Developing Better Posterior Predictive Checks for Gravitational-wave Population Analyses

Hundreds of merging binary black holes have been observed via gravitational waves by the LIGO and Virgo detectors, allowing for measurements of the astrophysical population distribution of their source properties, such as mass and spin. Model checking, which confirms that a measured distribution is indeed a good fit to the data, is essential to ensure that conclusions drawn from population studies are astrophysical and not spuriously caused by choices about a model's functional form. The leading tool for model checking in gravitational-wave population analyses is the "posterior predictive check" (PPC), where catalogs of signals predicted by a given model are compared to the observed data. For parameters which are poorly constrained for individual events – like black hole spin – we show that traditional PPCs are unable to identify known discrepancies between a model and the true underlying parameter distribution. We then propose alternative population model checking procedures that avoid these shortcomings.