blind, but constrained to be based on sources with high membership probabilities, and thus is highly consistent with the distribution in the proper motion space.

When the iterations converged to a stable solution (defined by no change in membership for any source in two consecutive iterations), we computed membership probabilities for incomplete sources (i.e., sources with missing data) by again applying Bayes’ theorem, with a likelihood model obtained by marginalising the complete maximum-likelihood model derived in the previous section over the missing variables:

$$p(\vec{m}_{measured}|\mathcal{C}_i)=\int p(\vec{m}|\mathcal{C}_i) \cdot {\rm d}\vec{m}_{missing},
\label{eq:missing}$$

where $\vec{m}=\{\vec{m}_{measured},\vec{m}_{missing}\}$, and $\vec{m}_{measured}$ and $\vec{m}_{missing}$ are the subsets of $\vec{m}$ that are measured and missing, respectively. Since the model for $p(\vec{m}|\mathcal{C}_i)$ is a mixture of Gaussians, the result of the integral is again a mixture of Gaussians with means and covariance matrices that correspond to the projection of the original ones onto the subspace of measured variables. Uncertainties are handled in the same way as described in Eq. \[uncertainties\].

Representation space {#sect:repspace}
====================

It is well known that not all variables are equally informative for the determination of membership probabilities. As a matter of fact, apparent magnitudes alone may be insufficient for the selection of member candidates, and it is 