Satellite conjunction assessment: Statistical space oddity?

Satellite conjunctions involving "near misses" of space objects are becoming increasingly likely. One approach to risk analysis for them involves the computation of the collision probability, but this has been regarded as having some counter-intuitive properties, and its meaning as a probability is unclear. We formulate an alternative approach based on a simple statistical model that allows highly accurate inference on the miss distance between the two objects, show that this provides a close approximation to a default Bayesian approach, illustrate the method with a case study, and give Monte Carlo results to show its excellent performance.