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Abstract The observed distributions of the source properties from gravitational-wave (GW) detections are biased due to the selection effects and detection criteria in the detections, analogous to the Malmquist bias. In this work, this observation bias is investigated through its fundamental statistical and physical origins. An efficient semi-analytical formulation for its estimation is derived, which is as accurate as the standard method of numerical simulations, with only a millionth of the computational cost. Then, the estimated bias is used for unmodeled inferences on the binary black hole population. These inferences show additional structures, specifically two peaks in the joint mass distribution around binary masses ∼10 M ⊙ and ∼30 M ⊙ . Example ready-to-use scripts and some produced data sets for this method are shared in an online repository.
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Growing pains: understanding the impact of likelihood uncertainty on hierarchical Bayesian inference for gravitational-wave astronomy
ABSTRACT Observations of gravitational waves emitted by merging compact binaries have provided tantalizing hints about stellar astrophysics, cosmology, and fundamental physics. However, the physical parameters describing the systems (mass, spin, distance) used to extract these inferences about the Universe are subject to large uncertainties. The most widely used method of performing these analyses requires performing many Monte Carlo integrals to marginalize over the uncertainty in the properties of the individual binaries and the survey selection bias. These Monte Carlo integrals are subject to fundamental statistical uncertainties. Previous treatments of this statistical uncertainty have focused on ensuring that the precision of the inferred inference is unaffected; however, these works have neglected the question of whether sufficient accuracy can also be achieved. In this work, we provide a practical exploration of the impact of uncertainty in our analyses and provide a suggested framework for verifying that astrophysical inferences made with the gravitational-wave transient catalogue are accurate. Applying our framework to models used by the LIGO–Virgo–KAGRA collaboration and in the wider literature, we find that Monte Carlo uncertainty in estimating the survey selection bias is the limiting factor in our ability to probe narrow population models and this will rapidly grow more problematic as the size of the observed population increases.
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- Award ID(s):
- 2207758
- PAR ID:
- 10533734
- Publisher / Repository:
- Oxford University Press on behalf of Royal Astronomical Society
- Date Published:
- Journal Name:
- Monthly Notices of the Royal Astronomical Society
- Volume:
- 526
- Issue:
- 3
- ISSN:
- 0035-8711
- Page Range / eLocation ID:
- 3495 to 3503
- Subject(s) / Keyword(s):
- gravitational waves compact binaries statistical uncertainties Bayesian inference
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript
- Journal Article:
- https://doi.org/10.1093/mnras/stad2968
