Is there an excess of black holes around $20 M_{\odot}$? Optimising the complexity of population models with the use of reversible jump MCMC

Some analyses of the third gravitational wave catalogue released by the LIGO-Virgo-KAGRA collaboration (LVK) suggest an excess of black holes around $15-20 M_{\odot}$. In order to investigate this feature, we introduce two flexible population models, a semi-parametric one and a non-parametric one. Both make use of reversible jump Markov chain Monte-Carlo to optimise their complexity. We also illustrate how the latter can be used to efficiently perform model selection. Our parametric model broadly agrees with the fiducial analysis of the LVK, but finds a peak of events at slightly larger masses. Our non-parametric model shows this same displacement. Moreover, it also suggests the existence of an excess of black holes around $20 M_{\odot}$. We assess the robustness of this prediction by performing mock injections and running hierarchical analyses on those. We find that such a feature might be due to statistical fluctuations, given the small number of events observed so far, with a $5\%$ probability. We estimate that with a few hundreds of observations, as expected for O4, our non-parametric model will, be able to robustly determine the presence of this excess. It will then allow for an efficient agnostic inference of the properties of black holes.
Comment: correct typo in equation 5