk numbers don't make any sense." Dr. Balch looked into how collision risk was being calculated in conjunction analysis; that is, the analysis that a satellite navigator does when his satellite is projected to pass near another satellite or piece of debris. Dr. Balch quickly came to the conclusion that his colleague was right: The "probability" of collision numbers didn't make any sense. The problem was a phenomenon called probability dilution. As uncertainty in the satellite trajectory estimate increased, the risk of collision appeared to decrease. And the idea that noisier data make a system safer is foolish on its face. In fact, under ordinary operating conditions, probability dilution would lead an unwary satellite navigator to under-predict their collision risk exposure by several orders of magnitude.
In 2016, Dr. Balch presented a paper detailing his early work on the problem. Since then, we have developed a proprietary algorithm for computing collision risk in rigorous frequentist terms. This algorithm delivers a collision risk metric that is statistically reliable in the same way that the ellipse (or ellipsoid) overlap approach is, while also being flexible in the same way that "probability" of collision was supposed to be. Our algorithm is also more efficient than ellipse overlap, in terms of its ability to discriminate between conjunctions that will or will not result in a collision. Moreover, this work led to a break-through in our general understanding of epistemic uncertainties resulting from statistical inference. Representing such uncertainties using a probability distribution results in a phenomenon that can be aptly described as false confidence, in which particular propositions (e.g., "this satellite conjunction will not result in a collision") are guaranteed to be assigned a high confidence value, regardless of whether or not they are true. Probability dilution in satellite conjunction analysis is a manifestation of this more general defect. Dr. Balch published these findings (with co-authors Ryan Martin and Scott Ferson) in the Proceedings of the Royal Society A. R-Scripts for producing Figures One, Two, and Three from the 2019 RSPA paper, Satellite conjunction analysis and the false confidence theorem, are attached below. |

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