Anomalous orbits are found when minimum-chi^{2} estimation is applied tosynthetic Gaia data for orbits with astrometric signatures comparable to thesingle-scan measurement error (Pourbaix 2002). These orbits are nearlyparabolic, edge-on, and their major axes align with the line-of-sight to theobserver. Such orbits violate the Copernican principle (CPr) and as such couldbe rejected. However, the preferred alternative is to develop a statisticaltechnique that incorporates the CPr as a fundamental postulate. This can beachieved in a Bayesian context by defining a Copernican prior. Pourbaix'sanomalous orbits then no longer arise. Instead, the selected orbits have asomewhat higher chi^{2} but do not violate the CPr. The problem of detecting aweak additional orbit in an astrometric binary with a well-determined orbit isalso treated.
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