Incorporation of model accuracy in gravitational wave Bayesian inference

Inferring the properties of colliding black holes from gravitational-wave observations is subject to systematic errors arising from modelling uncertainties. Although the accuracy of each model can be calculated through comparison to theoretical expectations from general relativity, Bayesian analyses are yet to incorporate this information. As such, a mixture model is typically used where results obtained with different gravitational-wave models are combined with either equal weight, or based on their relative Bayesian evidence. In this work we present a novel method to incorporate the accuracy of multiple models in gravitational-wave Bayesian analyses. By analysing simulated gravitational-wave signals in zero-noise, we show that our technique uses $30\%$ less computational resources, and more faithfully recovers the true parameters than existing techniques. We further apply our method to a real gravitational-wave signal and, when assuming the binary black hole hypothesis, demonstrate that the source of GW191109_010717 has unequal component masses, with the primary having a $69\%$ probability that it lies above the maximum black hole mass from stellar collapse. We envisage that this method will become an essential tool within ground-based gravitational-wave astronomy.