Gwtc2 Bbh Mass Distribution Eval

gwtc2-bbh-mass-distribution-eval

Ain't No Mountain High Enough: Semi-Parametric Modeling of LIGO-Virgos Binary Black Hole Mass Distribution — Edelman et al. (2021) (arXiv:2109.06137, 2021)

What this evaluates

Evaluates the ability of semi-parametric and parametric models to recover the astrophysical primary mass distribution of binary black holes from gravitational wave observations, specifically testing for features like the ~35 M⊙ peak and low-mass structure.

Datasets

• GWTC-2 catalog — total 46; splits: full (46)

Metrics

• marginal likelihood (primary) — range: other
  • Computed via hierarchical Bayesian inference to compare model fit and select the number of spline knots. Higher values indicate better evidence for the model given the data.
• percentile of zero perturbation — range: percent
  • The percentile in the posterior distribution where the perturbation function f(m1)=0 falls. Values near 50% indicate no deviation from the power law; extreme values indicate credible features.

Input / output format

Input: Posterior samples for each of the 46 BBH events, combined with a gravitational wave injection set to estimate selection effects.

Output: Inferred hyperparameters for the mass distribution model, perturbation function f(m1) at specific masses, and sets of predicted event catalogs for posterior predictive checks.

Scoring recipe

# For each model (spline variants, Powerlaw+Peak, etc.):
# 1. Run hierarchical Bayesian inference to get posterior on hyperparameters.
# 2. Compute marginal likelihood Z_n.
# 3. For posterior predictive checks:
#    - Reweight injection set to inferred population for N_draw=500 draws.
#    - Draw N_obs=46 predicted events per draw.
#    - Reweight event posteriors to inferred population, draw 1 fair draw per event per draw.
#    - Compare predicted vs observed CDFs and relative errors visually.
# 4. For feature credibility:
#    - Calculate percentile where f(m1)=0 in the posterior at target masses (7.5, 10, 35 M_sun).

Common pitfalls

• Small number statistics (N=46) can cause the model to latch onto data fluctuations, especially at low masses where sensitive volume is small.
• Spline models are inherently more likely to find peak-like features than power-law breaks, which must be accounted for when comparing to parametric models.
• Posterior predictive checks are primarily visual/qualitative in this work, relying on band overlap rather than a single scalar score.

Evidence (verbatim from paper)

We calculate the percentile where f=0 falls in the posterior distribution for each of these three cuts, which would be near 50% in the presence of no deviations to the power law or equivalently for draws from the spline model prior. The percentiles of zero perturbation for the combined model with the conservative (wide) priors are 70.8% (72.6%), 19.4% (13.1%), and 0.8% (2.5%) at 7.5 M⊙, 10 M⊙, and 35 M⊙, respectively.

Citation

@misc{edelman2021semi,
  title={Ain't No Mountain High Enough: Semi-Parametric Modeling of LIGO-Virgos Binary Black Hole Mass Distribution},
  author={Edelman et al. (2021)},
  year={2021},
  note={arXiv:2109.06137}
}

• arXiv: 2109.06137