Related papers: Estimating Cosmological Parameter Covariance
The asymptotic variance of the maximum likelihood estimate is proved to decrease when the maximization is restricted to a subspace that contains the true parameter value. Maximum likelihood estimation allows a systematic fitting of…
The advent of Stage IV weak lensing surveys will open up a new era in precision cosmology. These experiments will offer more than an order-of-magnitude leap in precision over existing surveys, and we must ensure that the accuracy of our…
Several ongoing and upcoming large scale structure surveys aim to explore the nonlinear regime of structure formation with high precision. Making reliable cosmological inferences from these observations necessitates precise theoretical…
Most parameter constraints obtained from cosmic microwave background (CMB) anisotropy data are based on power estimates and rely on approximate likelihood functions; computational difficulties generally preclude an exact analysis based on…
Weak gravitational lensing (WL) causes distortions of galaxy images and probes massive structures on large scales, allowing us to understand the late-time evolution of the Universe. One way to extract the cosmological information from WL is…
We study the minimal sample size N=N(n) that suffices to estimate the covariance matrix of an n-dimensional distribution by the sample covariance matrix in the operator norm, with an arbitrary fixed accuracy. We establish the optimal bound…
Cosmological $N$-body simulations provide numerical predictions of the structure of the Universe against which to compare data from ongoing and future surveys, but the growing volume of the Universe mapped by surveys requires…
The application of standard sufficient dimension reduction methods for reducing the dimension space of predictors without losing regression information requires inverting the covariance matrix of the predictors. This has posed a number of…
With the advent of large-scale weak lensing surveys there is a need to understand how realistic, scale-dependent systematics bias cosmic shear and dark energy measurements, and how they can be removed. Here we describe how spatial…
When the copula of the conditional distribution of two random variables given a covariate does not depend on the value of the covariate, two conflicting intuitions arise about the best possible rate of convergence attainable by…
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…
Correlated random fields are a common way to model dependence struc- tures in high-dimensional data, especially for data collected in imaging. One important parameter characterizing the degree of dependence is the asymp- totic variance…
Causal discovery algorithms infer causal relations from data based on several assumptions, including notably the absence of measurement error. However, this assumption is most likely violated in practical applications, which may result in…
To explore the limits of a stochastic gradient method, it may be useful to consider an example consisting of an infinite number of quadratic functions. In this context, it is appropriate to determine the expected value and the covariance…
The disconnected part of the power spectrum covariance matrix (also known as the "Gaussian" covariance) is the dominant contribution on large scales for galaxy clustering and weak lensing datasets. The presence of a complicated sky mask…
A separable covariance model for a random matrix provides a parsimonious description of the covariances among the rows and among the columns of the matrix, and permits likelihood-based inference with a very small sample size. However, in…
Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…
What do the data, as distinguished from cosmological models, tell us about cosmological parameters that determined the model of the universe? In this paper, we address this question in the context of the WMAP angular power spectra for the…
The spectra of empirical correlation matrices, constructed from multivariate data, are widely used in many areas of sciences, engineering and social sciences as a tool to understand the information contained in typically large datasets. In…
We measure the covariance of the non-linear matter power spectrum from N-body simulations using two methods. In the first case, the covariance of power is estimated from the scatter over many random realizations of the density field. In the…