Related papers: Data Compression and Covariance Matrix Inspection:…
Covariance matrices are important tools for obtaining reliable parameter constraints. Advancements in cosmological surveys lead to larger data vectors and, consequently, increasingly complex covariance matrices, whose number of elements…
We show how the massive data compression algorithm MOPED can be used to reduce, by orders of magnitude, the number of simulated datasets that are required to estimate the covariance matrix required for the analysis of gaussian-distributed…
In many fields including cosmology, statistical inference often relies on Gaussian likelihoods whose covariance matrices are estimated from a finite number of simulations. This finite-sample estimation introduces noise into the covariance,…
Future large scale cosmological surveys will provide huge data sets whose analysis requires efficient data compression. Calculating accurate covariances is extremely challenging with increasing number of statistics used. Here we introduce a…
Cosmological weak lensing by the large scale structure of the Universe, cosmic shear, is coming of age as a powerful probe of the parameters describing the cosmological model and matter power spectrum. It complements CMB studies, by…
We explore linear and non-linear dimensionality reduction techniques for statistical inference of parameters in cosmology. Given the importance of compressing the increasingly complex data vectors used in cosmology, we address questions…
Data re-sampling methods such as the delete-one jackknife are a common tool for estimating the covariance of large scale structure probes. In this paper we investigate the concepts of internal covariance estimation in the context of cosmic…
In recent years cosmic shear, the weak gravitational lensing effect by the large-scale structure of the Universe, has proven to be one of the observational pillars on which the cosmological concordance model is founded. Several cosmic shear…
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…
We present a new method, called $x$-cut cosmic shear, which optimally removes sensitivity to poorly modeled scales from the two-point cosmic shear signal. We show that the $x$-cut cosmic shear covariance matrix can be computed from the…
We present simulations of a cosmic shear survey and show how the survey geometry influences the accuracy of determination of cosmological parameters. We numerically calculate the full covariance matrices Cov of two-point statistics of…
Weak gravitational lensing is a powerful probe of cosmology, with second-order shear statistics commonly used to constrain parameters such as the matter density $\Omega_\mathrm{m}$ and the clustering amplitude $S_8$. However, parameter…
We derive in this paper expressions for the covariance matrix of the cosmic shear two-point correlation functions which are readily applied to any survey geometry. Furthermore, we consider the more special case of a simple survey geometry…
$ $Future surveys could obtain tighter constraints on the cosmological parameters with the galaxy power spectrum than with the Cosmic Microwave Background. However, the inclusion of multiple overlapping tracers, redshift bins, and more…
In cosmic shear likelihood analyses the covariance is most commonly assumed to be constant in parameter space. Therefore, when calculating the covariance matrix (analytically or from simulations), its underlying cosmology should not…
3D data compression techniques can be used to determine the natural basis of radial eigenmodes that encode the maximum amount of information in a tomographic large-scale structure survey. We explore the potential of the Karhunen-Lo\`eve…
Covariance and histogram image descriptors provide an effective way to capture information about images. Both excel when used in combination with special purpose distance metrics. For covariance descriptors these metrics measure the…
We propose a method for estimating a covariance matrix that can be represented as a sum of a low-rank matrix and a diagonal matrix. The proposed method compresses high-dimensional data, computes the sample covariance in the compressed…
Creating accurate and low-noise covariance matrices represents a formidable challenge in modern-day cosmology. We present a formalism to compress arbitrary observables into a small number of bins by projection into a model-specific subspace…
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,…