Related papers: The Value of $H_0$ from Gaussian Processes
Accurate estimation of the Hubble constant, and other cosmological parameters, from distances measured by cosmic gravitational wave sirens requires sufficient allowance for the dark energy evolution. We demonstrate how model independent…
In this paper we propose the first non-parametric Bayesian model using Gaussian Processes to make inference on Poisson Point Processes without resorting to gridding the domain or to introducing latent thinning points. Unlike competing…
The standard cosmological model, the $\Lambda$CDM model, is the most suitable description for our universe. This framework can explain the accelerated expansion phase of the universe but still is not immune to open problems when it comes to…
Gaussian process (GP) models are effective non-linear models for numerous scientific applications. However, computation of their hyperparameters can be difficult when there is a large number of training observations (n) due to the O(n^3)…
Gravitational lensing is now widely and successfully used to study a range of astronomical phenomena, from individual objects, like galaxies and clusters, to the mass distribution on various scales, to the overall geometry of the Universe.…
The correlation length-scale next to the noise variance are the most used hyperparameters for the Gaussian processes. Typically, stationary covariance functions are used, which are only dependent on the distances between input points and…
Gaussian processes offers a convenient way to perform nonparametric reconstructions of observational data assuming only a kernel which describes the covariance between neighbouring points in a data set. We approach the ambiguity in the…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…
Determining the relevant spatial covariates is one of the most important problems in the analysis of point patterns. Parametric methods may lead to incorrect conclusions, especially when the model of interactions between points is wrong.…
The measurement of the Hubble constant $H_0$ plays an important role in the study of cosmology. In this letter, we propose a new method to constrain the Hubble constant using the strongly lensed gravitational wave (GW) signals. By…
We report the outcome of a 3-day workshop on the Hubble constant (H_0) that took place during February 6-8 2012 at the Kavli Institute for Particle Astrophysics and Cosmology, on the campus of Stanford University. The participants met to…
We study the expected variance of measurements of the Hubble constant, $H_0$, as calculated in either linear perturbation theory or using non-linear velocity power spectra derived from $N$-body simulations. We compare the variance with that…
Gaussian process regression is used throughout statistics and machine learning for prediction and uncertainty quantification. A Gaussian process is specified by its mean and covariance functions. Many covariance functions, including…
Gaussian process is a theoretically appealing model for nonparametric analysis, but its computational cumbersomeness hinders its use in large scale and the existing reduced-rank solutions are usually heuristic. In this work, we propose a…
Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…
In this paper we present new constraints on the Hubble parameter $H_0$ using: (i) the available data on $H(z)$ obtained from cosmic chronometers (CCH); (ii) the Hubble rate data points extracted from the supernovae of Type Ia (SnIa) of the…
Uncertainty quantification based on generalized polynomial chaos has been used in many applications. It has also achieved great success in variation-aware design automation. However, almost all existing techniques assume that the parameters…
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of…
In this paper we study algorithms to find a Gaussian approximation to a target measure defined on a Hilbert space of functions; the target measure itself is defined via its density with respect to a reference Gaussian measure. We employ the…
In the present work, we apply consistency relation tests to several cosmological models, including the flat and non-flat $\Lambda$CDM models, as well as the flat XCDM model. The analysis uses a non-parametric Gaussian Processes method to…