Related papers: Wavelet Moments for Cosmological Parameter Estimat…
We investigate the use of wavelet transforms in detecting and characterising non-Gaussian structure in maps of the cosmic microwave background (CMB). We apply the method to simulated maps of the Kaiser-Stebbins effect due to cosmic strings…
The analysis of gravitational-wave (GW) signals is one of the most challenging application areas of signal processing. Wavelet transforms are specially helpful in detecting and analyzing GW transients and several analysis pipelines are…
The cosmic microwave background (CMB) is a relic radiation of the Big Bang and as such it contains a wealth of cosmological information. Statistical analyses of the CMB, in conjunction with other cosmological observables, represent some of…
The two-point summary statistics is one of the most commonly used tools in the study of cosmological structure. Starting from the theoretical power spectrum defined in the 3D volume and obtained via the process of ensemble averaging, we…
Using distribution theory we present the moment asymptotic expansion of continuous wavelet transform in different distributional spaces for large and small values of dilation parameter $a$. We also obtain asymptotic expansions for certain…
We focus on the complex relationship between the shape of dark matter halos and the cosmological models underlying their formation. We used three realistic cosmological models from the Dark Energy Universe Simulation suite. They have…
Recent measurements of the cosmic microwave background radiation (CMB), particularly when combined with other datasets, have revolutionised our knowledge of the values of the basic cosmological parameters. Here we summarize the state of…
We study the cosmological information contained in the cosmic web, categorized as four structure types: nodes, filaments, walls, and voids, using the Quijote simulations and a modified nexus+ algorithm. We show that splitting the density…
We derive constraints on cosmological parameters using the power spectrum of galaxy clustering measured from the final two-degree field galaxy redshift survey (2dFGRS) and a compilation of measurements of the temperature power spectrum and…
We study non-parametric regression estimates for random fields. The data satisfies certain strong mixing conditions and is defined on the regular $N$-dimensional lattice structure. We show consistency and obtain rates of convergence. The…
This chapter is dedicated to recent developments in the field of wavelet analysis for scattered data. We introduce the concept of samplets, which are signed measures of wavelet type and may be defined on sets of arbitrarily distributed data…
The power spectrum has long been the workhorse summary statistics for large-scale structure cosmological analyses. However, gravitational non-linear evolution moves precious cosmological information from the two-point statistics (such as…
Many flexible parameterizations exist to represent data on the sphere. In addition to the venerable spherical harmonics, we have the Slepian basis, harmonic splines, wavelets and wavelet-like Slepian frames. In this paper we focus on the…
We develop a novel statistical strong lensing approach to probe the cosmological parameters by exploiting multiple redshift image systems behind galaxies or galaxy clusters. The method relies on free-form mass inversion of strong lenses and…
This work is concerned with the study of the adaptivity properties of nonparametric regression estimators over the $d$-dimensional sphere within the global thresholding framework. The estimators are constructed by means of a form of…
Covariance matrices are essential cosmological probes of fundamental physics, providing information on numerous fundamental physical parameters and varying with any change in the underlying cosmology. However, this cosmology dependence,…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
Massive neutrinos influence the background evolution of the Universe as well as the growth of structure. Being able to model this effect and constrain the sum of their masses is one of the key challenges in modern cosmology. Weak-lensing…
In data science, one is often confronted with a time series representing measurements of some quantity of interest. Usually, as a first step, features of the time series need to be extracted. These are numerical quantities that aim to…
We discuss Spherical Needlets and their properties. Needlets are a form of spherical wavelets which do not rely on any kind of tangent plane approximation and enjoy good localization properties in both pixel and harmonic space; moreover…