Catalog Construction and Selection Effects

A gravitational-wave catalog is the output of a versioned measurement process, not a source list discovered independently of that process. Calibrated detector time, search pipelines, ranking backgrounds, association rules, thresholds, signal–noise mixtures, parameter products, and injection-measured efficiency jointly determine which records appear and which population claims they can support. This chapter reconstructs that chain without yet inferring astrophysical population distributions.

Helpful background. Injection Campaigns and Search Sensitivity explains how efficiency is measured, and The Gravitational-Wave Likelihood supplies the event-level statistical interface.

Enter the catalog construction problem

Three search quantities are often confused:

$$\mathrm{FAR}(x), \qquad p_{\mathrm{astro}}(x), \qquad p_{\mathrm{det}}(\theta).$$

The false-alarm rate describes a search’s noise background above rank $x$. The astrophysical probability is a signal–noise mixture membership under assumed rates and densities. The detection probability describes the chance that a source with parameters $\theta$ enters the catalog under the complete search and reporting rule. None can be substituted for another.

For a population model $\pi(\theta\mid\Lambda)$, the selection normalization is

$$\alpha(\Lambda) =\int d\theta\, p_{\mathrm{det}}(\theta) \pi(\theta\mid\Lambda).$$

This quantity connects catalog construction to the hierarchical inference of the next chapter. It must use the same detector/source-frame measure, observing epochs, search versions, and threshold that generated the analyzed event set.

The event-likelihood, interim-prior, rate, and selection measures must remain distinct in that transition Thrane and Talbot 2019, § 5 and Appendices E–F, corrected PDF v9.

Two routes through the chapter

Catalog provenance route. Follow From Search Triggers to Catalog Events, Detection Thresholds and False-Alarm Accounting, and Catalog Versions and Scientific Updates. This route is for readers evaluating whether an event count, membership statement, or product can be reproduced.

Preparing a population analysis. Begin with Selection Functions from Injections, continue to Completeness and Search Heterogeneity, and then study Astrophysical Probability and Mixture Membership. This route is for readers preparing a contamination- and selection-aware likelihood.

The routes meet at the threshold. The catalog inclusion rule determines which triggers become records, which injections count as recovered, and which mixture model applies near the boundary.

Chapter map

1. From Search Triggers to Catalog Events preserves pipeline, data-quality, association, and parameter-product provenance.
2. Detection Thresholds and False-Alarm Accounting connects ranking backgrounds, analyzed time, trials, and inclusion loss functions.
3. Selection Functions from Injections derives importance-weighted efficiency and its support and Monte Carlo diagnostics.
4. Completeness and Search Heterogeneity shows why completeness is conditional on source region, detector epoch, search union, and product availability.
5. Astrophysical Probability and Mixture Membership derives model-dependent signal membership and compares pipeline-specific, unified, and coherent-odds treatments.
6. Catalog Versions and Scientific Updates binds every current claim to immutable release inputs and a dated assessment.

After the chapter, a reader should be able to trace an event-level claim back to its search and release, distinguish contamination from inefficiency, and decide whether a catalog subset and injection set support a proposed downstream analysis.

Recurring failure modes

A row is treated as an unconditioned source. Catalog membership depends on a pipeline and rule. Preserve the search and version that produced it.

FAR is read as a candidate’s noise probability. FAR is a background-event rate. $p_{\mathrm{astro}}$ additionally uses signal/noise rate and shape models.

Selection is corrected by weighting detected point estimates. The selection factor normalizes the generative population likelihood; it is not generally an inverse-efficiency patch on noisy event summaries.

Several pipelines are assumed independent. They share strain, signal strength, glitches, and waveform support. Measure the union efficiency and joint background with common triggers or injections.

A cumulative release is called uniformly complete. Sensitivity, duty cycle, calibration, search domain, and product coverage vary across epochs and source classes.

What the results establish

All release-specific examples in this chapter are frozen at 2026-08-18. The current baseline is the official GWTC-5.0 release, interpreted with its Methods paper and Observations paper. Stable probability identities remain useful after a new release; membership values, row sets, thresholds, injection products, and completeness claims require a freshness review.

Review the chapter

1. Diagnose a classification claim. A candidate has a FAR of $0.1\,\mathrm{yr}^{-1}$. A report states that it therefore has a 90% probability of being astrophysical. What is missing?

Solution

FAR is a noise-trigger rate, not a posterior membership probability. Computing $p_{\mathrm{astro}}$ requires at least the local signal and noise ranking densities and their expected rates, plus the pipeline, epoch, and source-population model. The stated 90% does not follow from the FAR.

2. Check selection support. An injection proposal contains only $q\gt0.5$ binaries, but a target population allows $q\ge0.1$. Can importance weighting provide the full selection factor?

Solution

No. The proposal density is zero for $0.1\le q\le0.5$, so injections supply no information about detection probability there. The importance ratio is undefined on that part of the target support. A new campaign or a second proposal covering the missing region is required.

3. Transfer task. Two correlated searches have individual efficiencies $0.7$ and $0.6$. Why can neither $1.3$ nor $1-(0.3)(0.4)=0.88$ be accepted automatically as their union efficiency?

Solution

Adding efficiencies double-counts jointly recovered sources and can exceed one. The value $0.88$ assumes conditional independence, but searches on the same strain are correlated through source strength, detector state, glitches, and shared waveform coverage. Pass common injections through both searches and the actual de-duplication rule to estimate the union directly.

Continue to Source Populations and Hierarchical Inference for the selection-normalized likelihood that combines event data, rates, and population distributions.

References

• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration (2026). “GWTC-5.0: Methods for Identifying and Characterizing Gravitational-Wave Transients.” arXiv:2605.27224. Open PDF.
• LIGO Scientific Collaboration, Virgo Collaboration, and KAGRA Collaboration (2026). “GWTC-5.0: Observations from the Second Part of the Fourth LIGO-Virgo-KAGRA Observing Run and Updates to the Gravitational-Wave Transient Catalog.” arXiv:2605.27225. Open PDF.
• Thrane, E., and Talbot, C. (2019). “An Introduction to Bayesian Inference in Gravitational-Wave Astronomy: Parameter Estimation, Model Selection, and Hierarchical Models.” Publications of the Astronomical Society of Australia 36, e010. DOI. Open PDF v9, including the selection erratum.