Related papers: Errors on errors - Estimating cosmological paramet…
We are now beginning to learn detailed information about cosmological parameters from the shapes of the matter and radiation power spectra, together with their relative normalization. As more high quality data are gathered from galaxy…
The good agreement between large-scale observations and the predictions of the now-standard $\Lambda$CDM theory gives us hope that this will become a lasting foundation for cosmology. After briefly reviewing the current status of the key…
We develop a general formalism for analysing parameter information from non-Gaussian cosmic fields. The method can be adapted to include the nonlinear effects in galaxy redshift surveys, weak lensing surveys and cosmic velocity field…
A very common task in data visualization is to plot many data points with some measured y-value as a function of fixed x-values. Uncertainties on the y-values are typically presented as vertical error bars that represent either a…
Estimating and quantifying uncertainty in unknown system parameters from limited data remains a challenging inverse problem in a variety of real-world applications. While many approaches focus on estimating constant parameters, a subset of…
Forecasts and analyses of cosmological observations often rely on the assumption of a perfect theoretical model over a defined range of scales. We explore how model uncertainties and nuisance parameters in perturbative models of the matter…
Measurements of the peculiar velocities of large samples of galaxies enable new tests of the standard cosmological model, including determination of the growth rate of cosmic structure that encodes gravitational physics. With the size of…
I discuss whether the standard cosmological models fit the WMAP data well enough to justify parameter estimation with standard assumptions. The observed quadrupole is low (but has significant foreground uncertainty) and drives weak evidence…
Modern scientific cosmology pushes the boundaries of knowledge and the knowable. This is prompting questions on the nature of scientific knowledge. A central issue is what defines a 'good' model. When addressing global properties of the…
The Cosmic Microwave Background (CMB) is an abundant source of cosmological information. However, this information is encoded in non-trivial ways in a signal that is difficult to observe. The resulting challenges in extracting this…
Accurate and precise covariance matrices will be important in enabling planned cosmological surveys to detect new physics. Standard methods imply either the need for many N-body simulations in order to obtain an accurate estimate, or a…
In this brief paper we revisit the Fisher information content of cosmological power spectra or two-point functions of Gaussian fields in order to comment on the assumption of Gaussian estimators and the use of parameter-dependent covariance…
Bayesian statistics and Markov Chain Monte Carlo (MCMC) algorithms have found their place in the field of Cosmology. They have become important mathematical and numerical tools, especially in parameter estimation and model comparison. In…
We present general, analytic methods for Cosmological likelihood analysis and solve the "many-parameters" problem in Cosmology. Maxima are found by Newton's Method, while marginalization over nuisance parameters, and parameter errors and…
Stochastic inverse problems considered in this article consist of estimating the probability distributions of intrinsically random inputs of computer models. These estimations are based on observable outputs affected by model noise, and…
A new approach to the phenomenon of large numbers coincidence leads to unexpected results. No matter how strange it might sound, the exact value of cosmological parameters and their analytical expression through fundamental constants have…
Due to lack of scientific understanding, some mechanisms may be missing in mathematical modeling of complex phenomena in science and engineering. These mathematical models thus contain some uncertainties such as uncertain parameters. One…
In this review, we outline the expected tests of gravity that will be achieved at cosmological scales in the upcoming decades. We focus mainly on constraints on phenomenologically parameterized deviations from general relativity, which…
Our aim is to quantify the impact of systematic effects on the inference of cosmological parameters from cosmic shear. We present an end-to-end approach that introduces sources of bias in a modelled weak lensing survey on a galaxy-by-galaxy…
This paper deals with the problem of estimating the covariance matrix of a series of independent multivariate observations, in the case where the dimension of each observation is of the same order as the number of observations. Although…