Toward the incorporation of marginal events into the gravitational-wave population inference of compact binaries

The fourth Gravitational-Wave Transient Catalog (GWTC-4.0) from the latest observing run has nearly doubled the number of confidently detected compact binary coalescences, providing unprecedented statistical power to probe the astrophysical population of black holes. While GWTC-4.0 reveals possible new features in the binary black hole population, additional astrophysical information may reside in marginal candidates below the standard event selection thresholds. We present a new hierarchical framework that incorporates such marginal events while accounting for potential noise contamination. Using a toy-model analysis based on the GWTC-3.0 dataset, we demonstrate that this method robustly infers both signal and noise population properties with minimal bias across varying event selection thresholds. We further apply the framework to the GWTC-4.0 dataset, highlighting its potential to extract additional astrophysical insights.