  The paper presents an approach to the modelling of epistemic uncertainty in
Conjunction Data Messages (CDM) and the classification of conjunction events
according to the confidence in the probability of collision. The approach
proposed in this paper is based on the Dempster-Shafer Theory (DSt) of evidence
and starts from the assumption that the observed CDMs are drawn from a family
of unknown distributions. The Dvoretzky-Kiefer-Wolfowitz (DKW) inequality is
used to construct robust bounds on such a family of unknown distributions
starting from a time series of CDMs. A DSt structure is then derived from the
probability boxes constructed with DKW inequality. The DSt structure
encapsulates the uncertainty in the CDMs at every point along the time series
and allows the computation of the belief and plausibility in the realisation of
a given probability of collision. The methodology proposed in this paper is
tested on a number of real events and compared against existing practices in
the European and French Space Agencies. We will show that the classification
system proposed in this paper is more conservative than the approach taken by
the European Space Agency but provides an added quantification of uncertainty
in the probability of collision.
