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 increased, the risk of collision appeared to decrease. And the idea that worse data make a system safer is foolish on its face.
In 2016, Dr. Balch presented a paper detailing his early work on the problem. Since then, we have developed a full-scale algorithm for computing collision risk in rigorous frequentist terms. Moreover, this work led to a break-through in our general understanding of epistemic uncertainties resulting from statistical inference. Specifically, we found that representing such uncertainties probabilistically results in a phenomenon that can be aptly described as false confidence. Probability dilution in satellite conjunction analysis is a manifestation of this more general difficulty. Dr. Balch has written a paper with co-authors Ryan Martin and Scott Ferson detailing these findings. It is entitled "Satellite Conjunction Analysis and the False Confidence Theorem," currently under peer review. R-Scripts for producing the Figures One, Two, and Three from "Satellite Conjunction Analysis and the False Confidence Theorem" are attached below. |

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