Galactic Double Neutron Star total masses and Gaussian mixture model selection

Abstract

[eng] Huang et al. (2018) have analysed the population of 15 known Galactic double neutron stars (DNSs) regarding the total masses of these systems. They suggest the existence of two subpopulations, and report likelihood-based preference for a two-component Gaussian mixture model over a single-Gaussian distribution. This note offers a cautionary perspective on model selection for this data set: especially for such a small sample size, a pure likelihood ratio test can encourage overfitting. This can be avoided by penalizing models with a higher number of free parameters. Re-examining the DNS total mass data set within the class of Gaussian mixture models, this can be achieved through several simple and well-established statistical tests, including information criteria (AICc, BIC), cross-validation, Bayesian evidence ratios, and a penalized EM-test. While this reanalysis confirms the basic finding that a two-component mixture is consistent with the data, the model selection criteria consistently indicate that there is no robust preference for it over a single-component fit. Additional DNS discoveries will be needed to settle the question of subpopulations.