Kernel-, mean- and noise-marginalised Gaussian processes for exoplanet transits and $H_0$ inference
This work addresses uncertainty quantification in Gaussian Processes for astrophysics, specifically in exoplanet transits and cosmology, but is incremental as it extends existing Bayesian methods with marginalization techniques.
The paper tackles the problem of improving Gaussian Process regression by marginalizing over kernel choice, hyperparameters, mean functions, and noise models using a fully Bayesian approach with transdimensional sampling, and applies this to exoplanet transit simulations and Hubble parameter inference, resulting in inferred H0 values of 66 ± 6, 67 ± 10, and 69 ± 6 km/s/Mpc from different datasets.
Using a fully Bayesian approach, Gaussian Process regression is extended to include marginalisation over the kernel choice and kernel hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher-dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light curve simulations. Subsequently, the method was extended to marginalisation over mean functions and noise models and applied to the inference of the present-day Hubble parameter, $H_0$, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and $Λ$CDM-dependent baryon acoustic oscillation observations. The inferred $H_0$ values from the cosmic chronometers, baryon acoustic oscillations and combined datasets are $H_0= 66 \pm 6\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, $H_0= 67 \pm 10\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$ and $H_0= 69 \pm 6\, \mathrm{km}\,\mathrm{s}^{-1}\,\mathrm{Mpc}^{-1}$, respectively. The kernel posterior of the cosmic chronometers dataset prefers a non-stationary linear kernel. Finally, the datasets are shown to be not in tension with $\ln R=12.17\pm 0.02$.