Related papers: New Interpretable Statistics for Large Scale Struc…
Extracting non-Gaussian information from the non-linear regime of structure formation is key to fully exploiting the rich data from upcoming cosmological surveys probing the large-scale structure of the universe. However, due to theoretical…
Optimal extraction of the non-Gaussian information encoded in the Large-Scale Structure (LSS) of the universe lies at the forefront of modern precision cosmology. We propose achieving this task through the use of the Wavelet Scattering…
It is well known that the power spectrum is not able to fully characterize the statistical properties of non-Gaussian density fields. Recently, many different statistics have been proposed to extract information from non-Gaussian…
High-dimensional data sets are expected from the next generation of large-scale surveys. These data sets will carry a wealth of information about the early stages of galaxy formation and cosmic reionization. Extracting the maximum amount of…
Traditional statistical mechanics is constrained by the binary paradigms of identical/distinguishable and bosonic/fermionic particle statistics, leading to a fundamental logical gap in describing systems with partial distinguishability. We…
Large-scale structure (LSS) analysis in galaxy surveys is a powerful cosmological probe but is limited by tracer bias, which can obscure underlying information and weaken parameter constraints. Existing methods either model bias or restrict…
Clustering of large-scale structure provides significant cosmological information through the power spectrum of density perturbations. Additional information can be gained from higher-order statistics like the bispectrum, especially to…
Nonparametric estimation of the mean and covariance functions is ubiquitous in functional data analysis and local linear smoothing techniques are most frequently used. Zhang and Wang (2016) explored different types of asymptotic properties…
In this paper, we systematically review weighted persistent homology (WPH) models and their applications in biomolecular data analysis. Essentially, the weight value, which reflects physical, chemical and biological properties, can be…
Building upon the recent pioneering work by Mazenko and by Das and Mazenko, we develop a microscopic, non-equilibrium, statistical field theory for initially correlated canonical ensembles of classical microscopic particles obeying…
Most statistical inference from cosmic large-scale structure relies on two-point statistics, i.e.\ on the galaxy-galaxy correlation function (2PCF) or the power spectrum. These statistics capture the full information encoded in the Fourier…
We present a self-consistent framework to perform the wavelet analysis of two-dimensional statistical distributions. The analysis targets the 2D probability density function (p.d.f.) of an input sample, in which each object is characterized…
We investigate the Wavelet Scattering Transform (WST) as a tool for the study of Primordial non-Gaussianity (PNG) in Large Scale Structure (LSS), and compare its performance with that achievable via a joint analysis with power spectrum and…
We present a detailed review of large-scale structure (LSS) study using the discrete wavelet transform (DWT). After describing how one constructs a wavelet decomposition we show how this bases can be used as a complete statistical…
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…
We propose a new image representation for texture categorization and facial analysis, relying on the use of higher-order local differential statistics as features. It has been recently shown that small local pixel pattern distributions can…
Statistical models often include thousands of parameters. However, large models decrease the investigator's ability to interpret and communicate the estimated parameters. Reducing the dimensionality of the parameter space in the estimation…
We consider the statistical analysis of data on high-dimensional spheres and shape spaces. The work is of particular relevance to applications where high-dimensional data are available--a commonly encountered situation in many disciplines.…
Continuous wavelet analysis is gaining popularity in science and engineering for its ability to analyze data across spatial and scale domains simultaneously. In this study, we introduce a wavelet-based method to identify halos and assess…
We apply a suite of different estimators to the Quijote-PNG halo catalogues to find the best approach to constrain Primordial non-Gaussianity (PNG) at non-linear cosmological scales, up to $k_{\rm max} = 0.5 \, h\,{\rm Mpc}^{-1}$. The set…