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Handling big data has largely been a major bottleneck in traditional statistical models. Consequently, when accurate point prediction is the primary target, machine learning models are often preferred over their statistical counterparts for…
We investigate the form of the one-point probability distribution function (pdf) for the density field of the interstellar medium using numerical simulations that successively reduce the number of physical processes included.…
Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…
The simplest theory describing large-scale redshift-space distortions (RSD), based on linear theory and distant galaxies, depends on the growth of cosmological structure, suggesting that strong tests of General Relativity can be constructed…
Numerical simulations show that redshift space distortions (RSD) introduce strong scale dependence in the power spectra of halos, with ten percent deviations relative to linear theory predictions even on relatively large scales (k<0.1h/Mpc)…
Given sufficiently many components, it is often cited that finite mixture models can approximate any other probability density function (pdf) to an arbitrary degree of accuracy. Unfortunately, the nature of this approximation result is…
In Part I of this series, we introduced the Spherical Collapse (SC) approximation in Lagrangian space as a way of estimating the cumulants $\xi_J$ of density fluctuations in cosmological Perturbation Theory (PT). Within this approximation,…
Theoretical investigations into the deflection angle caused by microlenses offer a direct path to uncovering principles of the cosmological microlensing effect. This work specifically concentrates on the the probability density function…
We study the statistical properties of the Luminous Red Galaxies sample from the Sloan Digital Sky Survey. In particular we test, by determining the probability density function (PDF) of galaxy (conditional) counts in spheres, whether…
We create mock pencil-beam redshift surveys from very large cosmological $N$-body simulations of two Cold Dark Matter cosmogonies, an Einstein-de Sitter model ($\tau$CDM) and a flat model with $\Omega_0 =0.3$ and a cosmological constant…
The Central Limit Theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization…
The CSL dynamical collapse structure, adapted to the relativistically invariant model where the collapse-generating operator is a one-dimensional scalar field $\hat\phi(x,t)$ (mass $m$) is discussed. A complete solution for the density…
We present a numerically cheap approximation to super-sample covariance (SSC) of large scale structure cosmological probes, first in the case of angular power spectra. It necessitates no new elements besides those used for the prediction of…
We show that an analogy between crowding in fluid and jammed phases of hard spheres captures the density dependence of the kissing number for a family of numerically generated jammed states. We extend this analogy to jams of mixtures of…
A precise determination of the mass function is an important tool to verify cosmological predictions of the $\Lambda$CDM model and to infer more precisely the better model describing the evolution of the Universe. Galaxy clusters have been…
In this work, we studied the impact of galaxy morphology on photometric redshift (photo-$z$) probability density functions (PDFs). By including galaxy morphological parameters like the radius, axis-ratio, surface brightness and the S\'ersic…
Supersonic turbulence occurs in many environments, particularly in astrophysics. In the crucial case of isothermal turbulence, the probability density function (PDF) of the logarithmic density, $s$, is well measured, but a theoretical…
We report on results from the Durham/UKST Galaxy Redshift Survey where we have found large scale ``cellular'' features in the galaxy distribution. These have spatial 2-point correlation function power significantly in excess of the…
Three density theorems for three suitable subspaces of $SBD$ functions, in the strong $BD$ topology, are proven. The spaces are $SBD$, $SBD^p_\infty$, where the absolutely continuous part of the symmetric gradient is in $L^p$, with $p>1$,…
We propose the notion of a sample distortion (SD) function for independent and identically distributed (i.i.d) compressive distributions to fundamentally quantify the achievable reconstruction performance of compressed sensing for certain…