Bayesian Framework to Follow-up Continuous Gravitational Wave Candidates from Deep Surveys

TL;DR

The paper introduces a Bayesian, automated follow-up framework for deep all-sky searches of continuous gravitational waves, integrating the F-statistic within a hierarchical Bayesian pipeline and using nested sampling to obtain posteriors and evidences. By propagating posterior information as priors across increasing coherence times, the method achieves substantial reductions in manual intervention and computational cost while maintaining consistency with deterministic follow-ups on real data. Gaussian mixture modeling of posteriors, DBSCAN clustering, and an inverse-transform sampling scheme enable efficient per-candidate priors and scalable handling of millions of candidates. Application to Einstein@Home O3a data demonstrates effective separation of true-signal-like candidates from noise, with hardware injections validating the approach and a two-stage variant offering favorable bias and cost characteristics for future large-scale CW follow-ups.

Abstract

Broad all-sky searches for continuous gravitational waves have high computational costs and require hierarchical pipelines. The sensitivity of these approaches is set by the initial search and by the number of candidates from that stage that can be followed up. The current follow-up schemes for the deepest surveys require careful tuning and set-up, have a significant human-labor cost and this impacts the number of follow-ups that can be afforded. Here we present and demonstrate a new follow-up framework based on Bayesian parameter estimation for the rapid, highly automated follow-up of candidates produced by the early stages of deep, wide-parameter space searches for continuous waves.

Figures (11)

• Figure 1: Posterior distribution for a fake signal near the ecliptic equator ($\beta\approx 0$) added to O3a data and using the semi-coherent $\mathcal{F}$-statistic with $T_\mathrm{coh} = 120\,\unit{h}$. The posterior shows a bimodal distribution, split between the hemispheres. The plot indicates the $\Delta(C = 0.99)$ region of each mode of the fitted Gaussian mixture model following \ref{['eq:credible_regions_gmm']}.
• Figure 2: Circles defining two uncertainty regions on the ecliptic plane and their projection to the ecliptic sphere. The size of the uncertainty regions is exaggerated. (Red) Uncertainty region for a candidate that is intersecting the ecliptic equator. (Blue) The extension of the uncertainty region onto the opposing hemisphere. (Green) Uncertainty region of a candidate at higher frequency, which corresponds to a smaller circle on the ecliptic plane.
• Figure 3: Left: the fraction of missed test signals for search configurations with different prior volumes. Right: the average number of per-signal likelihood evaluations for the recovered signals. Vertical bars show the 99$^{\mathrm{th}}$ quantile. In both plots, vertical colored areas mark configurations listed in \ref{['tab:stagesetups']}. The volumes are given in terms of the number of unit-mismatch hyperellipsoids contained in the search region, $N_\star$.
• Figure 4: Log-evidences $\log(Z^{2})$ recorded for each candidate and simulated test signal. The candidates corresponding to hardware injections and the candidate remaining compatible with the test signal population after Stage 7 are emphasized.
• Figure 5: Log-evidences $\log Z^i$ recorded across all follow-ups at stages $i=3,\ldots,7$ and the relative change $R^i$. The candidates corresponding to hardware injections and the remaining significant candidate are emphasized. Two hardware injections closely match in $\log Z^i$ and $R^i$ and coincide in the plots at each stage.