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Using overlap of sky localization probability maps for filtering potentially lensed pairs of gravitational-wave signals

Henry W. Y. Wong, Lok W. L. Chan, Isaac C. F. Wong, Rico K. L. Lo, Tjonnie G. F. Li

TL;DR

This work proposes a fast, low-latency filter for identifying strongly lensed gravitational-wave pairs by exploiting the overlap of sky localization probability maps (skymaps) rather than performing costly joint-parameter estimation. It introduces three overlap statistics—posterior overlap, 90% credible region overlap, and cross-HPD—and validates their performance on 200 simulated lensed pairs across five SNRs, demonstrating that at a fixed false-positive rate of $10^{-2}$, more than 99% of nonlensed pairs can be rejected while retaining all lensed pairs. Using rapid skymaps from low-latency pipelines like BAYESTAR, each statistic can be computed in under a few seconds, enabling near real-time screening of event pairs. The results support deploying a dense, SNR-conditioned ROC mapping to set adaptive thresholds in production pipelines, significantly reducing the computational burden of lensing analyses while preserving sensitivity to lensing pairs.

Abstract

Strong gravitational lensing creates multiple images of a gravitational wave transient. The current state-of-the-art method for identifying such lensing events is a computationally expensive full Bayesian analysis. In this paper, we investigate the feasibility and efficiency of using the overlap of sky localization probability maps (skymaps) to quickly filter potentially lensed gravitational wave signal pairs. We introduce three overlap statistics and test their performance using 200 simulated lensed pairs of gravitational-wave signals across five sets of signal-to-noise ratios. By setting a threshold with a false positive rate of $\mathrm{FPR} = 10^{-2}$ for the three overlap statistics, we find that we can filter out over $99\%$ of nonlensed events while retaining all lensed events. The statistics for each event pair can be computed instantly, and can be used in practice to quickly analyze existing events using the skymaps from the low-latency localization pipelines when results from the full parameter estimation are not available.

Using overlap of sky localization probability maps for filtering potentially lensed pairs of gravitational-wave signals

TL;DR

This work proposes a fast, low-latency filter for identifying strongly lensed gravitational-wave pairs by exploiting the overlap of sky localization probability maps (skymaps) rather than performing costly joint-parameter estimation. It introduces three overlap statistics—posterior overlap, 90% credible region overlap, and cross-HPD—and validates their performance on 200 simulated lensed pairs across five SNRs, demonstrating that at a fixed false-positive rate of , more than 99% of nonlensed pairs can be rejected while retaining all lensed pairs. Using rapid skymaps from low-latency pipelines like BAYESTAR, each statistic can be computed in under a few seconds, enabling near real-time screening of event pairs. The results support deploying a dense, SNR-conditioned ROC mapping to set adaptive thresholds in production pipelines, significantly reducing the computational burden of lensing analyses while preserving sensitivity to lensing pairs.

Abstract

Strong gravitational lensing creates multiple images of a gravitational wave transient. The current state-of-the-art method for identifying such lensing events is a computationally expensive full Bayesian analysis. In this paper, we investigate the feasibility and efficiency of using the overlap of sky localization probability maps (skymaps) to quickly filter potentially lensed gravitational wave signal pairs. We introduce three overlap statistics and test their performance using 200 simulated lensed pairs of gravitational-wave signals across five sets of signal-to-noise ratios. By setting a threshold with a false positive rate of for the three overlap statistics, we find that we can filter out over of nonlensed events while retaining all lensed events. The statistics for each event pair can be computed instantly, and can be used in practice to quickly analyze existing events using the skymaps from the low-latency localization pipelines when results from the full parameter estimation are not available.
Paper Structure (13 sections, 9 equations, 3 figures, 2 tables)

This paper contains 13 sections, 9 equations, 3 figures, 2 tables.

Table of Contents

  1. Introduction
  2. Skymap
  3. Posterior distribution
  4. Sky localization probability map
  5. Overlap Statistics
  6. Posterior overlap
  7. 90% credible region overlap
  8. Cross-HPD statistic
  9. Results and Discussion
  10. Injection campaign
  11. Coverage of samples
  12. Performance of statistics
  13. Conclusions

Figures (3)

  • Figure 1: Contours of 90% credible region of 200 skymaps with $\mathrm{SNR}=8$ are shown in the figure. Details of the injection campaign are referred to Table \ref{['table:injection']}. The figure shows the sky coverage of the injections with $\mathrm{SNR} = 8$.
  • Figure 2: ROC curves of event pairs with one event $\mathrm{SNR}=8$. The black solid line $x=y$ represents the ROC curve of a random classifier. ROC curves indicate the performance of the overlap statistics. The classifier is better if it can achieve a higher true positive rate given a false positive rate. The three statistics do not show a large difference in the region of FPR between $10^{-2}$ and 1.
  • Figure 3: ROC curves of event pairs with one event $\mathrm{SNR}=50$. The black solid line $x=y$ represents the ROC curve of a random classifier. The classifier is better if it can achieve a higher true positive rate given a false positive rate. The three statistics do not show a large difference in the region of FPR between $10^{-2}$ and 1.