Testing General Relativity with GWTC-4.0 through mixture models

Gravitational-wave observations of compact binary mergers have enabled precision tests of gravity in the strong-field dynamical regime. Current approaches combine single-event results that assume deviations from General Relativity (GR) are uniformly distributed across events, limiting their flexibility and potentially biasing the inferred evidence. We introduce a simple mixture-model framework in which a fraction $\zeta$ of events is consistent with GR, while a fraction $1 - \zeta$ deviates from it, without imposing constraints on the population distribution of the deviation parameters. We apply this method to publicly available results from the LIGO-Virgo-KAGRA (LVK) collaboration on O1-O4a compact binary mergers obtained through FTI, pSEOBNR, and KerrPostMerger tests. We find that the data are consistent with all events satisfying GR. However, we obtain respective Bayes factors $B^{\zeta=1}_{\zeta \neq 1} \simeq 20$, $10$ and $15$, which are much smaller than those inferred from existing LVK analyses, indicating that the data require greater flexibility in modelling possible deviations than standard approaches permit. In light of our results, we recommend using flexible mixture models to test GR across compact-merger catalogues, unless there are obvious physical motivations to impose more restrictive models, as in the case of graviton-mass estimates.