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tokens: We thank the anonymous referee for their thorough comments which helped to improve the method and the manuscript. We gratefully acknowledge the support of the UK's Science Technology Facilities Council (STFC Grant ST/H00260X/1 and ST/J500914/1). The calculations for this paper were performed on Cray XT4 at Center for Computational Astrophysics, CfCA, of the National Astronomical Observatory of Japan and the DiRAC facilities (through the COSMOS consortium) including the COSMOS Shared Memory system at DAMTP, University of Cambridge operated on behalf of the STFC DiRAC HPC Facility. This equipment is funded by BIS National E-infrastructure capital grant ST/J005673/1 and STFC grants ST/H008586/1, ST/K00333X/1 ST/J001341/1. The authors acknowledge the use of the IRIDIS High Performance Computing Facility, and associated support services at the University of Southampton. We would also like to thank PRACE for the use of the Cartesius facility. This work was carried out, in part, through the Gaia Research for European Astronomy Training (GREAT-ITN) network. The research leading to these results has received funding from the European Union Seventh Framework Programme ([FP7/2007-2013] under grant agreement number 264895). DK acknowledges the generous support and hospitality of the Kavli Institute for Theoretical Physics (KITP), University of California Santa Barbara during the ‘Galactic Archaeology and Precision Stellar Astrophysics’ programme, where some of this research was performed. This research was supported in part by the National Science Foundation under Grant No. NSF PHY11-25915. We would also like to thank Mercè Romero-Gómez and Francesca Figueras for providing the subroutine to calculate the Gaia performance errors, including the update to post-launch estimates, Sanjib Sharma for providing the galaxia extinction maps and isochrones and Sami Niemi for the suggestion of using KDE's to visualize the velocity distributions.