  We derive Bayesian distances for all stars in the RV sample of Gaia DR2, and
use the statistical method of Schoenrich, Binney & Asplund(2012) to validate
the distances and test the Gaia parallaxes. In contrast to other methods, which
rely on special sources, our method directly tests the distances to all stars
in our sample. We find clear evidence for a near-linear trend of distance bias
f with distance s, proving a parallax offset delta p. On average, we find delta
p = -0.054 mas (parallaxes in Gaia DR2 need to be increased) when accounting
for the parallax uncertainty under-estimate in the Gaia set (delta p = -0.048
mas on the raw parallax errors) with negligible formal error and a systematic
uncertainty of about 0.006 mas. The value is in concordance with results from
asteroseismic measurements, but differs from the much lower bias found on
quasar samples. We further use our method to compile a comprehensive set of
quality cuts in colour, apparent magnitude, and astrometric parameters. Last,
we find that for this sample delta p appears to strongly depend on the parallax
uncertainty sigma_p (when including the additional 0.043 mas) with a
statistical confidence far in excess of 10\sigma and a proportionality factor
close to 1, though the dependence varies somewhat with sigma_p. Correcting for
the sigma_p dependence also resolves otherwise unexplained correlations of the
offset with the number of observation periods n_{vis} and ecliptic latitude.
Every study using Gaia DR2 parallaxes/distances should investigate the
sensitivity of their results on the parallax biases described here and - for
fainter samples - in the DR2 astrometry paper.
