And Gaussian process is independent of any specific parameterized forms of function.
Thus by transformations these generic cosmography parameters can be used to constrain a cosmological model and dark energy model directly at the kinematics level of our Universe.May 7, 2023.
Gaussian Process is a machine learning technique.
You can use it to do regression, classification, among many other things..
In probability theory and statistics, a Gaussian process is a stochastic process (a collection of random variables indexed by time or space), such that every finite collection of those random variables has a multivariate normal distribution, i.e. every finite linear combination of them is normally distributed..
And Gaussian process is independent of any specific parameterized forms of function.
Thus by transformations these generic cosmography parameters can be used to constrain a cosmological model and dark energy model directly at the kinematics level of our Universe.May 7, 2023.
It means, that the cosmological perturbations satisfy Gaussian initial conditions.
This means, that the probability of the perturbation amplitude has a Gaussian shape about the mean value.
Considering linear perturbation theory, the initial Gaussian probability distribution will remain Gaussian for all times, e.g. today.
To the best of our knowledge, the Euclidean setting is (so far) the only one used in cosmology.
The second component of the GKF is a twice differentiable, constant mean, Gaussian random field, , with constant variance.
There is no requirement of stationarity or isotropy, only of constant mean and variance.
One of the principal topological characteristics of Gaussian fields is their relative simplicity, in that the three Betti numbers dominate the topology at different density ranges.
In this sense, Gaussian field are rather unique.
Our statistical study of 3D Gaussian field homology consists of Betti number curves β 0, β 1, and β 2 as a function of density field threshold ν of the corresponding superlevel set of a Gaussian field realization.
The curves are averaged over 100 field realizations for each separate power spectrum.
