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Table G.1.

Bayesian evidence, maximum log likelihood value, and number of parameters for the cosτ models (relative to the reference LVK model of Eq. B.1).

Run lnEvidence lnMaxL # spin pars
Isotropic −0.8 −3.2 -2

LVK default ref ref ref

Isotropic + Gaussianμ ∈ [ − 1, 1] −0.3 −0.4 +1

Isotropic + Gaussianμ ∈ [ − 5, 5] −0.4 −0.2 +1

Isotropic + Beta +0.4 +0.4 +1

Isotropic + Tukey −0.2 +0.7 +2

Isotropic + correlated Gaussian (m) −0.4 −0.6 +3

Isotropic + correlated Gaussian (q) −0.5 −0.1 +3

Isotropic + correlated Gaussian (χ) −0.6 −0.4 +3

Isotropic + correlated Gaussian (Mtot) −0.7 −0.1 +3

Isotropic + correlated Beta (m) −0.4 +0.0 +3

Isotropic + correlated Beta (q) −0.1 −0.3 +3

Isotropic + correlated Beta (χ) +0.3 −0.6 +3

Isotropic + correlated Beta (Mtot) −0.3 −0.7 +3

Isotropic + Gaussian + Beta +0.3 −0.6 +4

Isotropic + 2 Gaussians ( − A = B = 1) −0.1 −0.3 +4

Isotropic + Gaussian + Tukey +0.1 +0.3 +5

Isotropic + 2 Gaussians +0.6 +0.2 +6

Notes: With our settings, the evidences carry a statistical uncertainty of ±0.15. Additional uncertainties in the log likelihood – and hence evidence – arise from the numerical evaluation of the integral in Eq. A.1. Golomb & Talbot (2022) estimate this extra uncertainty to be roughly Δlogℒ ± 1 when using the publicly released LVK injection sets to estimate selection effects. We also note that nested sampling algorithms do not aim to find the highest likelihood point, so it is possible that for nested models (e.g., LVK default and Isotropic + Gaussian) the broader model finds a slightly lower maximum likelihood point. Given these uncertainties, the only reliable – yet unsurprising – conclusions one may draw is that a purely isotropic model yields the worst match to the data.

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