An Order Statistics Post-Mortem on LIGO-Virgo GWTC-2 Events Analysed with Nested Sampling

TL;DR

This paper applies a statistical validation method to LIGO-Virgo gravitational wave event analyses, confirming that most posterior samples are unbiased, with minor exceptions, ensuring the reliability of source property inferences.

Contribution

It demonstrates the application of likelihood insertion order statistics to validate nested sampling analyses across all GWTC-1 and GWTC-2 events, highlighting the method's effectiveness.

Findings

Most events show unbiased posterior sampling

Weak evidence of bias at the catalog level

Validation method confirms analysis reliability

Abstract

The data analysis carried out by the LIGO-Virgo collaboration on gravitational-wave events utilizes nested sampling to compute Bayesian evidences and posterior distributions for inferring the source properties of compact binaries. 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 validating the performance of nested sampling, or identifying pathologies such as plateaus in the parameter space, using likelihood insertion order statistics. Here, this method is applied to nested sampling analyses of all events in the first and second gravitational wave transient catalogs (GWTC-1 and GWTC-2) of the LIGO-Virgo collaboration. The insertion order statistics are tested for uniformity across 45 events in the catalog and it is found that, with a few exceptions that have negligible effect on the final posteriors, the data from the analysis of events in the catalog is consistent with unbiased prior sampling. There is, however, weak evidence against uniformity at the catalog-level meta-test, yielding a Kolmogorov-Smirnov meta-p-value of 1.44 * 10-3.