The upper part of the table gives statistics for the [*Tycho*]{}-only stars, the lower part for the [Hipparcos]{} stars. As the priors are very different for the two subsets, they are separately discussed in the following.

### [*Tycho*]{}-only stars

Any attempt to solve five parameters with 0.5 yr of [*Gaia*]{} data without a prior utterly fails. Remarkably, however, the inclusion of the [*Tycho*]{} positions allows us to solve not only the proper motions, but also the parallaxes for the 2.5 million [*Tycho*]{} stars with sub-mas precision. Here the proper motions rely entirely on the [*Tycho*]{} positions, as shown by the strong variation of the uncertainty with magnitude, mainly reflecting the variation of positional uncertainty in the [*Tycho*]{} Catalogue. In spite of the fact that the prior parallaxes are set to zero, the posterior estimates have very little bias (the median parallax error is $-0.7~\mu$as).

### [Hipparcos]{} stars

It is interesting to compare the [Hipparcos]{} subset of this solution with the (conservative) HTPM case B, where only the positions were solved for the auxiliary non-[Hipparcos]{} stars (see Sect. 4.1 in the HTPM paper). The TGAS simulation is based on half as much [*Gaia*]{} data as HTPM-B, uses more conservative assumptions for 