  Anomalous orbits are found when minimum-chi^{2} estimation is applied to
synthetic Gaia data for orbits with astrometric signatures comparable to the
single-scan measurement error (Pourbaix 2002). These orbits are nearly
parabolic, edge-on, and their major axes align with the line-of-sight to the
observer. Such orbits violate the Copernican principle (CPr) and as such could
be rejected. However, the preferred alternative is to develop a statistical
technique that incorporates the CPr as a fundamental postulate. This can be
achieved in a Bayesian context by defining a Copernican prior. Pourbaix's
anomalous orbits then no longer arise. Instead, the selected orbits have a
somewhat higher chi^{2} but do not violate the CPr. The problem of detecting a
weak additional orbit in an astrometric binary with a well-determined orbit is
also treated.
