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Principal Component Analysis (PCA) is a highly useful topic within an introductory Linear Algebra course, especially since it can be used to incorporate a number of applied projects. This method represents an essential application and…
Determination of cosmological parameters is a major goal in cosmology at present. The availability of improved data sets necessitates the development of novel statistical tools to interpret the inference from a cosmological model. In this…
We consider Horndeski modified gravity models obeying stability, velocity of gravitational waves $c_T$ equals $c$ and quasistatic approximation (QSA) on subhorizon scales. We assume further a $\Lambda$CDM background expansion and a…
Principal component analysis (PCA) has been widely applied to dimensionality reduction and data pre-processing for different applications in engineering, biology and social science. Classical PCA and its variants seek for linear projections…
We study the estimators of various second-order weak lensing statistics such as the shear correlation functions xi_\pm and the aperture mass dispersion <M_ap^2> which can directly be constructed from weak lensing shear maps. We compare the…
We present an algorithm using Principal Component Analysis (PCA) to subtract galaxies from imaging data, and also two algorithms to find strong, galaxy-scale gravitational lenses in the resulting residual image. The combined method is…
We examine general physical parameterisations for viable gravitational models in the $f(R)$ framework. This is related to the mass of an additional scalar field, called the scalaron, that is introduced by the theories. Using a simple…
We show that the abundance and redshift distribution ($dN/dz$) of galaxy clusters in future high--yield cluster surveys, combined with the spatial power spectrum ($P_c(k)$) of the same clusters, can place significant constraints on the…
Principal component analysis (PCA) is a popular tool for linear dimensionality reduction and feature extraction. Kernel PCA is the nonlinear form of PCA, which better exploits the complicated spatial structure of high-dimensional features.…
Weak gravitational lensing (WL) surveys provide insight into the matter distribution over an extensive range of scales. Current WL results are in mild tension with cosmic microwave background measurements from the early Universe.…
Joint analysis of multiple phenotypes can increase statistical power in genetic association studies. Principal component analysis, as a popular dimension reduction method, especially when the number of phenotypes is high-dimensional, has…
In the last decade we have seen an enormous increase in the size and quality of spectroscopic galaxy surveys, both at low and high redshift. New statistical techniques to analyse large portions of galaxy spectra are now finding favour over…
Principal component analysis (PCA) is a standard tool for dimensional reduction of a set of $n$ observations (samples), each with $p$ variables. In this paper, using a matrix perturbation approach, we study the nonasymptotic relation…
We investigate the observational viability of a class of cosmological models in which the vacuum energy density decays linearly with the Hubble parameter, resulting in a production of cold dark matter particles at late times. Similarly to…
Weak gravitational lensing is one of the key probes of cosmology. Cosmic shear surveys aimed at measuring the distribution of matter in the universe are currently being carried out (Pan-STARRS) or planned for the coming decade (DES, LSST,…
Dark energy can be investigated in two complementary ways, by considering either general parameterizations or physically well-defined models. Following the second route, we explore the constraints on quintessence models where the…
We consider multi-class classification problems for high dimensional data. Following the idea of reduced-rank linear discriminant analysis (LDA), we introduce a new dimension reduction tool with a flavor of supervised principal component…
Weak lensing will play an important role in future cosmological surveys, including e.g. Euclid and SKA. Sufficiently accurate theoretical predictions are important for correctly interpreting these surveys and hence for extracting correct…
We explore the dependence of weak lensing phenomena on the background cosmology. We first generalise the relation between $P_\psi(\omega)$, the angular power spectrum of the distortion, and the power spectrum of density fluctuations to…
This paper introduces a robust approach to functional principal component analysis (FPCA) for relative data, particularly density functions. While recent papers have studied density data within the Bayes space framework, there has been…