Estimating distances from parallaxes. III. Distances of two million   stars in the Gaia DR1 catalogue
  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. 
Tri L. Astraatmadja (1,2) and Coryn A. L. Bailer-Jones (2) ((1)   Department of Terrestrial Magnetism, Carnegie Institution ...
astro-ph.GA astro-ph.IM astro-ph.SR