Fig. \[fig:correlated\] (left panel) this leads to a statistical correlation between the two datasets (correlation coefficient $+0.23$). As a result the differences between the parallaxes have a smaller spread than expected from their combined standard errors (right panel of Fig. \[fig:correlated\]).

To derive independent parallaxes, we propose a TGAS solution incorporating only the position and proper motion information from the [Hipparcos]{} Catalogue. This is achieved by setting the prior parallax value and the corresponding row and column in the [Hipparcos]{} prior normal matrix to zero before adding the information arrays. As shown in Fig. \[fig:uncorrelated\] this removes the correlation entirely (correlation coefficient $-0.0043$) at the expense of a moderate increase in astrometric uncertainties of the [Hipparcos]{} subset (Table \[tab:noParallaxPrior\]). The results for the [*Tycho*]{} subset are not shown since the values found are virtually identical to the nominal scenario in Table \[tab:results\].

[rrrrr]{} Mag. & Number & & &\
& & & &\
\
6–7 & 9381 & 158 & 270 & 18\
7–8 & 23679 & 147 & 241 & 23\
8–9 & 40729 & 142 & 232 & 30\
9–10 & 27912 & 147 & 244 & 40\
10–11 & 8563 & 164 & 276 & 60\
11–12 