Related papers: Validating the Fisher approach for stage IV spectr…
We study the accuracy with which cosmological parameters can be determined from real space power spectrum of matter density contrast at weakly nonlinear scales using analytical approaches. From power spectra measured in $N$-body simulations…
The growth rate of large-scale structure provides a powerful consistency test of the standard cosmological model and a probe of possible deviations from general relativity. We use a Fisher analysis to forecast constraints on the growth rate…
The intrinsic alignment (IA) of galaxy shapes probes the underlying gravitational tidal field, thus offering cosmological information complementary to galaxy clustering. In this paper, we perform a Fisher forecast to assess the benefit of…
A data-driven approach to elucidating the nature of the dark energy, in the form of a joint analysis of a full set of cosmological parameters, utilizing all available observational data is proposed. A parameterization of a generalized dark…
The main features of the statistical approach to inverse problems are described on the example of a linear model with additive noise. The approach does not use any Bayesian hypothesis regarding an unknown object; instead, the standard…
Quantum Fisher information matrix (QFIM) is a core concept in theoretical quantum metrology due to the significant importance of quantum Cram\'{e}r-Rao bound in quantum parameter estimation. However, studies in recent years have revealed…
Factor modeling is an essential tool for exploring intrinsic dependence structures among high-dimensional random variables. Much progress has been made for estimating the covariance matrix from a high-dimensional factor model. However, the…
We make the first detailed MCMC likelihood study of cosmological constraints that are expected from some of the largest, ongoing and proposed, cluster surveys in different wave-bands and compare the estimates to the prevalent Fisher matrix…
Gaussian Random Fields (GRFs) with Mat\'ern covariance functions have emerged as a powerful framework for modeling spatial processes due to their flexibility in capturing different features of the spatial field. However, the smoothness…
Data analysis from upcoming large galaxy redshift surveys, such as Euclid and DESI will significantly improve constraints on cosmological parameters. To optimally extract the information from these galaxy surveys, it is important to control…
We introduce a new theoretical framework based on Feynman diagrams to compute phase shifts in matter wave interferometry. The method allows for analytic computation of higher order quantum corrections, beyond the traditional semi-classical…
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…
Within the context of constraining an expansion of the dark energy equation of state w(z) we show that the eigendecomposition of Fisher matrices is sensitive to both the maximum order of the expansion and the basis set choice. We…
The Fisher information matrix (FIM) is a foundational concept in statistical signal processing. The FIM depends on the probability distribution, assumed to belong to a smooth parametric family. Traditional approaches to estimating the FIM…
Weak gravitational lensing provides a sensitive probe of cosmology by measuring the mass distribution and the geometry of the low redshift universe. We show how an all-sky weak lensing tomographic survey can jointly constrain different sets…
Classical Fisher-information asymptotics describe the covariance of regular efficient estimators through the local quadratic approximation of the log-likelihood, and thus capture first-order geometry only. In curved models, including…
In quantum multi-parameter estimation, the precision of estimating unknown parameters is bounded by the Cramer-Rao bound (CRB), defined via the inverse of the Fisher information matrix (FIM). However, in certain scenarios such as…
We demonstrate a methodology for optimizing the ability of future dark energy surveys to answer model selection questions, such as `Is acceleration due to a cosmological constant or a dynamical dark energy model?'. Model selection Figures…
Persistent homology naturally addresses the multi-scale topological characteristics of the large-scale structure as a distribution of clusters, loops, and voids. We apply this tool to the dark matter halo catalogs from the Quijote…
Using the Fisher matrix formalism, we quantitatively investigate the constraints on a 10 dimensional space of cosmological parameters which may be obtained with future cluster surveys. We explore the dependence of the Omega_m constraint on…