Variance of gravitational-wave populations

TL;DR

This paper investigates how the finite size of gravitational-wave catalogs affects population analysis uncertainties, revealing that catalog variance significantly broadens credible intervals and impacts inferred population features.

Contribution

It introduces a data-driven bootstrap method to quantify catalog variance, providing the first intrinsic uncertainty assessment for gravitational-wave population studies.

Findings

Catalog variance broadens population parameter uncertainties.

The 35 M_ont{\odot} peak in primary mass is diminished when accounting for variance.

Standard analyses underestimate true uncertainties without considering catalog variance.

Abstract

We quantify the impact of finite catalog size, or "catalog variance," on current gravitational-wave population analyses. The distribution of merging binary black holes is commonly reconstructed via hierarchical Bayesian inference, with uncertainties reported as credible intervals. Such intervals are conditioned on the specific realization of the observed events and are therefore themselves subject to variability arising from the finite size of the catalog. We estimate this "uncertainty on the uncertainty" using statistical bootstrapping applied to data segments containing both detected events and sensitivity injections. Applying this framework to GWTC-4, we find that the inferred population distributions exhibit substantially broader uncertainties than those obtained in a standard single-catalog analysis. In particular, the $\sim 35\,M_\odot$ peak in the primary-mass distribution is largely absorbed by statistical fluctuations once catalog variance is taken into account. Unlike other studies that rely on simulating catalogs by assuming an underlying population, this work provides the first data-driven assessment of the uncertainty intrinsic to the observed gravitational-wave catalog. Accounting for catalog variance is important for drawing robust astrophysical conclusions from gravitational-wave data, avoiding inferences driven by a particular finite realization rather than genuine population features.