Overlapping signals in next-generation gravitational wave observatories: A recipe for selecting the best parameter estimation technique

TL;DR

The paper addresses biases in parameter estimation caused by overlapping gravitational-wave signals in next-generation detectors and evaluates strategies to mitigate them. It demonstrates that joint parameter estimation combined with relative binning (RB) yields accurate posteriors for overlapping BBHs, including precession and higher-order modes, with substantial computational savings, and proposes an efficient bias-detection workflow based on posterior reweighting and Jensen-Shannon divergence. Prior-informed Fisher matrices can predict large biases but are unreliable for small biases, while time-frequency overlap is a robust indicator of bias, achieving ~86% accuracy for near-overlaps. The proposed posterior-reweighting method offers 99% accuracy in zero noise (98% in Gaussian noise) for deciding whether full JPE is needed, enabling a practical, PE-based bias assessment pipeline suitable for 3G-era analyses.

Abstract

Third-generation gravitational wave detectors such as Einstein Telescope and Cosmic Explorer will have significantly better sensitivities than current detectors, as well as a wider frequency bandwidth. This will increase the number and duration of the observed signals, leading to many signals overlapping in time. If not adequately accounted for, this can lead to biases in parameter estimation. In this work, we combine the joint parameter estimation method with relative binning to handle full parameter inference on overlapping signals from binary black holes, including precession effects and higher-order mode content. As this method is computationally more expensive than traditional single-signal parameter estimation, we test a prior-informed Fisher matrix and a time-frequency overlap method for estimating expected bias to help us decide when joint parameter estimation is necessary over the simpler methods. We improve upon previous Fisher matrix implementations by including the prior information and performing an optimization routine to better locate the maximum likelihood point point, but we still find the method unreliable. The time-frequency method is accurate in 86% of close binary black hole mergers. We end by developing our own method of estimating bias due overlaps, where we reweight the single signal parameter estimation posterior to quantify how much the overlapping signals affect it. We show it has 99% accuracy for zero noise injections (98% in Gaussian noise), at the cost of one additional standard sampling run when joint parameter estimation proves to be necessary.

Figures (16)

• Figure 1: RB is applied to two overlapping signals. They were chosen to be non-precessing and to contain just the dominant (2,2) mode, for clarity of the figure. Top: Frequency domain strain of the individual and the combined signals. They are strongly oscillating, requiring high sampling frequency to be captured properly. Bottom: Real part of the ratio of the strain to the reference strain. The ratio of the combined signal to the combined reference signal is much smoother than the absolute signal. The ratios of the composite signals are much smoother and are better suited for approximation by a piecewise linear function than the combined ratio.
• Figure 2: RB likelihood approximation error for an example overlapping signal. The scatter plot shows the distribution of likelihoods for all the points from the posterior. The x-axis shows the full unapproximated likelihood $\ln\mathcal{L}$ relative to the maximum likelihood sample $\ln\mathcal{L}_{max}$. The y-axis shows the absolute error $\delta\ln\mathcal{L}$ in the binned log-likelihood over the true likelihood. The relative error between the samples is at most 0.15, which leads to the effective sampling rate of $\eta_{eff}=99.96\%$.
• Figure 3: Comparison of different PE methods for overlapping signals and a representative signal in Gaussian noise. JPE is compared with SSPE and the second step of the HS method where the dominant signal is analized again after subtracting the estimation of signal B from the strain. For comparison, a posterior with only a single signal injected into the strain is also plotted. While both JPE and HS recover similar posteriors, they are statistically distinct. The contours in the corner plot indicate 0.86 credible regions.
• Figure 4: Comparison of different PE methods of overlapping signals for an extreme bias case. JPE is compared with SSPE and the second step of the HS method where the dominant signal is analized again after subtracting the estimation of signal B from the strain. For comparison, a posterior with only a single signal injected into the strain is also plotted. While both JPE and HS recover similar posteriors, they are statistically distinct. The contours in the corner plot indicate 0.86 credible regions. For this particular injection, SSPE case has a very small secondary peak closer to the injection, a feature very uncommon in the injections considered in this paper.
• Figure 5: Percentile-percentile plot for different analysis methods of overlapping signals. The x-axis is the percentile at which the injection was recovered. The y-axis is the fraction of events for which the injection was recovered for a given percentile. The shaded regions indicate expected deviation from the diagonal at 0.68, 0.95, and 0.997 probability levels. The legend notes the p-values of the individual parameters, while the combined p-value is quoted above the plots. Top: Recovery of the signal SSPE template. Only the louder signal can be recovered, resulting in 80 plotted injections. Middle: Recovery of both signals using the hierarchical subtraction method, 160 plotted injections. Bottom: Recovery of the signal with joint parameter estimation, 160 total signals.