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 itsss 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 A_v ∼ 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%).