Studying the gravitational-wave population without looking that FAR out

TL;DR

The paper addresses biases in gravitational-wave population inference arising from misestimated population likelihoods and noise transients. It evaluates a simple, scalable remedy—raising the detection threshold $\rho_*$ to focus on higher-significance events—using large mock BBH catalogs with full Bayesian parameter estimation to quantify impacts on uncertainty and computation. The results show that mass and spin distributions remain robust when moving to $\rho_*\approx13$–$15$, while redshift-evolution constraints weaken but stay informative; importantly, the Monte Carlo variance of the population likelihood decreases, enabling unbiased inference with reduced computational cost. The study provides a practical guideline for analyzing large future GW catalogs, suggesting that prioritizing higher-significance events can improve robustness and efficiency, albeit with caveats for next-generation detectors and the need for flexible population models.

Abstract

From catalogs of gravitational-wave transients, the population-level properties of their sources and the formation channels of merging compact binaries can be constrained. However, astrophysical conclusions can be biased by misspecification or misestimation of the population likelihood. Despite detection thresholds on the false-alarm rate (FAR) or signal-to-noise ratio (SNR), the current catalog is likely contaminated by noise transients. Further, computing the population likelihood becomes less accurate as the catalog grows. Current methods to address these challenges often scale poorly with the number of events and potentially become infeasible for future catalogs. Here, we evaluate a simple remedy: increasing the significance threshold for including events in population analyses. To determine the efficacy of this approach, we analyze simulated catalogs of up to 1600 gravitational-wave signals from black-hole mergers using full Bayesian parameter estimation with current detector sensitivities. We show that the growth in statistical uncertainty about the black-hole population, as we analyze fewer events but with higher SNR, depends on the source parameters of interest. When the SNR threshold is raised from 11 to 15 -- reducing our catalog size by two--thirds -- we find that statistical uncertainties on the mass distribution only grow by a few 10% and constraints on the spin distribution are essentially unchanged; meanwhile, uncertainties on the high-redshift cosmic merger rate more than double. Simultaneously, numerical uncertainty in the estimate of the population likelihood more than halves, allowing us to ensure unbiased inference without additional computational expense. Our results demonstrate that focusing on higher-significance events is an effective way to facilitate robust astrophysical inference with growing gravitational-wave catalogs.

Figures (14)

• Figure 1: PPDs of the merger rate density $\mathcal{R}$ over redshift $z$ (top) inferred from catalogs with increasing detection threshold on the SNR, $\rho_*$, indicated by colors from purple to yellow. Colored lines enclose the 90% CI and the dotted black line indicates the true distribution. In the bottom panel, we plot the width $\zeta$ of the 90% CI inferred in each analysis relative to our analysis at $\rho_* = 11$. We include a gray dashed line at $\zeta{} = 1$ (i.e., no growth in statistical uncertainty with increased $\rho_*$) for reference.
• Figure 2: PPD of the primary mass $m_1$ (top left) inferred from catalogs with increasing detection threshold on the SNR $\rho_*$. Colors and lines have the same meaning as Fig. \ref{['fig:mock-ppds-z']}. Additionally, the gray region fills in the 90% CI of the prior. In the top right, we show the width of the 90% CI of the PPD relative to our analysis at $\rho_* = 11$. In the bottom row, we show the posterior uncertainties on the integrated posterior population distributions over three subdomains of interest in $m_1$. Numbers on the left of each panel, colored according to SNR threshold, note the 90% CI width, relative to our analysis at $\rho_* = 11$, of the posterior on the fraction of events in each subdomain. Note, for $6\,M_\odot< m_1 < 12\,M_\odot$, the PPD mostly lie above the prior in density, and so no prior is visible in the bottom left panel. Conversely, the prior on the fraction of events lying in $50\,M_\odot< m_1 < 120\,M_\odot$ is strongly peaked at zero due to the sharp cutoff in our assumed population model which sends the prior population density to zero at high masses.
• Figure 3: The 90% CI of the PPD in mass ratio $q$ (top) and width of the 90% CI of the PPD relative to our analysis at $\rho_* = 11$ (bottom) at select thresholds $\rho_*$. Thresholds, shading, lines, and colors match those in the top row of Fig. \ref{['fig:mock-ppds-m1']}.
• Figure 4: PPD (top row), width of the 90% CI of the PPD relative to our analysis at $\rho_* = 11$ (middle row), and PPD integrated over select domains (bottom row) for spin magnitudes $a_{1,2}$ (left column) and tilts (right column). Thresholds, shading, lines, and colors match those in Fig. \ref{['fig:mock-ppds-m1']}.
• Figure 5: Joint posterior distributions for the total variance of the log-likelihood estimator $\mathcal{V}$ and integrated PPD. In the right panel, we histogram (with arbitrary normalization) the marginal posterior on the log-likelihood estimator variance. In all other panels, we show the 90% credible regions of joint distributions on $\mathcal{V}$ and the fraction of sources lying in select domains of primary mass, spin magnitude, or cosine-spin tilt. Colors from cooler to warmer denote the threshold $\rho_*$ and dotted black lines denote values in the true population.