Nested sampling cross-checks using order statistics
  Nested sampling (NS) is an invaluable tool in data analysis in modern
astrophysics, cosmology, gravitational wave astronomy and particle physics. We
identify a previously unused property of NS related to order statistics: the
insertion indexes of new live points into the existing live points should be
uniformly distributed. This observation enabled us to create a novel
cross-check of single NS runs. The tests can detect when an NS run failed to
sample new live points from the constrained prior and plateaus in the
likelihood function, which break an assumption of NS and thus leads to
unreliable results. We applied our cross-check to NS runs on toy functions with
known analytic results in 2 - 50 dimensions, showing that our approach can
detect problematic runs on a variety of likelihoods, settings and dimensions.
As an example of a realistic application, we cross-checked NS runs performed in
the context of cosmological model selection. Since the cross-check is simple,
we recommend that it become a mandatory test for every applicable NS run.
