  We infer distances and their asymmetric uncertainties for two million stars
using the parallaxes published in the Gaia DR1 (GDR1) catalogue. We do this
with two distance priors: A minimalist, isotropic prior assuming an
exponentially decreasing space density with increasing distance, and an
anisotropic prior derived from the observability of stars in a Milky Way model.
We validate our results by comparing our distance estimates for 105 Cepheids
which have more precise, independently estimated distances. For this sample we
find that the Milky Way prior performs better (the RMS of the scaled residuals
is 0.40) than the exponentially decreasing space density prior (RMS is 0.57),
although for distances beyond 2 kpc the Milky Way prior performs worse, with a
bias in the scaled residuals of -0.36 (vs. -0.07 for the exponentially
decreasing space density prior). We do not attempt to include the photometric
data in GDR1 due to the lack of reliable colour information. Our distance
catalogue is available at http://www.mpia.de/homes/calj/tgas
distances/main.html as well as at CDS. This should only be used to give
individual distances. Combining data or testing models should be done with the
original parallaxes, and attention paid to correlated and systematic
uncertainties.
