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. This method was
explored on synthetic data from exoplanet transit light curve simulations. The
true kernel was recovered in the low noise region while no kernel was preferred
for larger noise. Furthermore, inference of the physical exoplanet
hyperparameters was conducted. In the high noise region, either the bias in the
posteriors was removed, the posteriors were broadened or the accuracy of the
inference was increased. In addition, the uncertainty in mean function
predictive distribution increased due to the uncertainty in the kernel choice.
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 km/s/Mpc,
$H_0$ = 67$\pm$10 km/s/Mpc and $H_0$ = 69$\pm$6 km/s/Mpc, respectively. The
kernel posterior of the cosmic chronometers dataset prefers a non-stationary
linear kernel. Finally, the datasets are shown to be not in tension with
ln(R)=12.17$\pm$0.02.

使用完全贝叶斯方法将高斯过程回归扩展到包括核选择和核超参数的边际化。同时通过证据执行贝叶斯模型比较，实现了直接核比较。方法在合成数据和实际天体测量中得到了验证。

用于系外行星凌星和 $H_0$ 推断的核化、均值化和噪声化边际高斯过程

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

The time delay measured between the images of gravitationally lensed quasars
probes a combination of the angular diameter distance to the source-lens system
and the mass density profile of the lens. Observational campaigns to measure
such systems have reported a determination of the Hubble parameter H0 that
shows significant tension with independent determination based on the cosmic
microwave background (CMB) and large scale structure (LSS). We show that lens
mass models that exhibit a cored component, coexisting with a cusp, probe a
degenerate direction in the lens model parameter space, being an approximate
mass sheet transformation. This family of lens models has not been considered
by the cosmographic analyses. Once added to the model, the cosmographic error
budget should become dependent on stellar kinematics uncertainties. We propose
that a core component coexisting with a cusp could bring the lensing
measurements of H0 to accord with the CMB/LSS value.

通过测量引力透镜状星系图像之间的时差，对其源 - 透镜系统的角直径距离和透镜的质量密度轮廓的结合进行了研究，在该研究中，引入了含有一个中心核和一个尖峰的透镜质量模型，并将其接入到宇宙学分析模型中，提出了一种可将引力透镜测量结果与宇宙微波背景和大尺度结构数据一致的方法。