(H)DPGMM: A Hierarchy of Dirichlet Process Gaussian Mixture Models for the inference of the black hole mass function

Abstract: We introduce (H)DPGMM, a hierarchical Bayesian non-parametric method based on the Dirichlet Process Gaussian Mixture Model, designed to infer data-driven population properties of astrophysical objects without being committal to any specific physical model. We investigate the efficacy of our model on simulated datasets and demonstrate its capability to reconstruct correctly a variety of population models without the need of fine-tuning of the algorithm. We apply our method to the problem of inferring the black hole mass function given a set of gravitational wave observations from LIGO and Virgo, and find that the (H)DPGMM infers a binary black hole mass function that is consistent with previous estimates without the requirement of a theoretically motivated parametric model. Although the number of systems observed is still too small for a robust inference, (H)DPGMM confirms the presence of at least two distinct modes in the observed merging black holes mass function, hence suggesting in a model-independent fashion the presence of at least two classes of binary black hole systems.