and evolution. The study of different clusters reveals properties of the probabilistic distribution of initial masses (the initial mass function, IMF) and its dependence on parameters such as metallicity and age. The evolution of their dynamical scales and properties can help us understand the history of our own Galaxy and its components. But using clusters as one of the building blocks of our knowledge of the nearer Universe requires identifications of the cluster members as completely and accurately as possible. This work is the first in a series where we apply recent developments in statistics to the problem of estimating the cluster membership probabilities for a set of sources. We concentrate on data sets with both proper motions and multiband photometry.

Traditionally, the problem of estimating membership probabilities based on proper motion measurements has been treated with techniques that followed the pioneering work by [@1958AJ.....63..387V] and . These works modelled the distribution of sources in the vector point diagram (hereafter VPD) as the mixture of two bi-variate Gaussian distributions, one for the cluster members and another for the field sources. The cluster distribution was assumed to be circular in both cases because the astrometric uncertainties did not allow for the 