Fast and Efficient Bayesian Method to Search for Strongly Lensed Gravitational Waves
Bibliographic record
Abstract
Abstract A small fraction of the gravitational-wave (GW) signals from binary black holes observable by ground-based detectors will be strongly lensed by intervening objects such as galaxies and clusters. Strong lensing will produce nearly identical copies of the GW signals separated in time. These lensed signals must be identified against a background of unlensed pairs GW events, some of which may appear similar by accident. This is usually done using fast, but approximate methods that, for example, check for the overlap between the posterior distributions of a subset of binary parameters, or using slow, but accurate joint Bayesian parameter estimation. In this work, we present a modified version of the posterior overlap method dubbed “PO2.0” that is mathematically equivalent to joint parameter estimation while still remaining fast. We achieve a significant gain in efficiency by incorporating informative priors about the binary and lensing populations, selection effects, and all the inferred parameters of the binary. For binary black hole signals lensed by galaxies, our improved method can detect 65% lensed events at a pairwise false alarm probability of ∼2 × 10−6. Consequently, we have a 13% probability of detecting a strongly lensed event above 2.25σ significance during 18 months of observation by the LIGO-Virgo detectors at their current sensitivity. We also show how we can compute the joint posteriors of the lens and source parameters from a pair of lensed events by reweighting the posteriors of individual events in a computationally inexpensive way.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.013 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.003 | 0.003 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.009 | 0.002 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".