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We present a technique to perform dimensionality reduction on data that is subject to uncertainty. Our method is a generalization of traditional principal component analysis (PCA) to multivariate probability distributions. In comparison to…
We consider the impact of key astrophysical and measurement systematics on constraints on dark energy and modifications to gravity on cosmic scales. We focus on upcoming photometric "Stage III" and "Stage IV" large scale structure surveys…
Weak lensing surveys provide a powerful probe of dark energy through the measurement of the mass distribution of the local Universe. A number of ground-based and space-based surveys are being planned for this purpose. Here, we study the…
Ongoing and upcoming galaxy surveys are providing precision measurements of galaxy clustering. However a major obstacle in its cosmological application is the stochasticity in the galaxy bias. We explore whether the principal component…
Weak gravitational lensing provides a means of testing the long-range properties of gravity. Current measurements are consistent with standard Newtonian gravity and inconsistent with substantial modifications on Mpc scales. The data allows…
We study the sensitivity of weak lensing by large scale structures to the evolution of dark energy. We explore a 2-parameters model of dark energy evolution, inspired by tracking quintessence models. To this end, we compute the likelihood…
Principal component analysis (PCA) is often used for analyzing data in the most diverse areas. In this work, we report an integrated approach to several theoretical and practical aspects of PCA. We start by providing, in an intuitive and…
Focusing on the well motivated aperture mass statistics $\Map$, we study the possibility of constraining cosmological parameters using future space based SNAP class weak lensing missions. Using completely analytical results we construct the…
There is growing interest in using the close connection between differential geometry and statistics to model smooth manifold-valued data. In particular, much work has been done recently to generalize principal component analysis (PCA), the…
Upcoming stage 4 surveys, such as the Simons Observatory, LSST, and Euclid, are poised to measure weak gravitational lensing of the Cosmic Microwave Background (CMB) and galaxies with unprecedented precision. While the power spectrum is the…
Principal Component Analysis (PCA) is a workhorse of modern data science. While PCA assumes the data conforms to Euclidean geometry, for specific data types, such as hierarchical and cyclic data structures, other spaces are more…
Weak gravitational lensing is responsible for the shearing and magnification of the images of high-redshift sources due to the presence of intervening matter. The distortions are due to fluctuations in the gravitational potential, and are…
Inferring spatial curvature of the Universe with high-fidelity is a longstanding interest in cosmology. However, the strong degeneracy between dark energy equation-of-state parameter $w$ and curvature density parameter $\Omega_{\rm K}$ has…
In these lectures I give an overview of gravitational lensing, concentrating on theoretical aspects, including derivations of some of the important results. Topics covered include the determination of surface mass densities of intervening…
Modifications of the matter power spectrum due to baryonic physics are one of the major theoretical uncertainties in cosmological weak lensing measurements. Developing robust mitigation schemes for this source of systematic uncertainty…
In this paper we examine cosmological weak lensing on non-linear scales and show that there are Newtonian and relativistic contributions and that the latter can also be extracted from standard Newtonian simulations. We use the…
Weak lensing (WL) promises to be a particularly sensitive probe of both the growth of large scale structure (LSS) as well as the fundamental relation between matter density perturbations and metric perturbations, thus providing a powerful…
Principal Component Analysis (PCA) is applied to the residuals of six widely used nuclear mass models to uncover systematic deviations and identify missing physical effects in theoretical nuclear mass predictions. By analyzing the principal…
Dimensionality reduction is a crucial step for pattern recognition and data mining tasks to overcome the curse of dimensionality. Principal component analysis (PCA) is a traditional technique for unsupervised dimensionality reduction, which…
Weak gravitational lensing of distant galaxies by foreground structures has proven to be a powerful tool to study the mass distribution in the universe. The advent of panoramic cameras on 4m class telescope has led to a first generation of…