uncertainties into the derivation of the membership probabilities in a consistent way throughout the entire magnitude and proper motion range. We aim at producing membership probabilities with a method that treats astrometric and photometric measurements and their uncertainties consistently. We extend the original probabilistic formulation by [@1958AJ.....63..387V] and to include magnitudes and colour indices as part of the representation space where the modelling takes place, and incorporate all the measurement uncertainties (i.e. both astro- and photometric) into the derivation of probabilistic memberships. Another objective of this work is to provide an inference system capable of handling incomplete data (that is, data with non-detections, upper limits, or corrupt values).

In Section \[sect:rml\], we describe in more detail the general framework of our methods and the data set that drives the necessity to develop a methodology to infer membership probabilites. In Section \[sect:repspace\] we discuss the set of random variables used to represent sources in the modelling of the distribution corresponding to the cluster and the field, and alternative spaces tested in the experimentation phase. In Section \[sect:results\] we describe the results obtained with two sets of models, and in Section \[sect:sensitivity\] we analyse the sensitivity of these results to the various 