Verifying LIGO–Virgo GWTC-2 Nested Sampling with Order Statistics

The LIGO-Virgo Collaboration utilises nested sampling to infer the source properties of compact binaries, computing Bayesian evidences and posterior distributions. With poor sampling from the constrained prior, nested sampling algorithms may misbehave and fail to sample the posterior distribution faithfully. Fowlie et al. (2020) outlines a method of identifying pathologies such as plateaus in the parameter space, using likelihood insertion order statistics. We apply this method to nested sampling analyses of all events in the first and second gravitational wave transient catalogs. With a few exceptions that have negligible effect on the final posteriors, the data is consistent with uniform insertion order statistics and unbiased prior sampling. There is, however, weak evidence against uniformity at the catalog-level meta-test.