Related papers: Quantifying galactic clustering and departures fro…
A number of recent studies have estimated the inter-galactic void probability function and investigated its departure from various random models. We study a family of parametric statistical models based on gamma distributions, which do give…
Statistical inference more often than not involves models which are non-linear in the parameters thus leading to non-Gaussian posteriors. Many computational and analytical tools exist that can deal with non-Gaussian distributions, and…
We show that gamma distributions provide models for departures from randomness since every neighbourhood of an exponential distribution contains a neighbourhood of gamma distributions, using an information theoretic metric topology. We…
Large-scale structure of Universe includes galaxy clusters connected by filaments. Voids occupy the rest of cosmic volume. The search of any dependencities in filament structure can give answer to more general questions about origin of…
The information geometry of the 2-manifold of gamma probability density functions provides a framework in which pseudorandom number generators may be evaluated using a neighbourhood of the curve of exponential density functions. The process…
A novel over-dispersed discrete distribution, namely the PoiTG distribution is derived by the convolution of a Poisson variate and an independently distributed transmuted geometric random variable. This distribution generalizes the…
Galaxies are arranged in interconnected walls and filaments forming a cosmic web encompassing huge, nearly empty, regions between the structures. Many statistical methods have been proposed in the past in order to describe the galaxy…
In this dissertation, an abstract formalism extending information geometry is introduced. This framework encompasses a broad range of modelling problems, including possible applications in machine learning and in the information theoretical…
A grand challenge of the 21st century cosmology is to accurately estimate the cosmological parameters of our Universe. A major approach to estimating the cosmological parameters is to use the large-scale matter distribution of the Universe.…
In this paper a relative number density parameter, called the neighborhood function, is introduced so that the crowded nature of the neighborhood of individual sources can be described. With this parameter one can determine the probability…
Three methods for detecting and characterizing structure in point data, such as that generated by redshift surveys, are described: classification using self-organizing maps, segmentation using Bayesian blocks, and density estimation using…
This review presents a comprehensive overview of galaxy bias, that is, the statistical relation between the distribution of galaxies and matter. We focus on large scales where cosmic density fields are quasi-linear. On these scales, the…
Cosmic voids in the large-scale structure of the Universe affect the peculiar motions of objects in their vicinity. Although these motions are difficult to observe directly, the clustering pattern of their surrounding tracers in redshift…
We investigate the geometrical structure of probabilistic generative dimensionality reduction models using the tools of Riemannian geometry. We explicitly define a distribution over the natural metric given by the models. We provide the…
We present cosmological simulations of galaxy clusters, with focus on the cluster outskirts. We show that large-scale cosmic accretion and mergers produce significant internal gas motions and inhomogeneous gas distribution ("clumpiness") in…
Likelihood fitting to two-point clustering statistics made from galaxy surveys usually assumes a multivariate normal distribution for the measurements, with justification based on the central limit theorem given the large number of…
We introduce diffusion geometry as a new framework for geometric and topological data analysis. Diffusion geometry uses the Bakry-Emery $\Gamma$-calculus of Markov diffusion operators to define objects from Riemannian geometry on a wide…
Given a Poisson process on a bounded interval, its random geometric graph is the graph whose vertices are the points of the Poisson process and edges exist between two points if and only if their distance is less than a fixed given…
A new method for analyzing point patterns produced by the evolution of gravitational clustering is presented. The method is taken from the study of molecular liquids, where it has been introduced for making a statistical description of…
Multivariate generalized Gamma convolutions are distributions defined by a convolutional semi-parametric structure. Their flexible dependence structures, the marginal possibilities and their useful convolutional expression make them…