Miec: A Bayesian hierarchical model for the analysis of nearby young
  open clusters
  Context. The analysis of luminosity and mass distributions of young stellar
clusters is essential to understanding the star-formation process. However, the
gas and dust left over by this process extinct the light of the newborn stars
and can severely bias both the census of cluster members and its luminosity
distribution. Aims. We aim to develop a Bayesian methodology to infer, with
minimal biases due to photometric extinction, the candidate members and
magnitude distributions of embedded young stellar clusters. Methods. We improve
a previously published methodology and extend its application to embedded
stellar clusters. We validate the method using synthetically extincted data
sets of the Pleiades cluster with varying degrees of extinction. Results. Our
methodology can recover members from data sets extincted up to Av ~ 6 mag with
accuracies, true positive, and contamination rates that are better than 99%,
80%, and 9%, respectively. Missing values hamper our methodology by introducing
contaminants and artifacts into the magnitude distributions. Nonetheless, these
artifacts vanish through the use of informative priors in the distribution of
the proper motions. Conclusions. The methodology presented here recovers, with
minimal biases, the members and distributions of embedded stellar clusters from
data sets with a high percentage of sources with missing values (>96%).
