Compute Bayes-factor evidences for GP mass models

Compute evidences for Bayes-factor comparisons between the GP-1D and GP-2D Gaussian-process mass-distribution models used by CosmoPyro, thereby enabling direct model comparison beyond the capabilities of NUTS sampling.

Background

CosmoPyro implements two flexible non-parametric population models for compact-binary source-frame masses: GP-1D, which models the primary-mass distribution with a one-dimensional Gaussian process and uses a running power law for the mass ratio, and GP-2D, which models the joint mass distribution in logarithmic total mass and logarithmic mass ratio with a two-dimensional Gaussian process. The paper compares their inferred Hubble-constant posteriors and reconstructed mass distributions, but does not perform a Bayesian-evidence comparison between them.

The authors note that NUTS sampling does not directly provide model evidences. Computing these evidences would permit quantitative Bayes-factor comparisons between the GP-1D and GP-2D models and help assess which correlation structure is better supported by gravitational-wave catalogs, particularly as future datasets become larger and more informative.

References

Beyond the scope of this work, it would be desirable to compute evidences for Bayes-factor comparisons between the GP-1D and GP-2D models, something we leave for future work as this is not an immediate product from NUTS sampling.

— CosmoPyro: Gradients for Gravitational-Wave Cosmology  (2608.18281 - Leyde et al., 18 Aug 2026) in Section 5, Conclusions, p. 18

More targeted studies of population parameterizations in the two-dimensional mass plane will be needed to determine whether such shifts could become a source of systematic uncertainty as statistical errors shrink.

— A weakly modelled view of the joint compact-binary mass plane: population structure and spectral-siren cosmology  (2610.10535 - Renzis et al., 7 Oct 2026) in Section 3.3, paragraph beginning 'The change in population model'