Kernel-, mean-, and noise-marginalized Gaussian processes for exoplanet transits and H0 inference

Abstract

ABSTRACT Using a fully Bayesian approach, Gaussian process regression is extended to include marginalization over the kernel choice and 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 marginalization over mean functions and noise models and applied to the inference of the present-day Hubble parameter, H0, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and lambda-cold dark matter-dependent baryon acoustic oscillation observations. The inferred H0 values from the cosmic chronometers, baryon acoustic oscillations, and combined data sets are $H_0= 66 \pm 6,\, 67 \pm 10,\, \mathrm{ and}\,69 \pm 6\,\mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$, respectively. The kernel posterior of the cosmic chronometers data set prefers a non-stationary linear kernel. Finally, the data sets are shown to be not in tension with ln R = 12.17 ± 0.02.