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.