Related papers: Cosmic Statistics of Statistics
Studies of galaxy clusters have proved crucial in helping to establish the standard model of cosmology, with a universe dominated by dark matter and dark energy. A theoretical basis that describes clusters as massive, multi-component,…
We present a novel approach to measuring the expansion rate and the geometry of the Universe, which combine time-delay cosmography in lens galaxy clusters with pure samples of 'cosmic chronometers' (CCs) by probing the member galaxies. The…
In this study it is shown that the Tsallis q-extended statistical theory was found efficient to describe faithfully the space plasmas statistics in every case, from the planetic magnetospheres, to solar corona and solar dynamics, as well as…
We revisit the method of cumulants for analysing dynamic light scattering data in particle sizing applications. Here the data, in the form of the time correlation function of scattered light, is written as a series involving the first few…
The calculation of the characteristic function of the signal fluctuations due to clustered astrophysical sources is performed in this paper. For the typical case of power-law differential number counts and two-point angular correlation…
Conditional cumulants form a set of unique statistics which represent a sensible compromise between N-point correlation functions and cumulants measured from moments of counts in cells. They share accurate edge corrected estimators with…
This review outlines concepts of mathematical statistics, elements of probability theory, hypothesis tests and point estimation for use in the analysis of modern astronomical data. Least squares, maximum likelihood, and Bayesian approaches…
We describe an efficient algorithm for calculating the statistics of weak lensing by large-scale structure based on a tiled set of independent particle-mesh N-body simulations which telescope in resolution along the line of sight. This…
The accumulation of redshifts provides a significant observational bottleneck when using galaxy cluster surveys to constrain cosmological parameters. We propose a simple method to allow the use of samples where there is a fraction of the…
This survey provides a unified discussion of multiple integrals, moments, cumulants and diagram formulae associated with functionals of completely random measures. Our approach is combinatorial, as it is based on the algebraic formalism of…
Many important statistical models fall outside classical moment-based methods due to the non-existence of moments or moment generating functions. We propose a generalised probabilistic framework in which densities are replaced by pairs…
The advent of large data-set in cosmology has meant that in the past 10 or 20 years our knowledge and understanding of the Universe has changed not only quantitatively but also, and most importantly, qualitatively. Cosmologists rely on data…
Modern astronomy has been rapidly increasing our ability to see deeper into the universe, acquiring enormous samples of cosmic populations. Gaining astrophysical insights from these datasets requires a wide range of sophisticated…
Recently it has been shown that cumulants significantly simplify the analysis of multipartite weak measurements. Here we consider the mathematical structure that underlies this, and find that it can be formulated in terms of what we call…
Agekyan lambda-factor that accounts for the effect of multiple distant encounters with large impact factors is used for the first time to compute the diffusion coefficients in the velocity space of a stellar system. It is shown that in this…
Source confusion has been a long-standing problem in the astronomical history. In the previous formulation, sources are assumed to be distributed homogeneously on the sky. This fundamental assumption is not realistic in many applications.…
Non-extensive statistics, namely Tsallis statistics, is applied on a case of a supercritical string cosmology and interesting cosmological modifications are obtained. The two main results we focus on in this work are: fractal scaling for…
Beyond the linear regime, the power spectrum and higher order moments of the matter field no longer capture all cosmological information encoded in density fluctuations. While non-linear transforms have been proposed to extract this…
Several fundamental and closely interconnected issues related to factor models are reviewed and discussed: dynamic versus static loadings, rate-strong versus rate-weak factors, the concept of weakly common component recently introduced by…
Weak lensing surveys are expected to provide direct measurements of the statistics of the projected dark matter distribution. Most analytical studies of weak lensing statistics have been limited to quasilinear scales as they relied on…