in a future article in this series.

Both the initial list of Pleiades candidate members and the set of DANCe sources in the field are the result of a spatial selection on the celestial sphere and on the VPD diagram. Furthermore, since the likelihood model is only infered from complete observations, the spatial footprint of the different instruments included in the data set represents yet another source of biases. The selection based on celestial coordinates is defined by a circle of 5 degrees radius around the centre of the cluster; the selection in the VPD is bounded by maximum proper motions in any of the two axes of 100 mas$\cdot$yr$^{-1}$. This [*ab initio*]{} selection procedure defines the proportion of the two types of sources (field and cluster) and therefore affects the posterior probabilities via the likelihood and prior probability, as indicated in Eq. \[bayes.th\]. The posterior probabilities derived in this work are thus not an absolute scale, but are those derived from the actual data set, with the biases inherent to the preparation of the DANCe catalogue.

In Sect. \[sect:lim-concl\] we indicate a rigorous and consistent way to take these selection biases into account; this involves multilevel or hierarchical modelling 