Snr Detection Threshold

---
name: snr-detection-threshold
description: Evaluates the detection capability of the Lunar Gravitational-Wave Antenna (LGWA) for massive binary black hole mergers by computing the signal-to-noise ratio (SNR) of observed and simulated events against fixed thresholds. Use when the user has predictions and gold and needs to compute SNR.
metadata:
  skill_kind: metric
  source_arxiv: 2512.09978
  bibtex_key: iacovelli2025lgwa
  confidence: high
---

# snr-detection-threshold

> Gravitational-wave parameter estimation to the Moon and back: massive binaries and the case of GW231123 — Iacovelli et al. (2025) (arXiv:2512.09978, 2025)

## What this evaluates

Evaluates the detection capability of the Lunar Gravitational-Wave Antenna (LGWA) for massive binary black hole mergers by computing the signal-to-noise ratio (SNR) of observed and simulated events against fixed thresholds.

## Datasets

- **GWTC-3/4 (LVK Public Catalog)** — total 176; splits: test (176)
- **Simulated BBH Population Catalog** — total 110000; splits: simulation (110000)

## Metrics

- `SNR` **(primary)** — range: other
  - Signal-to-noise ratio computed by projecting the gravitational-wave strain signal onto the detector's noise power spectral density. Standard detection uses SNR ≥ 8, while archival searches use SNR ≥ 5.

## Input / output format

**Input**: Posterior parameter samples (masses, spins, sky location, inclination, polarization, coalescence time/phase) for binary black hole events, either from LVK public catalogs or simulated population models.

**Output**: Computed SNR value per event, classified as detected or undetected based on thresholds (SNR ≥ 8 or SNR ≥ 5).

## Scoring recipe

```python
def compute_snr(event_params, detector_noise_curve):
    strain = generate_waveform(event_params)
    snr = inner_product(strain, strain, detector_noise_curve)
    return snr

def evaluate_detection(events, snr_threshold=8):
    detections = 0
    for event in events:
        snr = compute_snr(event, lgwa_noise_curve)
        if snr >= snr_threshold:
            detections += 1
    return detections / len(events)
```

## Common pitfalls

- SNR values are highly sensitive to the assumed LGWA noise power spectral density, which varies with detector design choices and is not fixed in the paper.
- Using only maximum-likelihood parameters instead of full posterior samples ignores parameter uncertainty, leading to biased detection rate estimates.
- Confusing detector-frame vs. source-frame masses can cause mismatches when comparing simulated catalogs with LVK observations.

## Evidence (verbatim from paper)

> For each event, we extract 1000 samples from its posterior, and compute the LGWA SNR of those synthetic events. We find that, among the 176 events in the catalog, LGWA would have been able to observe 56 (+9/-5) (100 (+10/-8)) events with SNR larger than 8 (5). An SNR of 8 represents a suitable detection threshold, while an SNR of 5 has been identified as a viable threshold for archival searches of events detected with ground-based observatories in the case of LISA.

## Citation

```bibtex
@misc{iacovelli2025lgwa,
  title={Gravitational-wave parameter estimation to the Moon and back: massive binaries and the case of GW231123},
  author={Iacovelli et al. (2025)},
  year={2025},
  note={arXiv:2512.09978}
}
```

- arXiv: 2512.09978