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Many astronomical surveys are limited by the brightness of the sources, and gravitational-wave searches are no exception. The detectability of gravitational waves from merging binaries is affected by the mass and spin of the constituent compact objects. To perform unbiased inference on the distribution of compact binaries, it is necessary to account for this selection effect, which is known as Malmquist bias. Since systematic error from selection effects grows with the number of events, it will be increasingly important over the coming years to accurately estimate the observational selection function for gravitational-wave astronomy. We employ density estimation methods to accurately and efficiently compute the compact binary coalescence selection function. We introduce a simple pre-processing method, which significantly reduces the complexity of the required machine-learning models. We demonstrate that our method has smaller statistical errors at comparable computational cost than the method currently most widely used allowing us to probe narrower distributions of spin magnitudes. The currently used method leaves 10%–50% of the interesting black hole spin models inaccessible; our new method can probe >99% of the models and has a lower uncertainty for >80% of the models.

Gravitational-wave observations of binary neutron star mergers provide valuable information about neutron star structure and the equation of state of dense nuclear matter. Numerous methods have been proposed to analyze the population of observed neutron stars, and previous work has demonstrated the necessity of jointly fitting the astrophysical distribution and the equation of state in order to accurately constrain the equation of state. In this work, we introduce a new framework to simultaneously infer the distribution of binary neutron star masses and the nuclear equation of state using Gaussian mixture model density estimates, which mitigates some of the limitations previously used methods suffer from. Using our method, we reproduce previous projections for the expected precision of our joint mass distribution and equation-of-state inference with tens of observations. We also show that mismodeling the equation of state can bias our inference of the neutron star mass distribution. While we focus on neutron star masses and matter effects, our method is widely applicable to population inference problems.

As catalogs of gravitational-wave transients grow, new records are set for the most extreme systems observed to date. The most massive observed black holes probe the physics of pair-instability supernovae while providing clues about the environments in which binary black hole systems are assembled. The least massive black holes, meanwhile, allow us to investigate the purported neutron star–black hole mass gap, and binaries with unusually asymmetric mass ratios or large spins inform our understanding of binary and stellar evolution. Existing outlier tests generally implement leave-one-out analyses, but these do not account for the fact that the event being left out was by definition an extreme member of the population. This results in a bias in the evaluation of outliers. We correct for this bias by introducing a coarse-graining framework to investigate whether these extremal events are true outliers or whether they are consistent with the rest of the observed population. Our method enables us to study extremal events while testing for population model misspecification. We show that this ameliorates biases present in the leave-one-out analyses commonly used within the gravitational-wave community. Applying our method to results from the second LIGO–Virgo transient catalog, we find qualitative agreement with the conclusionsmore »of Abbott et al. GW190814 is an outlier because of its small secondary mass. We find that neither GW190412 nor GW190521 is an outlier.