Leveraging rapid parameter estimates for efficient gravitational-wave Bayesian inference via posterior repartitioning

TL;DR

The paper tackles the computational bottleneck of gravitational-wave Bayesian parameter estimation by marrying rapid, physics-informed constraints from simple-pe with the posterior repartitioning idea to steer nested sampling toward the most probable regions without altering the final prior. It trains a normalizing flow on simple-pe outputs to form a repartitioned prior and reweights the likelihood so that the product remains invariant, yielding identical posteriors to standard analyses but with far fewer likelihood evaluations. Validation on 100 injections shows unbiased posteriors and strong SNR-dependent speedups, with per-sample gains up to about $2.1$ at $\mathrm{SNR}=150$ and overall improvements up to $\sim2.2\times$; the method becomes increasingly beneficial for high-SNR events expected from current and next-generation detectors. The work also identifies limitations at low SNR and outlines future enhancements, such as automated widening and extension to precessing systems, positioning this approach as a practical, scalable tool for fast and robust gravitational-wave inference.

Abstract

Gravitational wave astronomy typically relies on rigorous, computationally expensive Bayesian analyses. Several methods have been developed to perform rapid Bayesian inference, but they are not yet used to inform our full analyses. We present a novel approach for doing this whilst ensuring that the Bayesian prior remains independent of the data, providing a statistically rigorous way to leverage low-latency information to accelerate the final inference. By combining the fast constraints from the simple-pe algorithm with the nested sampling acceleration technique of posterior repartitioning, we demonstrate that our method can guide the nested sampler towards the most probable regions of parameter space more efficiently for signal-to-noise ratios (SNR) greater than 20, while mathematically guaranteeing that the final inference is identical to that of a standard, uninformed analysis. We validate the method through an injection study, demonstrating that it produces statistically robust and unbiased results, whilst providing speedups of up to $2.2\times$ for binaries with SNRs $< 150$. Importantly, we show that the performance gain provided by our method scales with SNR, establishing it as a powerful technique to mitigate the cost of analysing signals from current and future gravitational-wave observatories.

Figures (17)

• Figure 1: Cartoon of nested sampling algorithm in two dimensions. Dead points define nested likelihood contours, indicated by $\mathcal{L}_{1}, \mathcal{L}_{2}, ...,$ in the parameter space, and the live points compress exponentially towards the peak of the likelihood as the algorithm proceeds. The fractional prior volumes enclosed between successive contours determine the weights of each dead point, used for calculating the Bayesian evidence and drawing posterior samples.
• Figure 2: Most of the computational time of nested sampling is spent in locating the bulk of the posterior, $\mathcal{P}$, within the much larger prior volume, $\pi$. In posterior repartitioning, this region of interest is first identified by an approximate method. The nested sampling run is then initialised within this smaller volume, $\pi'$, using a repartitioned likelihood (Eq. \ref{['eq:repartitioned_likelihood']}) to ensure the resulting posterior and evidence are identical to a standard analysis.
• Figure 3: A flowchart of our proposed algorithm. Our method (left) introduces several fast pre-processing steps before running a posterior repartitioned (PR) nested sampling analysis. This reduces the runtime compared to a traditional nested sampling (NS) analysis (right). The primary computational bottleneck in both methods is the nested sampling step itself. Provided the initial simple-pe distribution is sufficiently widened, our method produces the same posteriors as the traditional approach but with significantly fewer likelihood evaluations.
• Figure 4: Performance of the simple-pe-PR method relative to a standard nested sampling analysis as a function of network SNR. The speedup factor is the ratio of a metric for the standard analysis to that of the PR analysis. Top: Total speedup factors, showing the ratio of total likelihood evaluations (blue) and total sampling time (crimson). Bottom: Speedup factors normalised by the number of effective posterior samples. The dashed line at 1.0 indicates no change in performance. The shaded and non-shaded regions separate the two different regimes used for the widening factors.
• Figure 5: For the SNR 20 signal, simple-pe did not produce sufficient samples from the secondary mode of the true posterior in order for the flow to learn this feature. The widened flow is able to generate samples which lie in this secondary mode, but with very low probability. Since the sampler recognises that this region of the parameter space has a high repartitioned likelihood, it attempts to explore it, but inefficiently and unsuccessfully, leading a marginally slower analysis than standard NS and a slightly different final posterior. This issue can be mitigated by drawing more initial samples from simple-pe to make sure the secondary mode is sufficiently covered.