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Observations of gravitational waves emitted by merging compact binaries haveprovided tantalising hints about stellar astrophysics, cosmology, andfundamental physics. However, the physical parameters describing the systems,(mass, spin, distance) used to extract these inferences about the Universe aresubject to large uncertainties. The most widely-used method of performing theseanalyses requires performing many Monte Carlo integrals to marginalise over theuncertainty in the properties of the individual binaries and the surveyselection bias. These Monte Carlo integrals are subject to fundamentalstatistical uncertainties. Previous treatments of this statistical uncertaintyhas focused on ensuring the precision of the inferred inference is unaffected,however, these works have neglected the question of whether sufficient accuracycan also be achieved. In this work, we provide a practical exploration of theimpact of uncertainty in our analyses and provide a suggested framework forverifying that astrophysical inferences made with the gravitational-wavetransient catalogue are accurate. Applying our framework to models used by theLIGO-Virgo-KAGRA collaboration and in the wider literature, we find that MonteCarlo uncertainty in estimating the survey selection bias is the limitingfactor in our ability to probe narrow population models and this will rapidlygrow more problematic as the size of the observed population increases.

Growing Pains: Understanding the Impact of Likelihood Uncertainty on Hierarchical Bayesian Inference for Gravitational-Wave Astronomy