The seven sisters DANCe IV. Bayesian hierarchical model

TL;DR

This paper introduces a Bayesian hierarchical statistical tool for analyzing young open cluster populations, effectively handling missing data and heteroscedastic uncertainties, and demonstrating improved accuracy and bias reduction.

Contribution

A novel Bayesian hierarchical model for NYOC analysis that accounts for data uncertainties and missing values, providing more accurate cluster member identification.

Findings

Achieves 5.8% contamination rate in cluster member classification

Recovers approximately 90% of known candidates and finds 10% new members

Provides consistent luminosity functions and mass distributions with previous studies

Abstract

Aims. We develop, test and characterise of a new statistical tool (intelligent system) for the sifting and analysis of nearby young open cluster (NYOC) populations. Methods. Using a Bayesian formalism, this statistical tool is able to obtain the posterior distributions of parameters governing the cluster model. It also uses hierarchical bayesian models to establish weakly informative priors, and incorporates the treatment of missing values and non-homogeneous (heteroscedastic) observational uncertainties. Results. From simulations, we estimate that this statistical tool renders kinematic (proper motion) and photometric (luminosity) distributions of the cluster population with a contamination rate of $5.8 \pm 0.2$ %. The luminosity distributions and present day mass function agree with the ones found by Bouy et al. (2015b) on the completeness interval of the survey. At the probability threshold of maximum accuracy, the classifier recovers $\sim$ 90% of Bouy et al. (2015b) candidate members and finds 10% of new ones. Conclusions. A new statistical tool for the analysis of NYOC is introduced, tested and characterised. Its comprehensive modelling of the data properties allows it to get rid of the biases present in previous works. In particular, those resulting from the use of only completely observed (non-missing) data and the assumption of homoskedastic uncertainties. Also, its Bayesian framework allows it to properly propagate observational uncertainties into membership probabilities and cluster velocity and luminosity distributions. Our results are in a general agreement with those from the literature, although we provide the most up-to-date and extended list of candidate members of the Pleiades cluster.