相关论文: Precision matrix expansion - efficient use of nume…
The statistical analysis of covariance matrices occurs in many important applications, e.g. in diffusion tensor imaging and longitudinal data analysis. We consider the situation where it is of interest to estimate an average covariance…
The use of sparse precision (inverse covariance) matrices has become popular because they allow for efficient algorithms for joint inference in high-dimensional models. Many applications require the computation of certain elements of the…
Cosmological large-scale structure analyses based on two-point correlation functions often assume a Gaussian likelihood function with a fixed covariance matrix. We study the impact on cosmological parameter estimation of ignoring the…
We consider the problem of precision matrix estimation where, due to extraneous confounding of the underlying precision matrix, the data are independent but not identically distributed. While such confounding occurs in many scientific…
We quantify the information content of the non-linear matter power spectrum, the halo mass function, and the void size function, using the Quijote $N$-body simulations. We find that these three statistics exhibit very different degeneracies…
In practice, observations are often contaminated by noise, making the resulting sample covariance matrix to be an information-plus-noise-type covariance matrix. Aiming to make inferences about the spectra of the underlying true covariance…
Neutrino mass constraints are a primary focus of current and future large-scale structure (LSS) surveys. Non-linear LSS models rely heavily on cosmological simulations -- the impact of massive neutrinos should therefore be included in these…
Repeated measurements are common in many fields, where random variables are observed repeatedly across different subjects. Such data have an underlying hierarchical structure, and it is of interest to learn covariance/correlation at…
This paper studies the problem of estimating the covariance of a collection of vectors using only highly compressed measurements of each vector. An estimator based on back-projections of these compressive samples is proposed and analyzed. A…
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…
We offer a method to estimate a covariance matrix in the special case that \textit{both} the covariance matrix and the precision matrix are sparse --- a constraint we call double sparsity. The estimation method is maximum likelihood,…
The current generation of large galaxy surveys will test the cosmological model by combining multiple types of observational probes. Realising the statistical promise of these new datasets requires rigorous attention to all aspects of…
The estimation of uncertainties in cosmological parameters is an important challenge in Large-Scale-Structure (LSS) analyses. For standard analyses such as Baryon Acoustic Oscillations (BAO) and Full Shape, two approaches are usually…
A constrained L1 minimization method is proposed for estimating a sparse inverse covariance matrix based on a sample of $n$ iid $p$-variate random variables. The resulting estimator is shown to enjoy a number of desirable properties. In…
Ground and space-based sky surveys enable powerful cosmological probes based on measurements of galaxy properties and the distribution of galaxies in the Universe. These probes include weak lensing, baryon acoustic oscillations, abundance…
Many of the most exciting questions in astrophysics and cosmology, including the majority of observational probes of dark energy, rely on an understanding of the nonlinear regime of structure formation. In order to fully exploit the…
Estimating large covariance and precision matrices are fundamental in modern multivariate analysis. The problems arise from statistical analysis of large panel economics and finance data. The covariance matrix reveals marginal correlations…
Constraining neutrino mass through cosmological observations relies on precise simulations to calibrate their effects on large scale structure, while these simulations must overcome computational challenges like dealing with large velocity…
We present here the cosmo-SLICS, a new suite of simulations specially designed for the analysis of current and upcoming weak lensing data beyond the standard two-point cosmic shear. We sample the $[\Omega_{\rm m}, \sigma_8, h, w_0]$…
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…