Accelerating parameter estimation for parameterized tests of general relativity with gravitational-wave observations

TL;DR

The paper tackles the computational bottleneck in GR tests with gravitational waves posed by large parameter spaces from PN-deformation coefficients. It integrates relative binning into the TIGER framework to accelerate likelihood evaluations while preserving posterior accuracy, enabling full Bayesian inference for both GR-consistent and non-GR signals, including high-SNR XG-like observations. The authors demonstrate unbiased recoveries, quantify how bin resolution impacts accuracy (notably for the $-1$PN term), and report substantial speedups (order $10$–$10^2$) across frequency ranges and signal lengths. They validate the approach on simulated binaries, perform high-SNR XG forecasts, and apply it to GW150914 and GW250114, obtaining GR-consistent bounds that agree with prior results. The method enables scalable, multi-parameter GR tests and PCA analyses, significantly advancing the practicality of large ensembles and routine GR testing with current and next-generation GW detectors.

Abstract

Tests of general relativity (GR) with gravitational waves (GWs) introduce additional deviation parameters in the waveform model. The enlarged parameter space makes inference computationally costly, which has so far limited systematic, large-scale studies that are essential to quantify degeneracies, check effect of waveform systematics, and assess robustness across non-stationary and non-Gaussian noise effects. The need is even sharper for next-generation (XG) observatories where signals are longer, signal-to-noise ratios (SNRs) are higher, and likelihood evaluations increase substantially. We address this by applying relative binning to the TIGER framework for parameterized tests of GR. Relative binning replaces dense frequency evaluations with evaluations on adaptively chosen frequency bins, reducing the cost per likelihood call while preserving posterior accuracy. Using simulated binary black hole signals, we demonstrate unbiased recovery for GR-consistent cases and targeted non-GR deviations, and we map how bin resolution controls accuracy, with fine binning primarily required for the $-1$ post-Newtonian term. A high-SNR simulated signal at next-generation sensitivity further shows accurate recovery with tight posteriors. Applied to GW150914 and GW250114, both single and multi-parameter TIGER analyses finish within a day, yielding deviation bounds consistent with GR at 90\% credibility and in agreement with previous results. Across analyses, the method reduces wall time by factors of $\mathcal{O}(10)$ to $\mathcal{O}(100)$, depending on frequency range and binning, without degrading parameter estimation accuracy.

Figures (7)

• Figure 1: Validation of the linear approximation in relative binning across parameter variations and binning resolutions for a BBH system with $m_1 = 25\,M_\odot$ and $m_2 = 20\,M_\odot$. Columns correspond to binning resolutions: $\chi = 10$ ($621$ bins; left), $\chi = 50$ ($3104$ bins; center), and $\chi = 100$ ($6207$ bins; right). First row shows chirp mass variations $\Delta\mathcal{M}/\mathcal{M}_{\mathrm{true}} = \pm 1\%$; second row shows variations in the $-1$PN deviation parameter, $d\chi_{-2} = \pm 10$. The real part of the waveform ratio, $\mathfrak{R} \left[ {h}(f) /h_0(f) \right]$, is plotted as a function of frequency, with blue (red) curves representing positive (negative) parameter perturbations. Variations are shown in the first frequency bin for each binning scheme. In the chosen bins, all binning schemes show fairly linear waveform ratio for $\mathcal{M}$. However, for $d\chi_{-2}$, coarse binning ($\chi=10$; left) exhibits severe non-linear artifacts and non-monotonic behavior within the bin. Intermediate binning ($\chi=50$; center) shows improved linearity, and fine binning ($\chi=100$; right) achieves excellent linear approximation, validating Eq. \ref{['eq:linear_approx']}.
• Figure 2: Posterior distributions for precession parameters from GR parameter estimation runs. Violin plots compare results from two independent runs (Run 1 and Run 2) at different bin numbers ($\chi = 10$ and $\chi = 50$). All posteriors are consistent and centered around zero, as expected for GR signals.
• Figure 3: Posterior distributions for precession parameters from non-GR parameter estimation runs. Violin plots compare results from Run 1 and Run 2 at different bin numbers ($\chi = 10$ and $\chi = 50$). Most non-GR deviations are accurately recovered with the $\chi=10$ binning scheme. For $d\chi_{-2}$, using $\chi=10$ gives biased estimation, but increasing the number of bins with $\chi=50$ returns accurate posterior distributions.
• Figure 4: Posterior probability distribution showing accurate and precise inference of the parameter $d\chi_3$ for a non-GR Run 1-like simulated BBH signal in the 40 km Cosmic Explorer sensitivity. The red-dashed line shows the simulated value of $d\chi_3=-0.1$.
• Figure 5: Posterior distributions for deviation parameters from analysis of GW150914 (left) and GW250114 (right), with the $\chi=50$ binning scheme. All posteriors are consistent with GR, with distributions significantly more constrained for GW250114 due to higher SNR. The red dashed horizontal line shows the GR value of zero. The medians and 90% credible intervals are explicitly stated in Table \ref{['tab:GR_constraints_3dec']} in Appendix \ref{['app:GW_events']}.