Overcoming Dilution of Collision Probability in Satellite Conjunction Analysis via Confidence Distribution

In satellite conjunction analysis, dilution of collision probability has been recognized as a significant deficiency of probabilistic inference. A recent study identified the false confidence problem as another limitation and suggested a possible causal link between the two, arguing that addressing false confidence could be necessary to prevent dilution of collision probability. However, this paper clarifies the distinction between probability dilution and false confidence by investigating a confidence distribution (CD) with a point mass at zero. Although the point mass in CD has often been perceived as paradoxical, we demonstrate that it plays an essential role in satellite conjunction analysis by capturing the uncertainty in the data. Consequently, the CD resolves the probability dilution of probabilistic inference and the ambiguity in Neymanian confidence intervals, while addressing the false confidence for the hypothesis of interest in satellite conjunction analysis. Furthermore, the confidence derived from the CD offers a direct interpretation as a p-value for hypothesis testing related to collision risk.