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Ongoing and upcoming wide-field surveys at different wavelengths will measure the distribution of galaxy clusters with unprecedented precision, demanding accurate models for the two-point correlation function (2PCF) covariance. In this…
With the advent of high-quality surveys in cosmology the full three-point correlation function will be a valuable statistic for describing structure formation models. It contains information on cosmological parameters and detailed halo…
Many techniques for data science and uncertainty quantification demand efficient tools to handle Gaussian random fields, which are defined in terms of their mean functions and covariance operators. Recently, parameterized Gaussian random…
We study linear spectral statistics of high dimensional sample covariance matrices in a regime where the empirical spectral distribution remains governed by the classical sample covariance law but the fluctuation theory is nonclassical. Our…
We perform detailed comparison of the semi-analytic halo model predictions with measurements in numerical simulations of the two and three point correlation functions (3PCF), as well as power spectrum and bispectrum. We discuss the accuracy…
Surveys of cosmological large-scale structure (LSS) are sensitive to the presence of local primordial non-Gaussianity (PNG), and may be used to constrain models of inflation. Local PNG, characterized by fNL, the amplitude of the quadratic…
In a detailed analysis of the three point correlation function (3PCF) for the 2dF Galaxy Redshift Survey we have accurately measured the 3PCF for galaxies of different luminosity. The 3PCF amplitudes [$\Qsu$ or $\Qrpu$] of the galaxies…
The three-point correlation function (3PCF) is a crucial probe of non-Gaussianity and nonlinear structure formation. We develop a thermodynamic framework for the galaxy 3PCF by closing the BBGKY hierarchy with a physically motivated…
Ensemble Kalman filters are based on a Gaussian assumption, which can limit their performance in some non-Gaussian settings. This paper reviews two nonlinear, non-Gaussian extensions of the Ensemble Kalman Filter: Gaussian anamorphosis (GA)…
The three-point correlation function (3PCF) provides an important view into the clustering of galaxies that is not available to its lower order cousin, the two-point correlation function (2PCF). Higher order statistics, such as the 3PCF,…
We investigate the three-point correlation function (3PCF) in the squeezed limit by considering galaxy pairs as discrete objects and cross-correlating them with the galaxy field. We develop an efficient algorithm using Fast Fourier…
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 study pathwise invariances of centred random fields that can be controlled through the covariance. A result involving composition operators is obtained in second-order settings, and we show that various path properties including…
We constrain the linear and quadratic bias parameters from the configuration dependence of the three-point correlation function (3PCF) in both redshift and projected space, utilizing measurements of spectroscopic galaxies in the Sloan…
Accurately simulating the atmospheric turbulence behaviour is always challenging. The well-known FFT based method falls short in correctly predicting both the low and high frequency behaviours. Sub-harmonic compensation aids in…
Gaussian graphical models are of great interest in statistical learning. Because the conditional independencies between different nodes correspond to zero entries in the inverse covariance matrix of the Gaussian distribution, one can learn…
Super-sample covariance (SSC) is an important effect for cosmological analyses that use the deep structure of the cosmic web; it may, however, be nontrivial to include it practically in a pipeline. We solve this difficulty by presenting a…
In this study, we aim to develop a new methodology to estimate the cross-correlation function and uncertainties and apply it to the analysis of magnification bias in galaxy surveys. We adopt a new methodological framework that uses a…
An important topic of interest in imaging is the construction of protocols that are not diffraction limited. This can be achieved in a variety of ways, including classical superresolution techniques or quantum entanglement-based protocols.…
In climate studies, detecting spatial patterns that largely deviate from the sample mean still remains a statistical challenge. Although a Principal Component Analysis (PCA), or equivalently a Empirical Orthogonal Functions (EOF)…