Expect the unexpected: augmented mixture models for black-hole-population studies

TL;DR

The paper introduces the augmented mixture model ($AMM$), a Bayesian framework that blends parametric (astrophysical) models with a non-parametric component to robustly infer binary black-hole populations from gravitational-wave data. It leverages the Dirichlet distribution to weight different channels and employs collapsed Gibbs sampling (via HDPGMM/FIGARO) to explore a high-dimensional parameter space, including a non-parametric density $NP(\theta|\Theta)$. Validations on simulated datasets demonstrate the AMM’s ability to recover both known features and unforeseen ones, while applications to GWTC-3 BBH events yield results in agreement with current literature and reveal a non-parametric contribution of order a few tens of percent. The approach mitigates biases from misspecified parametric forms and sets the stage for future gravitational-wave catalogs (like GWTC-4.0) to reveal new formation channels through a flexible yet interpretable framework.

Abstract

Black hole population studies are currently performed either using astrophysically motivated models (informed but rigid in their functional forms) or via non-parametric methods (flexible but not directly interpretable). In this paper, we present a statistical framework to complement the predictive power of astrophysically motivated models with the flexibility of non-parametric methods. Our method makes use of the Dirichlet distribution to robustly infer the relative weights of different models as well as of the Gibbs sampling approach to efficiently explore the parameter space. After having validated our approach using simulated data, we apply this method to the BBH mergers observed during the first three Observing Runs of the LIGO-Virgo-KAGRA collaboration using both phenomenological and astrophysical models as parametric models, finding results in agreement with the currently available literature.

Figures (7)

• Figure 1: Inferred distribution for one-dimensional PowerLaw+Peak example presented in Section \ref{['sec:1dsim']} in the PL+NP case. The solid blue line marks the median reconstruction, the shaded areas correspond to the $68\%$ and $90\%$ credible regions, and the solid red line shows the true underlying distribution. The grey dashed line in the left panel corresponds to the selection function used.
• Figure 2: Inferred weights for different mixture models considered in Section \ref{['sec:1dsim']}.
• Figure 3: Inferred distributions for three-dimensional mock catalogue presented in Section \ref{['sec:3dsim']}. Left: Posterior distribution for $\Lambda_\mathrm{TPL}$. The blue cross-hairs mark the true values. Right: Non-parametric marginal $\mathrm{M}_1-z$ distribution. For each redshift value, the mass distribution has been normalised, and the shaded areas mark the $68\%$ credible regions.
• Figure 4: Posterior distribution for $\boldsymbol{\phi}$ using three-dimensional mock catalogue of Section \ref{['sec:3dsim']}. The blue cross-hairs mark the true values.
• Figure 5: Posterior distribution for $\Lambda_\mathrm{TPL}$ using GWTC-3.