Kernel-, mean- and noise-marginalised Gaussian processes for exoplanet transits and $H_0$ inference

TL;DR

This paper extends Gaussian Process regression with Bayesian marginalisation over kernels, hyperparameters, and models, applying it to exoplanet transits and $H_0$ inference, demonstrating improved model comparison and robust cosmological parameter estimation.

Contribution

It introduces a transdimensional Bayesian approach for kernel and model selection in Gaussian Processes, applied to astrophysical data for exoplanet transits and cosmological parameter inference.

Findings

Kernel recovery on synthetic exoplanet data was successful.

Inferred $H_0$ values are consistent with previous measurements.

Cosmic chronometers dataset prefers a non-stationary linear kernel.

Abstract

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 $\Lambda$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 $\ln R=12.17\pm 0.02$.